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Translocation Dynamics of High-Internal Phase Double Emulsions in Narrow Channels
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  • Andrea Montessori
    Andrea Montessori
    Istituto per le Applicazioni del Calcolo CNR, Via dei Taurini 19, Rome 00185, Italy
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  • Adriano Tiribocchi*
    Adriano Tiribocchi
    Istituto per le Applicazioni del Calcolo CNR, Via dei Taurini 19, Rome 00185, Italy
    Center for Life Nanoscience at la Sapienza, Istituto Italiano di Tecnologia, Viale Regina Elena 295, Rome 00161, Italy
    *Email: [email protected]
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    Orcidhttps://orcid.org/0000-0002-5314-9664
  • Michał Bogdan
    Michał Bogdan
    Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, Warsaw 01-224, Poland
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  • Fabio Bonaccorso
    Fabio Bonaccorso
    Center for Life Nanoscience at la Sapienza, Istituto Italiano di Tecnologia, Viale Regina Elena 295, Rome 00161, Italy
    Istituto per le Applicazioni del Calcolo CNR, Via dei Taurini 19, Rome 00185, Italy
    Dipartimento di Fisica, Università degli Studi di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, Rome 00133, Italy
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  • Marco Lauricella
    Marco Lauricella
    Istituto per le Applicazioni del Calcolo CNR, Via dei Taurini 19, Rome 00185, Italy
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    Orcidhttps://orcid.org/0000-0002-3862-5562
  • Jan Guzowski*
    Jan Guzowski
    Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, Warsaw 01-224, Poland
    *Email: [email protected], [email protected]
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  • Sauro Succi
    Sauro Succi
    Center for Life Nanoscience at la Sapienza, Istituto Italiano di Tecnologia, Viale Regina Elena 295, Rome 00161, Italy
    Istituto per le Applicazioni del Calcolo CNR, Via dei Taurini 19, Rome 00185, Italy
    Institute for Applied Computational Science, Harvard John A. Paulson School of Engineering and Applied Sciences, Cambridge, Massachusetts 02138, United States
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Langmuir

Cite this: Langmuir 2021, 37, 30, 9026–9033
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https://doi.org/10.1021/acs.langmuir.1c01026
Published July 22, 2021

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Abstract

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We numerically study the translocation dynamics of double emulsion drops with multiple close-packed inner droplets within constrictions. Such liquid architectures, which we refer to as HIPdEs (high-internal phase double emulsions), consist of a ternary fluid, in which monodisperse droplets are encapsulated within a larger drop in turn immersed in a bulk fluid. Extensive two-dimensional lattice Boltzmann simulations show that if the area fraction of the internal drops is close to the packing fraction limit of hard spheres and the height of the channel is much smaller than the typical size of the emulsion, the crossing yields permanent shape deformations persistent over long periods of time. Morphological changes and rheological response are quantitatively assessed in terms of the structure of the velocity field, circularity of the emulsion, and rate of energy dissipated by viscous forces. Our results may be used to improve the design of soft mesoscale porous materials, which employ HIPdEs as templates for tissue engineering applications.

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Introduction

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High-internal phase emulsions (HIPEs) are two-phase systems, in which a very high volume fraction of dispersed droplets, typically well above the close packing limit for spheres, arrange in a tightly packed, strongly deformed configuration. (1) An aliquot of such materials suspended in an external fluid forms a double-emulsion structure with highly packed “cores” encapsulated in a single “shell”, a structure that we further refer to as high-internal phase double emulsion (HIPdE). (2−14) Like in HIPEs, the cores generally occupy an area fraction ϕ larger than the close packing limit for hard spheres (ϕ ≃ 0.74); thus, they acquire a polyhedral, rather than perfectly spherical, shape (see Figure 1). A typical example of such a material is given by monodisperse aqueous droplets packed within an encapsulating shell containing an immiscible oil phase, in turn immersed within a bulk aqueous phase. This mixture is generally stabilized using a suitable surfactant adsorbed onto the water–oil interfaces. (1,12,15−18)

Figure 1

Figure 1. (a) Experimental result of a HIPdE made of approximately monodisperse drops encapsulated within a larger droplet. Three Newtonian liquids are used to formulate the mixture. The continuous fluid is made from a 1% solution of PFPE–PEG–PFPE in fluorinated oil FC40, and the lubricating fluid of the emulsion is a solution of 5cSt silicon oil, hexadecane, and SPAN80 in proportions 70:30:1. Finally, the innermost phase is water-painted with euroglaucine. Estimated values of viscosity of continuous and lubricating fluid are approximately 4.0 mPa·s, while the value of the innermost phase is 1.0 mPa·s. (b) Example of a HIPdE obtained by LB simulations. It is made of a dispersed droplet phase (white), an inter-droplet lubricating phase (blue) surrounded by a fluid interface (red), and an external fluid (black). The compact foam-like arrangement results from the translocation of the emulsion within a thin channel, followed by a slow relaxation in the downstream reservoir. See the section Results for more details.

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The resulting compartmentalized structure is highly desirable in numerous applications, ranging from cosmetic products (9,19) to functional foods, (20−22) and can be also used as a template for the fabrication of porous scaffolds for tissue engineering. (1,11,23−25) In addition, such soft granular aggregates provide an ideal tool to mimic the behavior of multicellular spheroids in confined environments or under external stresses, (26) such as clusters of tumor cells circulating within capillary-sized vessels (27−29) or fusing cell aggregates employed to fabricate large living constructs in tissue engineering applications. (30)
Densely packed emulsions exhibit intriguing and complex mechanical properties, in stark contrast with the characteristics of simple viscous liquids they are made of (water and oil). In particular, depending on the magnitude and rate (timescale) of externally applied stresses, the emulsions may behave either as a fluid (high stresses, long timescales) or as a solid (small stresses, short timescales). (31) These features are of particular relevance in the context of lab-on-chip devices, where tightly packed droplets (or bubbles), typically one hundred micrometers in diameter, are manipulated within channels of a few hundred microns width. (25,32) In such a confined environment, the applied stress, controlled by the flow rate, may be tuned to achieve a desired response of the droplet structures. Nonetheless, improper handling of these materials (such as by excessive stresses) may lead to droplet coalescence or fission, (33) thus irretrievably altering the “grain” size and/or polydispersity of the double emulsion while also dramatically affecting the topological arrangement of the internal drops. Hence, understanding the fluid–structure interactions governing the physics at these scales is of paramount importance for precise manufacturing and correct functioning of these soft granular materials.
From a theoretical standpoint, numerical simulations represent the only viable strategy to study the multiscale physics of these systems, due to the complex structure of the equations involved. (14,34−42) While efforts have been dedicated over the years to experimentally generate multicore emulsions with a high level of control, (9−11,16,43) to date, no theoretical studies have investigated the transport of a HIPdE structure through a narrow channel by fully incorporating hydrodynamic interactions. This work aims precisely at filling this gap using an extended version of a lattice Boltzmann (LB) method recently proposed to study dense emulsions produced in microfluidic channels. (44,45)
Here, we numerically investigate, by means of two-dimensional simulations, the translocation of dense double-emulsion drops through a constriction whose design is inspired by a typical microfluidic setting. The numerical experiment sets off with a HIPdE encapsulating multiple tightly packed cores initially relaxed in a wide inlet channel, subsequently driven by a uniform fluid flow through a narrow channel, and finally relaxed in a wide outlet chamber. The emulsion is made of three fluid components—a dispersed droplet phase (A), an inter-droplet lubricating phase (B), and an external bulk fluid (C) (see Figure 1).
Our results show that shape and mechanical properties of the resulting emulsion are critically influenced by (i) the area fraction ϕ of the internal cores and (ii) the height hs of the constriction with respect to the size of the HIPdE. During translocation, the double-emulsion drop undergoes dramatic shape deformations, which entail a considerable elongation of the shell combined with a substantial rearrangement of the cores. At low values of ϕ (generally smaller than ∼0.55), the emulsion collected in the outlet chamber essentially recovers the shape attained in the inlet channel, while at higher values of ϕ, the final shape considerably deviates from the initial one (before translocation). This behavior is evaluated in terms of quantitative parameters, such as circularity of the emulsion and energy dissipated during the crossing. Also, decreasing the height of the constriction favors deeper structural changes, whose dynamics is controlled by the ratio between viscous dissipation and the energy necessary to restore shape deformations. If the former dominates, substantial shape changes are inevitable. We finally note that our findings provide a precise mapping of observables, such as velocity gradients and topological changes within a dense emulsion, difficult to measure experimentally (46) but essential to predict the dynamic behavior of a HIPdE. Notwithstanding, the question whether some aspects of the dynamical behavior of various types of granular aggregates, such as active (46−48) and passive (10,49) ones, may be universal remains open, and here, we make a step toward better general understanding of the behavior of a purely passive system.
The paper is organized as follows. In the next section, we shortly outline the numerical method used in this work, while further details can be found in refs (34,34,44). In Results section, we initially discuss the typical shape deformations of a dense emulsion observed within a constriction, and then, we focus on memory-like effects induced by the area fraction of the cores and height of the channel on the final shape of the emulsion. Some final remarks conclude the manuscript.

Methods

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The numerical model employed in this work is based on a recently proposed LB color gradient approach for multicomponent flows with near-contact interactions. (34,44,45) Here, it is extended to simulate double emulsions with multicore morphology made of a three-component fluid—a droplet phase (A), an inter-droplet lubricating phase confined within a shell (B), and an external continuous phase (C) (see Figure 1).
This LB method is built starting from three sets of probability distribution functions (PDFs), whose evolution is governed by a discrete transport Boltzmann equation (50−54)
(1)
In the abovementioned equation, fik is the discrete distribution function (namely, the probability of finding a particle of the kth (k = A, B, C) fluid component at position x and time t) moving along the ith direction at a (discrete) velocity ci. The set of distributions streams along the directions identified by the lattice geometry, which is constructed with sufficient symmetry/isotropy to reproduce hydrodynamic moments up to the desired order. A nine-speed lattice in two dimensions (D2Q9) and 19 or 27 speeds in three-dimensions (D3Q19 and D3Q27), for example, hold moment isotropy up to the second order, enough to capture the physics of fluids up to the Navier–Stokes level. (50,55) In this work, we performed two-dimensional simulations; thus, we opted for a D2Q9 LB model.
The collision operator Ωik(fik,fieq,k) depends on the discrete set of PDFs and on the set of equilibrium distribution functions obtained by performing a Taylor expansion of the local Maxwell–Boltzmann distribution, up to the second order in the Mach number. (50) Within the color gradient framework, it is typical to split the collision operator into three parts
(2)
where (Ωik)1 stands for the standard relaxation operator of the set of distribution functions, (Ωik)2 codes for the perturbation step, contributing to the buildup of an interfacial tension between immiscible components, and (Ωik)3 is an anti-diffusion term, needed to guarantee the immiscibility between different fluid components and to minimize the thickness of the diffuse interface (more details can be found in refs (34,44)). Finally, to arrest the coarsening and prevent the coalescence between neighboring droplets in close contact, a mesoscale repulsive force, essentially capturing the effect due to a surfactant adsorbed onto the interfaces, is included in the model. In previous studies, (34,44) it has been shown that in the continuum limit, such an approach leads to a Navier–Stokes equation for a multicomponent system augmented with a surface-localized body force, which can be interpreted as a coarse-grained version of the short-range molecular forces acting at the nanometer and sub-nanometer scales.
This numerical approach provides a robust platform for the simulation of dense emulsions with double-emulsion morphology like those reported in Figure 1, which shows a qualitative comparison between two dense foam-like structures obtained experimentally (Figure 1a) and numerically (Figure 1b).

Numerical Details

The simulation setup consists of a two-dimensional microfluidic channel made of an inlet reservoir followed by a thinner channel connected to a further downstream reservoir (see Figure 2).The height of the chambers is h = 600 lattice units and that of the constriction varies from hs = 80 to hs = 200 lattice units, while its length is ls = 240 lattice units. At the walls, we impose a bounce-back rule for the distribution functions, while at the outlet, we employ absorbing (zero-gradient) boundary conditions. (52) As mentioned above, the triple emulsion consists of fluid droplets (component A, white squares in Figure 2a) immersed within an inter-droplet continuous phase (component B, blue lines) surrounded by an external bulk phase (component C, black region outside the emulsion). The emulsion is initialized as a checkerboard-like pattern within the inlet chamber and relaxed for ∼5000 time steps, enough to achieve a configuration essentially stable over long periods of time. The number of the cores Nd has been varied from 25 to 49, while their diameter d has been varied from 36 to 40 lattice sites to simulate different packing fractions. With these numbers, the area fraction ϕ = Ad/As ranges from 0.5 up to 0.9, where Ad is the area occupied by the cores and As is the area of the shell.

Figure 2

Figure 2. (a) Double emulsion with ϕ ≃ 0.9 and Nd = 49 is initialized as a checkerboard-like pattern within the inlet chamber. (b) Example of the structure of the emulsion attained after t = 5000 time steps. The height of the inlet and outer chambers is h = 600 lattice sites, while the total length of the microfluidic channel is L = 3.6h. The rectangular constriction is made of two opposite fluid-free squared regions (indicated by red lines) of length ls = 240 lattice units, placed at a distance hs (the height of the constriction) ranging from 80 to 200 lattice sites.

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Note that the shape of the emulsion decisively depends on ϕ. Indeed, while at low ϕ, the drops and the external interface essentially keep their circular shape; at higher area fractions, inner cores are heavily squeezed and the external interface displays a multifaceted structure, tightly fitted to that of the nearby cores. This occurs since the fluid confined within the emulsion is almost entirely substituted by the cores. As also detailed in the following, the viscous dissipation is expected to hinder the relaxation of the shell, thus opposing to surface tension forces, which would restore the circular shape of the interfaces.
Notwithstanding, a crude estimation of the typical size of the shell (such as its diameter) can be computed by simply summing the diameters of the cores along one direction, say, the vertical one, where one has about seven cores. Hence, the ratio hs/D, where D ≃∑idi is the diameter of the emulsion, ranges approximately between 0.3 and 0.8.
The physical parameters have been chosen as follows. The kinematic viscosity of the dispersed phase and of the shell is νB = νC = 0.167, while that of the droplet phase has been set to νA = 0.05. The surface tensions between different components have been set to σAB = 0.02, σBC = 0.05, and σAC = 0.01. Such values are reported in simulation (lattice) units (details about the conversion in physical units (52)) and are chosen to match viscosity ratios and surface tension ratios of water (A), hexadecane (B), and fluorocarbon fluid (C), mixtures often employed in microfluidic experiments (see Figure 1). (10)

Results

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We initially discuss the typical behavior of a dense emulsion flowing within a narrow channel, focusing on shape deformations of the drops and structure of the velocity field. Afterward, we study the dynamic response of the emulsion, evaluated by varying the number Nd of internal drops and height hs of the constriction.

Shape Deformations and Velocity Field within a Narrow Channel

In Figure 3a–d, we show an example of translocation of a dense emulsion. In our numerical experiment, a uniform velocity profile, of speed Uin = 2 × 10–3 (in simulation units), is imposed at the inlet, which pushes the emulsion, of ϕ ≃ 0.9 and Nd = 49, within a narrow constriction of height hs = 120 lattice units. A parabolic profile of the velocity starts at x ∼ 0.15L within the inlet chamber and fully develops within the constriction, where the average speed is approximately given by (Ain/Acon)Uin, with Ain and Acon being the cross-sections of the inlet and constriction, respectively. The value of the velocity ensures that capillary and Reynolds numbers remain well within the typical range of microfluidic experiments ( and , respectively).

Figure 3

Figure 3. Translocation of a dense emulsion within a narrow channel. Here, ϕ ≃ 0.9, Nd = 49, and hs = 120, and the black regions represent the walls. A uniform velocity field pushes the emulsion rightward, causing a flow of drops approximately arranged in a two-row structure (a). Afterward, the drops gradually fill the constriction, giving rise to a highly compact foam-like body, which, once out of the channel, expands and relaxes (b–d). The velocity field is generally rather uniform within the constriction, whereas it is irregular in the drops out of the channel. The color bar represents the ratio of the magnitude of the velocity field u with respect to its maximum value UM.

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Once the emulsion approaches the constriction, the leading edge of the outer shell gradually deforms, while the internal cores located nearby undergo a series of mutual rearrangements necessary to flow within the channel (Figure 3a). Note that due to the high area fraction, the shape of the cores is generally far from the circular one, and at this stage of the translocation, it is only mildly affected by the constriction. Afterward, the emulsion gradually fills the channel (Figure 3b,c), giving rise to flowing metastable clusters of drops approximately arranged in a two-row structure. Once the leading edge of this structure has left the constriction, the cores at the forefront slowly unpack, while those in the channel assemble in a compact foam-like flowing material made of highly deformed drops separated by thin fluid films. During such a process, the velocity field exhibits two distinct patterns: an irregular and chaotic structure within the cores located out of the channel and a more uniform and ordered one within. The former is essentially due to the coupling between the velocity field and interfaces of the cores, an effect significantly mitigated in the constriction where a heavier flow, caused by the confined geometry, drags the drops collectively rightward at a higher speed.
The translocation clearly entails a remarkably complex rearrangement of the material, whose shape is profoundly influenced by the geometry of the channel. However, to what extent the confined environment can reshape the emulsion? In other words, can the structural changes observed in this dense emulsion become permanent, thus resulting in a soft material with mechanical and topological properties radically different from the ones exhibited initially? The next section is precisely dedicated to explore these issues.

