# Performance enhancement of electrocatalytic hydrogen evolution through
coalescence-induced bubble dynamics

Aleksandr Bashkatov  [<EMAIL_ADDRESS>Sunghak Park  [  Çayan Demirkır
[  Jeffery A. Wood  [  Marc T.M. Koper  [  Detlef Lohse  [  Dominik Krug  [
<EMAIL_ADDRESS>
###### Abstract

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 hydrogen evolution reaction in 0.5 M H2SO4 using
dual platinum micro-electrode 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 for 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 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
favourable 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.

2_ESI font=sf,small Twente]Physics of Fluids Group, Max Planck Center for
Complex Fluid Dynamics and J. M. Burgers Centre for Fluid Dynamics, University
of Twente, Enschede, Netherlands Leiden]Leiden Institute of Chemistry, Leiden
University, Leiden, Netherlands Twente]Physics of Fluids Group, Max Planck
Center for Complex Fluid Dynamics and J. M. Burgers Centre for Fluid Dynamics,
University of Twente, Enschede, Netherlands Twente2]Soft Matter, Fluidics and
Interfaces, MESA+ Institute for Nanotechnology, J. M. Burgers Centre for Fluid
Dynamics, University of Twente, Enschede, Netherlands Leiden]Leiden Institute
of Chemistry, Leiden University, Leiden, Netherlands Twente]Physics of Fluids
Group, Max Planck Center for Complex Fluid Dynamics and J. M. Burgers Centre
for Fluid Dynamics, University of Twente, Enschede, Netherlands [MaxPlanck]Max
Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
Twente]Physics of Fluids Group, Max Planck Center for Complex Fluid Dynamics
and J. M. Burgers Centre for Fluid Dynamics, University of Twente, Enschede,
Netherlands

##  1 Introduction

Water electrolysis is likely to become a central technology in the CO2-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. ammonia
production for fertilisers) and steel industries (coal replacement), and
refineries (methanol, synthetic fuels) 1, 2, 3. Yet, the process efficiency
requires further improvement to compete on the energy market and enable large-
scale hydrogen production. In both conventional alkaline and proton exchange
membrane water electrolyzers a considerable part of the overpotentials and
hence losses can be attributed to the formation of H2 and O2 bubbles, present
at the electrodes and in the bulk.4, 5, 6, 7 These bubbles block the
electrodes by masking their active surface area, reducing the number of
nucleation sites. Additionally, they raise ohmic resistance by blocking the
ion-conducting pathways.8, 9, 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 11.

Various 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.12, 5, 7, 13
Passive methods, preferred for their energy-efficiency, primarily involve
surface modifications to alter the wettability14 of the catalytic surface.15
For example, superhydrophilic surfaces facilitate earlier bubble departure due
to the reduced contact angle at liquid-solid interfaces.16, 17, 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. This prevents bubble formation
within the catalyst, guiding the generated gas by capillary effects through
the hydrophobic layer 23, 24, 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. Also practically, this has been shown to be feasible using electrodes
partially covered with hydrophobic spots made of polytetrafluoroethylene
(PTFE)28, 29, 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, 29. Brussieux 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. This makes this removal process also
highly attractive in microgravity applications.32, 33, 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,39, 40, 41, 42, 43, 38, 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.

##  2 Methods

The pairs of H2 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 H2SO4.

The fabrication of dual micro-electrodes followed a previously established
method.45 Briefly, two Pt wires ($\varnothing$100 $\mu$m, 99.99%, Goodfellow)
were sealed into a soda-lime glass capillary (outer diameter $\varnothing$1.4
mm, inner diameter $\varnothing$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…1.35 V vs.
RHE , repeated 50 times) after being mechanically polished with sandpaper
(2000 grit), sonicated and rinsed with ultrapure water. The cell used here
closely resembles that used in earlier studies 46, 44, 45. The dual micro-
electrode (cathode) is inserted horizontally facing upward in the base of a
cuboid glass cuvette (Hellma) with dimensions of 10 $\times$ 10 $\times$ 40
mm3. The system is completed by the reference electrode (Ag/AgCl) and counter
electrode ($\varnothing$ 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.

Figure 1: (a) Schematic of the dual micro-electrode and two H2 bubbles sitting
on the carpet of micro-bubbles. 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).

The optically transparent cell allows visualization of the bubble dynamics
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 H2
bubbles presented in figure 6, monodisperse polystyrene particles
(microParticles GmbH) of $\varnothing$5 $\mu$m 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.

##  3 Single electrode

To set the baseline, we briefly report the results for the case where only a
single electrode is operated, which has been studied previously.48, 49, 50,
46, 51, 52, 47, 38, 44, 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.

Figure 2: (a) The electric current and radius over time representing three
complete cycles of bubble evolution at $\phi=-1.0$ V 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.

Finally, figure 2c summarizes how the average electric current
$\overline{I}_{s}$, where the overline denotes an average over $t$, the
departure radius ($\hat{R}_{s}$), and lifetime ($\hat{T}_{s}$) varies for
different cathodic potentials ($\phi$). 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 microbubbles44.
It continues to grow via the intensive coalescence with these microbubbles and
via gas diffusion59. In this case, departure of the bubble occurs once the
retaining forces due to the electric field44, thermal60, 61, 62, 63 and
solutal45 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 ($\phi\gtrapprox-0.7$ V in the present case)45. The
electric force is directly proportional to $\phi$ and therefore all retaining
forces diminish as the overpotential is reduced, which explains the decreasing
trend of the departure radius $\hat{R}_{s}$ as $|\phi|$ is made less negative.
Since the bubble captures almost all the produced gas46, 45, 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 $R_{s}^{3}/I$.

