# Thermodynamic Stability of Volatile Droplets and Thin Films Governed by Disjoining Pressure in Open and Closed ContainersClick to copy article linkArticle link copied!

- Magnus Aa. Gjennestad
*****Magnus Aa. GjennestadPoreLab/Department of Physics, Norwegian University of Science and Technology, 7491 Trondheim, Norway*****Email: [email protected], [email protected]More by Magnus Aa. Gjennestad - Øivind Wilhelmsen
*****Øivind WilhelmsenPoreLab/SINTEF Energy Research, 7034 Trondheim, NorwayDepartment of Energy and Process Engineering, Norwegian University of Science and Technology, 7491 Trondheim, Norway*****Email: [email protected]More by Øivind Wilhelmsen

## Abstract

Distributed thin films of water and their coexistence with droplets are investigated using a capillary description based on a thermodynamic fundamental relation for the film Helmholtz energy, derived from disjoining pressure isotherms and an accurate equation of state. Gas–film and film–solid interfacial tensions are derived, and the latter has a dependence on film thickness. The resulting energy functionals from the capillary description are discretized, and stationary states are identified. The thermodynamic stability of configurations with thin films in systems that are closed (canonical ensemble) or connected to a particle reservoir (grand canonical ensemble) is evaluated by considering the eigenvalues of the corresponding Hessian matrices. The conventional stability criterion from the literature states that thin flat films are stable when the derivative of the disjoining pressure with respect to the film thickness is negative. This criterion is found to apply only in open systems. A closer inspection of the eigenvectors of the negative eigenvalues shows that condensation/evaporation destabilizes the film in an open system. In closed systems, thin films can be stable even though the disjoining pressure derivative is positive, and their stability is governed by mechanical instabilities of a similar kind to those responsible for spinodal dewetting in nonvolatile systems. The films are stabilized when their thickness and disjoining pressure derivative are such that the minimum unstable wavelength is larger than the container diameter. Droplets in coexistence with thin films are found to be unstable for all considered examples in open systems. In closed systems, they are found to be stable under certain conditions. The unstable droplets in both open and closed systems are saddle points in their respective energy landscapes. In the closed system, they represent the activation barrier for the transition between a stable film and a stable droplet. In the open system, the unstable droplets represent the activation barrier for the transition from a film into a bulk liquid phase. Thin films are found to be the equilibrium configuration up to a certain value of the total density in a closed system. Beyond this value, there is a morphological phase transition to stable droplet configurations.

## Introduction

*h*> 0, where Π is the disjoining pressure and

*h*is the film thickness. (1,26,27) It has, however, been pointed out that this criterion is not necessarily valid for confined systems. (20,28) In fact, this has been exploited in computer simulations to calculate the disjoining pressure where it has a positive slope in

*h*. (29) The aim of this work is to compare, consistently and on equal terms, the thermodynamic stability of thin films in combination with droplets in open and closed systems. To this end, we derive a thermodynamic fundamental relation for the film phase from the disjoining pressure combined with an equation of state (EOS) that represents the bulk-phase properties. Pure water is used as an example, but the methodology is equally applicable to other fluids and can straightforwardly be extended to mixtures.

*h*> 0, in agreement with the conventional stability criterion.

## Fundamental Theory of Thin Films

### Disjoining Pressure

*p*

^{⊥}normal to the interfaces that differs from the pressure

*p*

^{∥}parallel to them.

*p*

^{g}, while in the right, there is a bulk liquid phase with pressure

*p*

^{b}. The film phase in the left container is connected to, and in chemical equilibrium with, the bulk liquid phase in the right through a tube. The system is also in mechanical force balance, but the pressures

*p*

^{g}and

*p*

^{b}are, in general, different.

### Fundamental Relation

*A*

^{fs}of a flat solid surface, as illustrated by the dotted white lines in Figure 2. Since the section is small, any variation in the film thickness across it may be considered small with respect to (w.r.t.) the thickness

*h*in the middle and can be approximated as linear. The Helmholtz energy differential for the film section may then be expressed as

*S*

^{f}is the entropy,

*T*is the temperature, μ

^{f}is the chemical potential,

*N*

^{f}is the number of particles,

*V*

^{f}is the volume of the film, and

*A*

^{gf}is the gas–film interfacial area. The interfacial tensions of the gas–film and film–solid interfaces are γ

^{gf}and γ

^{fs}, respectively. The reason for the appearance of

*p*

^{⊥}in eq 3 is that the only way to change

*V*

^{f}at constant

*A*

^{gf}and

*A*

^{fs}is to change the film thickness

*h*. The work required to change

*h*must be performed against the normal pressure in the film.

*T*,

*V*

^{f},

*A*

^{gf},

*A*

^{fs}, and

*N*

^{f}by integrating from a thick film of volume

*V*

_{∞}

^{f}, which has the desired areas

*A*

^{gf}and

*A*

^{fs}and is unaffected by the disjoining pressure, to a thin film with volume

*V*

^{f}

*F*

^{b}is a bulk-phase description of the fluid Helmholtz energy as given, e.g., by an EOS. Since the integration is performed with constant areas

*A*

^{gf}and

*A*

^{fs}, we may replace d

*V*

^{f}with

*A*

^{fs}d

*h*. Replacing the integrand in eq 4 by

*p*

^{⊥}=

*p*

^{b}+ Π from eq 2 and absorbing the resulting integral over

*p*

^{b}into

*F*

^{b}, we obtain

*h*=

*V*

^{f}/

*A*

^{fs}. For convenience, we introduce the shorthand notation

^{f}is a function of

*T*,

*V*

^{f}, and

*N*

^{f}. Furthermore, the gas–film interfacial tension is the same as the macroscopic gas–liquid interfacial tension

*V*

^{f},

*A*

^{gf},

*A*

^{fs}, and

*N*

^{f}

*A*

^{fs}yields the Helmholtz energy per area of solid substrate

*h*=

*V*

^{f}/

*A*

^{fs}, Γ =

*N*

^{f}/

*A*

^{fs}, and α =

*A*

^{gf}/

*A*

^{fs}. From the Euler relation (eq 11), we get

### Macroscopic Wetting Properties

*h*only. Young’s equation for the contact angle θ results from a balance of interfacial forces. In terms of the spreading coefficient, it can be expressed as

^{fs}using eqs 9 and eq 3 in the equations above gives

*h*

_{0}, which is such that Π(

*h*

_{0}) = 0. This simplifies eq 16 to

### Linear Stability Analysis

*h*< 0, and films corresponding to a negative slope in the disjoining pressure isotherm are therefore mechanically stable. When dΠ/d

*h*> 0, on the other hand, the interfacial tension acts to suppress disturbances with short wavelengths, while disturbances with wavelengths longer than λ

_{0}can grow. Films forming droplets by succumbing to such instabilities are said to undergo spinodal dewetting. (20) Locally stable films forming stable, energetically favorable droplets by overcoming some energy barrier do so through nucleation. If the substrate size is smaller than the shortest unstable wavelength, flat films may be stable even though dΠ/d

*h*> 0. (20,28)

## Models

_{∞}

^{gl}= 0.073 N m

^{–1}. Since γ

_{∞}

^{ls}only adds a constant to the Helmholtz energy that has no qualitative effect on the results, we have set γ

_{∞}

^{ls}= 0. In the section Fundamental Relation,

*V*

^{f},

*A*

^{gf},

*A*

^{fs}, and

*N*

^{f}refer to the volume, interfacial areas, and particle number of a small section of a film. From this point on, these symbols will refer to the entire distributed film.

### Disjoining Pressure Model

*h*

^{3}(ref (1), p 99) to more complex curves (38) that exhibit one or more local extrema; see, e.g., Figure 3 in ref (27). Disjoining pressure isotherms are usually modeled by adding terms that account for different types of forces acting between two interfaces, (39) resulting in a plethora of possibilities for combinations of terms. We will restrict the attention to a type of model that has been used to describe water films on a solid graphite surface. (27,40) This model has two terms

*h*

^{3}

*A*is the effective Hamaker constant. This is modeled by applying a mixing rule to the liquid and solid Hamaker constants

*A*

^{ll}= 4.4 × 10

^{–20}J and

*A*

^{ss}= 4.7 × 10

^{–19}J. (27,40)

*K*

_{sr}and

*L*

_{sr}are the strength and correlation length of the interactions, respectively. We will use

*L*

_{sr}= 0.6 nm (27,40) and consider

*K*

_{sr}= 0 and three different negative values of

*K*

_{sr}. The four resulting disjoining pressure curves are illustrated in Figure 4. The effect of the negative

*K*

_{sr}values is to create a minimum in the disjoining pressure curve that makes the liquid partially wetting and allows the existence of droplets in equilibrium with thin films. For each isotherm in the figure, the legends state the contact angle θ

_{0}predicted by eq 17 for a macroscopic droplet in mechanical force balance with a thin film.

### Equation of State for Bulk-Phase Properties

### Distributed Film in a Cylindrical Container

*R*, height

*H*, and volume

*V*= π

*R*

^{2}

*H*. Furthermore, we assume for simplicity that the film thickness

*h*is a cylindrically symmetric function of the radial coordinate

*r*. The film–solid interfacial area is then a constant

*h*over the area

*A*

^{fs}

*V*, and we will only consider the case when it is connected to a thermal reservoir with constant temperature

*T*. If the container is closed, i.e., it is in the canonical ensemble and contains a fixed number of particles

*N*, equilibrium is defined by the state that maximizes the total entropy of the system in the container and the reservoir subject to these constraints on

*T*,

*V*, and

*N*. This is equivalently described as a minimum in the Helmholtz energy for the system. (36) Equilibrium in an open container, which also has a fixed volume

*V*and temperature

*T*, but where the gas phase can exchange particles with an external particle reservoir at constant chemical potential, corresponds to a minimum in the grand canonical energy Ω.

*N*

^{g}=

*N*–

*N*

^{f}and

*V*

^{g}=

*V*–

*V*

^{f}. The Helmholtz energy of the film is obtained by integrating

*f*

^{f}over

*A*

^{fs}

*f*

^{f}using eq 13, and subsequently combining with eqs 8, eq 4, and eq 2, we get

*ḣ*= d

*h*/d

*r*. We restrict our attention to cases where there is chemical equilibrium within the film phase, i.e., μ

^{f}is uniform, and thus

*h*and a function of

*N*

^{f}.

^{g}= μ

^{f}, at a given value of Δ

*p*=

*p*

^{g}–

*p*

^{b}, mechanical equilibrium is defined by a minimum of the functional

*F*

_{μ}° is a constant and the integrand is

*F*

_{μ}closely resembles an effective interface Hamiltonian as presented, e.g., by MacDowell (28) and Dörfler et al. (20)

*F*

_{μ}and satisfy the Euler–Lagrange equation (44)

*L*and insert into the Euler–Lagrange equation to get

*r*= 0

*r*=

*R*

*h*

_{R}is some specified constant value.

*h*

_{R}, the Euler–Lagrange equation may have several solutions. We will consider two qualitatively different types of solutions. The first type is the trivial solution where

*h*is a constant. This corresponds to a flat film (Figure 3a). In this case, the curvature terms in eq 36 are zero and Δ

*p*=

*p*

^{g}–

*p*

^{b}is equal to Π, which is constant along the film profile. The other type of solution is a droplet and a film, as illustrated in Figure 3b. In this case, the disjoining pressure and curvature terms vary along the film profile, but their sum remains constant. Crucially, as the gas–liquid interface of the droplet approaches the solid surface, the disjoining pressure term balances the curvature terms in such a way that the gas–liquid interface flattens into a flat film.

*F*. However, the stability of these stationary points, i.e., whether they are minima, maxima, or saddle points, is likely to differ.

## Numerical Methods

*F*and Ω, and determining their stability by characterizing them as maxima, minima, or saddle points.

*h*as a function or

*r*, and corresponds to a specific value of Δ

*p*=

*p*

^{g}–

*p*

^{b}, the difference between the gas phase pressure and the pressure of the hypothetical bulk liquid phase with which the film would be in chemical equilibrium. A phase equilibrium calculation is performed next, where equality of the chemical potentials is used to determine the number of particles in the film and gas phases.

### Phase Equilibrium Calculations

*p*=

*p*

^{g}–

*p*

^{b}. Through eq 24, the film profile also specifies the volumes

*V*

^{f}and

*V*

^{g}. Phase equilibrium for a particular film profile can therefore be determined by finding the particle numbers

*N*

^{f}and

*N*

^{g}that give the necessary pressure difference and equality of the film and gas chemical potentials. This is accomplished by solving the nonlinear system of equations

^{b}= μ

^{f}according to eq 7. The pressures, chemical potentials, and the derivatives required to compute

**F**and its Jacobian are provided by the EOS. The scaling quantities are

*R*is the universal gas constant.

### Solving the Euler–Lagrange Equation

*r*= 0 and the other at

*r*=

*R*. Together, these boundary conditions and eq 36 constitute a two-point boundary value problem, which was solved using solve_bvp from Scipy’s integrate module. (47)

### Discrete Description of the Distributed Film

*h*(

*r*) by its values at discrete points and then use a quadrature rule to approximate the functional integrals. Stability of the stationary states can then be determined by considering the eigenvalues of a Hessian matrix, as will be described in the section Stability Analysis.

*A*

^{gf},

*W*, and

*V*

^{f}are functionals of

*h*. Specifically

*V*

^{f}is given by eq 24.

*h*be approximated by the vector

*M*discrete points along the

*r*-axis

*A*

^{gf}may then be approximated by the sum

*h*

_{0}=

*h*

_{1}and

*h*

_{M+1}=

*h*

_{M}. Analogous definitions apply for

*W*(

**h**) and

*V*

^{f}(

**h**).

**x**includes

*N*

^{f}in addition to

**h**

*i*∈ {2,

*M*+ 1}. The Hessian matrix may be found by further differentiation. Details of the procedure for calculating the derivatives of

*A*

^{gf},

*W*, and

*V*

^{f}w.r.t.

*x*

_{i}and a validation of the discretization procedure are given in ref (25) and its accompanying Supporting Information. An analogous procedure is applied to obtain a discrete approximation of the grand canonical energy and its derivatives.

### Stability Analysis

**x*** obtained with the above procedures will have Jacobian vectors equal to zero for both

*F*and Ω. The change in, e.g.,

*F*due to a small perturbation d

**x**of the stationary state

**x*** is thus determined by the Hessian matrix of

*F*

**Λ**is a diagonal matrix of eigenvalues and

**Q**is a matrix whose column

*i*is the eigenvector

**q**

^{(i)}corresponding to the eigenvalue Λ

^{(i)}. We will use the convention that all eigenvectors

**q**

^{(i)}have length 1 in the

*L*

_{2}-norm. Since the Hessian is symmetric, the eigenvectors are orthogonal. (25)

**x*** is locally stable in a closed container and represents a local minimum in

*F*if all of the eigenvalues of the Hessian matrix Λ

^{(i)}are positive. On the other hand, if one or more eigenvalues are negative, it is possible to choose the perturbation d

**x**along one of the associated eigenvectors

**q**

_{–}

^{(i)}. The subscripted minus sign indicates the negative eigenvalue. In this case, we choose d

**x**= d

**x**

_{–}∝

**q**

_{–}

^{(i)}and this will give a negative d

*F*. The stationary state

**x*** is then not a local minimum and is considered locally unstable. Stability in open containers is evaluated in a similar manner. Unstable states with both positive and negative eigenvalues are called saddle points, while only negative eigenvalues characterize a maximum.

## Results

*R*= 20 nm and

*H*= 10 nm. The number of grid points used in the discrete approximation is

*M*= 400.

### Flat Films

*h*< 0. This is in agreement with the conventional stability condition presented in the literature; see, e.g., the review paper by Boinovich and Emelyanenko (2) (or ref (1), p 56). A similar result was also obtained through dynamic considerations by Sharma, (34) assuming a constant gas pressure and a model for the evaporation rate. In the closed container, on the other hand, some films are found to be stable even if dΠ/d

*h*> 0.

**q**

_{–}

^{(i)}of Hessian matrices that are associated with negative eigenvalues correspond to perturbations d

**x**

_{–}∝

**q**

_{–}

^{(i)}that the film is unstable against. An unstable stationary state may have one or more such negative eigenvalues. The vectors d

**x**

_{–}are composed of two parts: d

*N*

_{–}

^{f}, the component describing the perturbation of the number of particles in the film; and d

**h**

_{–}, a vector representing the perturbation of the film profile. The vectors d

**h**

_{–}are here referred to as instability modes.

_{0}= 60° isotherm and two different film thicknesses in an open container. Specifically, Figure 6 displays the instability modes obtained when

*h*= 1.06 nm. This film thickness is well into the unstable region of the disjoining pressure isotherm with dΠ/d

*h*> 0. Each mode has resemblance to a sinusoidal function with some wavelength and corresponds to a specific number of internal extrema, indicated by their color (black, 0; blue, 1; yellow, 2; etc.). Instabilities in the closed system are similar, except that the zero-extrema mode (black) is absent. By moving along this mode, the open system can reduce its energy by condensing or evaporating the film while the film retains its flat profile. We call this mode a condensation–evaporation instability and find that it is present in the open system whenever the derivative of the disjoining pressure curve is positive. This type of mode thus causes the open system to be unstable whenever dΠ/d

*h*> 0. The other instability modes involve some degree of rearrangement of the film profile, and we therefore call these mechanical instability modes. The stability of the closed system is determined by this kind of instability. We emphasize that the mechanical instabilities also involve some exchange of particles. The distinction between condensation/evaporation and mechanical instabilities is based on whether or not the alteration of the gas–film interface shape occurs. We further observe that the exchange of particles is larger in the open system than in the closed system, which is due to the constrained total number of particles in the closed system.

*h*= 2.68 nm in an open container. This thickness corresponds to the rightmost red dot on the θ

_{0}= 60° isotherm of the closed container displayed in Figure 5a. The mechanical instability mode resembles in this case a sinusoidal function with a wavelength close to the diameter of the container. For thicker films, there are no unstable modes in the closed system and it is stable. In the open system however, the condensation/evaporation instability persists until the disjoining pressure derivative again becomes negative. The existence of condensation/evaporation inabilities in open systems and their absence in closed systems have recently been reported also for thick films in pores. (25)

*h*> 0 is a necessary condition for mechanical instabilities. This results in specific intervals of film thicknesses where mechanical instabilities may occur.

*r*-axis. We therefore estimate the wavelength as the distance from the container sidewall to the nearest internal extremum, multiplied by a factor 2. Figure 7 displays the resulting wavelengths as functions of film thickness. Results are presented for disjoining pressure isotherms with θ

_{0}= 40° (Figure 7a) and θ

_{0}= 60° (Figure 7b). Figure 7c displays results for the 40° isotherm and a wider container. The figures also show the container diameter 2

*R*(solid horizontal line) and the shortest unstable wavelength λ

_{0}as predicted by eq 18 (dashed line). The dotted vertical lines indicate where dΠ/d

*h*= 0 and λ

_{0}→ ∞. The disjoining pressure derivative is positive between them and, according to the linear stability analysis, mechanical instabilities should thus occur only for film thicknesses in between these lines.