Permanent Shape Deformations in Highly Dense Emulsions

To assess the effect produced by the inner drops on the shape of the emulsion once the translocation has occurred, we have performed a series of simulations by varying the number Nd of internal cores and their area fraction ϕ. As mentioned above, the numerical experiment essentially consists of an almost equilibrated dense emulsion placed at the inlet and pushed within a constriction by a uniform fluid flow. The material is finally collected in the outlet chamber and is let to relax for a sufficiently long period of time.
In Figure 4a, we show the results of three simulations obtained for ϕ = 0.55 (top, movie M1.avi), ϕ = 0.75 (middle, movie M2.avi), and ϕ = 0.9 (bottom, movie M3.avi), with Nd = 49 and diameter of the cores equal to d = 36 (top), d = 38 (middle), and d = 40 (bottom). Since hs = 120 lattice units, one has hs/D approximately equal to 0.45. Once the flow is switched on, the emulsion crosses the constriction undergoing considerable shape deformations, basically akin to those described in the previous section. However, the shape of the resulting material collected in the outer chamber crucially depends on the area fraction ϕ occupied by the cores and on the ratio hs/D.

Figure 4

Figure 4. (a) Translocation dynamics of a dense emulsion for ϕ = 0.55 (top), ϕ = 0.75 (middle), and ϕ = 0.9 (bottom). In all cases, Nd = 49 and hs/D ≃ 0.45. Once the emulsion crosses the constriction, the resulting shape observed in the outlet chamber crucially depends on the area fraction ϕ. At low ϕ, the emulsion expands and springs back close to its original shape; at increasing ϕ, deformations become permanent. Snapshots are taken at t = 25, 90, and 150 × 103 steps. Blue lines connecting the centers of neighboring droplets represent the Delaunay triangulation, while red dotted lines represent the Voronoi decomposition. (b) Time evolution of the circularity Λ for different values of ϕ and Nd. At low values of ϕ, the circular shape of the emulsion is basically restored after translocation, while at increasing ϕ, Λ considerably decreases, up to half of its initial value.

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Keeping hs/D fixed at ≃ 0.45, one can basically distinguish two relevant scenarios. Indeed, if ϕ = 0.55, the final shape resembles very closely the initial one observed before the translocation, whereas at increasing values of ϕ, the double-emulsion drop generally exhibits a highly elongated structure considerably different from the starting configuration. Such shape deformations are found to persist over long periods of time and can be considered permanent rather than temporary.
The departure of the emulsion from its circular shape can be monitored by computing the circularity of the external shell, defined as Λ = 4πA/P2, where A is the area of the shell and P is its perimeter. This quantity ranges between 1 (circular shape) and 0 (needle-like geometry).In Figure 4b, the time evolution of Λ for different values of ϕ and Nd and for hs = 120 is shown. At low values of ϕ (such as ϕ ∼ 0.55 and Nd = 49, hollow circles, or Nd = 25, dashed line) Λ goes back to ∼1 at late times, indications that deformations are negligible. For increasing values of ϕ (∼0.75, dotted line and hollow triangles, and ∼0.9 continuum line and filled circles), after the translocation, Λ attains values well below 1 kept essentially constant for a long period of time, thus quantitatively proving that shape changes can be considered essentially permanent. Note that finally, regardless of the area fraction, the minimum of Λ sets at roughly 0.4, basically because the height hs of the constriction has been kept constant in this set of simulations.
The complex topological rearrangements of the droplets can be quantitatively assessed by monitoring the time evolution of the number of hexagonal clusters NHex assembled in the process. This quantity, computed using a Delaunay triangulation, provides insights into how far such clusters are from the ordered hexagonal structure typical of a solid material. Like the circularity, NHex exhibits a minimum, roughly equal for all values of ϕ, when a large portion of the emulsion is within the constriction, whereas it attains a late time value, which decreases for increasing values of ϕ, once the translocation is completed (see Figure 5a). This result suggests that under extreme confinement, the crystal-like ordering dramatically drops, while it is only partially restored once the emulsion has relaxed in the outer chamber. In other words, the emulsion has undergone a permanent modification in its shape after the crossing within the narrow channel. We incidentally note that unlike this system, fully hexagonal clusters of droplets can survive within channels. This is the case, for example, of microfluidic crystals, (25) where droplets (or bubbles) are fed into the channel at a constant rate from a single tube without fluctuations, thus quickly jumping into local energy minima with a crystal-like configuration.

Figure 5

Figure 5. (a) In this figure, we show the time evolution of the number of hexagonal clusters NHex, computed by a Delaunay triangulation, observed during the translocation for ϕ ≃ 0.55 (black circles), ϕ ≃ 0.75 (empty circles), and ϕ ≃ 0.9 (squares). Like Λ, NHex exhibits a minimum, approximately equal for all values of ϕ, within the constriction, and attains a late time value, which decreases when ϕ augments. (b) Here, we show the behavior of the residual deformation Λr for different values of ϕ, Nd, and hs. In particular, hs = 200 and Nd = 25 (triangles), hs = 200 and Nd = 49 (plusses), hs = 120 and Nd = 25 (circles), and hs = 120 and Nd = 49 (asterisks). Λr is computed as the time average of the values of Λ obtained once the translocation is completed. As long as ϕ < 0.6, shape deformations are negligible, while for larger values of ϕ, Λr decreases faster for smaller values of hs (i.e., narrower channels).

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Finally, the effect produced by the constriction can be evaluated by computing the residual deformation Λr, calculated as a time average of the values of Λ obtained once the translocation ends (see Figure 5b). Such deformation is found to remain essentially constant and close to unity for ϕ ≤ 0.6 regardless of the values of hd, whereas it decreases down to ∼0.5 for higher values of ϕ and for narrower sizes of the channel. In this regime, the decrease is steeper for diminishing values of hd, a result proving, once again, that heavy shape changes observed during the translocation become stable and permanent for long periods of time.

Dynamical Characterization

The results discussed above show that the transition from a Newtonian behavior, in which shape changes are negligible, toward a viscoelastic one, in which on the contrary they become permanent, is observed for high values of ϕ (larger than 0.6), a regime in which fluid interfaces occupy a large portion of the emulsion. It is thus crucial to understand the role played by such interfaces and to what extent they affect the mechanical properties of the emulsion.
In Figure 6a,b, we show a map of the magnitude of the velocity gradients within the emulsion for ϕ ≃ 0.55 (a) and ϕ ≃ 0.9 (b). The spots highlighted in red represent regions in which |∇u| > |∇uth|, where and |∇uth| ∼ 10–3 is a threshold below which shear effects are negligible. The choice of the threshold is motivated as follows. By defining a grid capillary number as Cal = μ|∇u|Δx/σ, with μ ∼ 0.1, Δx = 1, σ = 0.01, and |∇u| = 10–3, we obtain Cal ∼ 10–2. Hence, if |∇u| < 10–3, it is reasonable to assume that the local shear stresses are negligible with respect to the surface tension forces. High values of |∇u| are generally concentrated between co-moving interfaces in close contact, and only at high ϕ, they form an interconnected path running through the tangle of the thin films sustained by the plateau of the droplet’s interfaces. Remarkably, once the emulsion has left the constriction, high gradients survive only if ϕ ≃ 0.9, whereas they are basically negligible for lower values.

Figure 6

Figure 6. (a,b) Map of the magnitude of the velocity gradients within the emulsion for ϕ ≃ 0.55 (a) and ϕ ≃ 0.9 (b). The spots highlighted in red represent regions in which |∇u| > |∇uth|. (c) Dissipation parameter η (i.e., viscous dissipation vs surface tension work) is plotted as a function of ϕ and for different values of the ratio hs/D, in particular hs/D ∼ 0.6 (open circles), hs/D ∼ 0.8 (open triangles), hs/D ∼ 0.35 (filled circles), and hs/D ∼ 0.5 (asterisks). Dotted, continuous, and dashed lines represent the best fit to asterisks, filled circles, and open circles, respectively.

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Since the interfaces are the source of the viscous dissipation in a fluid mixture, one may expect that in the high-ϕ regime, viscous forces become the dominant contribution with respect to the one stemming from surface tension, which opposes shape deformations. This is evaluated by introducing a dissipation parameter, η = ⟨PΨ⟩/⟨Pσ⟩, which essentially compares the loss of energy due to viscous dissipation to the work performed by surface forces to bring the droplets back to their spherical shape once the translocation is complete, thus favoring the relaxation of the external shell. Here, ⟨PΨ⟩ and ⟨Pσ⟩ represent time-averaged values of viscous and surface energy rates, respectively, defined as
(3)
and
(4)
In eq 3, the local (time–space) viscous function Ψ is defined as
(5)
where μ is the dynamic viscosity, is the local phase field varying between 1 (bulk of fluid A) and −1 (bulk of fluid B), and the term γ(∇ζ)2, with γ ∼ σAB, represents an interfacial free energy contribution, overall akin to the one of Landau theory of multicomponent fluids usually given by (k/2)(∇ζ)2, with k being the elastic constant. (52) Finally, in both equations, V is the volume occupied by the emulsion and T is the time integration interval.
In Figure 6c, η is plotted as a function of ϕ and for different values of the ratio hs/D. Its behavior is essentially independent of hs/D but steadily increasing with ϕ. The growth is linear for ϕ < 0.6, where the emulsion behaves as a Newtonian fluid, and follows a non-linear trend for higher values of ϕ, the region where viscoelastic features emerge. In this regime, η ≥ 10–2, a value above which the viscous dissipation, converted into thermal heating due to the high velocity gradients localized at the fluid interfaces, becomes a non-negligible fraction of the total surface energy. It is best fitted with a power law of the form Aϕ(1 – ϕ)α, where A is a constant and −3/2 ≤ α ≤ −4/3. This trend is reminiscent of the viscosity–concentration relation observed in packed emulsions (theoretically predicted by Bullard et al. (56)), which, unlike analogous soft materials displaying a first-order solid-to-liquid transition above a critical threshold, (31) follows a continuous power law behavior.
These results show that the ratio between the internal viscous forces (extensional force) and the surface tension (retraction/restoring force) controls the dynamics of a dense emulsion during the compression/expansion process. Indeed, while internal viscous forces retard the expansion of the external shell, the surface tension opposes the effect of the extensional stresses. This competition, together with the degree of confinement set by the constriction, modulates the final shape of the core emulsion.

Conclusions

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In this work, we have numerically investigated, using LB simulations, the dynamic behavior of double-emulsion drops with close-packed inner droplets crossing a narrow channel. Our system is a ternary fluid mixture, in which a dispersed droplet phase is immersed in an inter-droplet lubricating one, in turn surrounded by an external bulk fluid. The double-emulsion drops are initialized in an inlet chamber, subsequently driven by a uniform flow within a constriction, and finally collected in an outlet chamber, where they are let to relax.
Our results show that the shape of the double-emulsion drop obtained downstream crucially depends on (i) the area fraction of the internal droplets and (ii) the height of the narrow channel with respect to the typical size of the double-emulsion drop. For fixed values of height, but significantly smaller than the diameter the drop, we basically distinguish two scenarios. If the area fraction occupied by the cores remains below ∼0.55, once the translocation within the channel is completed, the double-emulsion drop essentially recovers the quasi-spherical shape attained before the crossing. On the contrary, for higher values of the area fraction, shape deformations induced by the constriction become permanent, and the drop generally attains a heavy elongated shape, in which highly packed inner droplets are separated by thin films of fluid. The deviation from the spherical shape is measured in terms of the circularity Λ, which is found to fall up to 0.5 for very dense emulsions (ϕ ≃ 0.9) and very narrow constrictions (hs/D ≃ 0.5 or lower values). The transition from a Newtonian fluid behavior toward a non-Newtonian one is captured with high accuracy using the dissipation parameter η, a dimensionless number representing the loss of energy due to viscous dissipation with respect to the work performed by surface forces necessary to round up deformations. This quantity follows a power law behavior, approximately linear for ϕ < 0.55 and highly non-linear for higher values; the latter is an indication that at a large area fraction, viscous forces dominate over surface tension ones, an effect very likely due to fluid interfaces occupying a large portion of the emulsion.
In summary, we find that our system develops memory-like effects induced by the combined action of confinement and viscous dissipation. Understanding the behavior of soft granular clusters, such as the double-emulsion drops studied here, can be of interest for the generation of compartmentalized capsules and vesicles useful, for example, in drug delivery. Their structure can give rise to a significant amount of internal dissipation, thereby considerably affecting the way they flow in complex geometries, such as obstacles and orifices. Under strong confinement, events such as topological transitions, coalescence, and rearrangement of droplets may crucially affect the stability and lead to morphological transitions, (25,32) such as fragmentation of the outer shell (breakup of a single HIPdE into multiple HIPdEs) or coalescence of the inner droplets. Control of such systems is also crucial for the preparation of dense emulsions and double emulsions as templates of porous materials with desired porosity and/or pore arrangement (e.g., ordered vs disordered). (1)
Besides their interest on its own, such largely unexplored complex states of flowing matter could also raise interest in fields such as biology and medicine. In the former case, our numerical experiments could be seen as a droplet microfluidic analogue of compression–relaxation experiments involving aggregates of cells (the inner cores in our emulsion). (47) In the latter context, modeling the migration of cell clusters within confined environments, such as across capillaries, is essential to assess how morphological changes affect their motion, a phenomenon of particular relevance in pathological diseases such as invasion and metastasis of cancer cells. (57,58)

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.langmuir.1c01026.

  • Translocation dynamics of a HIPdE with ϕ ≃ 0.55 (AVI)

  • Translocation dynamics of a HIPdE with ϕ ≃ 0.75 (AVI)

  • Translocation dynamics of a HIPdE with ϕ ≃ 0.9 (AVI)

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Author Information

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  • Corresponding Authors
  • Authors
    • Andrea Montessori - Istituto per le Applicazioni del Calcolo CNR, Via dei Taurini 19, Rome 00185, Italy
    • Michał Bogdan - Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, Warsaw 01-224, Poland
    • Fabio Bonaccorso - Center for Life Nanoscience at la Sapienza, Istituto Italiano di Tecnologia, Viale Regina Elena 295, Rome 00161, Italy;  Istituto per le Applicazioni del Calcolo CNR, Via dei Taurini 19, Rome 00185, Italy;  Dipartimento di Fisica, Università degli Studi di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, Rome 00133, Italy
    • Marco Lauricella - Istituto per le Applicazioni del Calcolo CNR, Via dei Taurini 19, Rome 00185, Italy;  Orcidhttps://orcid.org/0000-0002-3862-5562
    • Sauro Succi - Center for Life Nanoscience at la Sapienza, Istituto Italiano di Tecnologia, Viale Regina Elena 295, Rome 00161, Italy;  Istituto per le Applicazioni del Calcolo CNR, Via dei Taurini 19, Rome 00185, Italy;  Institute for Applied Computational Science, Harvard John A. Paulson School of Engineering and Applied Sciences, Cambridge, Massachusetts 02138, United States
  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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A.M., M.L., A.T., and S.S. acknowledge funding from the European Research Council under the European Union’s Horizon 2020 Framework Programme (no. FP/2014-2020) ERC grant agreement no.739964 (COPMAT). A.M. acknowledges the CINECA Computational Grant ISCRA-C IsC83 - “SDROMOL”, id. HP10CZXK6R under the ISCRA initiative, for the availability of high-performance computing resources and support. M.B. acknowledges European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant no. 847413 and PMW programme of the Minister of Science and Higher Education in the years 2020–2024, no. 5005/H2020-MSCA-COFUND/2019/2. J.G. acknowledges support from Foundation for Polish Science under program First Team (grant no. POIR.04.04.00-00-26C7/16-00).

