Performance Enhancement of Electrocatalytic Hydrogen Evolution through Coalescence-Induced Bubble Dynamics

The evolution of electrogenerated gas bubbles during water electrolysis can significantly hamper the overall process efficiency. Promoting the departure of electrochemically generated bubbles during (water) electrolysis is therefore beneficial. For a single bubble, a departure from the electrode surface occurs when buoyancy wins over the downward-acting forces (e.g., contact, Marangoni, and electric forces). In this work, the dynamics of a pair of H2 bubbles produced during the hydrogen evolution reaction in 0.5 M H2SO4 using a dual platinum microelectrode system is systematically studied by varying the electrode distance and the cathodic potential. By combining high-speed imaging and electrochemical analysis, we demonstrate the importance of bubble–bubble interactions in the departure process. We show that bubble coalescence may lead to substantially earlier bubble departure as compared to buoyancy effects alone, resulting in considerably higher reaction rates at a constant potential. However, due to continued mass input and conservation of momentum, repeated coalescence events with bubbles close to the electrode may drive departed bubbles back to the surface beyond a critical current, which increases with the electrode spacing. The latter leads to the resumption of bubble growth near the electrode surface, followed by buoyancy-driven departure. While less favorable at small electrode spacing, this configuration proves to be very beneficial at larger separations, increasing the mean current up to 2.4 times compared to a single electrode under the conditions explored in this study.


Introduction
Water electrolysis is likely to become a central technology in the CO 2 -neutral energy system of the future.Apart from being a potential energy carrier and fuel, hydrogen gas serves as a feedstock for the chemical (e.g.2][3] Yet, the process efficiency requires further improvement to compete on the energy market and enable large-scale hydrogen production.5][6][7] These bubbles block the electrodes by masking their active surface area, reducing the number of nucleation sites.
][10] It is therefore vital to maintain a bubble-free electrode area for continuous catalytic activity.
Enhanced removal of gas bubbles and deeper insights into their evolution processes will benefit further optimization of the system's energy efficiency. 11rious methods have been developed to aid bubble departure, categorized as active (e.g., sonication, centrifugal forces, mechanical convection, pressure modulation, external magnetic fields) and passive approaches. 5,7,12,13Passive methods, preferred for their energy-efficiency, primarily involve surface modifications to alter the wettability 14 of the catalytic surface. 15[18][19][20][21][22] The bubble removal process can also benefit from hydrophobic surfaces.One example is the bubble-free electrolysis concept that employs a hydrophobic porous layer adjacent to a porous electrode.4][25][26] A different concept to enhance gas removal, which was shown to hold promise based on theoretical analysis, 27 is the use of hydrophobic islands on the electrode as preferential nucleation sites.9][30] This allows to guide the produced gas away from the active areas of the electrode with the potential to lower the bubble-induced overpotentials. 28,29Brussieux et al. 30 demonstrated that, depending on the size of and distance between islets, parameters of the gas release such as bubble size and location can be controlled, but did not study the effect on electrode performance.More recently, Lake et al. 31 found that densely packed Pt-coated micropost arrays promote consistent release of smaller bubbles through their mutual coalescence.While this enhanced the stability of the current compared to untextured electrodes, it did not lead to performance gains when normalising by the active surface area in this system, due to additional bubbles forming in between the pillars.In this context, coalescence induced removal of bubbles is of particular interest.Coalescence leads to a reduction in surface energy and this difference is in part converted to kinetic energy, causing the bubble to jump off the surface without having to rely on buoyancy.[34][35][36][37][38] However, a detailed understanding of the mechanism and quantification of the extent to which coalescence-induced dynamics can be exploited to improve the performance of gas-evolving electrodes is still lacking.This also applies to parameter optimisation, which in view of complications such as a possible bubble return to the electrode surface, [38][39][40][41][42][43][44] is highly nontrivial.We address these open questions in the present work by studying the coalescence-driven dynamics of hydrogen bubbles produced at a dual micro-electrode during water electrolysis.This new setup allows precise control of important parameters such as the bubble size during coalescence, while also providing excellent observability of the dynamics.We demonstrate that coalescence events may lead to both premature bubble departure compared to buoyancy effects alone and the return of departed bubbles to the surface of the electrode, substantially altering the reaction rates.The dual micro-electrode configuration shows, depending on the applied potential and inter-electrode distance, up to a 2.4-fold increase in current compared to a single micro-electrode.