*h*> 0. We observe no mechanical instabilities with wavelengths longer than 2

*R*. As a concrete illustration, compare Figure 7a where

*R*= 20 nm with Figure 7c where the container size is increased to

*R*= 30 nm. In the latter case, the increased container size gives room for instabilities with longer wavelengths. This results in an increased interval of film thicknesses where films are mechanically unstable. The larger container also gives room for a larger number of extrema in instabilities with a given wavelength. For instance, the shortest-wavelength instabilities in Figure 7a have two internal extrema, whereas instabilities with approximately the same wavelength in Figure 7c have four. For both container sizes, it is clear that the mechanical instabilities with the longest wavelength disappear when they reach the 2

*R*-bound.

*R*, the measured unstable wavelengths are longer than λ

_{0}. Although derived with an assumption of translational invariance that does not apply in the present example, eq 18 appears to provide an accurate estimate for the lower bound for the unstable wavelengths.

_{0}= 40° isotherm (Figure 7a) to results from the θ

_{0}= 60° isotherm (Figure 7b). The latter disjoining pressure curve extends to larger negative values for the disjoining pressure. This results in unstable modes with shorter wavelengths and a larger number of internal extrema.

*R*increases. The films will then become mechanically unstable for a larger part of the interval where dΠ/d

*h*> 0. However, the dotted lines in Figure 7 display the film thicknesses for which the estimated lower bound for unstable wavelengths λ

_{0}diverges. The divergence of λ

_{0}means that there may be an interval on the

*h*-axis where a finite container is not large enough to support sufficiently long wavelengths for the film to be unstable no matter how large the container is. However, this region quickly becomes narrow as the container diameter is increased. As an example, consider the θ

_{0}= 40° isotherm and a container with 2

*R*= 1 μm. The lower bound, λ

_{0}, is larger than 1 μm only for film thicknesses between 5.41 nm and the thickness for which λ

_{0}diverges, 5.56 nm. The effect of mechanical stabilization due to finite container size is therefore expected to be small for large containers.

*h*< 0, applies only to open systems due to a condensation/evaporation instability that is present whenever this criterion is not satisfied. The stability of films in closed systems is governed by mechanical instabilities of a similar kind as those responsible for spinodal dewetting in nonvolatile systems. Similar to nonvolatile films, (20) we find that films in small closed containers may be stable even though dΠ/d

*h*> 0 due to the finite size of the container.

### Droplets and Films

_{0}= 60° isotherm. Here, the configurations with the largest droplets are stable. As the droplet size is reduced, the contact angle decreases and the film thickness increases. Thus, the droplet configurations gradually converge to a flat film as the film thickness approaches the minimum on the disjoining pressure curve where dΠ/d

*h*|

_{h=hR}= 0. At some point before the disjoining pressure in the thin-film part of the configurations reaches this minimum, however, the droplets become unstable. As we shall see in the next section, this point is associated with a minimum in the total density in the container. A similar behavior was obtained also for the θ

_{0}= 40° isotherm.

**h**

_{–}are shown in Figure 9. These modes are similar for the open and closed systems. However, as discussed for the flat film, the unstable perturbations d

**x**

_{–}∝

**q**

_{–}

^{(i)}for the open system involve a larger degree of particle exchange with the gas phase.

**x**

_{–}∝

**q**

_{–}

^{(i)}, we were able to form a path in the configuration space, with monotonically decreasing grand canonical energy, to a homogeneous liquid phase filling the entire container. By perturbing the system in the opposite direction, a path to a stable flat film was obtained. Sharma (34) observed a similar behavior by use of dynamic considerations. He assumed a constant gas pressure and a model for the evaporation rate. Time-stationary droplet solutions were then unstable, and droplets slightly smaller than the time-stationary state evaporated, shrunk, and eventually became a flat film, while slightly bigger droplets condensed further and grew in size. The unstable droplets in the open system thus represent activation barriers in the energy landscape, which correspond to stationary states with gas pressures above the saturation pressure.

*N*

^{f}changed very little. As an example, the decay of the unstable droplet in Figure 9 to a flat film resulted in a 5.5% reduction in

*N*

^{f}in the open system and only a 0.074% reduction in the closed system. A consequence of this is that the assumption of a nonvolatile film phase in the effective interface Hamiltonian approach used, e.g., by Dörfler et al. (20) appears reasonable for water in a closed system at the current temperature. However, this might not be the case for fluids closer to their critical temperature.

### Film–Droplet Transition

*N*/

*V*, we determine the equilibrium configuration in a closed system. This comparison is shown in Figure 10 for the θ

_{0}= 60° isotherm. The film thickness

*h*

_{R}at the container sidewall is plotted as a function of the total density for both types of configurations. Unstable configurations are indicated by red markers, locally stable configurations are indicated in green, and stable configurations that represent the lowest Helmholtz energy for a particular value of ρ are shown in blue. The gas spinodal density at the considered temperature is 0.35 mol L

^{–1}, and the liquid spinodal density is 43 mol L

^{–1}. Since the total densities of the configurations lie between the gas and liquid spinodals, a homogeneous fluid phase can be ruled out as a possible alternative equilibrium state since it is thermodynamically unstable. (46)

^{–1}, a value that depends both on the size and on the shape of the container.

^{–1}is shown in Figure 11b. A transition from the stable flat film to the stable droplet state will pass through the unstable droplet, as it represents a saddle point in the thermodynamic energy landscape.

*F*between the droplet configurations and the corresponding film configuration with the same total density is plotted. Like in Figure 10, the stationary droplet states fork out into a stable and an unstable branch. The Helmholtz energy of the unstable branch is always larger than the stable branch. Furthermore, the Helmholtz energy of the unstable branch approaches that of the flat film as the total density in increased.

*F*of the three states in Figure 11b are indicated by markers of corresponding colors in Figure 11a. It is clear that the large droplet has the lowest Helmholtz energy and is the equilibrium configuration. However, a transition from the stable flat configuration, which passes through the unstable small-droplet configuration, must overcome an energy barrier through an activated nucleation process. The probability of the transition to occur increases as the energy barrier decreases and eventually goes to zero as the total density is increased. The opposite transition, from a large droplet to a flat film, may also occur as an activated nucleation process below the transition density. A similar analysis for the θ

_{0}= 40° isotherm gives qualitatively similar results but a somewhat higher transition density of 3.88 mol L

^{–1}. Since the activation barriers for the film–droplet transition displayed in Figure 11a are rather small, we expect for this example that the morphological change will occur close to the transition density.

## Conclusions

*h*, and the existing bulk-phase equations of state, we derived a thermodynamic fundamental relation for a thin liquid film phase. From this fundamental relation, the film–gas and film–solid interfacial tensions were obtained, the latter of which was dependent on the film thickness. We verified that Derjaguin’s equation for the contact angle of a macroscopic droplet was reproduced by the fundamental relation, and it was next employed to derive a capillary model for a distributed film of varying thicknesses, with a homogeneous gas phase above it.

*h*< 0, was not satisfied. A closer inspection of the eigenvectors associated with the negative eigenvalues revealed that the stability was governed by mechanical instabilities of a similar kind as those responsible for spinodal dewetting in nonvolatile systems. In line with earlier works, (20,28) the films were stabilized when their thickness and disjoining pressure derivatives were such that the minimum unstable wavelength became larger than the container diameter.

## Acknowledgments

This work was partly supported by the Research Council of Norway through its Centres of Excellence funding scheme, project number 262644.

## Appendix A. Macroscopic Droplet Model

*R*, base area

*A*= π

*R*

^{2}, and height

*H*, giving a total volume

*V*=

*AH*. It contains a spherical droplet, large enough for the pressure inside it to be unaffected by the disjoining pressure, covering part of

*A*, while a thin film covers the rest. A gas phase occupies the remaining container volume. The gas–liquid interface of the droplet is a spherical cap, and the droplet volume can be expressed as

*a*is the base-area radius and

*b*is the height of the spherical cap. The parameters

*a*and

*b*are related to the radius of curvature in the droplet,

*r*, and the contact angle θ through

*h*is the film thickness. The gas volume is

^{f}is the film tension, i.e.,

*V*

^{g}= −d

*V*

^{f}– d

*V*

^{d}, d

*N*

^{g}= −d

*N*

^{f}– d

*N*

^{d}, and d

*A*

^{f}= – d

*A*

^{ds}, the differential may be expressed as

*h*,

*a*, and

*b*. This enables further manipulation of the differential to obtain

*F*.

*a*=

*R*/2 for progressively increasing values of

*R*. For each of these states, we compute the stationary state that has the same number of particles using the discrete approach with 600 grid points. We use the same fluid EOS and interfacial tensions as in the main paper and use the disjoining pressure isotherm with a macroscopic contact angle of θ

_{0}= 60°. Two examples are shown in Figure 12a,b for

*R*= 10 and 640 nm, respectively. There is a large discrepancy between the film profiles for the small container. In the large container, the two profiles are identical within the accuracy of the plots.

*L*

_{2}-norm of the relative difference between the film profiles obtained with the two different models. This is plotted in Figure 13 against the container radius. This shows that the film profiles obtained with the discrete method converge to those from the macroscopic model as the container size is increased.

## References

This article references 49 other publications.