References

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    Microemulsions have found a wide range of applications exploiting their chem. and phys. properties. Development of microfluidic-based approaches has allowed for the controlled prodn. of highly monodispersed emulsions, including the formation of multiple and hierarchical emulsions. Conventional poly(dimethylsiloxane)-based microfluidic systems require tight spatial control over the surface chem. when used for double emulsion generation, which can be challenging to achieve on the micrometer scale. Here, the authors present a two-dimensional device design, which can selectively be surface-treated in a straightforward manner and allows for the formation of uniform water/oil/water double emulsions by combining two distinct hydrophilic and hydrophobic surface properties. These surfaces are sufficiently sepd. in space to allow for imparting their functionalization without the requirement for lithog. approaches or complex flow control. The authors demonstrate that a mismatch between the wettability requirements of the continuous phase and the channel wall inherent in this approach can be tolerated over several hundreds of micrometers, opening up the possibility to use simple pressure-driven flows to achieve surface functionalization. The design architecture exhibits robust efficiency in emulsion generation while retaining simple device fabrication. The authors finally demonstrate the potential of this approach by generating water in oil in water emulsions with lipid mols. acting as surfactants.
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    Lee, J.; Kim, J. W.; Han, S. H.; Chang, I. S.; Kang, H. H.; Lee, O. S.; Oh, S. G.; Suh, K. D. The stabilization of L-ascorbic acid in aqueous solution and water-in-oil-in-water double emulsion by controlling pH and electrolyte concentration. Int. J. Cosmet. Sci. 2004, 26, 217,  DOI: 10.1111/j.0142-5463.2004.00223_1.x
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    Lee, M. C.; Tan, C.; Ravanfar, R.; Abbaspourrad, A. Ultrastable water-in-oil High internal phase emulsions featuring interfacial and biphasic network stabilization. ACS Appl. Mater. Interfaces 2019, 11, 26433– 26441,  DOI: 10.1021/acsami.9b05089
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    Ultrastable Water-in-Oil High Internal Phase Emulsions Featuring Interfacial and Biphasic Network Stabilization
    Lee, Michelle C.; Tan, Chen; Ravanfar, Raheleh; Abbaspourrad, Alireza
    ACS Applied Materials & Interfaces (2019), 11 (29), 26433-26441CODEN: AAMICK; ISSN:1944-8244. (American Chemical Society)
    The authors present gel-in-gel H2O-in-oil (W/O) high internal phase emulsions (HIPEs) that feature high stability by structuring both phases of the emulsion. Compared to significant advances made in oil-in-H2O (O/W) HIPEs, W/O HIPEs are extremely unstable and difficult to generate without introducing high concns. of surfactants. Another main challenge is the low viscosity of both H2O and oil phases which promotes the instability of W/O HIPEs. Here, the authors demonstrate ultrastable W/O HIPEs that feature biphasic structuring, in which hydrogels are dispersed in oleogels, and self-forming, low-concn. interfacial Pickering crystals provide added stability. These W/O HIPEs exhibit high tolerance toward pH shock and destabilizing environments. This novel ultrastable gel-in-gel W/O HIPE is sustainable and made solely with natural ingredients without the addn. of any synthetic stabilizers. By applying phase structuring within the HIPEs through the addn. of various carrageenans and beeswax as structurants, the authors can increase the emulsion's stability and viscoelastic rheol. properties. The performance of these gel-in-gel W/O HIPEs holds promise for a wide range of applications. As a proof of concept, the authors demonstrated herein the application as a gelled delivery system that enables the co-delivery of hydrophilic and hydrophobic materials at maximized loads, demonstrating high resistance to gastrointestinal pHs and a controlled-release profile.
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    Muschiolik, G.; Dickinson, E. Double Emulsions Relevant to Food Systems: Preparation, Stability, and Applications. Compr. Rev. Food Sci. Food Saf. 2017, 16, 532,  DOI: 10.1111/1541-4337.12261
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    Double Emulsions Relevant to Food Systems: Preparation, Stability, and Applications
    Muschiolik, Gerald; Dickinson, Eric
    Comprehensive Reviews in Food Science and Food Safety (2017), 16 (3), 532-555CODEN: CRFSBJ; ISSN:1541-4337. (Institute of Food Technologists)
    This review describes advances in the prepn. of food-relevant double emulsions (DEs) of the water-in-oil-in-water (W/O/W) and oil-in-water-in-oil (O/W/O) types with emphasis on research published within the last decade. The information is assembled and critically evaluated according to the following aspects: the food application area, the range of encapsulated components and emulsion compn., the emulsification prepn. methods, the balancing of the osmotic pressure, the stabilization by increased viscosity or gelation, the role of protein-polysaccharide interactions, and the techniques used to est. DE yield and emulsification efficiency. Particular focus is directed toward the control of encapsulation and release behavior, including strategies that have been employed to improve the retention ability of the inner phase droplets by modifying the outer oil-water interface through mixed ingredient interactions, Pickering stabilization by particles, and biopolymer gelation. We also briefly consider the incorporation of DEs into dried microcapsules and the stability of W/O/W emulsions during eating and digestion. It would appear that 2 outstanding issues are currently preventing full realization of the potential of DEs in food applications: (i) the lack of availability of large-scale prodn. equipment to ensure efficient nondestructive 2nd-stage emulsification, and (ii) the limited range of food-grade ingredients available to successfully replace polyglycerol polyricinoleate as the primary emulsifier in W/O/W formulations.
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    Jiang, H.; Zhang, T.; Smits, J.; Huang, X.; Maas, M.; Yin, S.; Ngai, T. Edible high internal phase Pickering emulsion with double-emulsion morphology. Food Hydrocolloids 2021, 111, 106405,  DOI: 10.1016/j.foodhyd.2020.106405
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    Edible high internal phase Pickering emulsion with double-emulsion morphology
    Jiang, Hang; Zhang, Tong; Smits, Joeri; Huang, Xiaonan; Maas, Michael; Yin, Shouwei; Ngai, To
    Food Hydrocolloids (2021), 111 (), 106405CODEN: FOHYES; ISSN:0268-005X. (Elsevier Ltd.)
    Food-grade high internal phase Pickering emulsions (HIPPEs) unify the stability of Pickering emulsions and the advantages of detergent-based high internal phase emulsions (HIPEs), making them attractive as nutritional products. However, as oral delivery systems, HIPPEs are usually prepd. in the form of o/w emulsions, which are suitable mainly for oleophilic active ingredients and may suffer from leakage during gastric digestion. To better protect and deliver hydrophilic cargo mols., we developed a HIPPE-based w/o/w double emulsion system. Zein nanoparticles and soybean lecithin are found to have a synergistic effect in stabilization - using both natural emulsifiers together results in the formation of w/o/w double emulsions with improved stability, which is further confirmed by the interfacial tension and rheol. of zein- and/or lecithin-laden oil-water interfaces. A combination of zein nanoparticles and lecithin achieves the fastest interfacial tension decrease, indicating an improved interfacial activity. Besides, lecithin contributes to the strong surface elasticity of the interfacial films, which makes the formed emulsions even stabler. Simulated digestion expts. suggest that the inner aq. droplets can be strongly protected from gastric fluids. This edible HIPPE with double emulsion morphol. provides new ideas for designing healthy foods for nutrients delivery.
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    Zhang, H.; Cooper, A. I. Synthesis and applications of emulsion-templated porous materials. Soft Matter 2005, 1, 107– 113,  DOI: 10.1039/b502551f
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    Synthesis and applications of emulsion-templated porous materials
    Zhang, Haifei; Cooper, Andrew I.
    Soft Matter (2005), 1 (2), 107-113CODEN: SMOABF; ISSN:1744-683X. (Royal Society of Chemistry)
    This review describes the use of macroemulsions as templates for the prodn. of porous materials. It is focussed on the use of high internal phase emulsions to produce interconnected open porous structures. The review encompasses porous hydrophobic polymers, hydrophilic polymers, composites, silica, metal oxides, and metals. The potential applications of these materials are also discussed.
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    Bokhari, M.; Carnachan, R. J.; Przyborski, S. A.; Cameron, N. R. Emulsion-Templated porous polymers as scaffolds for three dimensional cell culture: Effect of synthesis parameters on scaffold formation and homogeneity. J. Mater. Chem. 2007, 17, 4088– 4094,  DOI: 10.1039/b707499a
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    Emulsion-templated porous polymers as scaffolds for three dimensional cell culture: effect of synthesis parameters on scaffold formation and homogeneity
    Bokhari, Maria; Carnachan, Ross J.; Przyborski, Stefan A.; Cameron, Neil R.
    Journal of Materials Chemistry (2007), 17 (38), 4088-4094CODEN: JMACEP; ISSN:0959-9428. (Royal Society of Chemistry)
    Emulsion-templated porous polymers (PolyHIPEs) based on polystyrene have been prepd. and used for in vitro 3D cell culture of osteoblastic cells. It has been found that the method employed to prep. the emulsion precursor, namely the method of aq. phase addn., has a significant influence on the homogeneity of the morphol. of the material produced as well as the reproducibility of prepn. Addn. of the aq. phase in a controlled manner by means of a syringe pump produced a narrower void size distribution range than addn. from a dropping funnel, and the emulsions were obtained in a reproducible manner. Anal. of the morphol. of the materials revealed consistency of av. void and interconnect diam., within certain limits. The materials produced were subsequently sectioned into thin membranes which were then mounted to the base of com. available tissue culture plastic well inserts. Cell culture expts. using MG63 osteoblast-like cells indicated that the materials were capable of supporting cell growth for periods of up to 35 days, producing complex arrangements of cells interacting with one another and the scaffold. The functionality of cells grown on these materials, as indicated by viability assays and the prodn. of biomarkers (alk. phosphatase and osteocalcin), was found to be enhanced compared to cells grown on 2D substrates. We conclude that the 3D environment produced by these porous materials is more conducive to cell growth in vitro than existing 2D culture plastic.
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    Marmottant, P.; Raven, J.-P. Microfluidics with foams. Soft Matter 2009, 5, 3385– 3388,  DOI: 10.1039/b903276b
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    Microfluidics with foams
    Marmottant, Philippe; Raven, Jan-Paul
    Soft Matter (2009), 5 (18), 3385-3388CODEN: SMOABF; ISSN:1744-683X. (Royal Society of Chemistry)
    Lab-on-a-chip devices can handle very tiny amts. of fluids, as small as a picoliter. Samples of gas are conveniently encapsulated and transported within bubbles. The generation of these calibrated bubbles involves specific microfluidic devices that we describe. When the bubble concn. is high enough in a channel, they come into contact, and they flow as a cryst. foam. The flow of the foams depends strongly on the arrangement of bubbles within the channel, which entails original dynamical behaviors such as super-stability of the flow, or on the contrary spontaneous oscillations.
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    Liu, L.; Yu, M.; Lin, H.; Foty, R. Deformation and relaxation of an incompressible viscoelastic body with surface viscoelasticity. J. Mech. Phys. Solids 2017, 98, 309– 329,  DOI: 10.1016/j.jmps.2016.09.013
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    Deformation and relaxation of an incompressible viscoelastic body with surface viscoelasticity
    Liu, Liping; Yu, Miao; Lin, Hao; Foty, Ramsey
    Journal of the Mechanics and Physics of Solids (2017), 98 (), 309-329CODEN: JMPSA8; ISSN:0022-5096. (Elsevier Ltd.)
    Measuring mech. properties of cells or cell aggregates has proven to be an involved process due to their geometrical and structural complexity. Past measurements are based on material models that completely neglect the elasticity of either the surface membrane or the interior bulk. In this work, we consider general material models to account for both surface and bulk viscoelasticity. The boundary value problems are formulated for deformations and relaxations of a closed viscoelastic surface coupled with viscoelastic media inside and outside of the surface. The linearized surface elasticity models are derived for the const. surface tension model and the Helfrich-Canham bending model for coupling with the bulk viscoelasticity. For quasi-spherical surfaces, explicit solns. are obtained for the deformation, stress-strain and relaxation behaviors under a variety of loading conditions. These solns. can be applied to ext. the intrinsic surface and bulk viscoelastic properties of biol. cells or cell aggregates in the indentation, electro-deformation and relaxation expts.
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    Dong, Y.; Skelley, A. M.; Merdek, K. D.; Sprott, K. M.; Jiang, C.; Pierceall, W. E.; Lin, J.; Stocum, M.; Carney, W. P.; Smirnov, D. A. Microfluidics and circulating tumor cells. J. Mol. Diagn. 2013, 15, 149– 157,  DOI: 10.1016/j.jmoldx.2012.09.004
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    Microfluidics and circulating tumor cells
    Dong Yi; Skelley Alison M; Merdek Keith D; Sprott Kam M; Jiang Chunsheng; Pierceall William E; Lin Jessie; Stocum Michael; Carney Walter P; Smirnov Denis A
    The Journal of molecular diagnostics : JMD (2013), 15 (2), 149-57 ISSN:.
    Circulating tumor cells (CTCs) are shed from cancerous tumors, enter the circulatory system, and migrate to distant organs to form metastases that ultimately lead to the death of most patients with cancer. Identification and characterization of CTCs provides a means to study, monitor, and potentially interfere with the metastatic process. Isolation of CTCs from blood is challenging because CTCs are rare and possess characteristics that reflect the heterogeneity of cancers. Various methods have been developed to enrich CTCs from many millions of normal blood cells. Microfluidics offers an opportunity to create a next generation of superior CTC enrichment devices. This review focuses on various microfluidic approaches that have been applied to date to capture CTCs from the blood of patients with cancer.
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    Stott, S. L.; Hsu, C.-H.; Tsukrov, D. I.; Yu, M.; Miyamoto, D. T.; Waltman, B. A.; Rothenberg, S. M.; Shah, A. M.; Smas, M. E.; Korir, G. K.; Floyd, F. P., Jr.; Gilman, A. J.; Lord, J. B.; Winokur, D.; Springer, S.; Irimia, D.; Nagrath, S.; Sequist, L. V.; Lee, R. J.; Isselbacher, K. J.; Maheswaran, S.; Haber, D. A.; Toner, M. Isolation of circulating tumor cells using a microvortex-generating herringbone-chip. Proc. Natl. Acad. Sci. U.S.A. 2010, 107, 18392– 18397,  DOI: 10.1073/pnas.1012539107
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    Isolation of circulating tumor cells using a microvortex-generating herringbone-chip
    Stott, Shannon L.; Hsua, Chia-Hsien; Tsukrov, Dina I.; Yu, Min; Miyamoto, David T.; Waltman, Belinda A.; Rothenberg, S. Michael; Shah, Ajay M.; Smas, Malgorzata E.; Korir, George K.; Floyd, Frederick P., Jr.; Gilman, Anna J.; Lord, Jenna B.; Winokur, Daniel; Springer, Simeon; Irimia, Daniel; Nagrath, Sunitha; Sequist, Lecia V.; Lee, Richard J.; Isselbacher, Kurt J.; Maheswaran, Shyamala; Haber, Daniel A.; Toner, Mehmet
    Proceedings of the National Academy of Sciences of the United States of America (2010), 107 (43), 18392-18397, S18392/1-S18392/9CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
    Rare circulating tumor cells (CTCs) present in the bloodstream of patients with cancer provide a potentially accessible source for detection, characterization, and monitoring of nonhematol. cancers. We previously demonstrated the effectiveness of a microfluidic device, the CTC-Chip, in capturing these epithelial cell adhesion mol. (EpCAM)-expressing cells using antibody-coated microposts. Here, we describe a high-throughput microfluidic mixing device, the herringbone-chip, or "HB-Chip," which provides an enhanced platform for CTC isolation. The HB-Chip design applies passive mixing of blood cells through the generation of microvortices to significantly increase the no. of interactions between target CTCs and the antibody-coated chip surface. Efficient cell capture was validated using defined nos. of cancer cells spiked into control blood, and clin. utility was demonstrated in specimens from patients with prostate cancer. CTCs were detected in 14 of 15 (93%) patients with metastatic disease (median = 63 CTCs/mL, mean = 386 ± 238 CTCs/mL), and the tumor-specific TMPRSS2-ERG translocation was readily identified following RNA isolation and RT-PCR anal. The use of transparent materials allowed for imaging of the captured CTCs using std. clin. histopathol. stains, in addn. to immunofluorescence-conjugated antibodies. In a subset of patient samples, the low shear design of the HB-Chip revealed microclusters of CTCs, previously unappreciated tumor cell aggregates that may contribute to the hematogenous dissemination of cancer.
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    Dluska, E.; Markowska-Radomska, A.; Metera, A.; Tudek, B.; Kosicki, K. Multiple emulsions as effective platforms for controlled anti-cancer drug delivery. Nanomedicine 2017, 12, 18,  DOI: 10.2217/nnm-2017-0112
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    Kosztin, I.; Vunjak-Novakovic, G.; Forgacs, G. Colloquium: Modeling the dynamics of multicellular systems: Application to tissue engineering. Rev. Mod. Phys. 2012, 84, 1791– 1805,  DOI: 10.1103/revmodphys.84.1791
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    Lulli, M.; Benzi, R.; Sbragaglia, M. Metastability at the yield-stress transition in soft glasses. Phys. Rev. X 2018, 8, 021031,  DOI: 10.1103/physrevx.8.021031
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    Metastability at the Yield-Stress Transition in Soft Glasses
    Lulli, Matteo; Benzi, Roberto; Sbragaglia, Mauro
    Physical Review X (2018), 8 (2), 021031CODEN: PRXHAE; ISSN:2160-3308. (American Physical Society)
    We study the solid-to-liq. transition in a two-dimensional fully periodic soft-glassy model with an imposed spatially heterogeneous stress. The model we consider consists of droplets of a dispersed phase jammed together in a continuous phase. When the peak value of the stress gets close to the yield stress of the material, we find that the whole system intermittently tunnels to a metastable "fluidized" state, which relaxes back to a metastable "solid" state by means of an elastic-wave dissipation. This macroscopic scenario is studied through the microscopic displacement field of the droplets, whose time statistics displays a remarkable bimodality. Metastability is rooted in the existence, in a given stress range, of two distinct stable rheol. branches, as well as long-range correlations (e.g., large dynamic heterogeneity) developed in the system. Finally, we show that a similar behavior holds for a pressure-driven flow, thus suggesting possible exptl. tests.
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    Raven, J. P.; Marmottant, P. Microfluidic crystals: dynamic interplay between rearrangement waves and flow. Phys. Rev. Lett. 2009, 102, 084501,  DOI: 10.1103/PhysRevLett.102.084501
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    Microfluidic Crystals: Dynamic Interplay between Rearrangement Waves and Flow
    Raven, Jan-Paul; Marmottant, Philippe
    Physical Review Letters (2009), 102 (8), 084501/1-084501/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    Microfluidic crystals are assemblies of miniature bubbles or drops flowing in channels. We explore here the flow of these crystals, when submitted to a given driving pressure. The flow velocity is linked to the finite no. of elements in the channel width, and presents discontinuities when the crystal structure changes. At the transition from one structure to the other original dynamic features appear. The flow can self-regulate itself on a fixed velocity whatever the driving pressure, or, on the contrary, can spontaneously pulsate. All these features are predicted by simply considering the crystal's energy and friction, and looking at the propagation of structure rearrangements. We anticipate these results to improve the control over the structure of dense two-phase flows in microfluidic systems.
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    Rosenfeld, L.; Fan, L.; Chen, Y.; Swoboda, R.; Tang, S. K. Y. Break-up of droplets in a concentrated emulsion flowing through a narrow constriction. Soft Matter 2014, 10, 421– 430,  DOI: 10.1039/c3sm51843d