Methods
The pairs of H 2 bubbles sketched in figure 1a were generated at the surface of a dual platinum micro-electrode during the hydrogen evolution reaction (HER).The experiment was performed in a three-electrode electrochemical cell filled with 0.5 M H 2 SO 4 .
The fabrication of dual micro-electrodes followed a previously established method. 45iefly, two Pt wires (∅100 µm, 99.99%, Goodfellow) were sealed into a soda-lime glass capillary (outer diameter ∅1.4 mm, inner diameter ∅1.12 mm, Hilgenberg) by gently softening the capillary in a flame.Five different values for the interelectrode distance H were established and tested, as shown in fig.1b.The electrode surface underwent electrochemical cleaning (potential cycling between 0.03...1.35V vs. RHE , repeated 50 times) after being mechanically polished with sandpaper (2000 grit), sonicated and rinsed with ultrapure water.5][46] The dual micro-electrode (cathode) is inserted horizontally facing upward in the base of a cuboid glass cuvette (Hellma) with dimensions of 10 × 10 × 40 mm 3 .The system is completed by the reference electrode (Ag/AgCl) and counter electrode (∅ 0.5 mm Pt wire) both inserted vertically from the top.The electrochemical cell is controlled by a potentiostat (BioLogic, VSP-300, 6 channels) at a constant potential of -0.2 to -2.8 V (vs.RHE).Each of the two electrodes is connected to and controlled by a separate channel of the potentiostat.For each experimental run, the electric current was recorded with a sampling rate of at least 1 kHz over a period of 30 s.The optically transparent cell allows visualization of the bubble dy- namics using a shadowgraphy system.It consists of LED illumination (SCHOTT, KL 2500) with a microscope, connected to a high-speed camera (Photron, FASTCAM NOVA S16), providing a spatial resolution of 996 pix/mm.Image recording was typically performed at 5 kHz, unless otherwise stated.High-speed recording up to 264 kHz was used to resolve individual coalescence events.The bubble radius was extracted by standard image processing routine based on the Canny edge detection method in Matlab R2022b (for further details see Supplemental Material in Bashkatov et al. 47 ).To measure the velocity fields around H 2 bubbles presented in figure 6, monodisperse polystyrene particles (microParticles GmbH) of ∅5 µm were seeded into the electrolyte.These particles are neutrally buoyant with a mass density of 1.05 g/cm³.The resulting series of images, recorded at 1000 frames per second, were processed by the software DaViS 10, which employs a Particle Tracking Velocimetry (PTV) algorithm to track each particle over 25 ms shortly before departure.Due to the limited number of particles close to or at the bubble-electrolyte interface, the resulting tracks of the particles were collected for 60 bubbles.Subsequently, the tracks were converted into a vector field using a binning function that interpolates local tracks on a specified fine grid.

Single electrode
7][48][49][50][51][52][53][54][55] As an example, figure 2a shows the transient current (I s ) and radius (R s ) of the bubble for three complete bubble evolution cycles at -1.0 V. Shadowgraphs corresponding to a complete cycle from nucleation [56][57][58] to departure are included in figure 2b.This process is highly periodic with a bubble lifetime T s .The evolution of the bubble has a strong influence on the reaction current, for which the maxima in cathodic current marked by the red circles coincide with the departure of the bubble.This is immediately followed by the nucleation of a new bubble, whose growth in the vicinity of the electrode leads to a considerable reduction in I s of up to 50% in this case.This continues until the next bubble departure, after which the cycle repeats itself.
Finally, figure 2c summarizes how the average electric current I s , where the overline denotes an average over t, the departure radius ( Rs ), and lifetime ( Ts ) varies for different cathodic potentials (ϕ).All statistics are averaged over multiple bubble cycles with error bars representing the standard deviation.The figure also confirms that consistent results are obtained from both electrodes.
In this system, bubble formation occurs already at low overpotentials.Micron-sized bubbles form on the electrode surface and continuously coalesce to form a single larger bubble.This larger bubble is typically not in direct contact with the electrode surface, but rather resides on the layer of microbubbles. 44It continues to grow via the intensive coalescence with these microbubbles and via gas diffusion. 59In this case, departure of the bubble occurs once the retaining forces due to the electric field, 44 thermal 60-63 and solutal 45 Marangoni effects are overcome by buoyancy (see figure 1a).The thermal Marangoni effect is related to the Joule heating caused by the locally high current density (j) at the bubble foot as indicated in figure 1a.The effect therefore scales (via Ohm's law) with j 2 and prevails at high overpotentials.The solutal effect due to the depletion of the electrolyte at the electrode is expected to depend linearly on j and therefore dominates at lower overpotentials (ϕ ⪆ −0.7 V in the present case). 45The electric force is directly proportional to ϕ and therefore all retaining forces diminish as the overpotential is reduced, which explains the decreasing trend of the departure radius Rs as |ϕ| is made less negative.Since the bubble captures almost all the produced gas, 45,46 the departure period follows from the time it takes to produce the gas contained in the bubble volume and T s is therefore proportional to R 3 s /I.