**1**Churaev, N. V.; Derjaguin, B. V.; Muller, V. M.*Surface Forces*; Springer: New York, 1987.Google ScholarThere is no corresponding record for this reference.**2**Boinovich, L.; Emelyanenko, A. Wetting and surface forces.*Adv. Colloid Interface Sci.*2011,*165*, 60– 69, DOI: 10.1016/j.cis.2011.03.002Google Scholar2https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXmtVWnsLo%253D&md5=79c0a6da5f54d334fbf4582ed2775ebfWetting and surface forcesBoinovich, Ludmila; Emelyanenko, AlexandreAdvances in Colloid and Interface Science (2011), 165 (2), 60-69CODEN: ACISB9; ISSN:0001-8686. (Elsevier B.V.)In this review we discuss the fundamental role of surface forces, with a particular emphasis on the effect of the disjoining pressure, in establishing the wetting regime in the three phase systems with both plane and curved geometry. The special attention is given to the conditions of the formation of wetting/adsorption liq. films on the surface of poorly wetted substrate and the possibility of their thermodn. equil. with bulk liq. The calcns. of contact angles on the basis of the isotherms of disjoining pressure and the difference in wettability of flat and highly curved surfaces are discussed. Mechanisms of wetting hysteresis, related to the action of surface forces, are considered.**3**Boinovich, L.; Emelyanenko, A. The prediction of wettability of curved surfaces on the basis of the isotherms of the disjoining pressure.*Colloids Surf., A*2011,*383*, 10– 16, DOI: 10.1016/j.colsurfa.2010.12.020Google Scholar3https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXmtlCrtb0%253D&md5=4012fd751e90492045a2eff81a33fe79The prediction of wettability of curved surfaces on the basis of the isotherms of the disjoining pressureBoinovich, Ludmila; Emelyanenko, AlexandreColloids and Surfaces, A: Physicochemical and Engineering Aspects (2011), 383 (1-3), 10-16CODEN: CPEAEH; ISSN:0927-7757. (Elsevier B.V.)The generalization of Derjaguin-Frumkin approach for the description of wettability of curved interfaces is given. The equations for the calcns. of the contact angle on concave and convex cylindrical and spherical surfaces based on the isotherms of the disjoining pressure are derived. Anal. performed has shown that for the radius of curvature comparable to the range of surface forces action increasing the surface curvature for convex surfaces results in the contact angle increasing, whereas for concave surfaces the wetting improves. It is shown that curving the substrate surface may cause philic/phobic or phobic/philic wettability transition.**4**Moura, M.; Flekkøy, E. G.; Måløy, K. J.; Schäfer, G.; Toussaint, R. Connectivity enhancement due to film flow in porous media.*Phys. Rev. Fluids*2019,*4*, 094102 DOI: 10.1103/PhysRevFluids.4.094102Google ScholarThere is no corresponding record for this reference.**5**Zhao, B.; MacMinn, C. W.; Primkulov, B. K.; Chen, Y.; Valocchi, A. J.; Zhao, J.; Kang, Q.; Bruning, K.; McClure, J. E.; Miller, C. T.; Fakhari, A.; Bolster, D.; Hiller, T.; Brinkmann, M.; Cueto-Felgueroso, L.; Cogswell, D. A.; Verma, R.; Prodanović, M.; Maes, J.; Geiger, S.; Vassvik, M.; Hansen, A.; Segre, E.; Holtzman, R.; Yang, Z.; Yuan, C.; Chareyre, B.; Juanes, R. Comprehensive comparison of pore-scale models for multiphase flow in porous media.*Proc. Natl. Acad. Sci. U.S.A.*2019,*116*, 13799– 13806, DOI: 10.1073/pnas.1901619116Google Scholar5https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXhtlChu7fJ&md5=540016d8663e0ffc3df9fe92f09ca4beComprehensive comparison of pore-scale models for multiphase flow in porous mediaZhao, Benzhong; MacMinn, Christopher W.; Primkulov, Bauyrzhan K.; Chen, Yu; Valocchi, Albert J.; Zhao, Jianlin; Kang, Qinjun; Bruning, Kelsey; McClure, James E.; Miller, Cass T.; Fakhari, Abbas; Bolster, Diogo; Hiller, Thomas; Brinkmann, Martin; Cueto-Felgueroso, Luis; Cogswell, Daniel A.; Verma, Rahul; Prodanovic, Masa; Maes, Julien; Geiger, Sebastian; Vassvik, Morten; Hansen, Alex; Segre, Enrico; Holtzman, Ran; Yang, Zhibing; Yuan, Chao; Chareyre, Bruno; Juanes, RubenProceedings of the National Academy of Sciences of the United States of America (2019), 116 (28), 13799-13806CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)Multiphase flows in porous media are important in many natural and industrial processes. Pore-scale models for multiphase flows have seen rapid development in recent years and are becoming increasingly useful as predictive tools in both academic and industrial applications. However, quant. comparisons between different pore-scale models, and between these models and exptl. data, are lacking. Here, we perform an objective comparison of a variety of state-of-the-art pore-scale models, including lattice Boltzmann, stochastic rotation dynamics, vol.-of-fluid, level-set, phase-field, and pore-network models. As the basis for this comparison, we use a dataset from recent microfluidic expts. with precisely controlled pore geometry and wettability conditions, which offers an unprecedented benchmarking opportunity. We compare the results of the 14 participating teams both qual. and quant. using several std. metrics, such as fractal dimension, finger width, and displacement efficiency. We find that no single method excels across all conditions and that thin films and corner flow present substantial modeling and computational challenges.**6**Gjennestad, M. Aa.; Vassvik, M.; Kjelstrup, S.; Hansen, A. Stable and efficient time integration at low capillary numbers of a dynamic pore network model for immiscible two-phase flow in porous media.*Front. Phys.*2018,*6*, 56 DOI: 10.3389/fphy.2018.00056Google ScholarThere is no corresponding record for this reference.**7**Gjennestad, M. Aa.; Winkler, M.; Hansen, A. Pore network modeling of the effects of viscosity ratio and pressure gradient on steady-state incompressible two-phase flow in porous media.*Transp. Porous Media*2020,*132*, 355– 379, DOI: 10.1007/s11242-020-01395-zGoogle Scholar7https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXkvFCjsLY%253D&md5=16f0123f57b0ad0dd0baac19ebc8b33aPore Network Modeling of the Effects of Viscosity Ratio and Pressure Gradient on Steady-State Incompressible Two-Phase Flow in Porous MediaGjennestad, Magnus Aa.; Winkler, Mathias; Hansen, AlexTransport in Porous Media (2020), 132 (2), 355-379CODEN: TPMEEI; ISSN:0169-3913. (Springer)Abstr.: We perform steady-state simulations with a dynamic pore network model, corresponding to a large span in viscosity ratios and capillary nos. From these simulations, dimensionless steady-state time-averaged quantities such as relative permeabilities, residual saturations, mobility ratios and fractional flows are computed. These quantities are found to depend on three dimensionless variables, the wetting fluid satn., the viscosity ratio and a dimensionless pressure gradient. Relative permeabilities and residual saturations show many of the same qual. features obsd. in other exptl. and modeling studies. The relative permeabilities do not approach straight lines at high capillary nos. for viscosity ratios different from 1. Our conclusion is that this is because the fluids are not in the highly miscible near-crit. region. Instead they have a viscosity disparity and intermix rather than forming decoupled, similar flow channels. Ratios of av. mobility to their high capillary no. limit values are also considered. Roughly, these vary between 0 and 1, although values larger than 1 are also obsd. For a given satn., the mobilities are not always monotonically increasing with the pressure gradient. While increasing the pressure gradient mobilizes more fluid and activates more flow paths, when the mobilized fluid is more viscous, a redn. in av. mobility may occur.**8**Spernjak, D.; Prasad, A. K.; Advani, S. G. Experimental investigation of liquid water formation and transport in a transparent single-serpentine PEM fuel cell.*J. Power Sources*2007,*170*, 334– 344, DOI: 10.1016/j.jpowsour.2007.04.020Google Scholar8https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2sXmt1GrtLo%253D&md5=dd916e01879f57dc6e185806a5b56e8bExperimental investigation of liquid water formation and transport in a transparent single-serpentine PEM fuel cellSpernjak, Dusan; Prasad, Ajay K.; Advani, Suresh G.Journal of Power Sources (2007), 170 (2), 334-344CODEN: JPSODZ; ISSN:0378-7753. (Elsevier B.V.)Liq. water formation and transport were investigated by direct exptl. visualization in an operational transparent single-serpentine polymer electrolyte membrane (PEM) fuel cell. We examd. the effectiveness of various gas diffusion layer materials in removing water away from the cathode and through the flow field over a range of operating conditions. Complete polarization curves as well as time evolution studies after step changes in current draw were obtained with simultaneous liq. water visualization within the transparent cell. The level of cathode flow field flooding, under the same operating conditions and cell current, was recognized as a criterion for the water removal capacity of the gas diffusion layer materials. When compared at the same c.d. (i.e., water prodn. rate), higher amt. of liq. water in the cathode channel indicated that water had been efficiently removed from the catalyst layer. Visualization of the anode channel was used to investigate the influence of the microporous layer on water transport. No liq. water was obsd. in the anode flow field unless cathode gas diffusion layers had an microporous layer. Microporous layer on the cathode side creates a pressure barrier for water produced at the catalyst layer. Water is pushed across the membrane to the anode side, resulting in anode flow field flooding close to the H2 exit.**9**Thickett, S. C.; Neto, C.; Harris, A. T. Biomimetic surface coatings for atmospheric water capture prepared by dewetting of polymer films.*Adv. Mater.*2011,*23*, 3718– 3722, DOI: 10.1002/adma.201100290Google Scholar9https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXovVCmtbo%253D&md5=c8fa87586d070936c10386bd6b949a02Biomimetic Surface Coatings for Atmospheric Water Capture Prepared by Dewetting of Polymer FilmsThickett, Stuart C.; Neto, Chiara; Harris, Andrew T.Advanced Materials (Weinheim, Germany) (2011), 23 (32), 3718-3722CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH & Co. KGaA)Dewetting is the process by which unstable thin (=100 nm) liq. films spontaneously break apart on a substrate, driven by unfavorable intermol. forces at the interface between the two materials. The unstable film breaks apart into holes that grow with time, eventually transforming the film into a series of isolated droplets. Above its glass transition temp. (Tg), an unstable thin polymer film on a solid substrate spontaneously undergoes morphol. transformation via dewetting. When the polymer film is cooled below Tg, the resultant pattern is "frozen in," preserving the droplet morphol. We have exploited the resultant pattern to create biomimetic surfaces, whereby the dewetted polymer droplets mimic the hydrophilic bumps on the Stenocara exoskeleton. To create a final surface with wettability contrast between the droplet phase and the background, we investigated the dewetting of an immiscible polymer bilayer, consisting of a hydrophilic polymer layer on top of a hydrophobic polymer underlayer. The results presented here already demonstrate a facile and scalable methodol. to create surface coatings that capture significant vols. of water using low-cost materials and requiring only the cooling of the surface below the dew point. In many urban environments, water could be collected on these surfaces at night, taking advantage of radiative cooling of the substrate.**10**Xiao, R.; Maroo, S. C.; Wang, E. N. Negative pressures in nanoporous membranes for thin film evaporation.*Appl. Phys. Lett.*2013,*102*, 123103 DOI: 10.1063/1.4798243Google Scholar10https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXks1Oks78%253D&md5=05e6f231843388d6b6180c7ec5037c3eNegative pressures in nanoporous membranes for thin film evaporationXiao, Rong; Maroo, Shalabh C.; Wang, Evelyn N.Applied Physics Letters (2013), 102 (12), 123103/1-123103/4CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)We present a nanoporous membrane-based approach, which decouples the capillary pressure from the viscous resistance, to achieve high driving pressures and efficient liq. delivery for thin film evapn. By using Al2O3 membranes with ≈150 nm pore diams., abs. liq. pressures as low as -300 kPa were achieved using iso-Pr alc., while dissipating max. interfacial heat fluxes of ≈96 W/cm2. Design guidelines are provided to achieve higher interfacial heat fluxes with reduced membrane thicknesses. This work shows a promising approach to address thermal management needs for next generation electronic devices. (c) 2013 American Institute of Physics.**11**Zhao, J.-J.; Duan, Y.-Y.; Wang, X.-D.; Wang, B.-W. Effects of superheat and temperature-dependent thermophysical properties on evaporating thin liquid films in microchannels.*Int. J. Heat Mass Transfer*2011,*54*, 1259– 1267, DOI: 10.1016/j.ijheatmasstransfer.2010.10.026Google ScholarThere is no corresponding record for this reference.**12**Ju, Y. S.; Kaviany, M.; Nam, Y.; Sharratt, S.; Hwang, G. S.; Catton, I.; Fleming, E.; Dussinger, P. Planar vapor chamber with hybrid evaporator wicks for the thermal management of high-heat-flux and high-power optoelectronic devices.*Int. J. Heat Mass Transfer*2013,*60*, 163– 169, DOI: 10.1016/j.ijheatmasstransfer.2012.12.058Google Scholar12https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXktlCktr8%253D&md5=2db885be3f4825e974a35a10905e4ee7Planar vapor chamber with hybrid evaporator wicks for the thermal management of high-heat-flux and high-power optoelectronic devicesJu, Y. Sungtaek; Kaviany, M.; Nam, Y.; Sharratt, S.; Hwang, G. S.; Catton, I.; Fleming, E.; Dussinger, P.International Journal of Heat and Mass Transfer (2013), 60 (), 163-169CODEN: IJHMAK; ISSN:0017-9310. (Elsevier Ltd.)Heat spreaders based on compact vapor chambers offer one attractive approach to the thermal management of high-power electronics. We report our design and exptl. characterization of advanced evaporator wicks and thin planar vapor chambers incorporating these wicks. The hybrid wicks combine distributed high-permeability liq. supply structures with thin (monolayer) evapn. layers to achieve both low thermal resistance and high limiting heat fluxes over large heating areas. We model and exptl. characterize the capillary and heat transfer performance of liq. spreading layers consisting of mono-layers of Cu particles and identify a range of optimal particle diams. maximizing their performance. The thin liq. spreading layers are integrated with three different types of liq. supply structures, namely, columnar arteries, converging lateral arteries, and bi-porous structures. The resulting hybrid wicks show comparable heat transfer performances with crit. limiting heat fluxes >350 W/cm2 over heating areas of 1 cm2 and peak heat transfer coeffs. >20 W/cm2 K. These results confirm the effectiveness of our hybrid wick designs and also that evapn. heat transfer is dominated by the liq. spreading layers. A prototype vapor chamber incorporating CTE-tailored envelopes and the hybrid wick is developed for potential applications in the thermal management of laser diode arrays. We demonstrate an evaporator resistance of approx. 0.075 K/(W/cm2), while removing over 1500 W from a 4 cm2 heating area.**13**Kandlikar, S. G. Fundamental issues related to flow boiling in minichannels and microchannels.*Exp. Therm. Fluid Sci.*2002,*26*, 389– 407, DOI: 10.1016/S0894-1777(02)00150-4Google Scholar13https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD38XktlKgu7o%253D&md5=4ade7d4ceed0541ebac95e5b58a704a1Fundamental issues related to flow boiling in minichannels and microchannelsKandlikar, Satish G.Experimental Thermal and Fluid Science (2002), 26 (2-4), 389-407CODEN: ETFSEO; ISSN:0894-1777. (Elsevier Science Inc.)A review. Flow boiling in small hydraulic diam. channels is becoming increasingly important in many diverse applications. The previous studies addressing the effects of the channel size on the flow patterns, and heat transfer and pressure drop performance are reviewed. The fundamental questions related to the presence of nucleate boiling and characteristics of flow boiling in microchannels and minichannels in comparison to that in the conventional channel sizes (3 mm and above) are addressed. Also, the effect of heat exchanger configuration-single-channel and multichannel-on the heat transfer and pressure drop performance is reviewed. The areas for future research are identified.**14**Setu, S. A.; Dullens, R. P. A.; Hernández-Machado, A.; Pagonabarraga, I.; Aarts, D. G. A. L.; Ledesma-Aguilar, R. Superconfinement tailors fluid flow at micro-scales.*Nat. Commun.*2015,*6*, 7297 DOI: 10.1038/ncomms8297Google Scholar14https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXhtF2ktrvL&md5=7c086b672d64e3753da30a816bbe4f65Superconfinement tailors fluid flow at microscalesSetu, Siti Aminah; Dullens, Roel P. A.; Hernandez-Machado, Aurora; Pagonabarraga, Ignacio; Aarts, Dirk G. A. L.; Ledesma-Aguilar, RodrigoNature Communications (2015), 6 (), 7297CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)Understanding fluid dynamics under extreme confinement, where device and intrinsic fluid length scales become comparable, is essential to successfully develop the coming generations of fluidic devices. Here we report measurements of advancing fluid fronts in such a regime, which we dub superconfinement. We find that the strong coupling between contact-line friction and geometric confinement gives rise to a new stability regime where the max. speed for a stable moving front exhibits a distinctive response to changes in the bounding geometry. Unstable fronts develop into drop-emitting jets controlled by thermal fluctuations. Numerical simulations reveal that the dynamics in superconfined systems is dominated by interfacial forces. Henceforth, we present a theory that quantifies our expts. in terms of the relevant interfacial length scale, which in our system is the intrinsic contact-line slip length. Our findings show that length-scale overlap can be used as a new fluid-control mechanism in strongly confined systems.**15**McGraw, J. D.; Bäumchen, O.; Klos, M.; Haefner, S.; Lessel, M.; Backes, S.; Jacobs, K. Nanofluidics of thin polymer films: Linking the slip boundary condition at solidliquid interfaces to macroscopic pattern formation and microscopic interfacial properties.*Adv. Colloid Interface Sci.*2014,*210*, 13– 20, DOI: 10.1016/j.cis.2014.03.010Google Scholar15https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXmvFSjs7g%253D&md5=4f840f12feb822e039ab1ed21f8e50b5Nanofluidics of thin polymer films: Linking the slip boundary condition at solid-liquid interfaces to macroscopic pattern formation and microscopic interfacial propertiesMcGraw, Joshua D.; Baeumchen, Oliver; Klos, Mischa; Haefner, Sabrina; Lessel, Matthias; Backes, Sebastian; Jacobs, KarinAdvances in Colloid and Interface Science (2014), 210 (), 13-20CODEN: ACISB9; ISSN:0001-8686. (Elsevier B.V.)If a thin liq. film is not stable, different rupture mechanisms can be obsd. causing characteristic film morphologies: spinodal dewetting and dewetting by nucleation of holes. This rupturing entails liq. flow and opens new possibilities to study microscopic phenomena. Here we use this process of dewetting to gain insight on the slip boundary condition at the solid-liq. interface. Having established hydrodynamic models that allow for the detn. of the slip length in a dewetting expt. based on nucleation, we move on to the quantification and mol. description of slip effects in various systems. For the late stage of the dewetting process involving the Rayleigh-Plateau instability, several distinct droplet patterns can be obsd. We describe the importance of slip in detg. what pattern may be found. In order to control the slip length, we use polymeric liqs. on different hydrophobic coatings of silicon wafers. We find that subtle changes in the coating can lead to large changes in the slip length. Thus, we gain insight into the question of how the structure of the substrate affects the slip length.**16**Snustad, I.; Røe, I. T.; Brunsvold, A.; Ervik, A.; He, J.; Zhang, Z. A review on wetting and water condensation - Perspectives for CO_{2}condensation.*Adv. Colloid Interface Sci.*2018,*256*, 291– 304, DOI: 10.1016/j.cis.2018.03.008Google Scholar16https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXntlSmtb8%253D&md5=021109491e9024dbc7be46fc375e1314A review on wetting and water condensation - Perspectives for CO2 condensationSnustad, Ingrid; Roee, Ingeborg T.; Brunsvold, Amy; Ervik, Aasmund; He, Jianying; Zhang, ZhiliangAdvances in Colloid and Interface Science (2018), 256 (), 291-304CODEN: ACISB9; ISSN:0001-8686. (Elsevier B.V.)A review. Liquefaction of vapor is a necessary, but energy intensive step in several important process industries. This review identifies possible materials and surface structures for promoting dropwise condensation, known to increase efficiency of condensation heat transfer. Research on superhydrophobic and superomniphobic surfaces promoting dropwise condensation constitutes the basis of the review. In extension of this, knowledge is extrapolated to condensation of CO2. Global emissions of CO2 need to be minimized in order to reduce global warming, and liquefaction of CO2 is a necessary step in some carbon capture, transport and storage (CCS) technologies. The review is divided into three main parts: 1) An overview of recent research on superhydrophobicity and promotion of dropwise condensation of water, 2) An overview of recent research on superomniphobicity and dropwise condensation of low surface tension substances, and 3) Suggested materials and surface structures for dropwise CO2 condensation based on the two first parts.**17**Reiter, G. Dewetting of thin polymer films.*Phys. Rev. Lett.