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    Break-up of droplets in a concentrated emulsion flowing through a narrow constriction
    Rosenfeld, Liat; Fan, Lin; Chen, Yunhan; Swoboda, Ryan; Tang, Sindy K. Y.
    Soft Matter (2014), 10 (3), 421-430CODEN: SMOABF; ISSN:1744-683X. (Royal Society of Chemistry)
    This paper describes the break-up of droplets in a concd. emulsion during its flow as a 2D monolayer in a microchannel consisting of a narrow constriction. Anal. of the behavior of a large no. of drops (N > 4000) shows that the no. of break-ups increases with increasing flow rate, entrance angle to the constriction, and size of the drops relative to the width of the constriction. As single drops do not break at the highest flow rate used in the system, break-ups arise primarily from droplet-droplet interactions. Anal. of droplet properties at a high temporal resoln. of 10 μs makes it possible to relate droplet deformation with droplet break-up probability. Similar to previous studies on single drops, no break-up is obsd. below a set of crit. flow rates and droplet deformations. Unlike previous studies, however, not all drops undergo break-up above the crit. values. Instead, the probability of droplet break-up increases with flow rate and the deformation of the drops. The probabilistic nature of the break-up process arises from the stochastic variations in the packing configuration of the drops as they enter the constriction. Local break-up dynamics involves two primary drops. A close look at the interactions between the pair of drops reveals that the competing time scales of droplet rearrangement relative to the relaxation of the opposing drop govern whether break-up occurs or not. Practically, these results can be used to calc. the max. throughput of the serial interrogation process often employed in droplet microfluidics. For 40 pL-drops, the highest throughput with <1% droplet break-up was measured to be approx. 7000 drops per s. In addn., the results presented are useful for understanding the behavior of concd. emulsions in applications such as mobility control in enhanced oil recovery, and for extrapolating crit. parameters such as injection rates to ensure the stability of the fluids going through small pore throats.
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    Montessori, A.; Lauricella, M.; Tiribocchi, A.; Succi, S. Modeling pattern formation in soft flowing crystals. Phys. Rev. Fluids 2019, 4, 072201(R)  DOI: 10.1103/physrevfluids.4.072201
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    Wang, J.; Liu, J.; Han, J.; Guan, J. Effects of Complex Internal Structures on Rheology of Multiple Emulsions Particles in 2D from a Boundary Integral Method. Phys. Rev. Lett. 2013, 110, 066001,  DOI: 10.1103/PhysRevLett.110.066001
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    Effects of complex internal structures on rheology of multiple emulsions particles in 2D from a boundary integral method
    Wang, Jingtao; Liu, Jinxia; Han, Junjie; Guan, Jing
    Physical Review Letters (2013), 110 (6), 066001/1-066001/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    A boundary integral method is developed to investigate the effects of inner droplets and asymmetry of internal structures on rheol. of two-dimensional multiple emulsion particles with arbitrary nos. of layers and droplets within each layer. Under a modest extensional flow, the no. increment of layers and inner droplets, and the collision among inner droplets subject the particle to stronger shears. In addn., the coalescence or release of inner droplets changes the internal structure of the multiple emulsion particles. Since the rheol. of such particles is sensitive to internal structures and their change, modeling them as the core-shell particles to obtain the viscosity equation of a single particle should be modified by introducing the time-dependable vol. fraction Φ(t) of the core instead of the fixed Φ. An asym. internal structure induces an oriented contact and merging of the outer and inner interface. The start time of the interface merging is controlled by adjusting the viscosity ratio and enhancing the asymmetry, which is promising in the controlled release of inner droplets through hydrodynamics for targeted drug delivery.
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    Smith, K. A.; Ottino, J. M.; Olvera de la Cruz, M. Encapsulated Drop Breakup in Shear Flow. Phys. Rev. Lett. 2004, 93, 204501,  DOI: 10.1103/physrevlett.93.204501
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    Encapsulated Drop Breakup in Shear Flow
    Smith, K. A.; Ottino, J. M.; Olvera de la Cruz, M.
    Physical Review Letters (2004), 93 (20), 204501/1-204501/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    We investigate the deformation and breakup in shear flow of an encapsulated drop in which both the core and shell are Newtonian fluids. The equations of motion are solved numerically using a level set method to track interface motion. We consider the case of a drop stretched to a given length in const. shear and then allowed to relax. A range of morphologies is produced, and novel kinematics occur, due to the interaction of the core and outer interfaces. A phase diagram is presented to describe the morphologies produced over a range of capillary nos. and core interfacial tensions.
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    Chen, X.; Liu, Y.; Shi, M. Hydrodynamics of double emulsion droplet in shear flow. Appl. Phys. Lett. 2013, 102, 051609,  DOI: 10.1063/1.4789865
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    Hydrodynamics of double emulsion droplet in shear flow
    Chen, Yongping; Liu, Xiangdong; Shi, Mingheng
    Applied Physics Letters (2013), 102 (5), 051609/1-051609/5CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)
    Hydrodynamic behaviors of double emulsion droplets in shear flow, both deformation and breakup, are investigated numerically. We find that the inner drop is deformed in a uniform vortical flow interior to the outer drop under steady state deformation conditions and provides an addnl. deformation resistance for the integral droplet esp. when its vol. fraction is large. In particular, we report four types of breakup modes via three mechanisms (i.e., necking, end pinching, and capillary instability), resp., and present the corresponding phase diagrams to describe the breakup criteria (crit. capillary nos.) and morphologies. (c) 2013 American Institute of Physics.
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    Chen, Y.; Liu, X.; Zhao, Y. Deformation dynamics of double emulsion droplet under shear. Appl. Phys. Lett. 2015, 106, 141601,  DOI: 10.1063/1.4916623
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    Deformation dynamics of double emulsion droplet under shear
    Chen, Yongping; Liu, Xiangdong; Zhao, Yuanjin
    Applied Physics Letters (2015), 106 (14), 141601/1-141601/5CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)
    We combine exptl. observations with numerical simulations to explore the deformation dynamics of double emulsion droplet under shear. Two types of transient deformation topologies are identified via the resp. underlying phys. mechanisms. Esp., we demonstrate that the inner droplet can enhance the retracting of integral droplet, which leads to more intense transient deformation oscillations of double emulsion droplet than those of single-phase one. We further provide a regime diagram to quant. recognize the resp. regime of these two transient deformation topologies, depending on the capillary no. and radius ratio of inner droplet to the outer one. (c) 2015 American Institute of Physics.
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    Wang, N.; Semprebon, C.; Liu, H.; Zhang, C.; Kusumaatmaja, H. Modelling double emulsion formation in planar flow-focusing microchannels. J. Fluid Mech. 2020, 895, A22,  DOI: 10.1017/jfm.2020.299
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    Modelling double emulsion formation in planar flow-focusing microchannels
    Wang, Ningning; Semprebon, Ciro; Liu, Haihu; Zhang, Chuhua; Kusumaatmaja, Halim
    Journal of Fluid Mechanics (2020), 895 (), A22CODEN: JFLSA7; ISSN:0022-1120. (Cambridge University Press)
    Double emulsion formation in a hierarchical flow-focusing channel is systematically investigated using a free-energy ternary lattice Boltzmann model. A three-dimensional formation regime diagram is constructed based on the capillary nos. of the inner (Cai), middle (Cam) and outer (Cao) phase fluids. The results show that the formation diagram can be classified into periodic two-step region, periodic one-step region, and non-periodic region. By varying Cai and Cam in the two-step formation region, different morphologies are obtained, including the regular double emulsions, decussate regimes with one or two alternate empty droplets, and structures with multiple inner droplets contained in the continuous middle phase thread. Bidisperse behaviors are also frequently encountered in the two-step formation region. In the periodic one-step formation region, scaling laws are proposed for the double emulsion size and for the size ratio between the inner droplet and the overall double emulsion. Furthermore, we show that the interfacial tension ratio can greatly change the morphologies of the obtained emulsion droplets, and the channel geometry plays an important role in changing the formation regimes and the double emulsion sizes. In particular, narrowing the side inlets or the distance between the two side inlets promotes the conversion from the two-step formation regime to the one-step formation regime.
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    Tiribocchi, A.; Montessori, A.; Aime, S.; Milani, M.; Lauricella, M.; Succi, S.; Weitz, D. Novel nonequilibrium steady states in multiple emulsions. Phys. Fluids 2020, 32, 017102,  DOI: 10.1063/1.5134901
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    Novel nonequilibrium steady states in multiple emulsions
    Tiribocchi, A.; Montessori, A.; Aime, S.; Milani, M.; Lauricella, M.; Succi, S.; Weitz, D.
    Physics of Fluids (2020), 32 (1), 017102CODEN: PHFLE6; ISSN:1070-6631. (American Institute of Physics)
    We numerically investigate the rheol. response of a noncoalescing multiple emulsion under a sym. shear flow. We find that the dynamics significantly depends on the magnitude of the shear rate and on the no. of the encapsulated droplets, two key parameters whose control is fundamental to accurately select the resulting nonequil. steady states. The double emulsion, for instance, attains a static steady state in which the external droplet stretches under flow and achieves an elliptical shape (closely resembling the one obsd. in a sheared isolated fluid droplet), while the internal one remains essentially unaffected. Novel nonequil. steady states arise in a multiple emulsion. Under low/moderate shear rates, for instance, the encapsulated droplets display a nontrivial planetarylike motion that considerably affects the shape of the external droplet. Some features of this dynamic behavior are partially captured by the Taylor deformation parameter and the stress tensor. Besides a theor. interest on its own, our results can potentially stimulate further expts., as most of the predictions could be tested in the lab by monitoring droplets' shapes and position over time. (c) 2020 American Institute of Physics.
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    Tiribocchi, A.; Montessori, A.; Bonaccorso, F.; Lauricella, M.; Succi, S. Concentrated phase emulsion with multicore morphology under shear: A numerical study. Phys. Rev. Fluids 2020, 5, 113606,  DOI: 10.1103/physrevfluids.5.113606
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    Phase-Field Modeling of Multiple Emulsions Via Spinodal Decomposition
    Zhang, Haodong; Wu, Yanchen; Wang, Fei; Guo, Fuhao; Nestler, Britta
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    Currently, multiple emulsions via liq.-liq. phase sepn. in ternary polymer solns. have sparked considerable interest because of its remarkable potential in phys., medical, and biol. applications. The transient onion-like multilayers are highly dependent on the evolution kinetics, which is challenging to be scrutinized in expts. and has not yet been fully understood. Here, the authors report a thermodynamically consistent multicomponent Cahn-Hilliard model to study the kinetics of multiple emulsions by tracing the temporal evolution of the local compns. inside the emulsion droplets. The authors reveal that the mechanism governing the kinetics is attributed to the competition between surface energy minimization and phase sepn. Based on this concept, a generalized morphol. diagram for different emulsion patterns is achieved, showing a good accordance with previous expts. Also, combining the anal. for the kinetics and the morphol. diagram, the authors predict new emulsion structures that provide general guidelines to discovery, design, and manipulation of complex multiphase emulsions.
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    Soft Matter (2012), 8 (41), 10719-10724CODEN: SMOABF; ISSN:1744-683X. (Royal Society of Chemistry)
    We successfully encapsulate 2, 3, and 4 different inner drops inside double emulsions by a single-step emulsification technique. The microfluidic device fabrication is simple and the emulsification process highly robust. Optical microscopy images of double emulsion generation and of monodisperse double emulsions with discrete nos. of inner drops indicate the achievement of a high level of control with this technique. When the middle fluid transitions from dripping to jetting, 2 addnl. variations of double emulsions are produced: highly packed double emulsions and double emulsions with different sizes of inner drops. Finally, we successfully coalesce inner drops confined in a wax shell by applying heat. This demonstrates that these multi-component double emulsions may be useful as micro-reactors.
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    Mesoscale modelling of near-contact interactions for complex flowing interfaces
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    We present a mesoscale kinetic model for multicomponent flows, augmented with a short range forcing term, aimed at describing the combined effect of surface tension and near-contact interactions operating at the fluid interface level. Such a mesoscale approach is shown to (i) accurately capture the complex dynamics of bouncing colliding droplets for different values of the main governing parameters, (ii) predict quant. the effective viscosity of dense emulsions in micro-channels and (iii) simulate the formation of the so-called soft flowing crystals in microfluidic focusers.
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    Advances in microfluidic emulsification have enabled the creation of multiphase emulsion drops, which have emerged as promising templates for producing functional microcapsules. However, most previous micro-encapsulation methods have limitations in terms of capsule stability, functionality, and simplicity of fabrication procedures. Here, we report a simple single-step encapsulation technique that uses an optofluidic platform to efficiently and precisely encapsulate a specific no. of emulsion droplets in photocurable shell droplets. In particular, we show, for the first time, that densely confined core droplets within an oily shell droplet rearrange into a unique configuration that minimizes the interfacial energy, as confirmed here from theory. These structures are then consolidated into multi-cored microcapsules with structural and mech. stability through in situ photopolymn. of the shell in a continuous mode, which are capable of isolating active materials and releasing them in a controlled manner using well-defined nanohole arrays or nanoscopic silver architectures on thin membranes.
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    A review. This review discusses the lattice Boltzmann-particle dynamics (LBPD) multiscale paradigm for the simulation of complex states of flowing matter at the interface between physics, chem., and biol. In particular, current large-scale LBPD simulations of biopolymer translocation across cellular membranes, mol. transport in ion channels, and amyloid aggregation in cells are described. Prospects are provided for future LBPD explorations in the direction of cellular organization, the direct simulation of full biol. organelles, all the way up to physiol. scales of potential relevance to future precision-medicine applications, such as the accurate description of homeostatic processes. It is argued that, with the advent of Exascale computing, the mesoscale physics approach advocated in this review may come to age in the next decade and open up new exciting perspectives for physics-based computational medicine.
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    We review the state of the art of active fluids with particular attention to hydrodynamic continuous models and to the use of Lattice Boltzmann Methods (LBM) in this field. We present the thermodynamics of active fluids, in terms of liquid crystals modelling adapted to describe large-scale organization of active systems, as well as other effective phenomenological models. We discuss how LBM can be implemented to solve the hydrodynamics of active matter, starting from the case of a simple fluid, for which we explicitly recover the continuous equations by means of Chapman-Enskog expansion. Going beyond this simple case, we summarize how LBM can be used to treat complex and active fluids. We then review recent developments concerning some relevant topics in active matter that have been studied by means of LBM: spontaneous flow, self-propelled droplets, active emulsions, rheology, active turbulence, and active colloids.
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    The surface structure and compn. of a multi-component catalyst are crit. factors in detg. its catalytic performance. The surface compn. can depend on the local pressure of the reacting species, leading to the possibility that the flow through a nanoporous catalyst can affect its structure and reactivity. Here, we explore this possibility for oxidn. reactions on nanoporous gold, an AgAu bimetallic catalyst. We use microscopy and digital reconstruction to obtain the morphol. of a two-dimensional slice of a nanoporous gold sample. Using lattice Boltzmann fluid dynamics simulations along with thermodn. models based on first-principles total-energy calcns., we show that some sections of this sample have low local O2 partial pressures when exposed to reaction conditions, which leads to a pure Au surface in these regions, instead of the active bimetallic AgAu phase. We also explore the effect of temp. on the surface structure and find that moderate temps. (≈300-450 K) should result in the highest intrinsic catalytic performance, in apparent agreement with exptl. results. (c) 2017 American Institute of Physics.
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    Montessori, A.; Prestininzi, P.; La Rocca, M.; Succi, S. Lattice Boltzmann approach for complex nonequilibrium flows. Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 2015, 92, 043308,  DOI: 10.1103/physreve.92.069901
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    Lattice Boltzmann approach for complex nonequilibrium flows
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    We present a lattice Boltzmann realization of Grad's extended hydrodynamic approach to nonequil. flows. This is achieved by using higher-order isotropic lattices coupled with a higher-order regularization procedure. The method is assessed for flow across parallel plates and three-dimensional flows in porous media, showing excellent agreement of the mass flow with anal. and numerical solns. of the Boltzmann equation across the full range of Knudsen nos., from the hydrodynamic regime to ballistic motion.
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    Differential effective medium theory (D-EMT) has been used by a no. of investigators to derive expressions for the shear viscosity of a colloidal suspension or an emulsion as a function of the vol. fraction of the dispersed phase. Pal and Rhodes [R. Pal, E. Rhodes, J. Rheol. 33 (7) (1989) 1021-1045] used D-EMT to derive a viscosity-concn. expression for non-Newtonian emulsions, in which variations among different oil-water emulsions were accommodated by fitting the value of an empirical solvation factor by matching the vol. fraction at which the ratio of each emulsion was exptl. obsd. to have a viscosity 100 times greater than that of the pure solvent. When the particles in suspension have occluded vol. due to solvation or flocculation, we show that the application of D-EMT to the problem becomes more ambiguous than these investigators have indicated. In addn., the resulting equations either do not account for the limiting behavior near the crit. concn., i.e., the concn. at which the viscosity diverges, or they incorporate this crit. behavior in an ad hoc way. We suggest an alternative viscosity-concn. equation for emulsions, based on work by Bicerano and coworkers [J. Bicerano, J. F. Douglas, D. A. Brune, J. Macromol. Sci., Rev. Macromol. Chem. Phys. C 39 (4) (1999) 561-642]. This alternative equation has the advantages that (1) its parameters are more closely related to phys. properties of the suspension and (2) it recovers the correct limiting behavior both in the dil. limit and near the crit. concn. for rigid particles. In addn., the equation can account for the deformability of flexible particles in the semidilute regime. The proposed equation is compared to the equation proposed by Pal and Rhodes.
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  • Abstract