Modes of bubbles evolution
From now on, both electrodes are operated simultaneously, independently of each other, and at the same potential.Initially, we will only consider the pair with a separation of H = 117 µm.The measured currents for this configuration are plotted in figure 3a for different potentials.Time traces of the current for both electrodes ('left' and 'right') are included and for reference we also show the current signal measured when only a single electrode is operated at the same potential (grey line).Focusing initially on the lowest overpotential, ϕ = −0.3V, the current oscillations remain periodic during dual operation; however, both the period and amplitude are notably diminished.The reason for this can be understood from the corresponding shadowgraphs presented in figure 3b, which illustrate the bubble dynamics over one period (shown by black box in fig.3a).
Similar to what is observed for a single electrode, a larger bubble forms and grows initially at each of the two electrodes, leading to a gradual reduction in the current.This process continues until the two bubbles touch and coalesce, which is followed by the departure of the merged bubble along with a spike in the current (see inset at -0.3 V in fig.3a). Figure 3c details this coalescence process, which happens on the order of micro-seconds, and the emerging deformations of the bubble shape.The coalescence induced jump-off is powered by the released surface energy. 38,64,65While the majority of this energy is dissipated through the capillary waves seen in figure 3c, 37,66 the fraction that is transformed into kinetic energy (less than 1%, for details see Supporting Information) can cause bubble departure at much smaller radii than in the buoyancy-driven scenario, for the newly formed bubble.Together with the fact that each of the coalescing bubbles only contributes half the volume, this explains the significantly enhanced departure frequency.
At higher overpotential at ϕ = −0.5 V, events with a much longer period length start appearing intermittently in the current traces.These events become more frequent and dominate the signal at ϕ = −0.7 V, before almost fully superseding the high-frequency coalescence pattern at ϕ ≤ −1.0 V.In order to elucidate the underlying bubble dynamics, we provide an enlarged view of a segment of the current signal at ϕ = −0.7 V (green box) in figure 3d along with the size evolution of the bubbles.The first bubble departure included in figure 3d proceeds analogously to the one shown in figure 3b, and the bubble continues to rise away from the electrode after the coalescence induced take-off.We will refer to this as 'mode I' from now on.However, as the corresponding shadowgraphs in figure 3e show, even though the bubble also jumps off after the second coalescence event, it is eventually brought back to the surface through repeated coalescence with newly formed bubbles at both electrodes (see period between t = 0.8854 s and t = 0.8862 s).Following this return, the bubble rests between the two electrodes just above the surface.There, it continues to grow until a buoyancy driven departure (at R II = 158 µm vs. R I = 72 µm), which explains an order of magnitude longer lifetime (T II = 104.4ms vs. T I = 8.4 ms) of the bubble in this instance.We will denote this as 'comeback mode' or 'mode II'.
It is evident from figure 3a that the dynamics induced by coalescence have a strong impact not only on the current fluctuations, but also on the mean current at a specific potential.To analyse this, we compare period averaged currents for the two modes (I I and I II , taken to be the sum of the currents at both electrodes) to 2 × I s in figure 4. Note that it is possible to determine I I even at high potentials where mode II prevails by considering only the time until the first coalescence, leading to temporary departure of the bubble (see figure 3d).Despite the much faster gas removal, the current at low overpotentials (ϕ ⪆ −0.7 V) remains the same or even slightly decreases in dual operation compared to the single electrode case.This can be attributed to the additional shielding by the second bubble in the vicinity of the electrode and the diffusive competition between the two reaction sites, both of which lower performance.However, the benefits of the accelerated gas removal increasingly outweigh these effects as the overpotential is increased.This is particularly true for mode I, where the current is more than double than that of the single electrode at the same potential for the most negative values of ϕ investigated.While this clearly demonstrates the potential for performance enhancement through coalescence-induced gas removal, the effective performance enhancement is reduced to less than 50% for the current electrode spacing due to the prevalence of bubble return (mode II) at higher overpotentials.
The currents in mode II are consistently lower compared to mode I because the electrode separation is so small, that the returning bubble still blocks a large part of both electrodes (see figure 3e), even though it is located half-way between them.