*1992,*68*, 75, DOI: 10.1103/PhysRevLett.68.75Google Scholar17https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK38XmtVCltQ%253D%253D&md5=dcd6dc731f2f3eef5013e932fba95020Dewetting of thin polymer filmsReiter, GuenterPhysical Review Letters (1992), 68 (1), 75-8CODEN: PRLTAO; ISSN:0031-9007.Thin polystyrene films (<100 nm) on Si substrates undergo dewetting when annealed above the glass transition temp. Three different stages can be distinguished. The smooth films break up by the creation of cylindrical holes. The holes then grow and form rims ahead of them which finally contact each other creating "cellular" structures. The rims are unstable and decay into droplets. The influence of the film thickness on this process is investigated and compared to recent theor. predictions of spinodal decompn. of partially wetting thin films.**18**Mukherjee, R.; Sharma, A. Instability, self-organization and pattern formation in thin soft films.*Soft Matter*2015,*11*, 8717– 8740, DOI: 10.1039/C5SM01724FGoogle Scholar18https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXhsFamsb%252FL&md5=738b191eeb685ae4986e1c402da9997eInstability, self-organization and pattern formation in thin soft filmsMukherjee, Rabibrata; Sharma, AshutoshSoft Matter (2015), 11 (45), 8717-8740CODEN: SMOABF; ISSN:1744-683X. (Royal Society of Chemistry)The free surface of a thin soft polymer film is often found to become unstable and self-organizes into various meso-scale structures. In this article we classify the instability of a thin polymer film into three broad categories, which are: category 1: instability of an ultra-thin (<100 nm) viscous film engendered by amplification of thermally excited surface capillary waves due to interfacial dispersive van der Waals forces; category 2: instability arising from the attractive inter-surface interactions between the free surface of a soft film exhibiting room temp. elasticity and another rigid surface in its contact proximity; and category 3: instability caused by an externally applied field such as an elec. field or a thermal gradient, obsd. in both viscous and elastic films. We review the salient features of each instability class and highlight how characteristic length scales, feature morphologies, evolution pathways, etc. depend on initial properties such as film thickness, visco-elasticity (rheol.), residual stress, and film prepn. conditions. We emphasize various possible strategies for aligning and ordering of the otherwise isotropic structures by combining the essential concepts of bottom-up and top-down approaches. A perspective, including a possible future direction of research, novelty and limitations of the methods, particularly in comparison to the existing patterning techniques, is also presented for each setting.**19**Bhandaru, N.; Das, A.; Mukherjee, R. Confinement induced ordering in dewetting of ultra-thin polymer bilayers on nanopatterned substrates.*Nanoscale*2016,*8*, 1073– 1087, DOI: 10.1039/C5NR06690EGoogle Scholar19https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXhvVyhu73E&md5=8f342cd254a0a458d5231220dcd02a00Confinement induced ordering in dewetting of ultra-thin polymer bilayers on nanopatterned substratesBhandaru, Nandini; Das, Anuja; Mukherjee, RabibrataNanoscale (2016), 8 (2), 1073-1087CODEN: NANOHL; ISSN:2040-3372. (Royal Society of Chemistry)We report the dewetting of a thin bilayer of polystyrene (PS) and poly(methylmethacrylate) (PMMA) on a topog. patterned nonwettable substrate comprising an array of pillars, arranged in a square lattice. With a gradual increase in the concn. of the PMMA soln. (Cn-PMMA), the morphol. of the bottom layer changes to: (1) an aligned array of spin dewetted droplets arranged along substrate grooves at very low Cn-PMMA; (2) an interconnected network of threads surrounding each pillar at intermediate Cn-PMMA; and (3) a continuous bottom layer at higher Cn-PMMA. On the other hand the morphol. of the PS top layer depends largely on the nature of the pre-existing bottom layer, in addn. to Cn-PS. An ordered array of PMMA core-PS shell droplets forms right after spin coating when both Cn-PMMA and Cn-PS are very low. Bilayers with all other initial configurations evolve during thermal annealing, resulting in a variety of ordered structures. Unique morphologies realized include laterally coexisting structures of the two polymers confined within the substrate grooves due to initial rupture of the bottom layer on the substrate followed by a squeezing flow of the top layer; an array of core-shell and single polymer droplets arranged in an alternating order etc., to highlight a few. Such structures cannot be fabricated by any stand-alone lithog. technique.**20**Dörfler, F.; Rauscher, M.; Dietrich, S. Stability of thin liquid films and sessile droplets under confinement.*Phys. Rev. E*2013,*88*, 012402 DOI: 10.1103/PhysRevE.88.012402Google Scholar20https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BC3sfpvVSnsw%253D%253D&md5=1d914e1ddecf87facc0a6eeab29ac3ceStability of thin liquid films and sessile droplets under confinementDorfler Fabian; Rauscher Markus; Dietrich SPhysical review. E, Statistical, nonlinear, and soft matter physics (2013), 88 (1), 012402 ISSN:.The stability of nonvolatile thin liquid films and of sessile droplets is strongly affected by finite size effects. We analyze their stability within the framework of density functional theory using the sharp kink approximation, i.e., on the basis of an effective interface Hamiltonian. We show that finite size effects suppress spinodal dewetting of films because it is driven by a long-wavelength instability. Therefore nonvolatile films are stable if the substrate area is too small. Similarly, nonvolatile droplets connected to a wetting film become unstable if the substrate area is too large. This instability of a nonvolatile sessile droplet turns out to be equivalent to the instability of a volatile drop which can attain chemical equilibrium with its vapor.**21**MacDowell, L. G.; Shen, V. K.; Errington, J. R. Nucleation and cavitation of spherical, cylindrical, and slablike droplets and bubbles in small systems.*J. Chem. Phys.*2006,*125*, 034705 DOI: 10.1063/1.2218845Google Scholar21https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28XnsFeisLo%253D&md5=f7e027590ee8a700adf84e0029642ef9Nucleation and cavitation of spherical, cylindrical, and slablike droplets and bubbles in small systemsMacDowell, Luis G.; Shen, Vincent K.; Errington, Jeffrey R.Journal of Chemical Physics (2006), 125 (3), 034705/1-034705/15CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)Computer simulations are employed to obtain subcrit. isotherms of small finite sized systems inside the coexistence region. For all temps. considered, ranging from the triple point up to the crit. point, the isotherms gradually developed a sequence of sharp discontinuities as the system size increased from ∼8 to ∼21 mol. diams. For the smallest system sizes, and more so close to the crit. point, the isotherms appeared smooth, resembling the continuous van der Waals loop obtained from extrapolation of an analytic equation of state outside the coexistence region. As the system size was increased, isotherms in the chem. potential-d. plane developed first two, then four, and finally six discontinuities. Visual inspection of selected snapshots revealed that the obsd. discontinuities are related to structural transitions between droplets (on the vapor side) and bubbles (on the liq. side) of spherical, cylindrical, and tetragonal shapes. A capillary drop model was developed to qual. rationalize these observations. Analytic results were obtained and found to be in full agreement with the computer simulation results. The anal. shows that the shape of the subcrit. isotherms is dictated by a single characteristic vol. (or length scale), which depends on the surface tension, compressibility, and coexistence densities. For small reduced system vols., the model predicts that a homogeneous fluid is stable across the whole coexistence region, thus explaining the continuous van der Waals isotherms obsd. in the simulations. When the liq. and vapor free energies are described by means of an accurate mean-field equation of state and surface tensions from simulation are employed, the capillary model is found to describe the simulated isotherms accurately, esp. for large systems (i.e., larger than about 15 mol. diams.) at low temp. (lower than about 0.85 times the crit. temp.). This implies that the Laplace pressure differences can be predicted for drops as small as five mol. diams., and as few as about 500 mols. The theor. study also shows that the extrema or apparent spinodal points of the finite size loops are more closely related to (finite system size) bubble and dew points than to classical spinodals. Our results are of relevance to phase transitions in nanopores and show that first order corrections to nucleation energies in finite closed systems are power laws of the inverse vol.**22**Wilhelmsen, Ø.; Bedeaux, D.; Kjelstrup, S.; Reguera, D. Communication: Superstabilization of fluids in nanocontainer.*J. Chem. Phys.*2014,*141*, 071103 DOI: 10.1063/1.4893701Google Scholar22https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXhsVWksL7L&md5=051af6ae7012ef7098e46defa4cc1959Communication: Superstabilization of fluids in nanocontainersWilhelmsen, Oeivind; Bedeaux, Dick; Kjelstrup, Signe; Reguera, DavidJournal of Chemical Physics (2014), 141 (7), 071103/1-071103/5CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)One of the main challenges of thermodn. is to predict and measure accurately the properties of metastable fluids. Investigation of these fluids is hindered by their spontaneous transformation by nucleation into a more stable phase. We show how small closed containers can be used to completely prevent nucleation, achieving infinitely long-lived metastable states. Using a general thermodn. framework, we derive simple formulas to predict accurately the conditions (container sizes) at which this superstabilization takes place and it becomes impossible to form a new stable phase. This phenomenon opens the door to control nucleation of deeply metastable fluids at exptl. feasible conditions, having important implications in a wide variety of fields. (c) 2014 American Institute of Physics.**23**Wilhelmsen, Ø.; Reguera, D. Evaluation of finite-size effects in cavitation and droplet formation.*J. Chem. Phys.*2015,*142*, 064703 DOI: 10.1063/1.4907367Google Scholar23https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXis1Shtrs%253D&md5=25a148add9929ab2b4cb121551e39bbdEvaluation of finite-size effects in cavitation and droplet formationWilhelmsen, Oeivind; Reguera, DavidJournal of Chemical Physics (2015), 142 (6), 064703/1-064703/9CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)Nucleation of bubbles and droplets is of fundamental interest in science and technol. and has been widely investigated through expts., theory, and simulations. Giving the rare event nature of these phenomena, nucleation simulations are computationally costly and require the use of a limited no. of particles. Moreover, they are often performed in the canonical ensemble, i.e., by fixing the total vol. and no. of particles, to avoid the addnl. complexities of implementing a barostat. However, cavitation and droplet formation take place differently depending on the ensemble. Here, we analyze the importance of finite-size effects in cavitation and droplet formation. We present simple formulas which predict the finite-size corrections to the crit. size, the nucleation barrier, and the nucleation rates in the canonical ensemble very accurately. These results can be used to select an appropriate system-size for simulations and to get a more precise evaluation of nucleation in complex substances, by using a small no. of mols. and correcting for finite-size effects. (c) 2015 American Institute of Physics.**24**Yang, A. J.-M. The thermodynamical stability of the heterogeneous system with a spherical interface.*J. Chem. Phys.*1985,*82*, 2082– 2085, DOI: 10.1063/1.448344Google Scholar24https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaL2MXhsFGhtbs%253D&md5=7569c861a2646e5fce3e233281382aeaThe thermodynamical stability of the heterogeneous system with a spherical interfaceYang, Arthur Jing MinJournal of Chemical Physics (1985), 82 (4), 2082-5CODEN: JCPSA6; ISSN:0021-9606.A 1-component system, a liq. drop in equil. with its vapor, was studied in the discussion of the stability of a heterogeneous system with a spherical interface. Due to the complexity of the 2nd-order functional differentiation of the thermodynamical potential function, a simpler treatment with the use of surface thermodn. is provided instead. The Gibbs free energy and the Grand potential are at a saddle point if resp. natural thermodynamical variables are held const. The Helmholtz free energy for this system at const. temp., vol., and N is either at a saddle point or a min. depending on the relative ratio of the two phases. This agrees with a previous result. The method developed here can be used in a homogeneous nucleation to study the initial fluctuation which results in the formation of the crit. nucleus. The use of the surface thermodn. to study a kinetic process is discussed.**25**Gjennestad, M. Aa.; Wilhelmsen, Ø. Thermodynamic stability of droplets, bubbles and thick films in open and closed pores.*Fluid Phase Equilib.*2020,*505*, 112351 DOI: 10.1016/j.fluid.2019.112351Google Scholar25https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXitFamtb3J&md5=580c898f24427878271f0f5125a51164Thermodynamic stability of droplets, bubbles and thick films in open and closed poresGjennestad, Magnus Aa.; Wilhelmsen, OeivindFluid Phase Equilibria (2020), 505 (), 112351CODEN: FPEQDT; ISSN:0378-3812. (Elsevier B.V.)We combine a capillary description with the cubic-plus-assocn. equation of state to study the thermodn. stability of droplets, bubbles and films of water at 358 K in a cylindrically sym. pore. The equil. structure depends strongly on the size of the pore and whether the pore is closed or connected to a particle reservoir (grand canonical ensemble). A new methodol. is presented to analyze the thermodn. stability of films, where the integral that describes the total energy of the system is approximated by a quadrature rule. We show that, for large pores, the thermodn. stability limit of adsorbed droplets and bubbles in both open and closed pores is governed by their mech. stability, which is closely linked to the pore shape. In open pores, the film is chem. unstable except for very low film-phase contact angles and for a limited range in external pressure. This result emphasizes the need to invoke a complete thermodn. stability anal., and not restrict the discussion to mech. stability. A common feature for most of the heterogeneous structures examd. is the appearance of regions where the structure is metastable with respect to a pore filled with a homogeneous fluid. In the closed pores, these regions grow considerably in size when the pores become smaller. This can be understood from the larger energy cost of the interfaces relative to the energy gained from having two phases. Complete phase diagrams are presented that compare all the investigated structures.**26**Neimark, A. V.; Kornev, K. G. Classification of equilibrium configurations of wetting films on planar substrates.*Langmuir*2000,*16*, 5526– 5529, DOI: 10.1021/la000267bGoogle Scholar26https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3cXjsF2qtrw%253D&md5=7d64afc561b4328628c567683db25716Classification of Equilibrium Configurations of Wetting Films on Planar SubstratesNeimark, Alexander V.; Kornev, Konstantin G.Langmuir (2000), 16 (13), 5526-5529CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)The authors suggest a rigorous formulation of the problem of classification of equil. configurations of wetting films on solid surfaces and in pores taking into account capillary and adhesion forces. As example, cylindrical films and drops of a van der Waals liq. on planar substrates are considered. Rewritten as a dynamic system, the Derjaguin equation for equil. interfaces is analyzed in detail without numeric calcn. of interfacial profiles, providing a simple way for understanding the different wetting regimes. This method allows us to enrich the arsenal of well-known explicit solns. responsible for clarifying such phys. problems as wetting and dewetting, capillary condensation and desorption, imbibition and drainage, droplet formation, and foaming on inhomogeneous substrates and in pores.**27**Neimark, A. V. Thermodynamic equilibrium and stability of liquid films and droplets on fibers.*J. Adhes. Sci. Technol.*1999,*13*, 1137– 1154, DOI: 10.1163/156856199X00839Google Scholar27https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK1MXntlyhtrc%253D&md5=36b4cacbb33d8baee2468b2c519538d4Thermodynamic equilibrium and stability of liquid films and droplets on fibersNeimark, Alexander V.Journal of Adhesion Science and Technology (1999), 13 (10), 1137-1154CODEN: JATEE8; ISSN:0169-4243. (VSP BV)The modeling of liq. spreading and penetration into fibrous materials requires a better understanding of the interactions of thin liq. films and small droplets with single fibers. The wetting properties of fibers may differ significantly from those of plane solid surfaces. Convex surfaces of fibers imply a pos. Laplace pressure acting on the liq.-gas interface. This effect causes liq. film instability and hinders droplet spreading. Liq. films on fibers are stable when the destabilizing action of the Laplace pressure is balanced by liq.-solid adhesion. Equil. configurations of liq. droplets and films are detd. by the competition between capillary and adhesion forces. A general anal. soln. is presented for the equil. profile of the transition zone between a film and a droplet residing on a cylindrical fiber. A new equation for apparent contact angles on fibers is derived. Adhesion forces, including van der Waals and polar interactions, are expressed in terms of disjoining pressure. Explicit formulas for calcns. of equil. droplet profiles, film thicknesses, apparent contact angles, and stability factors are presented in the form of expressions which include both the measurable geometrical parameters and the presumably known parameters of liq.-solid interactions, such as apolar and polar spreading coeffs. The method is applicable for analyses of apparent contact angles and film stability on fibers and other cylindrical surfaces, particularly nanofibers. A transition from partial wetting to non-wetting may occur as the fiber diam. decreases. Depending on the fiber diam., contact angles of water on hydrophobic C fibers may vary from 75° (plane graphite surface) to 100-130° (C nanotubes).**28**MacDowell, L. G. Computer simulation of interface potentials: Towards a first principle description of complex interfaces.*Eur. Phys. J.: Spec. Top.*2011,*197*, 131– 145, DOI: 10.1140/epjst/e2011-01447-6Google Scholar28https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XntVGq&md5=8a00fb36bce66ab7ee057e4f496da7a3Computer simulation of interface potentials: towards a first principle description of complex interfaces?MacDowell, L. G.European Physical Journal: Special Topics (2011), 197 (Discussion and Debate: Wetting and Spreading Science: Quo Vadis?), 131-145CODEN: EPJSAC; ISSN:1951-6401. (EDP Sciences)We discuss the feasibility of a hierarchical protocol whereby the description and prediction of adsorbed fluids in confined systems at the mesoscopic scale is achieved by use of interface potentials that are obtained from raw mol. simulation data. Starting from a micro-scopic description of a fluid's interface on a flat substrate, we attempt to ext. the min. information that is required in order to predict the behavior of that fluid at larger length scales from coarse grained surface Hamiltonians. A crit. assessment of this procedure hinges on controversial aspects of wetting behavior and more generally on the meaning of metastability and instability of thermodn. systems.**29**MacDowell, L. G.; Benet, J.; Katcho, N. A. Capillary fluctuations and film-height-dependent surface tension of an adsorbed liquid film.*Phys. Rev. Lett.*2013,*111*, 047802 DOI: 10.1103/PhysRevLett.111.047802Google Scholar29https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXht1Ogt7vN&md5=fafd871b579540245e9abc0bda9ba871Capillary fluctuations and film-height-dependent surface tension of an adsorbed liquid filmMacDowell, Luis G.; Benet, Jorge; Katcho, Nebil A.Physical Review Letters (2013), 111 (4), 047802/1-047802/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)The understanding of both structure and dynamics of adsorbed liqs. heavily relies on the capillary wave Hamiltonian, but a thorough test of this model is still lacking. Here the capillary wave fluctuations of a liq. film with short-range forces adsorbed on a solid exhibiting van der Waals interactions were studied. The measured capillary wave spectrum right above the first order wetting transition provides an interface potential consistent with independent calcns. from thermodn. integration. However, the surface tension exhibits an oscillatory film thick dependence which reveals a hitherto unnoticed capillary wave broadening mechanism beyond mere interfacial displacements.**30**Pahlavan, A. A.; Cueto-Felgueroso, L.; Hosoi, A. E.; McKinley, G. H.; Juanes, R. Thin films in partial wetting: Stability, dewetting and coarsening.*J. Fluid Mech.