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    Figure 1

    Figure 1. (a) Experimental result of a HIPdE made of approximately monodisperse drops encapsulated within a larger droplet. Three Newtonian liquids are used to formulate the mixture. The continuous fluid is made from a 1% solution of PFPE–PEG–PFPE in fluorinated oil FC40, and the lubricating fluid of the emulsion is a solution of 5cSt silicon oil, hexadecane, and SPAN80 in proportions 70:30:1. Finally, the innermost phase is water-painted with euroglaucine. Estimated values of viscosity of continuous and lubricating fluid are approximately 4.0 mPa·s, while the value of the innermost phase is 1.0 mPa·s. (b) Example of a HIPdE obtained by LB simulations. It is made of a dispersed droplet phase (white), an inter-droplet lubricating phase (blue) surrounded by a fluid interface (red), and an external fluid (black). The compact foam-like arrangement results from the translocation of the emulsion within a thin channel, followed by a slow relaxation in the downstream reservoir. See the section Results for more details.

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    Figure 2

    Figure 2. (a) Double emulsion with ϕ ≃ 0.9 and Nd = 49 is initialized as a checkerboard-like pattern within the inlet chamber. (b) Example of the structure of the emulsion attained after t = 5000 time steps. The height of the inlet and outer chambers is h = 600 lattice sites, while the total length of the microfluidic channel is L = 3.6h. The rectangular constriction is made of two opposite fluid-free squared regions (indicated by red lines) of length ls = 240 lattice units, placed at a distance hs (the height of the constriction) ranging from 80 to 200 lattice sites.

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    Figure 3

    Figure 3. Translocation of a dense emulsion within a narrow channel. Here, ϕ ≃ 0.9, Nd = 49, and hs = 120, and the black regions represent the walls. A uniform velocity field pushes the emulsion rightward, causing a flow of drops approximately arranged in a two-row structure (a). Afterward, the drops gradually fill the constriction, giving rise to a highly compact foam-like body, which, once out of the channel, expands and relaxes (b–d). The velocity field is generally rather uniform within the constriction, whereas it is irregular in the drops out of the channel. The color bar represents the ratio of the magnitude of the velocity field u with respect to its maximum value UM.

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    Figure 4

    Figure 4. (a) Translocation dynamics of a dense emulsion for ϕ = 0.55 (top), ϕ = 0.75 (middle), and ϕ = 0.9 (bottom). In all cases, Nd = 49 and hs/D ≃ 0.45. Once the emulsion crosses the constriction, the resulting shape observed in the outlet chamber crucially depends on the area fraction ϕ. At low ϕ, the emulsion expands and springs back close to its original shape; at increasing ϕ, deformations become permanent. Snapshots are taken at t = 25, 90, and 150 × 103 steps. Blue lines connecting the centers of neighboring droplets represent the Delaunay triangulation, while red dotted lines represent the Voronoi decomposition. (b) Time evolution of the circularity Λ for different values of ϕ and Nd. At low values of ϕ, the circular shape of the emulsion is basically restored after translocation, while at increasing ϕ, Λ considerably decreases, up to half of its initial value.

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    Figure 5

    Figure 5. (a) In this figure, we show the time evolution of the number of hexagonal clusters NHex, computed by a Delaunay triangulation, observed during the translocation for ϕ ≃ 0.55 (black circles), ϕ ≃ 0.75 (empty circles), and ϕ ≃ 0.9 (squares). Like Λ, NHex exhibits a minimum, approximately equal for all values of ϕ, within the constriction, and attains a late time value, which decreases when ϕ augments. (b) Here, we show the behavior of the residual deformation Λr for different values of ϕ, Nd, and hs. In particular, hs = 200 and Nd = 25 (triangles), hs = 200 and Nd = 49 (plusses), hs = 120 and Nd = 25 (circles), and hs = 120 and Nd = 49 (asterisks). Λr is computed as the time average of the values of Λ obtained once the translocation is completed. As long as ϕ < 0.6, shape deformations are negligible, while for larger values of ϕ, Λr decreases faster for smaller values of hs (i.e., narrower channels).

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    Figure 6

    Figure 6. (a,b) Map of the magnitude of the velocity gradients within the emulsion for ϕ ≃ 0.55 (a) and ϕ ≃ 0.9 (b). The spots highlighted in red represent regions in which |∇u| > |∇uth|. (c) Dissipation parameter η (i.e., viscous dissipation vs surface tension work) is plotted as a function of ϕ and for different values of the ratio hs/D, in particular hs/D ∼ 0.6 (open circles), hs/D ∼ 0.8 (open triangles), hs/D ∼ 0.35 (filled circles), and hs/D ∼ 0.5 (asterisks). Dotted, continuous, and dashed lines represent the best fit to asterisks, filled circles, and open circles, respectively.