Phase diagram
To better understand under what conditions under which the return of the bubble after jump-off happens, figure 5 documents the probability (P ) of return for different interelectrode distances (H) and as a function of ϕ (figure 5a) and I I (figure 5b).As H is increased, the transition from mode I (P < 5%, circles), to a mixed regime (5% ≤ P ≤ 95%, triangles) and finally to mode II (P > 95%, squares) occurs at increasingly larger values of |ϕ|.In fact, the dependence on H is quite strong: for a fixed potential of ϕ = -1.3V, P changes from about 100% at H = 117 µm to almost 0 when the distance is increased to H = 270 µm.The sketch in figure 5c illustrates the relevant mechanism for the bubble return.A newly formed bubble (with radius R 0 ) on one of the electrodes catches up and coalesces with the departed bubble with radius RI .Due to momentum conservation, the resulting bubble is then located at the joint center of mass of the two coalescing bubbles, which implies a downward shift by ∆z compared to the location of the bubble with radius RI .Repeated coalescence events from both sides then bring the bubble back to the surface as seen in figure 3e.The transition between mode I and mode II is therefore governed by a competition between the departure or 'jump' velocity of a bubble after coalescence and the growth rate of bubbles at the electrode.
A larger magnitude of electric current, increasing approximately linearly with ϕ (see figure 6), enables faster formation of new bubbles which then increases the likelihood of their interaction with the previously departed bubble.Upon increasing H the bubble-successor needs to grow to a larger size, hence for a longer time before interacting with the already departed bubble, allowing the latter to move farther away.This will dramatically increase the current required for comeback mode.We can capture this in a simple model based on the geometry sketched in figure 5c to predict the minimum current I c for bubble return.
Our analysis considers the situation where the new bubble with radius R 0 has grown large enough to get in contact with the departing bubble.The time it takes for the bubble to grow to the radius R 0 is ∆t = kR 3 0 /I c , where RgT is a prefactor containing the Faraday constant F , the pressure inside the bubble P g , the gas constant R g and the temperature T (see Supporting Information for details).During this time interval, the departing bubble travels the distance ∆t • u I , with u I denoting the effective jump velocity.Based on the geometry of the triangle spanned by the centers of the two bubbles and the point A in figure 5c, the critical current for the mode transition as a function of R 0 is given by For any H, a value of R 0 can be determined for which I c reaches a minimum value, I * c .
To obtain the value of the current I * c in this critical configuration, an estimate of the jump velocity is required.To obtain this, we tracked bubbles departing after coalescence and then averaged their vertical velocity over the first 0.5 ms to obtain u I,0.5 ms .Note that u I varies widely depending on the position of both bubbles before coalescence (see Supporting Information for details).The results for this quantity are shown in figure 5d as a function of H. From these data, typical values for u I are found to be in the range from 60 mm/s to 110 mm/s with a slight tendency towards higher velocities as the bubble size increases at larger electrode separations H.In figure 5b, we have included results for 2 × I * c as a function of H and for different values of u I .It can be seen that the model very well captures the increase of the critical current as the electrode separation increases.The best agreement between the model and the data is for u I = 60 mm/s, which is close to, although slightly lower, than the measured jump velocities in figure 5d.Among potentially other factors, a reason for this slight difference is the fact that the new bubble with radius R 0 is also formed by coalescence and therefore also jumps off the electrode.Additionally, we do not account for shape oscillations of the larger bubbles, which become more prevalent at larger H.