*2018,*845*, 642– 681, DOI: 10.1017/jfm.2018.255Google Scholar30https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXitlKku77J&md5=c07ea3e85d875c62328480c8a6a861c1Thin films in partial wetting: stability, dewetting and coarseningPahlavan, A. Alizadeh; Cueto-Felgueroso, L.; Hosoi, A. E.; McKinley, G. H.; Juanes, R.Journal of Fluid Mechanics (2018), 845 (), 642-681CODEN: JFLSA7; ISSN:0022-1120. (Cambridge University Press)A uniform nanometric thin liq. film on a solid substrate can become unstable due to the action of van der Waals (vdW) forces. The instability leads to dewetting of the uniform film and the formation of drops. To minimize the total free energy of the system, these drops coarsen over time until one single drop remains. Here, using a thermodynamically consistent framework, we derive a new model for thin films in partial wetting with a free energy that resembles the Cahn-Hilliard form with a height-dependent surface tension that leads to a generalized disjoining pressure, and revisit the dewetting problem. Using both linear stability anal. and nonlinear simulations we show that the new model predicts a slightly smaller crit. instability wavelength and a significantly (up to six-fold) faster growth rate than the classical model in the spinodal regime; this faster growth rate brings the theor. predictions closer to published exptl. observations. During coarsening at intermediate times, the dynamics become self-similar and model-independent; we therefore observe the same scalings in both the classical (with and without thermal noise) and new models. Both models also lead to a mean-field Lifshitz-Slyozov-Wagner (LSW)-type droplet-size distribution at intermediate times for small drop sizes. We, however, observe a skewed drop-size distribution for larger drops in the new model; while the tail of the distribution follows a Smoluchowski equation, it is not assocd. with a coalescence-dominated coarsening, calling into question the assocn. made in some earlier expts. Our observations point to the importance of the height dependence of surface tension in the early and late stages of dewetting of nanometric films and motivate new high-resoln. exptl. observations to guide the development of improved models of interfacial flows at the nanoscale.**31**Kheshgi, H. S.; Scriven, L. Dewetting: Nucleation and growth of dry regions.*Chem. Eng. Sci.*1991,*46*, 519– 526, DOI: 10.1016/0009-2509(91)80012-NGoogle Scholar31https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK3MXhtVGjs7k%253D&md5=bd33a4450b0cef9f1c03355fbd9dbf60Dewetting: nucleation and growth of dry regionsKheshgi, Haroon S.; Scriven, L. E.Chemical Engineering Science (1991), 46 (2), 519-26CODEN: CESCAC; ISSN:0009-2509.Dewetting of a solid surface covered by a film of nonwetting liq. proceeds from a preexisting dry patch or edge or initiates from some film-thinning disturbance that grows until the film ruptures. Local thinning can be caused by evapn.; by drainage due to gravity or capillarity-driven flow, esp. from sharp surfaces; or by surface tension gradients, such as are caused by surfactants delivered by particles falling on the film. Once a nonwetting film is sufficiently thinned, conjoining (neg. disjoining) pressure can accelerate thinning until rupture. This catastrophic rupture is modeled by solving the Navier-Stokes system approximated for thickness variations over distances that are long compared with the mean film thickness, and augmented with conjoining pressure. Rupture leads to film retraction and formation of a dry patch. These phenomena are visualized via moire topog. Of special interest are local spreading disturbances, where airborne particles fall on the film surface; craters or dry patches often nucleate. Implications for coating operations are discussed.**32**Ruckenstein, E.; Jain, R. K. Spontaneous rupture of thin liquid films.*J. Chem. Soc., Faraday Trans. 2*1974,*70*, 132– 147, DOI: 10.1039/f29747000132Google Scholar32https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaE2cXhsV2htrs%253D&md5=ae4c4035bde3b1d88e4aa39b5d13657bSpontaneous rupture of thin liquid filmsRuckenstein, Eli; Jain, Rakesh K.Journal of the Chemical Society, Faraday Transactions 2: Molecular and Chemical Physics (1974), 70 (1), 132-47CODEN: JCFTBS; ISSN:0300-9238.Hydrodynamic linear stability theory was used to examine the rupture of a liq. film on a solid surface and of a free liq. film. The lubrication approxn. of the hydrodynamic equations of motion was used and the system described by the Navier-Stokes equations. The range of wavelengths of the applied perturbation for which instability occurred was estd. and the time of rupture was calcd. The effect of insol. and sol. surface active agents was examd. Exptl. data for condensation on a solid surface and coalescence of bubbles was discussed.**33**Silin, D.; Virnovsky, G. A variational model of disjoining pressure: Liquid film on a nonplanar surface.*Transp. Porous Media*2010,*82*, 485– 505, DOI: 10.1007/s11242-009-9424-zGoogle Scholar33https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXjvFagtro%253D&md5=8f4ba48cee74682a09b1b7d5b8bcc792A Variational Model of Disjoining Pressure: Liquid Film on a Nonplanar SurfaceSilin, Dmitriy; Virnovsky, GeorgeTransport in Porous Media (2010), 82 (3), 485-505CODEN: TPMEEI; ISSN:0169-3913. (Springer)Variational methods have been successfully used in modeling thin liq. films in numerous theor. studies of wettability. In this article, the variational model of the disjoining pressure is extended to the general case of a two-dimensional solid surface. The Helmholtz free energy functional depends both on the disjoining pressure isotherm and on the shape of the solid surface. The augmented Young-Laplace equation (AYLE) is a nonlinear second-order partial differential equation. A no. of solns. describing wetting films on spherical grains have been obtained. In the case of cylindrical films, the phase portrait technique describes the entire variety of math. feasible solns. It turns out that a periodic soln., which would describe wave-like wetting films, does not satisfy Jacobi's condition of the classical calculus of variations. Therefore, such a soln. is nonphys. The roughness of the solid surface significantly affects liq. film stability. AYLE solns. suggest that film rupture is more likely at a location where the pore-wall surface is most exposed into the pore space, and the curvature is pos.**34**Sharma, A. Equilibrium and dynamics of evaporating or condensing thin fluid domains: Thin film stability and heterogeneous nucleation.*Langmuir*1998,*14*, 4915– 4928, DOI: 10.1021/la971389fGoogle Scholar34https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK1cXkslGks7g%253D&md5=5dbfdb7f8638ba5c4db18306af31f998Equilibrium and Dynamics of Evaporating or Condensing Thin Fluid Domains: Thin Film Stability and Heterogeneous NucleationSharma, AshutoshLangmuir (1998), 14 (17), 4915-4928CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)A continuum theory is presented for the equil. and dynamics of evapg./condensing thin (<100 nm) fluid domains on solid surfaces. The local rate of evapn./condensation depends crucially on the local curvature and disjoining pressure. The phenomena of heterogeneous nucleation and thin film stability on partially wettable surfaces are considered. All of the results for these nanoscale phenomena are consistently interpreted in terms of the macroscopic parameters of wetting, e.g., the apolar van der Waals and the polar (e.g., acid-base) components of the spreading coeff. and the macroscopic equil. contact angle. Finite size effects (disjoining pressure) and adsorption can reduce the size, contact angle, and nucleation energy of crit. nuclei very substantially as compared to predictions of the classical theory of nucleation. The instability and dewetting (hole formation) of thin evapg. H2O films on partially wettable surfaces are caused by the hydrophobic attraction, whereas the van der Waals interaction promotes the film stability and wetting. Dynamic simulations are performed, and simple anal. results are obtained for the length and time scales of the surface instability for H2O films. Curiously, in contrast to the case of nonevaporating films, the no. d. of holes may decrease with increased strength of the hydrophobic attraction, because stronger attraction forces the onset of instability at higher thickness.**35**Berg, J. C.*An Introduction to Interfaces & Colloids: The Bridge to Nanoscience*; World Scientific, 2010.Google ScholarThere is no corresponding record for this reference.**36**Callen, H. B.*Thermodynamics and an Introduction to Thermostatistics*, 2nd ed.; John Wiley & Sons, 1985.Google ScholarThere is no corresponding record for this reference.**37**Vrij, A. Possible mechanism for the spontaneous rupture of thin, free liquid films.*Discuss. Faraday Soc.*1966,*42*, 23– 33, DOI: 10.1039/df9664200023Google ScholarThere is no corresponding record for this reference.**38**MacDowell, L. G.; Benet, J.; Katcho, N. A.; Palanco, J. M. Disjoining pressure and the film-height-dependent surface tension of thin liquid films: New insight from capillary wave fluctuations.*Adv. Colloid Interface Sci.*2014,*206*, 150– 171, DOI: 10.1016/j.cis.2013.11.003Google Scholar38https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXhvFGrsLrJ&md5=5806ffc1f81bd892d47713f9fabc9fc9Disjoining pressure and the film-height-dependent surface tension of thin liquid films: New insight from capillary wave fluctuationsMacDowell, Luis G.; Benet, Jorge; Katcho, Nebil A.; Palanco, Jose M. G.Advances in Colloid and Interface Science (2014), 206 (), 150-171CODEN: ACISB9; ISSN:0001-8686. (Elsevier B.V.)A review. Reviewed are simulation and exptl. studies of thermal capillary wave fluctuations as an ideal means for probing the underlying disjoining pressure and surface tensions, and more generally, fine details of the Interfacial Hamiltonian Model. Discussed are recent simulation results that reveal a film-height-dependent surface tension not accounted for in the classical Interfacial Hamiltonian Model. It is shown how this observation may be explained bottom-up from sound principles of statistical thermodn. and discuss some of its implications.**39**Boinovich, L. DLVO forces in thin liquid films beyond the conventional DLVO theory.*Curr. Opin. Colloid Interface Sci.*2010,*15*, 297– 302, DOI: 10.1016/j.cocis.2010.05.003Google Scholar39https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXhtVGhsrbF&md5=e13c0890edb50fea999f4f1f2d4ab492DLVO forces in thin liquid films beyond the conventional DLVO theoryBoinovich, LudmilaCurrent Opinion in Colloid & Interface Science (2010), 15 (5), 297-302CODEN: COCSFL; ISSN:1359-0294. (Elsevier B.V.)A review. Further progress has taken place in the theory of surface forces beyond the conventional DLVO theory. The major recent advances are related to more accurate accounting for the ionic nature of liq. interlayer in the calcns. of van der Waals forces and for the impact of dispersion interaction of ions with other ions or confining phases on the peculiarities of ion-electrostatic interactions in liq. films.**40**Thiele, U.; Mertig, M.; Pompe, W. Dewetting of an evaporating thin liquid film: Heterogeneous nucleation and surface instability.*Phys. Rev. Lett.*1998,*80*, 2869, DOI: 10.1103/PhysRevLett.80.2869Google Scholar40https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK1cXitVShtro%253D&md5=0d794da6911216b70147ef611518b1c9Dewetting of an evaporating thin liquid film: heterogeneous nucleation and surface instabilityThiele, Uwe; Mertig, Michael; Pompe, WolfgangPhysical Review Letters (1998), 80 (13), 2869-2872CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)Film rupture as the initial stage of dewetting is investigated for a volatile, spin-coated nonwetting film. During structure formation in the liq. film thickness is continuously reduced via evapn. The dynamical character of the expt. allows the study of hole formation caused by distinct rupture mechanisms occurring at different film thicknesses. Both heterogeneous nucleation for thick films as well as spinodal dewetting for film thickness below 10 nm have been obsd. The balance between both processes can be shifted by controlling the ambient humidity. The structures resulting from film rupture are quantified with respect to their different geometrical properties. For the first time we find that spinodal dewetting is caused by destabilizing polar interactions.**41**Emelyanenko, K. A.; Emelyanenko, A. M.; Boinovich, L. B. Van der waals forces in free and wetting liquid films.*Adv. Colloid Interface Sci.*2019, 357– 369, DOI: 10.1016/j.cis.2019.04.013Google Scholar41https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXhtVagur3M&md5=e549f0374c6f13d0de0f2f7986aa0afaVan der Waals forces in free and wetting liquid filmsEmelyanenko, Kirill A.; Emelyanenko, Alexandre M.; Boinovich, Ludmila B.Advances in Colloid and Interface Science (2019), 269 (), 357-369CODEN: ACISB9; ISSN:0001-8686. (Elsevier B.V.)Van der Waals interactions induced by fluctuations of electromagnetic field bear universal nature and act between individual atoms, condensed particles or bodies of any type. Continuously growing interest to theor. understanding as well as to precise evaluation of van der Waals forces is caused by their fundamental role in many phys., chem., and biol. processes. In this paper, we scrutinize progress in the studies of van der Waals forces, related to recent active development of Coupled Dipole Method (CDM) for the anal. of the behavior and properties of nanosized systems. The application of CDM for the anal. of thin liq. films allowed achieving substantial progress in understanding the behavior of free and wetting films. It was shown that both the macroscopic properties, such as excess free energy and Hamaker consts. and the local microscopic parameters, such as polarizabilities, can be successfully calcd. based only on properties of individual mols. The impact of lateral film confinement on the specific excess free energy and the film stability was elucidated, and effect of spatial constraints on the spectrum of vibrational states for liq. film and the underlying substrate was analyzed. It was shown that van der Waals interactions between mols. represent the universal mechanism for dynamic structuring and formation of boundary layers and that the CDM allows self-consistently calcg. the properties of these layers in both solid and liq. phases.**42**Kontogeorgis, G. M.; Voutsas, E. C.; Yakoumis, I. V.; Tassios, D. P. An equation of state for associating fluids.*Ind. Eng. Chem. Res.*1996,*35*, 4310– 4318, DOI: 10.1021/ie9600203Google Scholar42https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK28Xmt1GnsLg%253D&md5=4da4cf22fdac90c866145fe789b49065An Equation of State for Associating FluidsKontogeorgis, Georgios M.; Voutsas, Epaminondas C.; Yakoumis, Iakovos V.; Tassios, Dimitrios P.Industrial & Engineering Chemistry Research (1996), 35 (11), 4310-4318CODEN: IECRED; ISSN:0888-5885. (American Chemical Society)An equation of state (EoS) suitable for describing assocg. fluids is presented. The equation combines the simplicity of a cubic equation of state (the Soave-Redlich-Kwong), which is used for the phys. part and the theor. background of the perturbation theory employed for the chem. (or assocn.) part. The resulting EoS (Cubic Plus Assocn.) is not cubic with respect to vol. and contains five pure compd. parameters which are detd. using vapor pressures and satd. liq. densities. Excellent correlations of both vapor pressures and satd. liq. vols. are obtained for primary-alcs. (from methanol up to 1-tridecanol), phenol, tert-Bu alc., triethylene glycol, and water. Moreover, excellent prediction of satd. liq. vols. may be obtained from parameters which were estd. by regressing only vapor pressures. Finally, we suggest a method for reducing the no. of adjustable parameters for alcs. to three while maintaining the good correlation of vapor pressures and satd. liq. vols. We investigate the possibility of using the homomorph approach for estg. the EoS parameters and explain the problems obsd. The estd. pure compd. parameters were tested in the prediction of second virial coeffs. with satisfactory results.**43**Wilhelmsen, Ø.; Aasen, A.; Skaugen, G.; Aursand, P.; Austegard, A.; Aursand, E.; Gjennestad, M. Aa.; Lund, H.; Linga, G.; Hammer, M. Thermodynamic modeling with equations of state: present challenges with established methods.*Ind. Eng. Chem. Res.*2017,*56*, 3503– 3515, DOI: 10.1021/acs.iecr.7b00317Google Scholar43https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXktV2rsLo%253D&md5=5168dd9de5cbf69d7d6ca7641328d5c6Thermodynamic Modeling with Equations of State: Present Challenges with Established MethodsWilhelmsen, Oeivind; Aasen, Ailo; Skaugen, Geir; Aursand, Peder; Austegard, Anders; Aursand, Eskil; Gjennestad, Magnus Aa.; Lund, Halvor; Linga, Gaute; Hammer, MortenIndustrial & Engineering Chemistry Research (2017), 56 (13), 3503-3515CODEN: IECRED; ISSN:0888-5885. (American Chemical Society)A review. Equations of state (EoS) are essential in the modeling of a wide range of industrial and natural processes. Desired qualities of EoS are accuracy, consistency, computational speed, robustness and predictive ability outside of the domain where they have been fitted. In this work, we review present challenges assocd. with established models, and give suggestions on how to overcome them in the future. The most accurate EoS available, multiparameter EoS, have a second artificial Maxwell loop in the two-phase region that gives problems in phase-equil. calcns. and exclude them from important applications such as treatment of interfacial phenomena with mass based d. functional theory. Suggestions are provided on how this can be improved. Cubic EoS are among the most computationally efficient EoS, but they often lack sufficient accuracy. We show that extended corresponding state EoS are capable of providing significantly more accurate single-phase predictions than cubic EoS with only a doubling of the computational time. In comparison, the computational time of multiparameter EoS can be orders of magnitude larger. For mixts. in the two-phase region, however, the accuracy of extended corresponding state EoS has a large potential for improvement. The mol.-based SAFT family of EoS are preferred when predictive ability is important, e.g. for systems with strongly assocg. fluids or polymers where few exptl. data are available. We discuss some of their benefits and present challenges. A discussion is presented on why predictive thermodn. models for reactive mixts. such as CO2-NH3 and CO2-H2O-H2S must be developed in close combination with phase- and reaction equil. theory, regardless of the choice of EoS. After overcoming present challenges, a next-generation thermodn. modeling framework holds the potential to improve the accuracy and predictive ability in a wide range of applications such as process optimization, computational fluid dynamics, treatment of interfacial phenomena and processes with reactive mixts.**44**Troutman, J. L.*Variational Calculus and Optimal Control*, 2nd ed.; Springer, 1996.Google ScholarThere is no corresponding record for this reference.**45**Michelsen, M. L.; Mollerup, J. M.*Thermodynamic Models: Fundamentals & Computational Aspects*, 2nd ed.; Tie-Line Publications, 2007.Google ScholarThere is no corresponding record for this reference.**46**Aursand, P.; Gjennestad, M. Aa.; Aursand, E.; Hammer, M.; Wilhelmsen, Ø. The spinodal of single-and multi-component fluids and its role in the development of modern equations of state.*Fluid Phase Equilib.*2017,*436*, 98– 112, DOI: 10.1016/j.fluid.2016.12.018Google Scholar46https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXpsFyitw%253D%253D&md5=8fcc4bbe759df0412e2b5930db0a7a10The spinodal of single- and multi-component fluids and its role in the development of modern equations of stateAursand, Peder; Gjennestad, Magnus Aa.; Aursand, Eskil; Hammer, Morten; Wilhelmsen, OeivindFluid Phase Equilibria (2017), 436 (), 98-112CODEN: FPEQDT; ISSN:0378-3812. (Elsevier B.V.)The spinodal represents the limit of thermodn. stability of a homogeneous fluid. In this work, we present a robust methodol. to obtain the spinodal of multicomponent fluids described even with the most sophisticated equations of state (EoS) available. We elaborate how information about the spinodal and its uncertainty can contribute both in the development of modern EoS and to est. their uncertainty in the metastable regions. Inequality constraints are presented that can be exploited in the fitting of modern EoS of single-component fluids to avoid inadmissible pseudo-stable states between the vapor and liq. spinodals. We find that even cubic EoS violate some of these constraints. With the use of a selection of EoS representative of modern applications, we compare vapor and liq. spinodal curves, superheat and supersatn. limits from classic nucleation theory (CNT), and available exptl. data for the superheat limit. Computations are performed with pure species found in natural gas, binary mixts., as well as a multi-component natural gas mixt. in order to demonstrate the scalability of the approach. We demonstrate that there are large inconsistencies in predicted spinodals from a wide range of EoS such as cubic EoS, extended corresponding state EoS, SAFT and multiparameter EoS. The overall std. deviation in the prediction of the spinodal temps. were 1.4 K and 2.7 K for single- and multi-component liq.-spinodals and 6.3 K and 26.9 K for single- and multi-component vapor spinodals. The relationship between the measurable limit of superheat, or supersatn., and the theor. concept of the spinodal is discussed. While nucleation rates from CNT can deviate orders of magnitude from expts., we find that the limit of superheat from expts. agree within 1.0 K and 2.4 K with predictions from CNT for single- and multi-component fluids resp. We demonstrate that a large part of the metastable domain of the phase diagram is currently unavailable to expts., in particular for metastable vapor. Novel techniques, exptl. or with computational simulations, should be developed to characterize the thermodn. properties in these regions, and to identify the thermodn. states that define the spinodal.**47**Kierzenka, J.; Shampine, L. F. A BVP solver based on residual control and the Maltab PSE.*ACM Trans. Math. Software (TOMS)*2001,*27*, 299– 316, DOI: 10.1145/502800.502801Google ScholarThere is no corresponding record for this reference.**48**Jones, E.; Oliphant, T.; Peterson, P. SciPy: Open source scientific tools for Python, 2001. http://www.scipy.org/.Google ScholarThere is no corresponding record for this reference.**49**Anderson, E.; Bai, Z.; Bischof, C.; Blackford, S.; Demmel, J.; Dongarra, J.; Du Croz, J.; Greenbaum, A.; Hammarling, S.; McKenney, A.; Sorensen, D.*LAPACK Users’ Guide*, 3rd ed.; Society for Industrial and Applied Mathematics: Philadelphia, PA, 1999.Google ScholarThere is no corresponding record for this reference.