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      Generation of Polymerosomes from Double-Emulsions
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      Langmuir (2005), 21 (20), 9183-9186CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
      Diblock copolymers are known to spontaneously organize into polymer vesicles. Typically, this is achieved through the techniques of film rehydration or electroformation. We present a new method for generating polymer vesicles from double emulsions. We generate precision water-in-oil-in-water double emulsions from the breakup of concentric fluid streams; the hydrophobic fluid is a volatile mixt. of org. solvent that contains dissolved diblock copolymers. We collect the double emulsions and slowly evap. the org. solvent, which ultimately directs the self-assembly of the dissolved diblock copolymers into vesicular structures. Independent control over all three fluid streams enables precision assembly of polymer vesicles and provides for highly efficient encapsulation of active ingredients within the polymerosomes. We also use double emulsions with several internal drops to form new polymerosome structures.
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      Langmuir (2009), 25 (8), 4320-4323CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
      We present a simple microfluidics-based technique to fabricate Janus particles using double-emulsion droplets as templates. Since each half of the particles is templated from a different immiscible fluid, this method enables the formation of particles from two materials with vastly different properties. The use of microfluidics affords excellent control over the size, morphol., and monodispersity of the particles.
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      Monodisperse w/w/w Double Emulsion Induced by Phase Separation
      Song, Yang; Shum, Ho Cheung
      Langmuir (2012), 28 (33), 12054-12059CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
      We develop an approach to fabricate monodisperse water-in-water-in-water (wt./wt./w) double emulsion in microfluidic devices. A jet of aq. soln. contg. two incompatible solutes, dextran and polyethylene glycol (PEG), is periodically perturbed into water-in-water (wt./wt.) droplets. By extg. water out of the wt./wt. droplet, the solute concns. in the droplet phase increase; when the concns. exceed the miscibility limit, the droplet phase separates into two immiscible phases. Consequently, PEG-rich droplets are formed within the single emulsion templates. These PEG-rich droplets subsequently coalesce with each other, resulting in transiently stable wt./wt./w double emulsions with a high degree of size uniformity. These double emulsions are free of org. solvents and thus are ideal for use as droplet-vessels in protein purifn., as microreactors for biochem. reactions, and as templates for fabrication of biomaterials.
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      Wang, W.; Xie, R.; Ju, X. J.; Luo, T.; Liu, L.; Weitz, D. A.; Chu, L. Y. Controllable microfluidic production of multicomponent multiple emulsions. Lab Chip 2011, 11, 1587– 1592,  DOI: 10.1039/c1lc20065h
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      Controllable microfluidic production of multicomponent multiple emulsions
      Wang, Wei; Xie, Rui; Ju, Xiao-Jie; Luo, Tao; Liu, Li; Weitz, David A.; Chu, Liang-Yin
      Lab on a Chip (2011), 11 (9), 1587-1592CODEN: LCAHAM; ISSN:1473-0197. (Royal Society of Chemistry)
      A hierarchical and scalable microfluidic device constructed from a combination of three building blocks enables highly controlled generation of multicomponent multiple emulsions. The no., ratio and size of droplets, each with distinct contents being independently co-encapsulated in the same level, can be precisely controlled. The building blocks are a drop maker, a connector and a liq. extractor; combinations of these enable the scale-up of the device to create higher-order multicomponent multiple emulsions with exceptionally diverse structures. These multicomponent multiple emulsions offer a versatile and promising platform for precise encapsulation of incompatible actives or chems., for synergistic delivery and biochem. and chem. reactions, and for engineering multicompartment materials with controlled internal phases.
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      Li, Z.; Liu, H.; Zeng, L.; Liu, H.; Yang, S.; Wang, Y. Preparation of high internal water-phase double emulsions stabilized by a single anionic surfactant for fabricating interconnecting porous polymer microspheres. Langmuir 2014, 30, 12154– 12163,  DOI: 10.1021/la502564r
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      Preparation of High Internal Water-Phase Double Emulsions Stabilized by a Single Anionic Surfactant for Fabricating Interconnecting Porous Polymer Microspheres
      Li, Zichao; Liu, Huarong; Zeng, Lai; Liu, Hewen; Yang, Song; Wang, Yanmei
      Langmuir (2014), 30 (41), 12154-12163CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
      Herein we report a one-step method to prep. high internal water-phase double emulsions (W/O/W) via catastrophic phase inversion of water-in-oil high internal phase emulsions (W/O HIPEs) stabilized solely by 12-acryloxy-9-octadecenoic acid (AOA) through increasing the content of water phase. This is the first time for double emulsions to be stabilized solely by a single small mol. surfactant, which are usually costabilized by both hydrophilic and hydrophobic surfactants. After neutralized with ammonia, AOA is confirmed to be capable of stabilizing both W/O emulsions and O/W emulsions, which may account for its unique ability to stabilize double emulsions. The effects of different conditions (including changing the concns. of AOA and salt (NaCl), pH value, the polarity of oils, the addn. interval of water and stirring rate, etc.) on the formation and the stability of double emulsions as well as the inversion point have been investigated by using optical microscopy and cond. monitoring. Finally, porous polymer microspheres with high interconnection (polyHIPE microspheres) were fabricated by γ-ray initiated polymn. of the as-prepd. double emulsions composed of different monomers (styrene, or Bu acrylate, or Me methacrylate), which have been confirmed by SEM. Our method is facile and effective for prepg. high interconnecting porous polymer microspheres without tedious post-treatment of the products in common emulsion polymn. due to the use of polymerizable surfactant.
    9. 9
      Datta, S.; Abbaspourrad, A.; Amstad, E.; Fan, J.; Kim, S.; Romanowsky, M.; Shum, H.; Sun, B.; Utada, A.; Windbergs, M.; Zhou, S.; Weitz, D. 25th anniversary article: Double emulsion templated solid microcapsules: Mechanics and controlled release. Adv. Mater. 2014, 26, 2205,  DOI: 10.1002/adma.201305119
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      25th Anniversary Article: Double Emulsion Templated Solid Microcapsules: Mechanics And Controlled Release
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      A review. We describe how droplet microfluidics can be used to fabricate solid-shelled microcapsules having precisely controlled release behavior. Glass capillary devices enable the prodn. of monodisperse double emulsion drops, which can then be used as templates for microcapsule formation. The exquisite control afforded by microfluidics can be used to tune the compns. and geometrical characteristics of the microcapsules with exceptional precision. We review the use of this approach to fabricate microcapsules that only release their contents when exposed to a specific stimulus - such as a change in temp., exposure to light, a change in the chem. environment, or an external stress - only after a prescribed time delay, and at a prescribed rate.
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      Droplet clusters: exploring the phase space of soft mesoscale atoms
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      We report three-dimensional structures-mesoscale "atoms"-comprising up to N = 8 aq. droplets compressed in a liq. shell. In contrast to hard colloids that self-assemble into structures unique for a given N, we observe multiple metastable states. We attribute this unexpected richness of metastable structures to the deformability of the cores that introduces irreducible many-body interactions between the droplets. These exotic, often highly anisotropic, structures are locally stable. The structures displaying highly nonoptimum packing-and hence interfacial energy much higher than that of the lowest-energy state-exhibit finite energy barriers that prevent restructuring and relaxation of energy.
    11. 11
      Costantini, M.; Guzowski, J.; Zuk, P. J.; Mozetic, P.; De Panfilis, S.; Jaroszewicz, J.; Heljak, M.; Massimi, M.; Pierron, M.; Trombetta, M.; Dentini, M.; Swieszkowski, W.; Rainer, A.; Garstecki, P.; Barbetta, A. Electric Field Assisted Microfluidic Platform for Generation of Tailorable Porous Microbeads as Cell Carriers for Tissue Engineering. Adv. Funct. Mater. 2018, 28, 1800874,  DOI: 10.1002/adfm.201800874
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      Lei, L.; Zhang, Q.; Shi, S.; Zhu, S. High internal phase emulsion with double emulsion morphology and their templated porous polymer systems. J. Colloid Interface Sci. 2016, 483, 232– 240,  DOI: 10.1016/j.jcis.2016.08.034
      12
      High internal phase emulsion with double emulsion morphology and their templated porous polymer systems
      Lei, Lei; Zhang, Qi; Shi, Shuxian; Zhu, Shiping
      Journal of Colloid and Interface Science (2016), 483 (), 232-240CODEN: JCISA5; ISSN:0021-9797. (Elsevier B.V.)
      This paper reports synthesis of the first high internal phase emulsion (HIPE) system with double emulsion (DE) morphol. (HIPE-DE). HIPE is a highly concd. but highly stable emulsion system, which has a dispersed/internal phase fraction over 74 vol%. DE represents an emulsion system that hierarchically encapsulates two immiscible phases. The combination of HIPE and DE provides an efficient method for fabrication of complex structures. In this work, HIPE-DE having a water-in-oil-in-water (W/O/W) morphol. has been prepd. for the first time via a simple one-step emulsification method with poly(2-(diethylamino)ethyl methacrylate) (PDEA) microgel particles as Pickering stabilizer. An oil phase fraction up to 90 vol% was achieved by optimizing the microgel concn. in aq. phase. The mechanism of the DE formation has been elucidated. It was found that while PDEA microgels stabilized the oil droplets in water, small amt. protonated DEA monomers acted as surfactant and formed water-contg. micelles inside the oil droplets. It was demonstrated that the W/O/W HIPE-DE could be precisely converted into porous polymer structures. With styrene as the oil phase in W/O/W HIPE-DE, porous polystyrene particles were obtained upon polymn. With dissolved acrylamide as the aq. phase and toluene as the continuous phase, porous polyacrylamide matrixes were prepd. Elevating temp. required for polymn. did not change the W/O/W HIPE-DE morphologies. This simple approach provides a versatile platform for synthesis of a variety of porous polymer systems.
    13. 13
      Vladisavljevic, G. T.; Al Nuumani, R.; Nabavi, S. A. Microfluidic Production of Multiple Emulsions. Micromachines 2017, 8, 75,  DOI: 10.3390/mi8030075
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      Tiribocchi, A.; Montessori, A.; Lauricella, M.; Bonaccorso, F.; Succi, S.; Aime, S.; Milani, M.; Weitz, D. A. The vortex-driven dynamics of droplets within droplets. Nat. Commun. 2021, 12, 82,  DOI: 10.1038/s41467-020-20364-0
      14
      The vortex-driven dynamics of droplets within droplets
      Tiribocchi, A.; Montessori, A.; Lauricella, M.; Bonaccorso, F.; Succi, S.; Aime, S.; Milani, M.; Weitz, D. A.
      Nature Communications (2021), 12 (1), 82CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)
      Understanding the fluid-structure interaction is crucial for an optimal design and manufg. of soft mesoscale materials. Multi-core emulsions are a class of soft fluids assembled from cluster configurations of deformable oil-water double droplets (cores), often employed as building-blocks for the realization of devices of interest in bio-technol., such as drug-delivery, tissue engineering and regenerative medicine. Here, we study the physics of multi-core emulsions flowing in microfluidic channels and report numerical evidence of a surprisingly rich variety of driven non-equil. states (NES), whose formation is caused by a dipolar fluid vortex triggered by the sheared structure of the flow carrier within the microchannel. The obsd. dynamic regimes range from long-lived NES at low core-area fraction, characterized by a planetary-like motion of the internal drops, to short-lived ones at high core-area fraction, in which a pre-chaotic motion results from multi-body collisions of inner drops, as combined with self-consistent hydrodynamic interactions. The onset of pre-chaotic behavior is marked by transitions of the cores from one vortex to another, a process that we interpret as manifestations of the system to maximize its entropy by filling voids, as they arise dynamically within the capsule.
    15. 15
      Shum, H. C.; Lee, D.; Yoon, I.; Kodger, T.; Weitz, D. A. Double Emulsion Templated Monodisperse Phospholipid Vesicles. Langmuir 2008, 24, 7651– 7653,  DOI: 10.1021/la801833a
      15
      Double Emulsion Templated Monodisperse Phospholipid Vesicles
      Shum, Ho Cheung; Lee, Daeyeon; Yoon, Insun; Kodger, Tom; Weitz, David A.
      Langmuir (2008), 24 (15), 7651-7653CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
      We present a novel approach for fabricating monodisperse phospholipid vesicles with high encapsulation efficiency using controlled double emulsions as templates. Glass-capillary microfluidics is used to generate monodisperse double emulsion templates. We show that the high uniformity in size and shape of the templates are maintained in the final phospholipid vesicles after a solvent removal step. Our simple and versatile technique is applicable to a wide range of phospholipids.
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      Abate, A. R.; Weitz, D. A. High-order multiple emulsions formed in poly(dimethylsiloxane) microfluidics. Small 2009, 5, 2030– 2032,  DOI: 10.1002/smll.200900569
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      High-Order Multiple Emulsions Formed in Poly(dimethylsiloxane) Microfluidics
      Abate, A. R.; Weitz, D. A.
      Small (2009), 5 (18), 2030-2032CODEN: SMALBC; ISSN:1613-6810. (Wiley-VCH Verlag GmbH & Co. KGaA)
      Microfluidic devices prepd. by soft lithog. in PDMS had alternating wettability ideal for forming high-order multiple emulsions.
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      Ding, S.; Serra, C. A.; Vandamme, T. F.; Yu, W.; Anton, N. Double emulsions prepared by two–step emulsification: History, state-of-the-art and perspective. J. Controlled Release 2019, 295, 31,  DOI: 10.1016/j.jconrel.2018.12.037
      17
      Double emulsions prepared by two-step emulsification: History, state-of-the-art and perspective
      Ding, Shukai; Serra, Christophe A.; Vandamme, Thierry F.; Yu, Wei; Anton, Nicolas
      Journal of Controlled Release (2019), 295 (), 31-49CODEN: JCREEC; ISSN:0168-3659. (Elsevier B.V.)
      Attractive interest on double emulsions comes from their unique morphol., making them general multifunctional carriers able to encapsulate different hydrophilic and lipophilic mols. in the same particle. Over the past century, two different types of methods were followed to prep. double emulsions for pharmaceutics applications, so-called "one-step" and "two-step" processes. The two-step approach, consisting in two different emulsifications successively performed, allows the optimal and more efficient formulations due to simplicity of principle and controllability of the process. In this review, focused on the formulation of double emulsions by two-step process, we recount the historical development of this approach, along with the state-of-the-art, including a discussion on the role of the formulation parameters, surfactants, amphiphilic polymers, interface stabilization, vol. fraction, and so forth, on the final formulation stability, morphol. and properties as drug delivery system. Discussion was also extended to polymeric microparticles and nanoparticles made by solvent diffusion, on the basis of double emulsions made by two-step process, along with literature review on the impact of different formulation and processing parameters. In addn., the properties of the polymers used in the microparticles matrix (mol. wt., chem. nature) potentially impacting on the ones of the microparticles formed (drug release kinetics, stability, morphol.), were also discussed. Finally, the future trends in double emulsions application were addressed, emphasizing some new advances made in the emulsifications method as potentially able to open the range of applications, for example to nanoscale with spontaneous emulsification or low energy microfluidic emulsification.
    18. 18
      Kong, L.; Levin, A.; Toprakcioglu, Z.; Xu, Y.; Gang, H.; Ye, R.; Mu, B. Z.; Knowles, T. P. J. Lipid-Stabilized Double Emulsions Generated in Planar Microfluidic Devices. Langmuir 2020, 36, 2349– 2356,  DOI: 10.1021/acs.langmuir.9b03622
      18
      Lipid-Stabilized Double Emulsions Generated in Planar Microfluidic Devices
      Kong, Lingling; Levin, Aviad; Toprakcioglu, Zenon; Xu, Yufan; Gang, Hongze; Ye, Ruqiang; Mu, Bo-Zhong; Knowles, Tuomas P. J.
      Langmuir (2020), 36 (9), 2349-2356CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
      Microemulsions have found a wide range of applications exploiting their chem. and phys. properties. Development of microfluidic-based approaches has allowed for the controlled prodn. of highly monodispersed emulsions, including the formation of multiple and hierarchical emulsions. Conventional poly(dimethylsiloxane)-based microfluidic systems require tight spatial control over the surface chem. when used for double emulsion generation, which can be challenging to achieve on the micrometer scale. Here, the authors present a two-dimensional device design, which can selectively be surface-treated in a straightforward manner and allows for the formation of uniform water/oil/water double emulsions by combining two distinct hydrophilic and hydrophobic surface properties. These surfaces are sufficiently sepd. in space to allow for imparting their functionalization without the requirement for lithog. approaches or complex flow control. The authors demonstrate that a mismatch between the wettability requirements of the continuous phase and the channel wall inherent in this approach can be tolerated over several hundreds of micrometers, opening up the possibility to use simple pressure-driven flows to achieve surface functionalization. The design architecture exhibits robust efficiency in emulsion generation while retaining simple device fabrication. The authors finally demonstrate the potential of this approach by generating water in oil in water emulsions with lipid mols. acting as surfactants.
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      Lee, J.; Kim, J. W.; Han, S. H.; Chang, I. S.; Kang, H. H.; Lee, O. S.; Oh, S. G.; Suh, K. D. The stabilization of L-ascorbic acid in aqueous solution and water-in-oil-in-water double emulsion by controlling pH and electrolyte concentration. Int. J. Cosmet. Sci. 2004, 26, 217,  DOI: 10.1111/j.0142-5463.2004.00223_1.x
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      Lee, M. C.; Tan, C.; Ravanfar, R.; Abbaspourrad, A. Ultrastable water-in-oil High internal phase emulsions featuring interfacial and biphasic network stabilization. ACS Appl. Mater. Interfaces 2019, 11, 26433– 26441,  DOI: 10.1021/acsami.9b05089
      20
      Ultrastable Water-in-Oil High Internal Phase Emulsions Featuring Interfacial and Biphasic Network Stabilization
      Lee, Michelle C.; Tan, Chen; Ravanfar, Raheleh; Abbaspourrad, Alireza
      ACS Applied Materials & Interfaces (2019), 11 (29), 26433-26441CODEN: AAMICK; ISSN:1944-8244. (American Chemical Society)
      The authors present gel-in-gel H2O-in-oil (W/O) high internal phase emulsions (HIPEs) that feature high stability by structuring both phases of the emulsion. Compared to significant advances made in oil-in-H2O (O/W) HIPEs, W/O HIPEs are extremely unstable and difficult to generate without introducing high concns. of surfactants. Another main challenge is the low viscosity of both H2O and oil phases which promotes the instability of W/O HIPEs. Here, the authors demonstrate ultrastable W/O HIPEs that feature biphasic structuring, in which hydrogels are dispersed in oleogels, and self-forming, low-concn. interfacial Pickering crystals provide added stability. These W/O HIPEs exhibit high tolerance toward pH shock and destabilizing environments. This novel ultrastable gel-in-gel W/O HIPE is sustainable and made solely with natural ingredients without the addn. of any synthetic stabilizers. By applying phase structuring within the HIPEs through the addn. of various carrageenans and beeswax as structurants, the authors can increase the emulsion's stability and viscoelastic rheol. properties. The performance of these gel-in-gel W/O HIPEs holds promise for a wide range of applications. As a proof of concept, the authors demonstrated herein the application as a gelled delivery system that enables the co-delivery of hydrophilic and hydrophobic materials at maximized loads, demonstrating high resistance to gastrointestinal pHs and a controlled-release profile.
    21. 21
      Muschiolik, G.; Dickinson, E. Double Emulsions Relevant to Food Systems: Preparation, Stability, and Applications. Compr. Rev. Food Sci. Food Saf. 2017, 16, 532,  DOI: 10.1111/1541-4337.12261
      21
      Double Emulsions Relevant to Food Systems: Preparation, Stability, and Applications
      Muschiolik, Gerald; Dickinson, Eric
      Comprehensive Reviews in Food Science and Food Safety (2017), 16 (3), 532-555CODEN: CRFSBJ; ISSN:1541-4337. (Institute of Food Technologists)
      This review describes advances in the prepn. of food-relevant double emulsions (DEs) of the water-in-oil-in-water (W/O/W) and oil-in-water-in-oil (O/W/O) types with emphasis on research published within the last decade. The information is assembled and critically evaluated according to the following aspects: the food application area, the range of encapsulated components and emulsion compn., the emulsification prepn. methods, the balancing of the osmotic pressure, the stabilization by increased viscosity or gelation, the role of protein-polysaccharide interactions, and the techniques used to est. DE yield and emulsification efficiency. Particular focus is directed toward the control of encapsulation and release behavior, including strategies that have been employed to improve the retention ability of the inner phase droplets by modifying the outer oil-water interface through mixed ingredient interactions, Pickering stabilization by particles, and biopolymer gelation. We also briefly consider the incorporation of DEs into dried microcapsules and the stability of W/O/W emulsions during eating and digestion. It would appear that 2 outstanding issues are currently preventing full realization of the potential of DEs in food applications: (i) the lack of availability of large-scale prodn. equipment to ensure efficient nondestructive 2nd-stage emulsification, and (ii) the limited range of food-grade ingredients available to successfully replace polyglycerol polyricinoleate as the primary emulsifier in W/O/W formulations.
    22. 22
      Jiang, H.; Zhang, T.; Smits, J.; Huang, X.; Maas, M.; Yin, S.; Ngai, T. Edible high internal phase Pickering emulsion with double-emulsion morphology. Food Hydrocolloids 2021, 111, 106405,  DOI: 10.1016/j.foodhyd.2020.106405
      22
      Edible high internal phase Pickering emulsion with double-emulsion morphology