Performance vs. Inter-electrode distance, H
To understand how the current varies at different electrode separations, it is useful to first consider how the departure size of the bubbles changes for different H.In mode I, the departure is coalescence-driven so that RI is independent of ϕ and varies only with the interelectrode distance H. Due to lateral oscillations of the bubble position on the electrode and possibly a slight inclination of the electrode surfaces, the results for RI shown in figure 6a are about 10% lower than 2 −2/3 H, i.e. the value for the coalescence of two bubbles each with a radius of H/2.This small difference was taken into account when evaluating RI in equation 1.
Compared to the single electrode, the current in mode I shown in figure 6b is most enhanced at high overpotential and small H, because in this case the reduction in bubble departure size is maximal.There is only moderate decrease of I I for larger H primarily due to the relatively small range in H and, consequently, in RI , which is minor compared to variations observed in Rs at different potentials.At low overpotentials, RI ≈ Rs for the larger electrode separations studied and there is no increase of the current compared to I s , just as was observed at H = 117 µm in figure 4.
In mode II, the departure radius strongly depends on the potential but at most weakly on H, as shown in figure 6c.Remarkably, RII is approximately the same as for the single electrode case at the same potential (see grey symbols representing Rs ).An investigation of the force balance [67][68][69] leading to these trends in RII are beyond the scope of this study.
Nevertheless, we present clear evidence of Marangoni convection (see figures 6(e,f)), consistent with the presence of thermocapillary effects in the same potential range on single electrodes. 51,63Based on the flow direction, a resulting downward Marangoni force on the bubble is expected (see figure 1a).The convective motion is much more pronounced at H = 270 µm (figure 6f) compared to the narrower spacing of H = 117 µm in figure 6e, which is in line with the difference in current between the two cases (I II = 5.33 mA vs. 8.46 mA, respectively).Interestingly, this does not result in a noticeable difference in RII for the different interelectrode distances, which is presumably due to differences in the geometry dependent electric force. 69We confirmed that the continued coalescence with small bubble does not exert a significant apparent force on the bubble (see Supporting Information for details).
In contrast to mode I, the current in mode II shown in figure 6d shows a clear dependence on the electrode separation and increases strongly for larger H.This is because the bubble is now centered in between the two electrodes.Therefore the electrodes become more exposed as the distance between them increases, even if the bubble size remains the same.The continuous removal of the smaller bubbles on the electrode by coalescence with the larger one proves to be very beneficial and leads to maximum currents of more than twice I s , equalling the largest currents observed in mode I. To quantify the performance gain and to compensate for the ϕ dependence of the current, we normalise the current on the dual electrode by I s .This also accounts for small differences in I s between the different electrodes used in this study (see Supporting Information).In figure 7a, the ratio I I /I s is plotted for different H as a function of ϕ.As the figure shows, the interference effects at low overpotentials already discussed in the context of figure 3, cause I I to even fall below I s for ϕ ⪆ −0.5 V.This does not improve noticeably for larger electrode spacing, presumably due to a trade-off between reduced interference effects and the increase in the bubble size with H.For larger overpotentials, the benefits of the enhanced gas removal prevail, reflected in a ratio I I /I s > 1 which also consistently increases with increased overpotential exceeding a value of 2 at ϕ = −2.8V. Approximately the same values are also encountered for this potential for the ratio I II /I s in figure 7b.While the performance in mode II also improves slightly for higher overpotential, it most strongly depends on H.As the inset in figure 7b shows, the ratio I II /I s increases approximately linearly with H at constant potential.
Finally, figure 7c shows how the resulting effective current on the dual electrode I d changes relative to I s .In addition to variations in I I and I II , this quantity is also influenced by the probability P (H, ϕ) of bubble return (mode II).Given the results in figure 5a, the ratio I d /I s is therefore dominated by mode I at low and by mode II at large overpotentials.
This implies that the performance gains in mode I at high |ϕ| are not practically realisable.
However, this is only a limitation at smaller electrode separations, since the current in mode II even exceeds that of mode I for H = 242 µm and H = 270 µm (see inset of figure 7c).For these cases, the mode transition is therefore even beneficial.
Figure 7d shows snapshots for the parameter combination H = 270 µm and ϕ = −2.8V for which the highest ratio I d /I s = 2.4 was observed.Having the returned bubble located at the center in between the electrodes avoids the formation of larger bubbles directly on the electrodes.Notably, only a slight drop in the current is observed (see inset at t 0 = 0) as the outline of the bubble moves beyond the electrode positions.This contradicts the common practice of considering the region under the bubble as inactive but is in line with earlier conjectures. 31,70