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## References

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**1**Churaev, N. V.; Derjaguin, B. V.; Muller, V. M.*Surface Forces*; Springer: New York, 1987.There is no corresponding record for this reference.**2**Boinovich, L.; Emelyanenko, A. Wetting and surface forces.*Adv. Colloid Interface Sci.*2011,*165*, 60– 69, DOI: 10.1016/j.cis.2011.03.0022https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXmtVWnsLo%253D&md5=79c0a6da5f54d334fbf4582ed2775ebfWetting and surface forcesBoinovich, Ludmila; Emelyanenko, AlexandreAdvances in Colloid and Interface Science (2011), 165 (2), 60-69CODEN: ACISB9; ISSN:0001-8686. (Elsevier B.V.)In this review we discuss the fundamental role of surface forces, with a particular emphasis on the effect of the disjoining pressure, in establishing the wetting regime in the three phase systems with both plane and curved geometry. The special attention is given to the conditions of the formation of wetting/adsorption liq. films on the surface of poorly wetted substrate and the possibility of their thermodn. equil. with bulk liq. The calcns. of contact angles on the basis of the isotherms of disjoining pressure and the difference in wettability of flat and highly curved surfaces are discussed. Mechanisms of wetting hysteresis, related to the action of surface forces, are considered.**3**Boinovich, L.; Emelyanenko, A. The prediction of wettability of curved surfaces on the basis of the isotherms of the disjoining pressure.*Colloids Surf., A*2011,*383*, 10– 16, DOI: 10.1016/j.colsurfa.2010.12.0203https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXmtlCrtb0%253D&md5=4012fd751e90492045a2eff81a33fe79The prediction of wettability of curved surfaces on the basis of the isotherms of the disjoining pressureBoinovich, Ludmila; Emelyanenko, AlexandreColloids and Surfaces, A: Physicochemical and Engineering Aspects (2011), 383 (1-3), 10-16CODEN: CPEAEH; ISSN:0927-7757. (Elsevier B.V.)The generalization of Derjaguin-Frumkin approach for the description of wettability of curved interfaces is given. The equations for the calcns. of the contact angle on concave and convex cylindrical and spherical surfaces based on the isotherms of the disjoining pressure are derived. Anal. performed has shown that for the radius of curvature comparable to the range of surface forces action increasing the surface curvature for convex surfaces results in the contact angle increasing, whereas for concave surfaces the wetting improves. It is shown that curving the substrate surface may cause philic/phobic or phobic/philic wettability transition.**4**Moura, M.; Flekkøy, E. G.; Måløy, K. J.; Schäfer, G.; Toussaint, R. Connectivity enhancement due to film flow in porous media.*Phys. Rev. Fluids*2019,*4*, 094102 DOI: 10.1103/PhysRevFluids.4.094102There is no corresponding record for this reference.**5**Zhao, B.; MacMinn, C. W.; Primkulov, B. K.; Chen, Y.; Valocchi, A. J.; Zhao, J.; Kang, Q.; Bruning, K.; McClure, J. E.; Miller, C. T.; Fakhari, A.; Bolster, D.; Hiller, T.; Brinkmann, M.; Cueto-Felgueroso, L.; Cogswell, D. A.; Verma, R.; Prodanović, M.; Maes, J.; Geiger, S.; Vassvik, M.; Hansen, A.; Segre, E.; Holtzman, R.; Yang, Z.; Yuan, C.; Chareyre, B.; Juanes, R. Comprehensive comparison of pore-scale models for multiphase flow in porous media.*Proc. Natl. Acad. Sci. U.S.A.*2019,*116*, 13799– 13806, DOI: 10.1073/pnas.19016191165https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXhtlChu7fJ&md5=540016d8663e0ffc3df9fe92f09ca4beComprehensive comparison of pore-scale models for multiphase flow in porous mediaZhao, Benzhong; MacMinn, Christopher W.; Primkulov, Bauyrzhan K.; Chen, Yu; Valocchi, Albert J.; Zhao, Jianlin; Kang, Qinjun; Bruning, Kelsey; McClure, James E.; Miller, Cass T.; Fakhari, Abbas; Bolster, Diogo; Hiller, Thomas; Brinkmann, Martin; Cueto-Felgueroso, Luis; Cogswell, Daniel A.; Verma, Rahul; Prodanovic, Masa; Maes, Julien; Geiger, Sebastian; Vassvik, Morten; Hansen, Alex; Segre, Enrico; Holtzman, Ran; Yang, Zhibing; Yuan, Chao; Chareyre, Bruno; Juanes, RubenProceedings of the National Academy of Sciences of the United States of America (2019), 116 (28), 13799-13806CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)Multiphase flows in porous media are important in many natural and industrial processes. Pore-scale models for multiphase flows have seen rapid development in recent years and are becoming increasingly useful as predictive tools in both academic and industrial applications. However, quant. comparisons between different pore-scale models, and between these models and exptl. data, are lacking. Here, we perform an objective comparison of a variety of state-of-the-art pore-scale models, including lattice Boltzmann, stochastic rotation dynamics, vol.-of-fluid, level-set, phase-field, and pore-network models. As the basis for this comparison, we use a dataset from recent microfluidic expts. with precisely controlled pore geometry and wettability conditions, which offers an unprecedented benchmarking opportunity. We compare the results of the 14 participating teams both qual. and quant. using several std. metrics, such as fractal dimension, finger width, and displacement efficiency. We find that no single method excels across all conditions and that thin films and corner flow present substantial modeling and computational challenges.**6**Gjennestad, M. Aa.; Vassvik, M.; Kjelstrup, S.; Hansen, A. Stable and efficient time integration at low capillary numbers of a dynamic pore network model for immiscible two-phase flow in porous media.*Front. Phys.*2018,*6*, 56 DOI: 10.3389/fphy.2018.00056There is no corresponding record for this reference.**7**Gjennestad, M. Aa.; Winkler, M.; Hansen, A. Pore network modeling of the effects of viscosity ratio and pressure gradient on steady-state incompressible two-phase flow in porous media.*Transp. Porous Media*2020,*132*, 355– 379, DOI: 10.1007/s11242-020-01395-z7https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXkvFCjsLY%253D&md5=16f0123f57b0ad0dd0baac19ebc8b33aPore Network Modeling of the Effects of Viscosity Ratio and Pressure Gradient on Steady-State Incompressible Two-Phase Flow in Porous MediaGjennestad, Magnus Aa.; Winkler, Mathias; Hansen, AlexTransport in Porous Media (2020), 132 (2), 355-379CODEN: TPMEEI; ISSN:0169-3913. (Springer)Abstr.: We perform steady-state simulations with a dynamic pore network model, corresponding to a large span in viscosity ratios and capillary nos. From these simulations, dimensionless steady-state time-averaged quantities such as relative permeabilities, residual saturations, mobility ratios and fractional flows are computed. These quantities are found to depend on three dimensionless variables, the wetting fluid satn., the viscosity ratio and a dimensionless pressure gradient. Relative permeabilities and residual saturations show many of the same qual. features obsd. in other exptl. and modeling studies. The relative permeabilities do not approach straight lines at high capillary nos. for viscosity ratios different from 1. Our conclusion is that this is because the fluids are not in the highly miscible near-crit. region. Instead they have a viscosity disparity and intermix rather than forming decoupled, similar flow channels. Ratios of av. mobility to their high capillary no. limit values are also considered. Roughly, these vary between 0 and 1, although values larger than 1 are also obsd. For a given satn., the mobilities are not always monotonically increasing with the pressure gradient. While increasing the pressure gradient mobilizes more fluid and activates more flow paths, when the mobilized fluid is more viscous, a redn. in av. mobility may occur.**8**Spernjak, D.; Prasad, A. K.; Advani, S. G. Experimental investigation of liquid water formation and transport in a transparent single-serpentine PEM fuel cell.*J. Power Sources*2007,*170*, 334– 344, DOI: 10.1016/j.jpowsour.2007.04.0208https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2sXmt1GrtLo%253D&md5=dd916e01879f57dc6e185806a5b56e8bExperimental investigation of liquid water formation and transport in a transparent single-serpentine PEM fuel cellSpernjak, Dusan; Prasad, Ajay K.; Advani, Suresh G.Journal of Power Sources (2007), 170 (2), 334-344CODEN: JPSODZ; ISSN:0378-7753. (Elsevier B.V.)Liq. water formation and transport were investigated by direct exptl. visualization in an operational transparent single-serpentine polymer electrolyte membrane (PEM) fuel cell. We examd. the effectiveness of various gas diffusion layer materials in removing water away from the cathode and through the flow field over a range of operating conditions. Complete polarization curves as well as time evolution studies after step changes in current draw were obtained with simultaneous liq. water visualization within the transparent cell. The level of cathode flow field flooding, under the same operating conditions and cell current, was recognized as a criterion for the water removal capacity of the gas diffusion layer materials. When compared at the same c.d. (i.e., water prodn. rate), higher amt. of liq. water in the cathode channel indicated that water had been efficiently removed from the catalyst layer. Visualization of the anode channel was used to investigate the influence of the microporous layer on water transport. No liq. water was obsd. in the anode flow field unless cathode gas diffusion layers had an microporous layer. Microporous layer on the cathode side creates a pressure barrier for water produced at the catalyst layer. Water is pushed across the membrane to the anode side, resulting in anode flow field flooding close to the H2 exit.**9**Thickett, S. C.; Neto, C.; Harris, A. T. Biomimetic surface coatings for atmospheric water capture prepared by dewetting of polymer films.*Adv. Mater.*2011,*23*, 3718– 3722, DOI: 10.1002/adma.2011002909https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXovVCmtbo%253D&md5=c8fa87586d070936c10386bd6b949a02Biomimetic Surface Coatings for Atmospheric Water Capture Prepared by Dewetting of Polymer FilmsThickett, Stuart C.; Neto, Chiara; Harris, Andrew T.Advanced Materials (Weinheim, Germany) (2011), 23 (32), 3718-3722CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH & Co. KGaA)Dewetting is the process by which unstable thin (=100 nm) liq. films spontaneously break apart on a substrate, driven by unfavorable intermol. forces at the interface between the two materials. The unstable film breaks apart into holes that grow with time, eventually transforming the film into a series of isolated droplets. Above its glass transition temp. (Tg), an unstable thin polymer film on a solid substrate spontaneously undergoes morphol. transformation via dewetting. When the polymer film is cooled below Tg, the resultant pattern is "frozen in," preserving the droplet morphol. We have exploited the resultant pattern to create biomimetic surfaces, whereby the dewetted polymer droplets mimic the hydrophilic bumps on the Stenocara exoskeleton. To create a final surface with wettability contrast between the droplet phase and the background, we investigated the dewetting of an immiscible polymer bilayer, consisting of a hydrophilic polymer layer on top of a hydrophobic polymer underlayer. The results presented here already demonstrate a facile and scalable methodol. to create surface coatings that capture significant vols. of water using low-cost materials and requiring only the cooling of the surface below the dew point. In many urban environments, water could be collected on these surfaces at night, taking advantage of radiative cooling of the substrate.**10**Xiao, R.; Maroo, S. C.; Wang, E. N. Negative pressures in nanoporous membranes for thin film evaporation.*Appl. Phys. Lett.*2013,*102*, 123103 DOI: 10.1063/1.479824310https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXks1Oks78%253D&md5=05e6f231843388d6b6180c7ec5037c3eNegative pressures in nanoporous membranes for thin film evaporationXiao, Rong; Maroo, Shalabh C.; Wang, Evelyn N.Applied Physics Letters (2013), 102 (12), 123103/1-123103/4CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)We present a nanoporous membrane-based approach, which decouples the capillary pressure from the viscous resistance, to achieve high driving pressures and efficient liq. delivery for thin film evapn. By using Al2O3 membranes with ≈150 nm pore diams., abs. liq. pressures as low as -300 kPa were achieved using iso-Pr alc., while dissipating max. interfacial heat fluxes of ≈96 W/cm2. Design guidelines are provided to achieve higher interfacial heat fluxes with reduced membrane thicknesses. This work shows a promising approach to address thermal management needs for next generation electronic devices. (c) 2013 American Institute of Physics.**11**Zhao, J.-J.; Duan, Y.-Y.; Wang, X.-D.; Wang, B.-W. Effects of superheat and temperature-dependent thermophysical properties on evaporating thin liquid films in microchannels.*Int. J. Heat Mass Transfer*2011,*54*, 1259– 1267, DOI: 10.1016/j.ijheatmasstransfer.2010.10.026There is no corresponding record for this reference.**12**Ju, Y. S.; Kaviany, M.; Nam, Y.; Sharratt, S.; Hwang, G. S.; Catton, I.; Fleming, E.; Dussinger, P. Planar vapor chamber with hybrid evaporator wicks for the thermal management of high-heat-flux and high-power optoelectronic devices.*Int. J. Heat Mass Transfer*2013,*60*, 163– 169, DOI: 10.1016/j.ijheatmasstransfer.2012.12.05812https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXktlCktr8%253D&md5=2db885be3f4825e974a35a10905e4ee7Planar vapor chamber with hybrid evaporator wicks for the thermal management of high-heat-flux and high-power optoelectronic devicesJu, Y. Sungtaek; Kaviany, M.; Nam, Y.; Sharratt, S.; Hwang, G. S.; Catton, I.; Fleming, E.; Dussinger, P.International Journal of Heat and Mass Transfer (2013), 60 (), 163-169CODEN: IJHMAK; ISSN:0017-9310. (Elsevier Ltd.)Heat spreaders based on compact vapor chambers offer one attractive approach to the thermal management of high-power electronics. We report our design and exptl. characterization of advanced evaporator wicks and thin planar vapor chambers incorporating these wicks. The hybrid wicks combine distributed high-permeability liq. supply structures with thin (monolayer) evapn. layers to achieve both low thermal resistance and high limiting heat fluxes over large heating areas. We model and exptl. characterize the capillary and heat transfer performance of liq. spreading layers consisting of mono-layers of Cu particles and identify a range of optimal particle diams. maximizing their performance. The thin liq. spreading layers are integrated with three different types of liq. supply structures, namely, columnar arteries, converging lateral arteries, and bi-porous structures. The resulting hybrid wicks show comparable heat transfer performances with crit. limiting heat fluxes >350 W/cm2 over heating areas of 1 cm2 and peak heat transfer coeffs. >20 W/cm2 K. These results confirm the effectiveness of our hybrid wick designs and also that evapn. heat transfer is dominated by the liq. spreading layers. A prototype vapor chamber incorporating CTE-tailored envelopes and the hybrid wick is developed for potential applications in the thermal management of laser diode arrays. We demonstrate an evaporator resistance of approx. 0.075 K/(W/cm2), while removing over 1500 W from a 4 cm2 heating area.**13**Kandlikar, S. G. Fundamental issues related to flow boiling in minichannels and microchannels.*Exp. Therm. Fluid Sci.*2002,*26*, 389– 407, DOI: 10.1016/S0894-1777(02)00150-413https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD38XktlKgu7o%253D&md5=4ade7d4ceed0541ebac95e5b58a704a1Fundamental issues related to flow boiling in minichannels and microchannelsKandlikar, Satish G.Experimental Thermal and Fluid Science (2002), 26 (2-4), 389-407CODEN: ETFSEO; ISSN:0894-1777. (Elsevier Science Inc.)A review. Flow boiling in small hydraulic diam. channels is becoming increasingly important in many diverse applications. The previous studies addressing the effects of the channel size on the flow patterns, and heat transfer and pressure drop performance are reviewed. The fundamental questions related to the presence of nucleate boiling and characteristics of flow boiling in microchannels and minichannels in comparison to that in the conventional channel sizes (3 mm and above) are addressed. Also, the effect of heat exchanger configuration-single-channel and multichannel-on the heat transfer and pressure drop performance is reviewed. The areas for future research are identified.**14**Setu, S. A.; Dullens, R. P. A.; Hernández-Machado, A.; Pagonabarraga, I.; Aarts, D. G. A. L.; Ledesma-Aguilar, R. Superconfinement tailors fluid flow at micro-scales.*Nat. Commun.*2015,*6*, 7297 DOI: 10.1038/ncomms829714https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXhtF2ktrvL&md5=7c086b672d64e3753da30a816bbe4f65Superconfinement tailors fluid flow at microscalesSetu, Siti Aminah; Dullens, Roel P. A.; Hernandez-Machado, Aurora; Pagonabarraga, Ignacio; Aarts, Dirk G. A. L.; Ledesma-Aguilar, RodrigoNature Communications (2015), 6 (), 7297CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)Understanding fluid dynamics under extreme confinement, where device and intrinsic fluid length scales become comparable, is essential to successfully develop the coming generations of fluidic devices. Here we report measurements of advancing fluid fronts in such a regime, which we dub superconfinement. We find that the strong coupling between contact-line friction and geometric confinement gives rise to a new stability regime where the max. speed for a stable moving front exhibits a distinctive response to changes in the bounding geometry. Unstable fronts develop into drop-emitting jets controlled by thermal fluctuations. Numerical simulations reveal that the dynamics in superconfined systems is dominated by interfacial forces. Henceforth, we present a theory that quantifies our expts. in terms of the relevant interfacial length scale, which in our system is the intrinsic contact-line slip length. Our findings show that length-scale overlap can be used as a new fluid-control mechanism in strongly confined systems.**15**McGraw, J. D.; Bäumchen, O.; Klos, M.; Haefner, S.; Lessel, M.; Backes, S.; Jacobs, K. Nanofluidics of thin polymer films: Linking the slip boundary condition at solidliquid interfaces to macroscopic pattern formation and microscopic interfacial properties.*Adv. Colloid Interface Sci.*2014,*210*, 13– 20, DOI: 10.1016/j.cis.2014.03.01015https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXmvFSjs7g%253D&md5=4f840f12feb822e039ab1ed21f8e50b5Nanofluidics of thin polymer films: Linking the slip boundary condition at solid-liquid interfaces to macroscopic pattern formation and microscopic interfacial propertiesMcGraw, Joshua D.; Baeumchen, Oliver; Klos, Mischa; Haefner, Sabrina; Lessel, Matthias; Backes, Sebastian; Jacobs, KarinAdvances in Colloid and Interface Science (2014), 210 (), 13-20CODEN: ACISB9; ISSN:0001-8686. (Elsevier B.V.)If a thin liq. film is not stable, different rupture mechanisms can be obsd. causing characteristic film morphologies: spinodal dewetting and dewetting by nucleation of holes. This rupturing entails liq. flow and opens new possibilities to study microscopic phenomena. Here we use this process of dewetting to gain insight on the slip boundary condition at the solid-liq. interface. Having established hydrodynamic models that allow for the detn. of the slip length in a dewetting expt. based on nucleation, we move on to the quantification and mol. description of slip effects in various systems. For the late stage of the dewetting process involving the Rayleigh-Plateau instability, several distinct droplet patterns can be obsd. We describe the importance of slip in detg. what pattern may be found. In order to control the slip length, we use polymeric liqs. on different hydrophobic coatings of silicon wafers. We find that subtle changes in the coating can lead to large changes in the slip length. Thus, we gain insight into the question of how the structure of the substrate affects the slip length.**16**Snustad, I.; Røe, I. T.; Brunsvold, A.; Ervik, A.; He, J.; Zhang, Z. A review on wetting and water condensation - Perspectives for CO_{2}condensation.*Adv. Colloid Interface Sci.*2018,*256*, 291– 304, DOI: 10.1016/j.cis.2018.03.00816https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXntlSmtb8%253D&md5=021109491e9024dbc7be46fc375e1314A review on wetting and water condensation - Perspectives for CO2 condensationSnustad, Ingrid; Roee, Ingeborg T.; Brunsvold, Amy; Ervik, Aasmund; He, Jianying; Zhang, ZhiliangAdvances in Colloid and Interface Science (2018), 256 (), 291-304CODEN: ACISB9; ISSN:0001-8686. (Elsevier B.V.)A review. Liquefaction of vapor is a necessary, but energy intensive step in several important process industries. This review identifies possible materials and surface structures for promoting dropwise condensation, known to increase efficiency of condensation heat transfer. Research on superhydrophobic and superomniphobic surfaces promoting dropwise condensation constitutes the basis of the review. In extension of this, knowledge is extrapolated to condensation of CO2. Global emissions of CO2 need to be minimized in order to reduce global warming, and liquefaction of CO2 is a necessary step in some carbon capture, transport and storage (CCS) technologies. The review is divided into three main parts: 1) An overview of recent research on superhydrophobicity and promotion of dropwise condensation of water, 2) An overview of recent research on superomniphobicity and dropwise condensation of low surface tension substances, and 3) Suggested materials and surface structures for dropwise CO2 condensation based on the two first parts.**17**Reiter, G. Dewetting of thin polymer films.*Phys. Rev. Lett.