      Jiang, Hang; Zhang, Tong; Smits, Joeri; Huang, Xiaonan; Maas, Michael; Yin, Shouwei; Ngai, To
      Food Hydrocolloids (2021), 111 (), 106405CODEN: FOHYES; ISSN:0268-005X. (Elsevier Ltd.)
      Food-grade high internal phase Pickering emulsions (HIPPEs) unify the stability of Pickering emulsions and the advantages of detergent-based high internal phase emulsions (HIPEs), making them attractive as nutritional products. However, as oral delivery systems, HIPPEs are usually prepd. in the form of o/w emulsions, which are suitable mainly for oleophilic active ingredients and may suffer from leakage during gastric digestion. To better protect and deliver hydrophilic cargo mols., we developed a HIPPE-based w/o/w double emulsion system. Zein nanoparticles and soybean lecithin are found to have a synergistic effect in stabilization - using both natural emulsifiers together results in the formation of w/o/w double emulsions with improved stability, which is further confirmed by the interfacial tension and rheol. of zein- and/or lecithin-laden oil-water interfaces. A combination of zein nanoparticles and lecithin achieves the fastest interfacial tension decrease, indicating an improved interfacial activity. Besides, lecithin contributes to the strong surface elasticity of the interfacial films, which makes the formed emulsions even stabler. Simulated digestion expts. suggest that the inner aq. droplets can be strongly protected from gastric fluids. This edible HIPPE with double emulsion morphol. provides new ideas for designing healthy foods for nutrients delivery.
    23. 23
      Zhang, H.; Cooper, A. I. Synthesis and applications of emulsion-templated porous materials. Soft Matter 2005, 1, 107– 113,  DOI: 10.1039/b502551f
      23
      Synthesis and applications of emulsion-templated porous materials
      Zhang, Haifei; Cooper, Andrew I.
      Soft Matter (2005), 1 (2), 107-113CODEN: SMOABF; ISSN:1744-683X. (Royal Society of Chemistry)
      This review describes the use of macroemulsions as templates for the prodn. of porous materials. It is focussed on the use of high internal phase emulsions to produce interconnected open porous structures. The review encompasses porous hydrophobic polymers, hydrophilic polymers, composites, silica, metal oxides, and metals. The potential applications of these materials are also discussed.
    24. 24
      Bokhari, M.; Carnachan, R. J.; Przyborski, S. A.; Cameron, N. R. Emulsion-Templated porous polymers as scaffolds for three dimensional cell culture: Effect of synthesis parameters on scaffold formation and homogeneity. J. Mater. Chem. 2007, 17, 4088– 4094,  DOI: 10.1039/b707499a
      24
      Emulsion-templated porous polymers as scaffolds for three dimensional cell culture: effect of synthesis parameters on scaffold formation and homogeneity
      Bokhari, Maria; Carnachan, Ross J.; Przyborski, Stefan A.; Cameron, Neil R.
      Journal of Materials Chemistry (2007), 17 (38), 4088-4094CODEN: JMACEP; ISSN:0959-9428. (Royal Society of Chemistry)
      Emulsion-templated porous polymers (PolyHIPEs) based on polystyrene have been prepd. and used for in vitro 3D cell culture of osteoblastic cells. It has been found that the method employed to prep. the emulsion precursor, namely the method of aq. phase addn., has a significant influence on the homogeneity of the morphol. of the material produced as well as the reproducibility of prepn. Addn. of the aq. phase in a controlled manner by means of a syringe pump produced a narrower void size distribution range than addn. from a dropping funnel, and the emulsions were obtained in a reproducible manner. Anal. of the morphol. of the materials revealed consistency of av. void and interconnect diam., within certain limits. The materials produced were subsequently sectioned into thin membranes which were then mounted to the base of com. available tissue culture plastic well inserts. Cell culture expts. using MG63 osteoblast-like cells indicated that the materials were capable of supporting cell growth for periods of up to 35 days, producing complex arrangements of cells interacting with one another and the scaffold. The functionality of cells grown on these materials, as indicated by viability assays and the prodn. of biomarkers (alk. phosphatase and osteocalcin), was found to be enhanced compared to cells grown on 2D substrates. We conclude that the 3D environment produced by these porous materials is more conducive to cell growth in vitro than existing 2D culture plastic.
    25. 25
      Marmottant, P.; Raven, J.-P. Microfluidics with foams. Soft Matter 2009, 5, 3385– 3388,  DOI: 10.1039/b903276b
      25
      Microfluidics with foams
      Marmottant, Philippe; Raven, Jan-Paul
      Soft Matter (2009), 5 (18), 3385-3388CODEN: SMOABF; ISSN:1744-683X. (Royal Society of Chemistry)
      Lab-on-a-chip devices can handle very tiny amts. of fluids, as small as a picoliter. Samples of gas are conveniently encapsulated and transported within bubbles. The generation of these calibrated bubbles involves specific microfluidic devices that we describe. When the bubble concn. is high enough in a channel, they come into contact, and they flow as a cryst. foam. The flow of the foams depends strongly on the arrangement of bubbles within the channel, which entails original dynamical behaviors such as super-stability of the flow, or on the contrary spontaneous oscillations.
    26. 26
      Liu, L.; Yu, M.; Lin, H.; Foty, R. Deformation and relaxation of an incompressible viscoelastic body with surface viscoelasticity. J. Mech. Phys. Solids 2017, 98, 309– 329,  DOI: 10.1016/j.jmps.2016.09.013
      58
      Deformation and relaxation of an incompressible viscoelastic body with surface viscoelasticity
      Liu, Liping; Yu, Miao; Lin, Hao; Foty, Ramsey
      Journal of the Mechanics and Physics of Solids (2017), 98 (), 309-329CODEN: JMPSA8; ISSN:0022-5096. (Elsevier Ltd.)
      Measuring mech. properties of cells or cell aggregates has proven to be an involved process due to their geometrical and structural complexity. Past measurements are based on material models that completely neglect the elasticity of either the surface membrane or the interior bulk. In this work, we consider general material models to account for both surface and bulk viscoelasticity. The boundary value problems are formulated for deformations and relaxations of a closed viscoelastic surface coupled with viscoelastic media inside and outside of the surface. The linearized surface elasticity models are derived for the const. surface tension model and the Helfrich-Canham bending model for coupling with the bulk viscoelasticity. For quasi-spherical surfaces, explicit solns. are obtained for the deformation, stress-strain and relaxation behaviors under a variety of loading conditions. These solns. can be applied to ext. the intrinsic surface and bulk viscoelastic properties of biol. cells or cell aggregates in the indentation, electro-deformation and relaxation expts.
    27. 27
      Dong, Y.; Skelley, A. M.; Merdek, K. D.; Sprott, K. M.; Jiang, C.; Pierceall, W. E.; Lin, J.; Stocum, M.; Carney, W. P.; Smirnov, D. A. Microfluidics and circulating tumor cells. J. Mol. Diagn. 2013, 15, 149– 157,  DOI: 10.1016/j.jmoldx.2012.09.004
      26
      Microfluidics and circulating tumor cells
      Dong Yi; Skelley Alison M; Merdek Keith D; Sprott Kam M; Jiang Chunsheng; Pierceall William E; Lin Jessie; Stocum Michael; Carney Walter P; Smirnov Denis A
      The Journal of molecular diagnostics : JMD (2013), 15 (2), 149-57 ISSN:.
      Circulating tumor cells (CTCs) are shed from cancerous tumors, enter the circulatory system, and migrate to distant organs to form metastases that ultimately lead to the death of most patients with cancer. Identification and characterization of CTCs provides a means to study, monitor, and potentially interfere with the metastatic process. Isolation of CTCs from blood is challenging because CTCs are rare and possess characteristics that reflect the heterogeneity of cancers. Various methods have been developed to enrich CTCs from many millions of normal blood cells. Microfluidics offers an opportunity to create a next generation of superior CTC enrichment devices. This review focuses on various microfluidic approaches that have been applied to date to capture CTCs from the blood of patients with cancer.
    28. 28
      Stott, S. L.; Hsu, C.-H.; Tsukrov, D. I.; Yu, M.; Miyamoto, D. T.; Waltman, B. A.; Rothenberg, S. M.; Shah, A. M.; Smas, M. E.; Korir, G. K.; Floyd, F. P., Jr.; Gilman, A. J.; Lord, J. B.; Winokur, D.; Springer, S.; Irimia, D.; Nagrath, S.; Sequist, L. V.; Lee, R. J.; Isselbacher, K. J.; Maheswaran, S.; Haber, D. A.; Toner, M. Isolation of circulating tumor cells using a microvortex-generating herringbone-chip. Proc. Natl. Acad. Sci. U.S.A. 2010, 107, 18392– 18397,  DOI: 10.1073/pnas.1012539107
      27
      Isolation of circulating tumor cells using a microvortex-generating herringbone-chip
      Stott, Shannon L.; Hsua, Chia-Hsien; Tsukrov, Dina I.; Yu, Min; Miyamoto, David T.; Waltman, Belinda A.; Rothenberg, S. Michael; Shah, Ajay M.; Smas, Malgorzata E.; Korir, George K.; Floyd, Frederick P., Jr.; Gilman, Anna J.; Lord, Jenna B.; Winokur, Daniel; Springer, Simeon; Irimia, Daniel; Nagrath, Sunitha; Sequist, Lecia V.; Lee, Richard J.; Isselbacher, Kurt J.; Maheswaran, Shyamala; Haber, Daniel A.; Toner, Mehmet
      Proceedings of the National Academy of Sciences of the United States of America (2010), 107 (43), 18392-18397, S18392/1-S18392/9CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
      Rare circulating tumor cells (CTCs) present in the bloodstream of patients with cancer provide a potentially accessible source for detection, characterization, and monitoring of nonhematol. cancers. We previously demonstrated the effectiveness of a microfluidic device, the CTC-Chip, in capturing these epithelial cell adhesion mol. (EpCAM)-expressing cells using antibody-coated microposts. Here, we describe a high-throughput microfluidic mixing device, the herringbone-chip, or "HB-Chip," which provides an enhanced platform for CTC isolation. The HB-Chip design applies passive mixing of blood cells through the generation of microvortices to significantly increase the no. of interactions between target CTCs and the antibody-coated chip surface. Efficient cell capture was validated using defined nos. of cancer cells spiked into control blood, and clin. utility was demonstrated in specimens from patients with prostate cancer. CTCs were detected in 14 of 15 (93%) patients with metastatic disease (median = 63 CTCs/mL, mean = 386 ± 238 CTCs/mL), and the tumor-specific TMPRSS2-ERG translocation was readily identified following RNA isolation and RT-PCR anal. The use of transparent materials allowed for imaging of the captured CTCs using std. clin. histopathol. stains, in addn. to immunofluorescence-conjugated antibodies. In a subset of patient samples, the low shear design of the HB-Chip revealed microclusters of CTCs, previously unappreciated tumor cell aggregates that may contribute to the hematogenous dissemination of cancer.
    29. 29
      Dluska, E.; Markowska-Radomska, A.; Metera, A.; Tudek, B.; Kosicki, K. Multiple emulsions as effective platforms for controlled anti-cancer drug delivery. Nanomedicine 2017, 12, 18,  DOI: 10.2217/nnm-2017-0112
      There is no corresponding record for this reference.
    30. 30
      Kosztin, I.; Vunjak-Novakovic, G.; Forgacs, G. Colloquium: Modeling the dynamics of multicellular systems: Application to tissue engineering. Rev. Mod. Phys. 2012, 84, 1791– 1805,  DOI: 10.1103/revmodphys.84.1791
      There is no corresponding record for this reference.
    31. 31
      Lulli, M.; Benzi, R.; Sbragaglia, M. Metastability at the yield-stress transition in soft glasses. Phys. Rev. X 2018, 8, 021031,  DOI: 10.1103/physrevx.8.021031
      30
      Metastability at the Yield-Stress Transition in Soft Glasses
      Lulli, Matteo; Benzi, Roberto; Sbragaglia, Mauro
      Physical Review X (2018), 8 (2), 021031CODEN: PRXHAE; ISSN:2160-3308. (American Physical Society)
      We study the solid-to-liq. transition in a two-dimensional fully periodic soft-glassy model with an imposed spatially heterogeneous stress. The model we consider consists of droplets of a dispersed phase jammed together in a continuous phase. When the peak value of the stress gets close to the yield stress of the material, we find that the whole system intermittently tunnels to a metastable "fluidized" state, which relaxes back to a metastable "solid" state by means of an elastic-wave dissipation. This macroscopic scenario is studied through the microscopic displacement field of the droplets, whose time statistics displays a remarkable bimodality. Metastability is rooted in the existence, in a given stress range, of two distinct stable rheol. branches, as well as long-range correlations (e.g., large dynamic heterogeneity) developed in the system. Finally, we show that a similar behavior holds for a pressure-driven flow, thus suggesting possible exptl. tests.
    32. 32
      Raven, J. P.; Marmottant, P. Microfluidic crystals: dynamic interplay between rearrangement waves and flow. Phys. Rev. Lett. 2009, 102, 084501,  DOI: 10.1103/PhysRevLett.102.084501
      31
      Microfluidic Crystals: Dynamic Interplay between Rearrangement Waves and Flow
      Raven, Jan-Paul; Marmottant, Philippe
      Physical Review Letters (2009), 102 (8), 084501/1-084501/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      Microfluidic crystals are assemblies of miniature bubbles or drops flowing in channels. We explore here the flow of these crystals, when submitted to a given driving pressure. The flow velocity is linked to the finite no. of elements in the channel width, and presents discontinuities when the crystal structure changes. At the transition from one structure to the other original dynamic features appear. The flow can self-regulate itself on a fixed velocity whatever the driving pressure, or, on the contrary, can spontaneously pulsate. All these features are predicted by simply considering the crystal's energy and friction, and looking at the propagation of structure rearrangements. We anticipate these results to improve the control over the structure of dense two-phase flows in microfluidic systems.
    33. 33
      Rosenfeld, L.; Fan, L.; Chen, Y.; Swoboda, R.; Tang, S. K. Y. Break-up of droplets in a concentrated emulsion flowing through a narrow constriction. Soft Matter 2014, 10, 421– 430,  DOI: 10.1039/c3sm51843d
      32
      Break-up of droplets in a concentrated emulsion flowing through a narrow constriction
      Rosenfeld, Liat; Fan, Lin; Chen, Yunhan; Swoboda, Ryan; Tang, Sindy K. Y.
      Soft Matter (2014), 10 (3), 421-430CODEN: SMOABF; ISSN:1744-683X. (Royal Society of Chemistry)
      This paper describes the break-up of droplets in a concd. emulsion during its flow as a 2D monolayer in a microchannel consisting of a narrow constriction. Anal. of the behavior of a large no. of drops (N > 4000) shows that the no. of break-ups increases with increasing flow rate, entrance angle to the constriction, and size of the drops relative to the width of the constriction. As single drops do not break at the highest flow rate used in the system, break-ups arise primarily from droplet-droplet interactions. Anal. of droplet properties at a high temporal resoln. of 10 μs makes it possible to relate droplet deformation with droplet break-up probability. Similar to previous studies on single drops, no break-up is obsd. below a set of crit. flow rates and droplet deformations. Unlike previous studies, however, not all drops undergo break-up above the crit. values. Instead, the probability of droplet break-up increases with flow rate and the deformation of the drops. The probabilistic nature of the break-up process arises from the stochastic variations in the packing configuration of the drops as they enter the constriction. Local break-up dynamics involves two primary drops. A close look at the interactions between the pair of drops reveals that the competing time scales of droplet rearrangement relative to the relaxation of the opposing drop govern whether break-up occurs or not. Practically, these results can be used to calc. the max. throughput of the serial interrogation process often employed in droplet microfluidics. For 40 pL-drops, the highest throughput with <1% droplet break-up was measured to be approx. 7000 drops per s. In addn., the results presented are useful for understanding the behavior of concd. emulsions in applications such as mobility control in enhanced oil recovery, and for extrapolating crit. parameters such as injection rates to ensure the stability of the fluids going through small pore throats.
    34. 34
      Montessori, A.; Lauricella, M.; Tiribocchi, A.; Succi, S. Modeling pattern formation in soft flowing crystals. Phys. Rev. Fluids 2019, 4, 072201(R)  DOI: 10.1103/physrevfluids.4.072201
      There is no corresponding record for this reference.
    35. 35
      Wang, J.; Liu, J.; Han, J.; Guan, J. Effects of Complex Internal Structures on Rheology of Multiple Emulsions Particles in 2D from a Boundary Integral Method. Phys. Rev. Lett. 2013, 110, 066001,  DOI: 10.1103/PhysRevLett.110.066001
      34
      Effects of complex internal structures on rheology of multiple emulsions particles in 2D from a boundary integral method
      Wang, Jingtao; Liu, Jinxia; Han, Junjie; Guan, Jing
      Physical Review Letters (2013), 110 (6), 066001/1-066001/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      A boundary integral method is developed to investigate the effects of inner droplets and asymmetry of internal structures on rheol. of two-dimensional multiple emulsion particles with arbitrary nos. of layers and droplets within each layer. Under a modest extensional flow, the no. increment of layers and inner droplets, and the collision among inner droplets subject the particle to stronger shears. In addn., the coalescence or release of inner droplets changes the internal structure of the multiple emulsion particles. Since the rheol. of such particles is sensitive to internal structures and their change, modeling them as the core-shell particles to obtain the viscosity equation of a single particle should be modified by introducing the time-dependable vol. fraction Φ(t) of the core instead of the fixed Φ. An asym. internal structure induces an oriented contact and merging of the outer and inner interface. The start time of the interface merging is controlled by adjusting the viscosity ratio and enhancing the asymmetry, which is promising in the controlled release of inner droplets through hydrodynamics for targeted drug delivery.
    36. 36
      Smith, K. A.; Ottino, J. M.; Olvera de la Cruz, M. Encapsulated Drop Breakup in Shear Flow. Phys. Rev. Lett. 2004, 93, 204501,  DOI: 10.1103/physrevlett.93.204501
      35
      Encapsulated Drop Breakup in Shear Flow
      Smith, K. A.; Ottino, J. M.; Olvera de la Cruz, M.
      Physical Review Letters (2004), 93 (20), 204501/1-204501/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      We investigate the deformation and breakup in shear flow of an encapsulated drop in which both the core and shell are Newtonian fluids. The equations of motion are solved numerically using a level set method to track interface motion. We consider the case of a drop stretched to a given length in const. shear and then allowed to relax. A range of morphologies is produced, and novel kinematics occur, due to the interaction of the core and outer interfaces. A phase diagram is presented to describe the morphologies produced over a range of capillary nos. and core interfacial tensions.
    37. 37
      Chen, X.; Liu, Y.; Shi, M. Hydrodynamics of double emulsion droplet in shear flow. Appl. Phys. Lett. 2013, 102, 051609,  DOI: 10.1063/1.4789865
      36
      Hydrodynamics of double emulsion droplet in shear flow
      Chen, Yongping; Liu, Xiangdong; Shi, Mingheng
      Applied Physics Letters (2013), 102 (5), 051609/1-051609/5CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)
      Hydrodynamic behaviors of double emulsion droplets in shear flow, both deformation and breakup, are investigated numerically. We find that the inner drop is deformed in a uniform vortical flow interior to the outer drop under steady state deformation conditions and provides an addnl. deformation resistance for the integral droplet esp. when its vol. fraction is large. In particular, we report four types of breakup modes via three mechanisms (i.e., necking, end pinching, and capillary instability), resp., and present the corresponding phase diagrams to describe the breakup criteria (crit. capillary nos.) and morphologies. (c) 2013 American Institute of Physics.
    38. 38
      Chen, Y.; Liu, X.; Zhao, Y. Deformation dynamics of double emulsion droplet under shear. Appl. Phys. Lett. 2015, 106, 141601,  DOI: 10.1063/1.4916623
      37
      Deformation dynamics of double emulsion droplet under shear
      Chen, Yongping; Liu, Xiangdong; Zhao, Yuanjin
      Applied Physics Letters (2015), 106 (14), 141601/1-141601/5CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)
      We combine exptl. observations with numerical simulations to explore the deformation dynamics of double emulsion droplet under shear. Two types of transient deformation topologies are identified via the resp. underlying phys. mechanisms. Esp., we demonstrate that the inner droplet can enhance the retracting of integral droplet, which leads to more intense transient deformation oscillations of double emulsion droplet than those of single-phase one. We further provide a regime diagram to quant. recognize the resp. regime of these two transient deformation topologies, depending on the capillary no. and radius ratio of inner droplet to the outer one. (c) 2015 American Institute of Physics.
    39. 39
      Wang, N.; Semprebon, C.; Liu, H.; Zhang, C.; Kusumaatmaja, H. Modelling double emulsion formation in planar flow-focusing microchannels. J. Fluid Mech. 2020, 895, A22,  DOI: 10.1017/jfm.2020.299
      38
      Modelling double emulsion formation in planar flow-focusing microchannels
      Wang, Ningning; Semprebon, Ciro; Liu, Haihu; Zhang, Chuhua; Kusumaatmaja, Halim
      Journal of Fluid Mechanics (2020), 895 (), A22CODEN: JFLSA7; ISSN:0022-1120. (Cambridge University Press)
      Double emulsion formation in a hierarchical flow-focusing channel is systematically investigated using a free-energy ternary lattice Boltzmann model. A three-dimensional formation regime diagram is constructed based on the capillary nos. of the inner (Cai), middle (Cam) and outer (Cao) phase fluids. The results show that the formation diagram can be classified into periodic two-step region, periodic one-step region, and non-periodic region. By varying Cai and Cam in the two-step formation region, different morphologies are obtained, including the regular double emulsions, decussate regimes with one or two alternate empty droplets, and structures with multiple inner droplets contained in the continuous middle phase thread. Bidisperse behaviors are also frequently encountered in the two-step formation region. In the periodic one-step formation region, scaling laws are proposed for the double emulsion size and for the size ratio between the inner droplet and the overall double emulsion. Furthermore, we show that the interfacial tension ratio can greatly change the morphologies of the obtained emulsion droplets, and the channel geometry plays an important role in changing the formation regimes and the double emulsion sizes. In particular, narrowing the side inlets or the distance between the two side inlets promotes the conversion from the two-step formation regime to the one-step formation regime.
    40. 40
      Tiribocchi, A.; Montessori, A.; Aime, S.; Milani, M.; Lauricella, M.; Succi, S.; Weitz, D. Novel nonequilibrium steady states in multiple emulsions. Phys. Fluids 2020, 32, 017102,  DOI: 10.1063/1.5134901
      39
      Novel nonequilibrium steady states in multiple emulsions