Conclusions
We have explored the coalescence dynamics of electrogenerated bubbles and their influence on the electrochemical reaction rate using dual platinum micro-electrodes.We found that the coalescence of two adjacent bubbles leads to an initial jump-off of the merged bubble and premature escape from the surface.However, the continued coalescence with newly formed successors may result in a return to the electrode, hence prolonged growth.The latter mode is increasingly prevalent the higher the current and the smaller the interelectrode distance.We proposed a simple model to capture these trends and predict the critical magnitude of the current required to initiate the return process.This comeback mode negates the potential performance improvement achieved through direct departure following the coalescence event at smaller H (up to a 1.7-vs.2.3-fold increase in current at constant potential when compared to a single electrode).However, even in cases of bubble return, the effective current at larger H increased by up to 2.4 times because the bubble was then located between the electrodes, exposing a greater electrode area for the reaction.Therefore, this mode is promising, especially since, given the dependence on electrode separation, even greater performance gains can be expected by further increasing H.In practice, a similar configuration may be achieved on extended electrodes using hydrophobic islands, which should be spaced to favour coalescence-based departure and minimize the probability of bubble return, thus avoiding the blocking of the active surface area.periodical evolution of bubbles.The quite similar current between various H suggests that the surfaces of these electrodes are alike.However, the small differences are enough to affect the dynamics of H 2 bubbles and significantly alter the lifetime and size at the departure.to the effects of drag force, particularly in the moments following the jump.Interestingly, the "terminal" velocity of the bubble, which can be read from the slope of the curves and i.e. ca. after 2 ms, increased at a larger overpotential (-0.5 V).This might be explained by the wake behind the rising bubble-predecessor.This flow drags, hence accelerates the merged bubble in the moment of departure.The wake enhances with the faster departure of bubbles-predecessors (smaller T ) which is the case at a more negative potential.denote mode II, i.e. when the once departed bubble following the coalescence event comes back to the surface, continues to grow, and departs at a later stage due to buoyancy.Note that u I varies widely depending on the position of both bubbles before coalescence and their size ratio.(ii) at higher potential, hence current, the bubble would come back to the electrode more often moving away with even higher jumping velocity, as already emphasized in the manuscript (see figure 5).

Single electrode: characterization
Upon coalescence of two bubbles, there is a release of surface energy (∆G s ) given as where R l , R r and R I are the left, right and merged bubbles, respectively.γ ≈ 0.072 N/m is the surface tension of the electrolyte.The released energy partly dissipates by the bubble oscillations, working against viscous drag.When in the proximity to the surface, the remaining energy is converted to the kinetic energy (E k ) driving the resultant (merged) bubble to jump off the electrode. 1The kinetic energy is where C M is added mass coefficient, ρ l electrolyte density and u I is the initial jumping velocity.For a spherical bubble C M = 0.5, however, when the bubble is in proximity to the wall the coefficient is larger. 2In detail, when two bubbles approach each other, the thin film of electrolyte separating them gradually drains O µs and eventually ruptures.
This leads to the formation of a neck, i.e. an open cavity, and a series of capillary waves of varying strengths that propagate along the electrolyte-gas interface.These waves move away from the neck region until they meet at the opposite apex of the coalescence point (see manuscript, fig.3c).The strength of these waves decreases as they travel along the interface due to continuous viscous dissipation. 3Meanwhile, the surface tension γ drives the retraction of the remaining capillary waves towards a spherical shape, deforming the bubble shape.Once the excess surface energy overcomes the work done by the bubble against viscous drag (W µ ) during the expansion and retraction processes, the resultant net component of momentum perpendicular to the surface causes the bubble to jump off the electrode.As neither of the bubbles is attached to the electrode, the adhesion energy W a is neglected.The process is controlled by surface tension and viscosity and is often characterized in terms of the Ohnesorge number (Oh = µ √ ργR I ). 3 µ is the dynamic viscosity of the electrolyte.The influence of gravity during the coalescence, before lift-off, is negligible. 2 While the process is considered highly inefficient, with only a small portion of surface energy translating into kinetic energy, 2 it is sufficient for a resultant bubble (R I ) to jump off the electrode acquiring an initial velocity u I .

Figure 1 :
Figure 1: (a) Schematic of the dual micro-electrode and two H 2 bubbles sitting on the carpet of microbubbles.Each growing bubble is subject to a force balance including buoyancy, electric, and Marangoni forces.The red lines represent current density (j) and the black streamlines on the right represent the Marangoni convection with velocity u M .E k is the kinetic energy released during the coalescence of the left (R l ) and right (R r ) bubbles.(b) Top view of the five dual micro-electrodes with different interelectrode distance (H).