*1992,*68*, 75, DOI: 10.1103/PhysRevLett.68.7517https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK38XmtVCltQ%253D%253D&md5=dcd6dc731f2f3eef5013e932fba95020Dewetting of thin polymer filmsReiter, GuenterPhysical Review Letters (1992), 68 (1), 75-8CODEN: PRLTAO; ISSN:0031-9007.Thin polystyrene films (<100 nm) on Si substrates undergo dewetting when annealed above the glass transition temp. Three different stages can be distinguished. The smooth films break up by the creation of cylindrical holes. The holes then grow and form rims ahead of them which finally contact each other creating "cellular" structures. The rims are unstable and decay into droplets. The influence of the film thickness on this process is investigated and compared to recent theor. predictions of spinodal decompn. of partially wetting thin films.**18**Mukherjee, R.; Sharma, A. Instability, self-organization and pattern formation in thin soft films.*Soft Matter*2015,*11*, 8717– 8740, DOI: 10.1039/C5SM01724F18https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXhsFamsb%252FL&md5=738b191eeb685ae4986e1c402da9997eInstability, self-organization and pattern formation in thin soft filmsMukherjee, Rabibrata; Sharma, AshutoshSoft Matter (2015), 11 (45), 8717-8740CODEN: SMOABF; ISSN:1744-683X. (Royal Society of Chemistry)The free surface of a thin soft polymer film is often found to become unstable and self-organizes into various meso-scale structures. In this article we classify the instability of a thin polymer film into three broad categories, which are: category 1: instability of an ultra-thin (<100 nm) viscous film engendered by amplification of thermally excited surface capillary waves due to interfacial dispersive van der Waals forces; category 2: instability arising from the attractive inter-surface interactions between the free surface of a soft film exhibiting room temp. elasticity and another rigid surface in its contact proximity; and category 3: instability caused by an externally applied field such as an elec. field or a thermal gradient, obsd. in both viscous and elastic films. We review the salient features of each instability class and highlight how characteristic length scales, feature morphologies, evolution pathways, etc. depend on initial properties such as film thickness, visco-elasticity (rheol.), residual stress, and film prepn. conditions. We emphasize various possible strategies for aligning and ordering of the otherwise isotropic structures by combining the essential concepts of bottom-up and top-down approaches. A perspective, including a possible future direction of research, novelty and limitations of the methods, particularly in comparison to the existing patterning techniques, is also presented for each setting.**19**Bhandaru, N.; Das, A.; Mukherjee, R. Confinement induced ordering in dewetting of ultra-thin polymer bilayers on nanopatterned substrates.*Nanoscale*2016,*8*, 1073– 1087, DOI: 10.1039/C5NR06690E19https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXhvVyhu73E&md5=8f342cd254a0a458d5231220dcd02a00Confinement induced ordering in dewetting of ultra-thin polymer bilayers on nanopatterned substratesBhandaru, Nandini; Das, Anuja; Mukherjee, RabibrataNanoscale (2016), 8 (2), 1073-1087CODEN: NANOHL; ISSN:2040-3372. (Royal Society of Chemistry)We report the dewetting of a thin bilayer of polystyrene (PS) and poly(methylmethacrylate) (PMMA) on a topog. patterned nonwettable substrate comprising an array of pillars, arranged in a square lattice. With a gradual increase in the concn. of the PMMA soln. (Cn-PMMA), the morphol. of the bottom layer changes to: (1) an aligned array of spin dewetted droplets arranged along substrate grooves at very low Cn-PMMA; (2) an interconnected network of threads surrounding each pillar at intermediate Cn-PMMA; and (3) a continuous bottom layer at higher Cn-PMMA. On the other hand the morphol. of the PS top layer depends largely on the nature of the pre-existing bottom layer, in addn. to Cn-PS. An ordered array of PMMA core-PS shell droplets forms right after spin coating when both Cn-PMMA and Cn-PS are very low. Bilayers with all other initial configurations evolve during thermal annealing, resulting in a variety of ordered structures. Unique morphologies realized include laterally coexisting structures of the two polymers confined within the substrate grooves due to initial rupture of the bottom layer on the substrate followed by a squeezing flow of the top layer; an array of core-shell and single polymer droplets arranged in an alternating order etc., to highlight a few. Such structures cannot be fabricated by any stand-alone lithog. technique.**20**Dörfler, F.; Rauscher, M.; Dietrich, S. Stability of thin liquid films and sessile droplets under confinement.*Phys. Rev. E*2013,*88*, 012402 DOI: 10.1103/PhysRevE.88.01240220https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BC3sfpvVSnsw%253D%253D&md5=1d914e1ddecf87facc0a6eeab29ac3ceStability of thin liquid films and sessile droplets under confinementDorfler Fabian; Rauscher Markus; Dietrich SPhysical review. E, Statistical, nonlinear, and soft matter physics (2013), 88 (1), 012402 ISSN:.The stability of nonvolatile thin liquid films and of sessile droplets is strongly affected by finite size effects. We analyze their stability within the framework of density functional theory using the sharp kink approximation, i.e., on the basis of an effective interface Hamiltonian. We show that finite size effects suppress spinodal dewetting of films because it is driven by a long-wavelength instability. Therefore nonvolatile films are stable if the substrate area is too small. Similarly, nonvolatile droplets connected to a wetting film become unstable if the substrate area is too large. This instability of a nonvolatile sessile droplet turns out to be equivalent to the instability of a volatile drop which can attain chemical equilibrium with its vapor.**21**MacDowell, L. G.; Shen, V. K.; Errington, J. R. Nucleation and cavitation of spherical, cylindrical, and slablike droplets and bubbles in small systems.*J. Chem. Phys.*2006,*125*, 034705 DOI: 10.1063/1.221884521https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28XnsFeisLo%253D&md5=f7e027590ee8a700adf84e0029642ef9Nucleation and cavitation of spherical, cylindrical, and slablike droplets and bubbles in small systemsMacDowell, Luis G.; Shen, Vincent K.; Errington, Jeffrey R.Journal of Chemical Physics (2006), 125 (3), 034705/1-034705/15CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)Computer simulations are employed to obtain subcrit. isotherms of small finite sized systems inside the coexistence region. For all temps. considered, ranging from the triple point up to the crit. point, the isotherms gradually developed a sequence of sharp discontinuities as the system size increased from ∼8 to ∼21 mol. diams. For the smallest system sizes, and more so close to the crit. point, the isotherms appeared smooth, resembling the continuous van der Waals loop obtained from extrapolation of an analytic equation of state outside the coexistence region. As the system size was increased, isotherms in the chem. potential-d. plane developed first two, then four, and finally six discontinuities. Visual inspection of selected snapshots revealed that the obsd. discontinuities are related to structural transitions between droplets (on the vapor side) and bubbles (on the liq. side) of spherical, cylindrical, and tetragonal shapes. A capillary drop model was developed to qual. rationalize these observations. Analytic results were obtained and found to be in full agreement with the computer simulation results. The anal. shows that the shape of the subcrit. isotherms is dictated by a single characteristic vol. (or length scale), which depends on the surface tension, compressibility, and coexistence densities. For small reduced system vols., the model predicts that a homogeneous fluid is stable across the whole coexistence region, thus explaining the continuous van der Waals isotherms obsd. in the simulations. When the liq. and vapor free energies are described by means of an accurate mean-field equation of state and surface tensions from simulation are employed, the capillary model is found to describe the simulated isotherms accurately, esp. for large systems (i.e., larger than about 15 mol. diams.) at low temp. (lower than about 0.85 times the crit. temp.). This implies that the Laplace pressure differences can be predicted for drops as small as five mol. diams., and as few as about 500 mols. The theor. study also shows that the extrema or apparent spinodal points of the finite size loops are more closely related to (finite system size) bubble and dew points than to classical spinodals. Our results are of relevance to phase transitions in nanopores and show that first order corrections to nucleation energies in finite closed systems are power laws of the inverse vol.**22**Wilhelmsen, Ø.; Bedeaux, D.; Kjelstrup, S.; Reguera, D. Communication: Superstabilization of fluids in nanocontainer.*J. Chem. Phys.*2014,*141*, 071103 DOI: 10.1063/1.489370122https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXhsVWksL7L&md5=051af6ae7012ef7098e46defa4cc1959Communication: Superstabilization of fluids in nanocontainersWilhelmsen, Oeivind; Bedeaux, Dick; Kjelstrup, Signe; Reguera, DavidJournal of Chemical Physics (2014), 141 (7), 071103/1-071103/5CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)One of the main challenges of thermodn. is to predict and measure accurately the properties of metastable fluids. Investigation of these fluids is hindered by their spontaneous transformation by nucleation into a more stable phase. We show how small closed containers can be used to completely prevent nucleation, achieving infinitely long-lived metastable states. Using a general thermodn. framework, we derive simple formulas to predict accurately the conditions (container sizes) at which this superstabilization takes place and it becomes impossible to form a new stable phase. This phenomenon opens the door to control nucleation of deeply metastable fluids at exptl. feasible conditions, having important implications in a wide variety of fields. (c) 2014 American Institute of Physics.**23**Wilhelmsen, Ø.; Reguera, D. Evaluation of finite-size effects in cavitation and droplet formation.*J. Chem. Phys.*2015,*142*, 064703 DOI: 10.1063/1.490736723https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXis1Shtrs%253D&md5=25a148add9929ab2b4cb121551e39bbdEvaluation of finite-size effects in cavitation and droplet formationWilhelmsen, Oeivind; Reguera, DavidJournal of Chemical Physics (2015), 142 (6), 064703/1-064703/9CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)Nucleation of bubbles and droplets is of fundamental interest in science and technol. and has been widely investigated through expts., theory, and simulations. Giving the rare event nature of these phenomena, nucleation simulations are computationally costly and require the use of a limited no. of particles. Moreover, they are often performed in the canonical ensemble, i.e., by fixing the total vol. and no. of particles, to avoid the addnl. complexities of implementing a barostat. However, cavitation and droplet formation take place differently depending on the ensemble. Here, we analyze the importance of finite-size effects in cavitation and droplet formation. We present simple formulas which predict the finite-size corrections to the crit. size, the nucleation barrier, and the nucleation rates in the canonical ensemble very accurately. These results can be used to select an appropriate system-size for simulations and to get a more precise evaluation of nucleation in complex substances, by using a small no. of mols. and correcting for finite-size effects. (c) 2015 American Institute of Physics.**24**Yang, A. J.-M. The thermodynamical stability of the heterogeneous system with a spherical interface.*J. Chem. Phys.*1985,*82*, 2082– 2085, DOI: 10.1063/1.44834424https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaL2MXhsFGhtbs%253D&md5=7569c861a2646e5fce3e233281382aeaThe thermodynamical stability of the heterogeneous system with a spherical interfaceYang, Arthur Jing MinJournal of Chemical Physics (1985), 82 (4), 2082-5CODEN: JCPSA6; ISSN:0021-9606.A 1-component system, a liq. drop in equil. with its vapor, was studied in the discussion of the stability of a heterogeneous system with a spherical interface. Due to the complexity of the 2nd-order functional differentiation of the thermodynamical potential function, a simpler treatment with the use of surface thermodn. is provided instead. The Gibbs free energy and the Grand potential are at a saddle point if resp. natural thermodynamical variables are held const. The Helmholtz free energy for this system at const. temp., vol., and N is either at a saddle point or a min. depending on the relative ratio of the two phases. This agrees with a previous result. The method developed here can be used in a homogeneous nucleation to study the initial fluctuation which results in the formation of the crit. nucleus. The use of the surface thermodn. to study a kinetic process is discussed.**25**Gjennestad, M. Aa.; Wilhelmsen, Ø. Thermodynamic stability of droplets, bubbles and thick films in open and closed pores.*Fluid Phase Equilib.*2020,*505*, 112351 DOI: 10.1016/j.fluid.2019.11235125https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXitFamtb3J&md5=580c898f24427878271f0f5125a51164Thermodynamic stability of droplets, bubbles and thick films in open and closed poresGjennestad, Magnus Aa.; Wilhelmsen, OeivindFluid Phase Equilibria (2020), 505 (), 112351CODEN: FPEQDT; ISSN:0378-3812. (Elsevier B.V.)We combine a capillary description with the cubic-plus-assocn. equation of state to study the thermodn. stability of droplets, bubbles and films of water at 358 K in a cylindrically sym. pore. The equil. structure depends strongly on the size of the pore and whether the pore is closed or connected to a particle reservoir (grand canonical ensemble). A new methodol. is presented to analyze the thermodn. stability of films, where the integral that describes the total energy of the system is approximated by a quadrature rule. We show that, for large pores, the thermodn. stability limit of adsorbed droplets and bubbles in both open and closed pores is governed by their mech. stability, which is closely linked to the pore shape. In open pores, the film is chem. unstable except for very low film-phase contact angles and for a limited range in external pressure. This result emphasizes the need to invoke a complete thermodn. stability anal., and not restrict the discussion to mech. stability. A common feature for most of the heterogeneous structures examd. is the appearance of regions where the structure is metastable with respect to a pore filled with a homogeneous fluid. In the closed pores, these regions grow considerably in size when the pores become smaller. This can be understood from the larger energy cost of the interfaces relative to the energy gained from having two phases. Complete phase diagrams are presented that compare all the investigated structures.**26**Neimark, A. V.; Kornev, K. G. Classification of equilibrium configurations of wetting films on planar substrates.*Langmuir*2000,*16*, 5526– 5529, DOI: 10.1021/la000267b26https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3cXjsF2qtrw%253D&md5=7d64afc561b4328628c567683db25716Classification of Equilibrium Configurations of Wetting Films on Planar SubstratesNeimark, Alexander V.; Kornev, Konstantin G.Langmuir (2000), 16 (13), 5526-5529CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)The authors suggest a rigorous formulation of the problem of classification of equil. configurations of wetting films on solid surfaces and in pores taking into account capillary and adhesion forces. As example, cylindrical films and drops of a van der Waals liq. on planar substrates are considered. Rewritten as a dynamic system, the Derjaguin equation for equil. interfaces is analyzed in detail without numeric calcn. of interfacial profiles, providing a simple way for understanding the different wetting regimes. This method allows us to enrich the arsenal of well-known explicit solns. responsible for clarifying such phys. problems as wetting and dewetting, capillary condensation and desorption, imbibition and drainage, droplet formation, and foaming on inhomogeneous substrates and in pores.**27**Neimark, A. V. Thermodynamic equilibrium and stability of liquid films and droplets on fibers.*J. Adhes. Sci. Technol.*1999,*13*, 1137– 1154, DOI: 10.1163/156856199X0083927https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK1MXntlyhtrc%253D&md5=36b4cacbb33d8baee2468b2c519538d4Thermodynamic equilibrium and stability of liquid films and droplets on fibersNeimark, Alexander V.Journal of Adhesion Science and Technology (1999), 13 (10), 1137-1154CODEN: JATEE8; ISSN:0169-4243. (VSP BV)The modeling of liq. spreading and penetration into fibrous materials requires a better understanding of the interactions of thin liq. films and small droplets with single fibers. The wetting properties of fibers may differ significantly from those of plane solid surfaces. Convex surfaces of fibers imply a pos. Laplace pressure acting on the liq.-gas interface. This effect causes liq. film instability and hinders droplet spreading. Liq. films on fibers are stable when the destabilizing action of the Laplace pressure is balanced by liq.-solid adhesion. Equil. configurations of liq. droplets and films are detd. by the competition between capillary and adhesion forces. A general anal. soln. is presented for the equil. profile of the transition zone between a film and a droplet residing on a cylindrical fiber. A new equation for apparent contact angles on fibers is derived. Adhesion forces, including van der Waals and polar interactions, are expressed in terms of disjoining pressure. Explicit formulas for calcns. of equil. droplet profiles, film thicknesses, apparent contact angles, and stability factors are presented in the form of expressions which include both the measurable geometrical parameters and the presumably known parameters of liq.-solid interactions, such as apolar and polar spreading coeffs. The method is applicable for analyses of apparent contact angles and film stability on fibers and other cylindrical surfaces, particularly nanofibers. A transition from partial wetting to non-wetting may occur as the fiber diam. decreases. Depending on the fiber diam., contact angles of water on hydrophobic C fibers may vary from 75° (plane graphite surface) to 100-130° (C nanotubes).**28**MacDowell, L. G. Computer simulation of interface potentials: Towards a first principle description of complex interfaces.*Eur. Phys. J.: Spec. Top.*2011,*197*, 131– 145, DOI: 10.1140/epjst/e2011-01447-628https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XntVGq&md5=8a00fb36bce66ab7ee057e4f496da7a3Computer simulation of interface potentials: towards a first principle description of complex interfaces?MacDowell, L. G.European Physical Journal: Special Topics (2011), 197 (Discussion and Debate: Wetting and Spreading Science: Quo Vadis?), 131-145CODEN: EPJSAC; ISSN:1951-6401. (EDP Sciences)We discuss the feasibility of a hierarchical protocol whereby the description and prediction of adsorbed fluids in confined systems at the mesoscopic scale is achieved by use of interface potentials that are obtained from raw mol. simulation data. Starting from a micro-scopic description of a fluid's interface on a flat substrate, we attempt to ext. the min. information that is required in order to predict the behavior of that fluid at larger length scales from coarse grained surface Hamiltonians. A crit. assessment of this procedure hinges on controversial aspects of wetting behavior and more generally on the meaning of metastability and instability of thermodn. systems.**29**MacDowell, L. G.; Benet, J.; Katcho, N. A. Capillary fluctuations and film-height-dependent surface tension of an adsorbed liquid film.*Phys. Rev. Lett.*2013,*111*, 047802 DOI: 10.1103/PhysRevLett.111.04780229https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXht1Ogt7vN&md5=fafd871b579540245e9abc0bda9ba871Capillary fluctuations and film-height-dependent surface tension of an adsorbed liquid filmMacDowell, Luis G.; Benet, Jorge; Katcho, Nebil A.Physical Review Letters (2013), 111 (4), 047802/1-047802/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)The understanding of both structure and dynamics of adsorbed liqs. heavily relies on the capillary wave Hamiltonian, but a thorough test of this model is still lacking. Here the capillary wave fluctuations of a liq. film with short-range forces adsorbed on a solid exhibiting van der Waals interactions were studied. The measured capillary wave spectrum right above the first order wetting transition provides an interface potential consistent with independent calcns. from thermodn. integration. However, the surface tension exhibits an oscillatory film thick dependence which reveals a hitherto unnoticed capillary wave broadening mechanism beyond mere interfacial displacements.**30**Pahlavan, A. A.; Cueto-Felgueroso, L.; Hosoi, A. E.; McKinley, G. H.; Juanes, R. Thin films in partial wetting: Stability, dewetting and coarsening.*J. Fluid Mech.