      Tiribocchi, A.; Montessori, A.; Aime, S.; Milani, M.; Lauricella, M.; Succi, S.; Weitz, D.
      Physics of Fluids (2020), 32 (1), 017102CODEN: PHFLE6; ISSN:1070-6631. (American Institute of Physics)
      We numerically investigate the rheol. response of a noncoalescing multiple emulsion under a sym. shear flow. We find that the dynamics significantly depends on the magnitude of the shear rate and on the no. of the encapsulated droplets, two key parameters whose control is fundamental to accurately select the resulting nonequil. steady states. The double emulsion, for instance, attains a static steady state in which the external droplet stretches under flow and achieves an elliptical shape (closely resembling the one obsd. in a sheared isolated fluid droplet), while the internal one remains essentially unaffected. Novel nonequil. steady states arise in a multiple emulsion. Under low/moderate shear rates, for instance, the encapsulated droplets display a nontrivial planetarylike motion that considerably affects the shape of the external droplet. Some features of this dynamic behavior are partially captured by the Taylor deformation parameter and the stress tensor. Besides a theor. interest on its own, our results can potentially stimulate further expts., as most of the predictions could be tested in the lab by monitoring droplets' shapes and position over time. (c) 2020 American Institute of Physics.
    41. 41
      Tiribocchi, A.; Montessori, A.; Bonaccorso, F.; Lauricella, M.; Succi, S. Concentrated phase emulsion with multicore morphology under shear: A numerical study. Phys. Rev. Fluids 2020, 5, 113606,  DOI: 10.1103/physrevfluids.5.113606
      There is no corresponding record for this reference.
    42. 42
      Zhang, H.; Wu, Y.; Wang, F.; Guo, F.; Nestler, B. Phase-Field Modeling of Multiple Emulsions Via Spinodal Decomposition. Langmuir 2021, 37, 5275– 5281,  DOI: 10.1021/acs.langmuir.1c00275
      41
      Phase-Field Modeling of Multiple Emulsions Via Spinodal Decomposition
      Zhang, Haodong; Wu, Yanchen; Wang, Fei; Guo, Fuhao; Nestler, Britta
      Langmuir (2021), 37 (17), 5275-5281CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
      Currently, multiple emulsions via liq.-liq. phase sepn. in ternary polymer solns. have sparked considerable interest because of its remarkable potential in phys., medical, and biol. applications. The transient onion-like multilayers are highly dependent on the evolution kinetics, which is challenging to be scrutinized in expts. and has not yet been fully understood. Here, the authors report a thermodynamically consistent multicomponent Cahn-Hilliard model to study the kinetics of multiple emulsions by tracing the temporal evolution of the local compns. inside the emulsion droplets. The authors reveal that the mechanism governing the kinetics is attributed to the competition between surface energy minimization and phase sepn. Based on this concept, a generalized morphol. diagram for different emulsion patterns is achieved, showing a good accordance with previous expts. Also, combining the anal. for the kinetics and the morphol. diagram, the authors predict new emulsion structures that provide general guidelines to discovery, design, and manipulation of complex multiphase emulsions.
    43. 43
      Adams, L. L. A.; Kodger, T. E.; Kim, S. H.; Shum, H. C.; Franke, T.; Weitz, D. A. High internal phase emulsion with double emulsion morphology and their templated porous polymer systems. Soft Matter 2012, 8, 10719– 10724,  DOI: 10.1039/c2sm25953b
      42
      Single step emulsification for the generation of multi-component double emulsions
      Adams, L. L. A.; Kodger, Thomas E.; Kim, Shin-Hyun; Shum, Ho Cheng; Franke, Thomas; Weitz, David A.
      Soft Matter (2012), 8 (41), 10719-10724CODEN: SMOABF; ISSN:1744-683X. (Royal Society of Chemistry)
      We successfully encapsulate 2, 3, and 4 different inner drops inside double emulsions by a single-step emulsification technique. The microfluidic device fabrication is simple and the emulsification process highly robust. Optical microscopy images of double emulsion generation and of monodisperse double emulsions with discrete nos. of inner drops indicate the achievement of a high level of control with this technique. When the middle fluid transitions from dripping to jetting, 2 addnl. variations of double emulsions are produced: highly packed double emulsions and double emulsions with different sizes of inner drops. Finally, we successfully coalesce inner drops confined in a wax shell by applying heat. This demonstrates that these multi-component double emulsions may be useful as micro-reactors.
    44. 44
      Montessori, A.; Lauricella, M.; Tirelli, N.; Succi, S. Mesoscale modelling of near-contact interactions for complex flowing interfaces. J. Fluid Mech. 2019, 872, 327,  DOI: 10.1017/jfm.2019.372
      43
      Mesoscale modelling of near-contact interactions for complex flowing interfaces
      Montessori, A.; Lauricella, M.; Tirelli, N.; Succi, S.
      Journal of Fluid Mechanics (2019), 872 (), 327-347CODEN: JFLSA7; ISSN:0022-1120. (Cambridge University Press)
      We present a mesoscale kinetic model for multicomponent flows, augmented with a short range forcing term, aimed at describing the combined effect of surface tension and near-contact interactions operating at the fluid interface level. Such a mesoscale approach is shown to (i) accurately capture the complex dynamics of bouncing colliding droplets for different values of the main governing parameters, (ii) predict quant. the effective viscosity of dense emulsions in micro-channels and (iii) simulate the formation of the so-called soft flowing crystals in microfluidic focusers.
    45. 45
      Montessori, A.; Tiribocchi, A.; Lauricella, M.; Bonaccorso, F.; Succi, S. Wet to dry self-transitions in dense emulsions: From order to disorder and back. Phys. Rev. Fluids 2021, 6, 023606,  DOI: 10.1103/physrevfluids.6.023606
      There is no corresponding record for this reference.
    46. 46
      Marmottant, P.; Mgharbel, A.; Käfer, J.; Audren, B.; Rieu, J.-P.; Vial, J.-C.; van der Sanden, B.; Marée, A. F. M.; Graner, F.; Delanoë-Ayari, H. The role of fluctuations and stress on the effective viscosity of cell aggregates. Proc. Natl. Acad. Sci. U.S.A. 2009, 106, 17271– 17275,  DOI: 10.1073/pnas.0902085106
      45
      The role of fluctuations and stress on the effective viscosity of cell aggregates
      Marmottant, Philippe; Mgharbel, Abbas; Kaefer, Jos; Audren, Benjamin; Rieu, Jean-Paul; Vial, Jean-Claude; van der Sanden, Boudewijn; Maree, Athanasius F. M.; Graner, Francois; Delanoe-Ayari, Helene
      Proceedings of the National Academy of Sciences of the United States of America (2009), 106 (41), 17271-17275, S17271/1-S17271/10CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
      Cell aggregates are a tool for in vitro studies of morphogenesis, cancer invasion, and tissue engineering. They respond to mech. forces as a complex rather than simple liq. To change an aggregate's shape, cells have to overcome energy barriers. If cell shape fluctuations are active enough, the aggregate spontaneously relaxes stresses ("fluctuation-induced flow"). If not, changing the aggregate's shape requires a sufficiently large applied stress ("stress-induced flow"). To capture this distinction, we develop a mech. model of aggregates based on their cellular structure. At stress lower than a characteristic stress τ*, the aggregate as a whole flows with an apparent viscosity η*, and at higher stress it is a shear-tinning fluid. An increasing cell-cell tension results in a higher η* (and thus a slower stress relaxation time tc). Our constitutive equation fits expts. of aggregate shape relaxation after compression or decompression in which irreversibility can be measured; we find tc of the order of 5 h for F9 cell lines. Predictions also match numerical simulations of cell geometry and fluctuations. We discuss the deviations from liq. behavior, the possible overestimation of surface tension in parallel-plate compression measurements, and the role of measurement duration.
    47. 47
      Foty, R. A.; Forgacs, G.; Pfleger, C. M.; Steinberg, M. S. Liquid properties of embryonic tissues: Measurement of interfacial tensions. Phys. Rev. Lett. 1994, 72, 2298– 2301,  DOI: 10.1103/physrevlett.72.2298
      46
      Liquid properties of embryonic tissues: Measurement of interfacial tensions
      Foty; Forgacs; Pfleger; Steinberg
      Physical review letters (1994), 72 (14), 2298-2301 ISSN:.
      There is no expanded citation for this reference.
    48. 48
      Douezan, S.; Guevorkian, K.; Naouar, R.; Dufour, S.; Cuvelier, D.; Brochard-Wyart, F. Spreading dynamics and wetting transition of cellular aggregates. Proc. Natl. Acad. Sci. U.S.A. 2011, 108, 7315– 7320,  DOI: 10.1073/pnas.1018057108
      47
      Spreading dynamics and wetting transition of cellular aggregates
      Douezan, Stephane; Guevorkian, Karine; Naouar, Randa; Dufour, Sylvie; Cuvelier, Damien; Brochard-Wyart, Francoise
      Proceedings of the National Academy of Sciences of the United States of America (2011), 108 (18), 7315-7320, S7315/1-S7315/3CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
      We study the spreading of spheroidal aggregates of cells, expressing a tunable level of E-cadherin mols., on glass substrates decorated with mixed fibronectin and polyethylene glycol. We observe the contact area by optical interferometry and the profile by side-view microscopy. We find a universal law of aggregate spreading at short times, which we interpret through an analogy with the spreading of viscoelastic droplets. At long times, we observe either partial wetting or complete wetting, with a precursor film of cells spreading around the aggregate with two possible states. In strongly cohesive aggregates this film is a cellular monolayer in the liq. state, whereas in weakly cohesive aggregates, cells escape from the aggregate, forming a 2D gas. The escape of isolated cells is a phys. mechanism that appears also to be present in the progression of a noninvasive tumor into a metastatic malignant carcinoma, known as the epithelial-mesenchymal transition.
    49. 49
      Kim, S.-H.; Hwang, H.; Lim, C. H.; Shim, J. W.; Yang, S.-M. Packing of Emulsion Droplets: Structural and Functional Motifs for Multi-Cored Microcapsules. Adv. Funct. Mater. 2011, 21, 1608– 1615,  DOI: 10.1002/adfm.201002316
      48
      Packing of Emulsion Droplets: Structural and Functional Motifs for Multi-Cored Microcapsules
      Kim, Shin-Hyun; Hwang, Hyerim; Lim, Che Ho; Shim, Jae Won; Yang, Seung-Man
      Advanced Functional Materials (2011), 21 (9), 1608-1615CODEN: AFMDC6; ISSN:1616-301X. (Wiley-VCH Verlag GmbH & Co. KGaA)
      Advances in microfluidic emulsification have enabled the creation of multiphase emulsion drops, which have emerged as promising templates for producing functional microcapsules. However, most previous micro-encapsulation methods have limitations in terms of capsule stability, functionality, and simplicity of fabrication procedures. Here, we report a simple single-step encapsulation technique that uses an optofluidic platform to efficiently and precisely encapsulate a specific no. of emulsion droplets in photocurable shell droplets. In particular, we show, for the first time, that densely confined core droplets within an oily shell droplet rearrange into a unique configuration that minimizes the interfacial energy, as confirmed here from theory. These structures are then consolidated into multi-cored microcapsules with structural and mech. stability through in situ photopolymn. of the shell in a continuous mode, which are capable of isolating active materials and releasing them in a controlled manner using well-defined nanohole arrays or nanoscopic silver architectures on thin membranes.
    50. 50
      Succi, S. The Lattice Boltzmann Equation: For Complex States of Flowing Matter; Oxford University Press, 2018.
      There is no corresponding record for this reference.
    51. 51
      Bernaschi, M.; Melchionna, S.; Succi, S. Mesoscopic simulations at the physics-chemistry-biology interface. Rev. Mod. Phys. 2019, 91, 025004,  DOI: 10.1103/revmodphys.91.025004
      50
      Mesoscopic simulations at the physics-chemistry-biology interface
      Bernaschi, Massimo; Melchionna, Simone; Succi, Sauro
      Reviews of Modern Physics (2019), 91 (2), 025004CODEN: RMPHAT; ISSN:1539-0756. (American Physical Society)
      A review. This review discusses the lattice Boltzmann-particle dynamics (LBPD) multiscale paradigm for the simulation of complex states of flowing matter at the interface between physics, chem., and biol. In particular, current large-scale LBPD simulations of biopolymer translocation across cellular membranes, mol. transport in ion channels, and amyloid aggregation in cells are described. Prospects are provided for future LBPD explorations in the direction of cellular organization, the direct simulation of full biol. organelles, all the way up to physiol. scales of potential relevance to future precision-medicine applications, such as the accurate description of homeostatic processes. It is argued that, with the advent of Exascale computing, the mesoscale physics approach advocated in this review may come to age in the next decade and open up new exciting perspectives for physics-based computational medicine.
    52. 52
      Krüger, T.; Kusumaatmaja, H.; Kuzmin, A.; Shardt, O.; Silva, G.; Viggen, E. M. The lattice Boltzmann method; Springer International Publishing, 2017; Vol. 10, pp 978– 983.
      There is no corresponding record for this reference.
    53. 53
      Carenza, L. N.; Gonnella, G.; Lamura, A.; Negro, G.; Tiribocchi, A. Lattice Boltzmann methods and active fluids. Eur. Phys. J. E 2019, 42, 81,  DOI: 10.1140/epje/i2019-11843-6
      52
      Lattice Boltzmann methods and active fluids
      Carenza Livio Nicola; Gonnella Giuseppe; Negro Giuseppe; Lamura Antonio; Tiribocchi Adriano
      The European physical journal. E, Soft matter (2019), 42 (6), 81 ISSN:.
      We review the state of the art of active fluids with particular attention to hydrodynamic continuous models and to the use of Lattice Boltzmann Methods (LBM) in this field. We present the thermodynamics of active fluids, in terms of liquid crystals modelling adapted to describe large-scale organization of active systems, as well as other effective phenomenological models. We discuss how LBM can be implemented to solve the hydrodynamics of active matter, starting from the case of a simple fluid, for which we explicitly recover the continuous equations by means of Chapman-Enskog expansion. Going beyond this simple case, we summarize how LBM can be used to treat complex and active fluids. We then review recent developments concerning some relevant topics in active matter that have been studied by means of LBM: spontaneous flow, self-propelled droplets, active emulsions, rheology, active turbulence, and active colloids.
    54. 54
      Montemore, M. M.; Montessori, A.; Succi, S.; Barroo, C.; Falcucci, G.; Bell, D. C.; Kaxiras, E. Effect of nanoscale flows on the surface structure of nanoporous catalysts. J. Chem. Phys. 2017, 146, 214703,  DOI: 10.1063/1.4984614
      53
      Effect of nanoscale flows on the surface structure of nanoporous catalysts
      Montemore, Matthew M.; Montessori, Andrea; Succi, Sauro; Barroo, Cedric; Falcucci, Giacomo; Bell, David C.; Kaxiras, Efthimios
      Journal of Chemical Physics (2017), 146 (21), 214703/1-214703/8CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      The surface structure and compn. of a multi-component catalyst are crit. factors in detg. its catalytic performance. The surface compn. can depend on the local pressure of the reacting species, leading to the possibility that the flow through a nanoporous catalyst can affect its structure and reactivity. Here, we explore this possibility for oxidn. reactions on nanoporous gold, an AgAu bimetallic catalyst. We use microscopy and digital reconstruction to obtain the morphol. of a two-dimensional slice of a nanoporous gold sample. Using lattice Boltzmann fluid dynamics simulations along with thermodn. models based on first-principles total-energy calcns., we show that some sections of this sample have low local O2 partial pressures when exposed to reaction conditions, which leads to a pure Au surface in these regions, instead of the active bimetallic AgAu phase. We also explore the effect of temp. on the surface structure and find that moderate temps. (≈300-450 K) should result in the highest intrinsic catalytic performance, in apparent agreement with exptl. results. (c) 2017 American Institute of Physics.
    55. 55
      Montessori, A.; Prestininzi, P.; La Rocca, M.; Succi, S. Lattice Boltzmann approach for complex nonequilibrium flows. Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 2015, 92, 043308,  DOI: 10.1103/physreve.92.069901
      54
      Lattice Boltzmann approach for complex nonequilibrium flows
      Montessori, A.; Prestininzi, P.; La Rocca, M.; Succi, S.
      Physical Review E: Statistical, Nonlinear, and Soft Matter Physics (2015), 92 (4-B), 043308/1-043308/6CODEN: PRESCM; ISSN:1539-3755. (American Physical Society)
      We present a lattice Boltzmann realization of Grad's extended hydrodynamic approach to nonequil. flows. This is achieved by using higher-order isotropic lattices coupled with a higher-order regularization procedure. The method is assessed for flow across parallel plates and three-dimensional flows in porous media, showing excellent agreement of the mass flow with anal. and numerical solns. of the Boltzmann equation across the full range of Knudsen nos., from the hydrodynamic regime to ballistic motion.
    56. 56
      Bullard, J. W.; Pauli, A. T.; Garboczi, E. J.; Martys, N. S. A comparison of viscosity-concentration relationships for emulsions. J. Colloid Interface Sci. 2009, 330, 186– 193,  DOI: 10.1016/j.jcis.2008.10.046
      55
      A comparison of viscosity-concentration relationships for emulsions
      Bullard, Jeffrey W.; Pauli, Adam T.; Garboczi, Edward J.; Martys, Nicos S.
      Journal of Colloid and Interface Science (2009), 330 (1), 186-193CODEN: JCISA5; ISSN:0021-9797. (Elsevier B.V.)
      Differential effective medium theory (D-EMT) has been used by a no. of investigators to derive expressions for the shear viscosity of a colloidal suspension or an emulsion as a function of the vol. fraction of the dispersed phase. Pal and Rhodes [R. Pal, E. Rhodes, J. Rheol. 33 (7) (1989) 1021-1045] used D-EMT to derive a viscosity-concn. expression for non-Newtonian emulsions, in which variations among different oil-water emulsions were accommodated by fitting the value of an empirical solvation factor by matching the vol. fraction at which the ratio of each emulsion was exptl. obsd. to have a viscosity 100 times greater than that of the pure solvent. When the particles in suspension have occluded vol. due to solvation or flocculation, we show that the application of D-EMT to the problem becomes more ambiguous than these investigators have indicated. In addn., the resulting equations either do not account for the limiting behavior near the crit. concn., i.e., the concn. at which the viscosity diverges, or they incorporate this crit. behavior in an ad hoc way. We suggest an alternative viscosity-concn. equation for emulsions, based on work by Bicerano and coworkers [J. Bicerano, J. F. Douglas, D. A. Brune, J. Macromol. Sci., Rev. Macromol. Chem. Phys. C 39 (4) (1999) 561-642]. This alternative equation has the advantages that (1) its parameters are more closely related to phys. properties of the suspension and (2) it recovers the correct limiting behavior both in the dil. limit and near the crit. concn. for rigid particles. In addn., the equation can account for the deformability of flexible particles in the semidilute regime. The proposed equation is compared to the equation proposed by Pal and Rhodes.
    57. 57
      Cuddapah, V. A.; Robel, S.; Watkins, S.; Sontheimer, H. A neurocentric perspective on glioma invasion. Nat. Rev. Neurosci. 2014, 15, 455– 465,  DOI: 10.1038/nrn3765
      56
      A neurocentric perspective on glioma invasion
      Cuddapah, Vishnu Anand; Robel, Stefanie; Watkins, Stacey; Sontheimer, Harald
      Nature Reviews Neuroscience (2014), 15 (7), 455-465CODEN: NRNAAN; ISSN:1471-003X. (Nature Publishing Group)
      A review. Malignant gliomas are devastating tumors that frequently kill patients within 1 yr of diagnosis. The major obstacle to a cure is diffuse invasion, which enables tumors to escape complete surgical resection and chemo- and radiation therapy. Gliomas use the same tortuous extracellular routes of migration that are travelled by immature neurons and stem cells, frequently using blood vessels as guides. They repurpose ion channels to dynamically adjust their cell vol. to accommodate to narrow spaces and breach the blood-brain barrier through disruption of astrocytic endfeet, which envelop blood vessels. The unique biol. of glioma invasion provides hitherto unexplored brain-specific therapeutic targets for this devastating disease.
    58. 58
      Davidson, P. M.; Sliz, J.; Isermann, P.; Denais, C.; Lammerding, J. Design of a microfluidic device to quantify dynamic intra-nuclear deformation during cell migration through confining enviornments. Integr. Biol. 2015, 7, 1534– 1546,  DOI: 10.1039/c5ib00200a
      57
      Design of a microfluidic device to quantify dynamic intra-nuclear deformation during cell migration through confining environments
      Davidson, Patricia M.; Sliz, Josiah; Isermann, Philipp; Denais, Celine; Lammerding, Jan
      Integrative Biology (2015), 7 (12), 1534-1546CODEN: IBNIFL; ISSN:1757-9694. (Royal Society of Chemistry)
      The ability of cells to migrate through tissues and interstitial spaces is an essential factor during development and tissue homeostasis, immune cell mobility, and in various human diseases. Deformation of the nucleus and its assocd. lamina during 3-D migration is gathering increasing interest in the context of cancer metastasis, with the underlying hypothesis that a softer nucleus, resulting from reduced levels of lamin A/C, may aid tumor spreading. However, current methods to study the migration of cells in confining three dimensional (3-D) environments are limited by their imprecise control over the confinement, physiol. relevance, and/or compatibility with high resoln. imaging techniques. We describe the design of a polydimethylsiloxane (PDMS) microfluidic device composed of channels with precisely-defined constrictions mimicking physiol. environments that enable high resoln. imaging of live and fixed cells. The device promotes easy cell loading and rapid, yet long-lasting (>24 h) chemotactic gradient formation without the need for continuous perfusion. Using this device, we obtained detailed, quant. measurements of dynamic nuclear deformation as cells migrate through tight spaces, revealing distinct phases of nuclear translocation through the constriction, buckling of the nuclear lamina, and severe intranuclear strain. Furthermore, we found that lamin A/C-deficient cells exhibited increased and more plastic nuclear deformations compared to wild-type cells but only minimal changes in nuclear vol., implying that low lamin A/C levels facilitate migration through constrictions by increasing nuclear deformability rather than compressibility. The integration of our migration devices with high resoln. time-lapse imaging provides a powerful new approach to study intracellular mechanics and dynamics in a variety of physiol.-relevant applications, ranging from cancer cell invasion to immune cell recruitment.

  • Supporting Information

    Supporting Information

    The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.langmuir.1c01026.

    • Translocation dynamics of a HIPdE with ϕ ≃ 0.55 (AVI)

    • Translocation dynamics of a HIPdE with ϕ ≃ 0.75 (AVI)

    • Translocation dynamics of a HIPdE with ϕ ≃ 0.9 (AVI)


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