Figure 2 :
Figure 2: (a) The electric current and radius over time representing three complete cycles of bubble evolution at ϕ = −1.0V at a single micro-electrode.The red circles mark nucleation and departure instants of time.(b) Shadowgraphs displaying the evolution cycle, marked in grey in (a).(c) The averaged electric current (circles), departure radius (triangles) and lifetime (squares) versus the potential for the right (black) and left (orange) electrodes, run separately.Image recording performed at 500 frames/second.

Figure 3 :
Figure 3: (a) Electric current over 2 seconds (out of 30 seconds) of the experimental run at various potentials (ϕ).The black and orange curves represent the electric current measured at the right and left electrodes, respectively.Grey lines represent corresponding results for single electrode operation.(b) Snapshots depict the bubble evolution following mode I as indicated in (a) by the black rectangular inset at -0.3 V. (c) Snapshots detailing the coalescence-driven departure process recorded at -0.5 V. t 0 is one frame before the coalescence process begins.(d) A zoomed-in view of the current at -0.7 V, shown by the green rectangle in (a), with corresponding evolution of R(t).The orange and blue shades correspond to modes I and II, respectively.(e) Mode II of bubble evolution from (d).The red line indicates the maximum height reached by the departed bubble.Recordings in (b) and (e) were performed at 5 kHz, and at 264 kHz in (c).

Figure 4 :
Figure 4: Electric current (I) vs. potential (ϕ) for single electrode (black) and for modes I (blue) and II (red) at dual micro-electrode.Both I I and I II are the sum of the currents at the left and right electrodes.

Figure 5 :
Figure 5: Phase diagram representing the probability (P) of the bubble coming back after initial departure shown in terms of (a) Potential and (b) Current vs. H.The color bar scales the probability from 0 to 100%.The circles denote Scenario I, i.e. when P is less than 5%, and squares denote Scenario II, with P more than 95%.The triangles are for a mixed regime, where the probability varies widely from 5 to 95%.The red lines plot 2 × I * c using eq. 1. (c) The sketch illustrating the relevant geometry for the bubble return.(d) Vertical jump velocity u I.0.5 ms averaged over the first 0.5 ms of the jump vs. H for numerous bubbles.The line represents the averaged values at each H, completed with standard deviation.

Figure 6 :
Figure 6: Departure radius (a) RI , (c) RII and electric current (b) I I , (d) I II for Modes I and II, respectively.RI is given as a function of H. RII , I I and I II are shown as functions of potential and for various H. Grey curves are for single electrode.(e) and (f) Velocity fields, |u M |, representing Marangoni convection during mode II at -2.8 V and H = 117 µm and H = 270 µm, respectively.The velocity is measured in a period of 25 ms before the bubble departure.

Figure 7 :
Figure 7: The electric current (a) I I , (b) I II and (c) I d , all in dimensionless form with reference to I s .Data are presented as a function of potential (ϕ) and interelectrode distance (H).The inset in (b) shows I II /I s vs. H at -1.8, -2.3 and -2.8 V.The inset in (c) documents I I /I II vs. ϕ.I d is the current averaged over both mode I (I I ) and mode II (I II ).(d) Snapshots throughout the bubble evolution at -2.8V and H = 270 µm.t 0 = 0 marks an instant of time one image before the coalescence of two bubbles (with radii R l and R r , respectively) followed by the jump of the merged bubble off the electrode and its consecutive return.The inset shows the electric current throughout the entire evolution, with the red circles marking the corresponding snapshots.

Figure
Figure S1 documents the electric current over 5 seconds (out of 30 seconds) of the experimental run at various potentials (ϕ).The currents are shown for H = 117 µm for left and right electrodes (see figure 1a in the manuscript), run separately.

Figure S1 :
Figure S1: The electric current over time for left and right electrodes.

Figure
Figure S2 characterizes five electrodes in terms of the electric current (2 × I s ), lifetime ( Ts ), and radius at the departure ( Rs ) vs. ϕ.I s is averaged over 30 seconds and the left and right electrodes.Ts and Rs are averaged for multiple bubbles and accompanied by the standard deviations.The low standard deviation for Rs and Ts demonstrates the highly

Figure S2 :
Figure S2: The electric current, lifetime and departure radius for H 2 bubbles produced at single electrode vs. ϕ for different electrodes (H).The error bars represent standard deviation.