*2018,*845*, 642– 681, DOI: 10.1017/jfm.2018.25530https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXitlKku77J&md5=c07ea3e85d875c62328480c8a6a861c1Thin films in partial wetting: stability, dewetting and coarseningPahlavan, A. Alizadeh; Cueto-Felgueroso, L.; Hosoi, A. E.; McKinley, G. H.; Juanes, R.Journal of Fluid Mechanics (2018), 845 (), 642-681CODEN: JFLSA7; ISSN:0022-1120. (Cambridge University Press)A uniform nanometric thin liq. film on a solid substrate can become unstable due to the action of van der Waals (vdW) forces. The instability leads to dewetting of the uniform film and the formation of drops. To minimize the total free energy of the system, these drops coarsen over time until one single drop remains. Here, using a thermodynamically consistent framework, we derive a new model for thin films in partial wetting with a free energy that resembles the Cahn-Hilliard form with a height-dependent surface tension that leads to a generalized disjoining pressure, and revisit the dewetting problem. Using both linear stability anal. and nonlinear simulations we show that the new model predicts a slightly smaller crit. instability wavelength and a significantly (up to six-fold) faster growth rate than the classical model in the spinodal regime; this faster growth rate brings the theor. predictions closer to published exptl. observations. During coarsening at intermediate times, the dynamics become self-similar and model-independent; we therefore observe the same scalings in both the classical (with and without thermal noise) and new models. Both models also lead to a mean-field Lifshitz-Slyozov-Wagner (LSW)-type droplet-size distribution at intermediate times for small drop sizes. We, however, observe a skewed drop-size distribution for larger drops in the new model; while the tail of the distribution follows a Smoluchowski equation, it is not assocd. with a coalescence-dominated coarsening, calling into question the assocn. made in some earlier expts. Our observations point to the importance of the height dependence of surface tension in the early and late stages of dewetting of nanometric films and motivate new high-resoln. exptl. observations to guide the development of improved models of interfacial flows at the nanoscale.**31**Kheshgi, H. S.; Scriven, L. Dewetting: Nucleation and growth of dry regions.*Chem. Eng. Sci.*1991,*46*, 519– 526, DOI: 10.1016/0009-2509(91)80012-N31https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK3MXhtVGjs7k%253D&md5=bd33a4450b0cef9f1c03355fbd9dbf60Dewetting: nucleation and growth of dry regionsKheshgi, Haroon S.; Scriven, L. E.Chemical Engineering Science (1991), 46 (2), 519-26CODEN: CESCAC; ISSN:0009-2509.Dewetting of a solid surface covered by a film of nonwetting liq. proceeds from a preexisting dry patch or edge or initiates from some film-thinning disturbance that grows until the film ruptures. Local thinning can be caused by evapn.; by drainage due to gravity or capillarity-driven flow, esp. from sharp surfaces; or by surface tension gradients, such as are caused by surfactants delivered by particles falling on the film. Once a nonwetting film is sufficiently thinned, conjoining (neg. disjoining) pressure can accelerate thinning until rupture. This catastrophic rupture is modeled by solving the Navier-Stokes system approximated for thickness variations over distances that are long compared with the mean film thickness, and augmented with conjoining pressure. Rupture leads to film retraction and formation of a dry patch. These phenomena are visualized via moire topog. Of special interest are local spreading disturbances, where airborne particles fall on the film surface; craters or dry patches often nucleate. Implications for coating operations are discussed.**32**Ruckenstein, E.; Jain, R. K. Spontaneous rupture of thin liquid films.*J. Chem. Soc., Faraday Trans. 2*1974,*70*, 132– 147, DOI: 10.1039/f2974700013232https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaE2cXhsV2htrs%253D&md5=ae4c4035bde3b1d88e4aa39b5d13657bSpontaneous rupture of thin liquid filmsRuckenstein, Eli; Jain, Rakesh K.Journal of the Chemical Society, Faraday Transactions 2: Molecular and Chemical Physics (1974), 70 (1), 132-47CODEN: JCFTBS; ISSN:0300-9238.Hydrodynamic linear stability theory was used to examine the rupture of a liq. film on a solid surface and of a free liq. film. The lubrication approxn. of the hydrodynamic equations of motion was used and the system described by the Navier-Stokes equations. The range of wavelengths of the applied perturbation for which instability occurred was estd. and the time of rupture was calcd. The effect of insol. and sol. surface active agents was examd. Exptl. data for condensation on a solid surface and coalescence of bubbles was discussed.**33**Silin, D.; Virnovsky, G. A variational model of disjoining pressure: Liquid film on a nonplanar surface.*Transp. Porous Media*2010,*82*, 485– 505, DOI: 10.1007/s11242-009-9424-z33https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXjvFagtro%253D&md5=8f4ba48cee74682a09b1b7d5b8bcc792A Variational Model of Disjoining Pressure: Liquid Film on a Nonplanar SurfaceSilin, Dmitriy; Virnovsky, GeorgeTransport in Porous Media (2010), 82 (3), 485-505CODEN: TPMEEI; ISSN:0169-3913. (Springer)Variational methods have been successfully used in modeling thin liq. films in numerous theor. studies of wettability. In this article, the variational model of the disjoining pressure is extended to the general case of a two-dimensional solid surface. The Helmholtz free energy functional depends both on the disjoining pressure isotherm and on the shape of the solid surface. The augmented Young-Laplace equation (AYLE) is a nonlinear second-order partial differential equation. A no. of solns. describing wetting films on spherical grains have been obtained. In the case of cylindrical films, the phase portrait technique describes the entire variety of math. feasible solns. It turns out that a periodic soln., which would describe wave-like wetting films, does not satisfy Jacobi's condition of the classical calculus of variations. Therefore, such a soln. is nonphys. The roughness of the solid surface significantly affects liq. film stability. AYLE solns. suggest that film rupture is more likely at a location where the pore-wall surface is most exposed into the pore space, and the curvature is pos.**34**Sharma, A. Equilibrium and dynamics of evaporating or condensing thin fluid domains: Thin film stability and heterogeneous nucleation.*Langmuir*1998,*14*, 4915– 4928, DOI: 10.1021/la971389f34https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK1cXkslGks7g%253D&md5=5dbfdb7f8638ba5c4db18306af31f998Equilibrium and Dynamics of Evaporating or Condensing Thin Fluid Domains: Thin Film Stability and Heterogeneous NucleationSharma, AshutoshLangmuir (1998), 14 (17), 4915-4928CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)A continuum theory is presented for the equil. and dynamics of evapg./condensing thin (<100 nm) fluid domains on solid surfaces. The local rate of evapn./condensation depends crucially on the local curvature and disjoining pressure. The phenomena of heterogeneous nucleation and thin film stability on partially wettable surfaces are considered. All of the results for these nanoscale phenomena are consistently interpreted in terms of the macroscopic parameters of wetting, e.g., the apolar van der Waals and the polar (e.g., acid-base) components of the spreading coeff. and the macroscopic equil. contact angle. Finite size effects (disjoining pressure) and adsorption can reduce the size, contact angle, and nucleation energy of crit. nuclei very substantially as compared to predictions of the classical theory of nucleation. The instability and dewetting (hole formation) of thin evapg. H2O films on partially wettable surfaces are caused by the hydrophobic attraction, whereas the van der Waals interaction promotes the film stability and wetting. Dynamic simulations are performed, and simple anal. results are obtained for the length and time scales of the surface instability for H2O films. Curiously, in contrast to the case of nonevaporating films, the no. d. of holes may decrease with increased strength of the hydrophobic attraction, because stronger attraction forces the onset of instability at higher thickness.**35**Berg, J. C.*An Introduction to Interfaces & Colloids: The Bridge to Nanoscience*; World Scientific, 2010.There is no corresponding record for this reference.**36**Callen, H. B.*Thermodynamics and an Introduction to Thermostatistics*, 2nd ed.; John Wiley & Sons, 1985.There is no corresponding record for this reference.**37**Vrij, A. Possible mechanism for the spontaneous rupture of thin, free liquid films.*Discuss. Faraday Soc.*1966,*42*, 23– 33, DOI: 10.1039/df9664200023There is no corresponding record for this reference.**38**MacDowell, L. G.; Benet, J.; Katcho, N. A.; Palanco, J. M. Disjoining pressure and the film-height-dependent surface tension of thin liquid films: New insight from capillary wave fluctuations.*Adv. Colloid Interface Sci.*2014,*206*, 150– 171, DOI: 10.1016/j.cis.2013.11.00338https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXhvFGrsLrJ&md5=5806ffc1f81bd892d47713f9fabc9fc9Disjoining pressure and the film-height-dependent surface tension of thin liquid films: New insight from capillary wave fluctuationsMacDowell, Luis G.; Benet, Jorge; Katcho, Nebil A.; Palanco, Jose M. G.Advances in Colloid and Interface Science (2014), 206 (), 150-171CODEN: ACISB9; ISSN:0001-8686. (Elsevier B.V.)A review. Reviewed are simulation and exptl. studies of thermal capillary wave fluctuations as an ideal means for probing the underlying disjoining pressure and surface tensions, and more generally, fine details of the Interfacial Hamiltonian Model. Discussed are recent simulation results that reveal a film-height-dependent surface tension not accounted for in the classical Interfacial Hamiltonian Model. It is shown how this observation may be explained bottom-up from sound principles of statistical thermodn. and discuss some of its implications.**39**Boinovich, L. DLVO forces in thin liquid films beyond the conventional DLVO theory.*Curr. Opin. Colloid Interface Sci.*2010,*15*, 297– 302, DOI: 10.1016/j.cocis.2010.05.00339https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXhtVGhsrbF&md5=e13c0890edb50fea999f4f1f2d4ab492DLVO forces in thin liquid films beyond the conventional DLVO theoryBoinovich, LudmilaCurrent Opinion in Colloid & Interface Science (2010), 15 (5), 297-302CODEN: COCSFL; ISSN:1359-0294. (Elsevier B.V.)A review. Further progress has taken place in the theory of surface forces beyond the conventional DLVO theory. The major recent advances are related to more accurate accounting for the ionic nature of liq. interlayer in the calcns. of van der Waals forces and for the impact of dispersion interaction of ions with other ions or confining phases on the peculiarities of ion-electrostatic interactions in liq. films.**40**Thiele, U.; Mertig, M.; Pompe, W. Dewetting of an evaporating thin liquid film: Heterogeneous nucleation and surface instability.*Phys. Rev. Lett.*1998,*80*, 2869, DOI: 10.1103/PhysRevLett.80.286940https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK1cXitVShtro%253D&md5=0d794da6911216b70147ef611518b1c9Dewetting of an evaporating thin liquid film: heterogeneous nucleation and surface instabilityThiele, Uwe; Mertig, Michael; Pompe, WolfgangPhysical Review Letters (1998), 80 (13), 2869-2872CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)Film rupture as the initial stage of dewetting is investigated for a volatile, spin-coated nonwetting film. During structure formation in the liq. film thickness is continuously reduced via evapn. The dynamical character of the expt. allows the study of hole formation caused by distinct rupture mechanisms occurring at different film thicknesses. Both heterogeneous nucleation for thick films as well as spinodal dewetting for film thickness below 10 nm have been obsd. The balance between both processes can be shifted by controlling the ambient humidity. The structures resulting from film rupture are quantified with respect to their different geometrical properties. For the first time we find that spinodal dewetting is caused by destabilizing polar interactions.**41**Emelyanenko, K. A.; Emelyanenko, A. M.; Boinovich, L. B. Van der waals forces in free and wetting liquid films.*Adv. Colloid Interface Sci.*2019, 357– 369, DOI: 10.1016/j.cis.2019.04.01341https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXhtVagur3M&md5=e549f0374c6f13d0de0f2f7986aa0afaVan der Waals forces in free and wetting liquid filmsEmelyanenko, Kirill A.; Emelyanenko, Alexandre M.; Boinovich, Ludmila B.Advances in Colloid and Interface Science (2019), 269 (), 357-369CODEN: ACISB9; ISSN:0001-8686. (Elsevier B.V.)Van der Waals interactions induced by fluctuations of electromagnetic field bear universal nature and act between individual atoms, condensed particles or bodies of any type. Continuously growing interest to theor. understanding as well as to precise evaluation of van der Waals forces is caused by their fundamental role in many phys., chem., and biol. processes. In this paper, we scrutinize progress in the studies of van der Waals forces, related to recent active development of Coupled Dipole Method (CDM) for the anal. of the behavior and properties of nanosized systems. The application of CDM for the anal. of thin liq. films allowed achieving substantial progress in understanding the behavior of free and wetting films. It was shown that both the macroscopic properties, such as excess free energy and Hamaker consts. and the local microscopic parameters, such as polarizabilities, can be successfully calcd. based only on properties of individual mols. The impact of lateral film confinement on the specific excess free energy and the film stability was elucidated, and effect of spatial constraints on the spectrum of vibrational states for liq. film and the underlying substrate was analyzed. It was shown that van der Waals interactions between mols. represent the universal mechanism for dynamic structuring and formation of boundary layers and that the CDM allows self-consistently calcg. the properties of these layers in both solid and liq. phases.**42**Kontogeorgis, G. M.; Voutsas, E. C.; Yakoumis, I. V.; Tassios, D. P. An equation of state for associating fluids.*Ind. Eng. Chem. Res.*1996,*35*, 4310– 4318, DOI: 10.1021/ie960020342https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK28Xmt1GnsLg%253D&md5=4da4cf22fdac90c866145fe789b49065An Equation of State for Associating FluidsKontogeorgis, Georgios M.; Voutsas, Epaminondas C.; Yakoumis, Iakovos V.; Tassios, Dimitrios P.Industrial & Engineering Chemistry Research (1996), 35 (11), 4310-4318CODEN: IECRED; ISSN:0888-5885. (American Chemical Society)An equation of state (EoS) suitable for describing assocg. fluids is presented. The equation combines the simplicity of a cubic equation of state (the Soave-Redlich-Kwong), which is used for the phys. part and the theor. background of the perturbation theory employed for the chem. (or assocn.) part. The resulting EoS (Cubic Plus Assocn.) is not cubic with respect to vol. and contains five pure compd. parameters which are detd. using vapor pressures and satd. liq. densities. Excellent correlations of both vapor pressures and satd. liq. vols. are obtained for primary-alcs. (from methanol up to 1-tridecanol), phenol, tert-Bu alc., triethylene glycol, and water. Moreover, excellent prediction of satd. liq. vols. may be obtained from parameters which were estd. by regressing only vapor pressures. Finally, we suggest a method for reducing the no. of adjustable parameters for alcs. to three while maintaining the good correlation of vapor pressures and satd. liq. vols. We investigate the possibility of using the homomorph approach for estg. the EoS parameters and explain the problems obsd. The estd. pure compd. parameters were tested in the prediction of second virial coeffs. with satisfactory results.**43**Wilhelmsen, Ø.; Aasen, A.; Skaugen, G.; Aursand, P.; Austegard, A.; Aursand, E.; Gjennestad, M. Aa.; Lund, H.; Linga, G.; Hammer, M. Thermodynamic modeling with equations of state: present challenges with established methods.*Ind. Eng. Chem. Res.*2017,*56*, 3503– 3515, DOI: 10.1021/acs.iecr.7b0031743https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXktV2rsLo%253D&md5=5168dd9de5cbf69d7d6ca7641328d5c6Thermodynamic Modeling with Equations of State: Present Challenges with Established MethodsWilhelmsen, Oeivind; Aasen, Ailo; Skaugen, Geir; Aursand, Peder; Austegard, Anders; Aursand, Eskil; Gjennestad, Magnus Aa.; Lund, Halvor; Linga, Gaute; Hammer, MortenIndustrial & Engineering Chemistry Research (2017), 56 (13), 3503-3515CODEN: IECRED; ISSN:0888-5885. (American Chemical Society)A review. Equations of state (EoS) are essential in the modeling of a wide range of industrial and natural processes. Desired qualities of EoS are accuracy, consistency, computational speed, robustness and predictive ability outside of the domain where they have been fitted. In this work, we review present challenges assocd. with established models, and give suggestions on how to overcome them in the future. The most accurate EoS available, multiparameter EoS, have a second artificial Maxwell loop in the two-phase region that gives problems in phase-equil. calcns. and exclude them from important applications such as treatment of interfacial phenomena with mass based d. functional theory. Suggestions are provided on how this can be improved. Cubic EoS are among the most computationally efficient EoS, but they often lack sufficient accuracy. We show that extended corresponding state EoS are capable of providing significantly more accurate single-phase predictions than cubic EoS with only a doubling of the computational time. In comparison, the computational time of multiparameter EoS can be orders of magnitude larger. For mixts. in the two-phase region, however, the accuracy of extended corresponding state EoS has a large potential for improvement. The mol.-based SAFT family of EoS are preferred when predictive ability is important, e.g. for systems with strongly assocg. fluids or polymers where few exptl. data are available. We discuss some of their benefits and present challenges. A discussion is presented on why predictive thermodn. models for reactive mixts. such as CO2-NH3 and CO2-H2O-H2S must be developed in close combination with phase- and reaction equil. theory, regardless of the choice of EoS. After overcoming present challenges, a next-generation thermodn. modeling framework holds the potential to improve the accuracy and predictive ability in a wide range of applications such as process optimization, computational fluid dynamics, treatment of interfacial phenomena and processes with reactive mixts.**44**Troutman, J. L.*Variational Calculus and Optimal Control*, 2nd ed.; Springer, 1996.There is no corresponding record for this reference.**45**Michelsen, M. L.; Mollerup, J. M.*Thermodynamic Models: Fundamentals & Computational Aspects*, 2nd ed.; Tie-Line Publications, 2007.There is no corresponding record for this reference.**46**Aursand, P.; Gjennestad, M. Aa.; Aursand, E.; Hammer, M.; Wilhelmsen, Ø. The spinodal of single-and multi-component fluids and its role in the development of modern equations of state.*Fluid Phase Equilib.*2017,*436*, 98– 112, DOI: 10.1016/j.fluid.2016.12.01846https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXpsFyitw%253D%253D&md5=8fcc4bbe759df0412e2b5930db0a7a10The spinodal of single- and multi-component fluids and its role in the development of modern equations of stateAursand, Peder; Gjennestad, Magnus Aa.; Aursand, Eskil; Hammer, Morten; Wilhelmsen, OeivindFluid Phase Equilibria (2017), 436 (), 98-112CODEN: FPEQDT; ISSN:0378-3812. (Elsevier B.V.)The spinodal represents the limit of thermodn. stability of a homogeneous fluid. In this work, we present a robust methodol. to obtain the spinodal of multicomponent fluids described even with the most sophisticated equations of state (EoS) available. We elaborate how information about the spinodal and its uncertainty can contribute both in the development of modern EoS and to est. their uncertainty in the metastable regions. Inequality constraints are presented that can be exploited in the fitting of modern EoS of single-component fluids to avoid inadmissible pseudo-stable states between the vapor and liq. spinodals. We find that even cubic EoS violate some of these constraints. With the use of a selection of EoS representative of modern applications, we compare vapor and liq. spinodal curves, superheat and supersatn. limits from classic nucleation theory (CNT), and available exptl. data for the superheat limit. Computations are performed with pure species found in natural gas, binary mixts., as well as a multi-component natural gas mixt. in order to demonstrate the scalability of the approach. We demonstrate that there are large inconsistencies in predicted spinodals from a wide range of EoS such as cubic EoS, extended corresponding state EoS, SAFT and multiparameter EoS. The overall std. deviation in the prediction of the spinodal temps. were 1.4 K and 2.7 K for single- and multi-component liq.-spinodals and 6.3 K and 26.9 K for single- and multi-component vapor spinodals. The relationship between the measurable limit of superheat, or supersatn., and the theor. concept of the spinodal is discussed. While nucleation rates from CNT can deviate orders of magnitude from expts., we find that the limit of superheat from expts. agree within 1.0 K and 2.4 K with predictions from CNT for single- and multi-component fluids resp. We demonstrate that a large part of the metastable domain of the phase diagram is currently unavailable to expts., in particular for metastable vapor. Novel techniques, exptl. or with computational simulations, should be developed to characterize the thermodn. properties in these regions, and to identify the thermodn. states that define the spinodal.**47**Kierzenka, J.; Shampine, L. F. A BVP solver based on residual control and the Maltab PSE.*ACM Trans. Math. Software (TOMS)*2001,*27*, 299– 316, DOI: 10.1145/502800.502801There is no corresponding record for this reference.**48**Jones, E.; Oliphant, T.; Peterson, P. SciPy: Open source scientific tools for Python, 2001. http://www.scipy.org/.There is no corresponding record for this reference.**49**Anderson, E.; Bai, Z.; Bischof, C.; Blackford, S.; Demmel, J.; Dongarra, J.; Du Croz, J.; Greenbaum, A.; Hammarling, S.; McKenney, A.; Sorensen, D.*LAPACK Users’ Guide*, 3rd ed.; Society for Industrial and Applied Mathematics: Philadelphia, PA, 1999.There is no corresponding record for this reference.