Figure S4 :
Figure S4: The electric current vs. time plotted for 1 second out of 30 seconds of the experimental run for various potentials ϕ and interelectrode distance: (a) H = 242 µm, (b) H = 270 µm.

Figure
Figure S5 documents the lifetime of the bubbles produced at dual electrode vs. potential (ϕ) for Modes I (left) and II (right) and for different electrodes.T is averaged for multiple bubbles and accompanied by the standard deviations.Two main trends can be observed: (i)Since the departure radius in mode I is independent of the ϕ, TI reduces at larger overpotentials, owing to higher electric current.It also increases together with H, especially at larger ϕ. -This is because the pair of bubbles need to grow to a bigger size before coalescence at larger H; (ii) On the other hand, TII increases at larger overpotentials and reduces at larger H.As already mentioned in the manuscript, larger overpotentials imply larger downwardacting forces increasing the departure size of the bubble.Therefore the bubble would grow for a longer time.However, the separation of two electrodes away from each other for larger

Figure S5 :
Figure S5: The lifetime at dual electrode as a function of potential (ϕ) and interelectrode distance (H).TI and TII are for mode I and mode II, respectively.The error bars represent standard deviation.

Figure
Figure S6 demonstrates the traveling distance in vertical direction of the merged bubble in the first 5 milliseconds after the jump-off of the electrode driven by the coalescence event at H = 117 µm.The results are shown for ϕ = −0.3 and −0.5 V and three bubbles in each case.The curves document that the jumping velocity notably decays over time (∆t) due

Figure
Figure S7 represents the vertical jumping velocity u I.0.5 ms for numerous bubbles, averaged over the first 0.5 ms of the jump, vs. parent size ratio R s /R l .The experiments performed at H = 117 and (a) ϕ = −0.5 V, (b) ϕ = −1.0V. R s and R l are radii for smaller and larger bubbles, respectively.The geometric parameters are shown in figure S7c.The color bar scales another geometric parameter Y max given in dimensionless form.It represents the relative position of the bubble i.e. the distance from the bubble bottom to the electrode, chosen as the maximum value between the smaller and bigger bubbles.The bubble sits at the electrode if Y = 1 and is away from the electrode if Y > 1.The circles represent mode I, i.e. when the bubble departs into the bulk following the coalescence event, and squares

Figure S6 :
Figure S6: The trajectory of bubble at -0.3 V and -0.5 V over the first 5 milliseconds after coalescence driven jump-off.t 0 = 0 is one frame before coalescence.Each potential is presented by three bubbles.The interelectrode distance H = 117 µm.

Figure S7 :
Figure S7: (a),(b) The vertical jumping velocity (u I,0.5ms ) vs.. R s /R l at ϕ = −0.5 V and ϕ = −1.0V.The color bar scales the relative position of the bubble shown in (c), i.e. the maximum of either smaller or bigger bubbles, prior to coalescence at H = 117.Image recording performed at 10 kHz.

Figure
Figure S8 documents an estimation of the ratio between the translated kinetic energy (E k ) and the released surface energy (∆G s ) as a function of (a) R I and (b) H.The data points in fig.S8a is calculated using eq. 1 and eq. 2 by taking corresponding R l , R r , R I and u I,0.5ms for the bubbles presented in fig.S7a, i.e. at H = 117 µm and ϕ = −0.5 V.The circles represent the bubbles following mode I and squares mode II.The data points in fig.S8b is based on the RI from fig. 6a and u I,0.5ms from fig. 5d in the manuscript, assuming that R l = R r , hence R l = RI 2 1/3 .

Figure S8 :
Figure S8: The ratio between the translated kinetic energy (E k ) and the released surface energy (∆G s ) as a function of (a) R I and (b) H.

Figure
FigureS9documents a comparison between the buoyancy force and apparent force, calculated using eq.17 at I = −8 mA (which corresponds to approximately the maximum current observed in this study), against the bubble radius R. The buoyancy force defined as F b = (ρ g − ρ H2 )gV , where g represents gravitational acceleration.Fig.S9demonstrates that the continued coalescence with the carpet of microbubbles does not impose a significant apparent force on the bubble.-This force decays rapidly with increasing R and becomes smaller than the buoyancy force at at approximately R = 16 µm.