##  4 Dual electrode

###  4.1 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 $H=117$ $\mu$m. 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, $\phi=-0.3$ V, 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).

Figure 3:  (a) Electric current over 2 seconds (out of 30 seconds) of the
experimental run at various potentials ($\phi$). 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).

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 energy64, 65, 38. While the majority of this
energy is dissipated through the capillary waves seen in figure 3c 66, 37, 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 $\phi=-0.5$ 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 $\phi=-0.7$ V, before almost
fully superseding the high-frequency coalescence pattern at $\phi\leq-1.0$ V.
In order to elucidate the underlying bubble dynamics, we provide an enlarged
view of a segment of the current signal at $\phi=-0.7$ 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
$R_{II}=158\>\mu$m vs. $R_{I}=72\>\mu$m), which explains an order of magnitude
longer lifetime ($T_{II}$ = 104.4 ms 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 ($\overline{I}_{I}$ and $\overline{I}_{II}$, taken
to be the sum of the currents at both electrodes) to $2\times\overline{I}_{s}$
in figure 4.

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

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 ($\phi\gtrapprox-0.7$ 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 $\phi$
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.

###  4.2 Phase diagram

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 $2\times
I_{c}^{*}$ using eq. 1. (c) The sketch illustrating the relevant geometry for
the bubble return. (d) Vertical jump velocity $\overline{u}_{I.0.5\>ms}$
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.

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
$\phi$ (figure 5a) and $\overline{I}_{I}$ (figure 5b). As $H$ is increased,
the transition from mode I ($P<5\%$, circles), to a mixed regime ($5\%\leq
P\leq 95\%$, triangles) and finally to mode II ($P>95\%$, squares) occurs at
increasingly larger values of $|\phi|$. In fact, the dependence on $H$ is
quite strong: for a fixed potential of $\phi=$ -1.3 V, $P$ changes from about
100% at $H=117\>\mu$m to almost 0 when the distance is increased to
$H=270\>\mu$m. 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
$\hat{R}_{I}$. 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 $\Delta z$ compared to the location of the bubble
with radius $\hat{R}_{I}$. 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 $\phi$ (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 $\Delta
t=kR_{0}^{3}/I_{c}$, where $k=\frac{8\pi}{3}\frac{FP_{g}}{R_{g}T}$ 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 $\Delta t\cdot u_{I}$, 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

$I_{c}(R_{0};u_{I},H)=\frac{u_{I}R_{0}^{3}k}{\left[(\hat{R}_{I}+R_{0})^{2}-\left(\frac{H}{2}\right)^{2}\right]^{1/2}-\hat{R}_{I}+R_{0}}.$
(1)

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 $\overline{u}_{I,0.5\
ms}$. 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 $2\times I_{c}^{*}$ 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 $H$.

###  4.3 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
$\hat{R}_{I}$ is independent of $\phi$ 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 $\hat{R}_{I}$ 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
$\hat{R}_{I}$ in equation 1.

Figure 6: Departure radius (a) $\hat{R}_{I}$, (c) $\hat{R}_{II}$ and electric
current (b) $\overline{I}_{I}$, (d) $\overline{I}_{II}$ for Modes I and II,
respectively. $\hat{R}_{I}$ is given as a function of $H$. $\hat{R}_{II}$,
$\overline{I}_{I}$ and $\overline{I}_{II}$ 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 $H=117$ $\mu$m and $H=270$ $\mu$m, respectively. The velocity is measured
in a period of 25 ms before the bubble departure.

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 $\overline{I}_{I}$ for larger $H$ primarily due to the relatively small
range in $H$ and, consequently, in $\hat{R}_{I}$, which is minor compared to
variations observed in $\hat{R}_{s}$ at different potentials. At low
overpotentials, $\hat{R}_{I}\approx\hat{R}_{s}$ for the larger electrode
separations studied and there is no increase of the current compared to
$I_{s}$, just as was observed at $H=117\>\mu$m 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, $\hat{R}_{II}$ is
approximately the same as for the single electrode case at the same potential
(see grey symbols representing $\hat{R}_{s}$). An investigation of the force
balance 67, 68, 69 leading to these trends in $\hat{R}_{II}$ 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.63,
51 Based 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 $H=270\>\mu$m (figure 6f) compared to the narrower spacing of
$H=117\>\mu$m in figure 6e, which is in line with the difference in current
between the two cases ($\overline{I}_{II}=5.33$ mA vs. 8.46 mA, respectively).
Interestingly, this does not result in a noticeable difference in
$\hat{R}_{II}$ for the different interelectrode distances, which is presumably
due to differences in the geometry dependent electric force.69 We 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
$\overline{I}_{s}$, equalling the largest currents observed in mode I.

Figure 7: The electric current (a) $\overline{I}_{I}$, (b) $\overline{I}_{II}$
and (c) $\overline{I}_{d}$, all in dimensionless form with reference to
$\overline{I}_{s}$. Data are presented as a function of potential ($\phi$) and
interelectrode distance (H). The inset in (b) shows
$\overline{I}_{II}/\overline{I}_{s}$ vs. $H$ at -1.8, -2.3 and -2.8 V. The
inset in (c) documents $\overline{I}_{I}/\overline{I}_{II}$ vs. $\phi$.
$\overline{I}_{d}$ is the current averaged over both mode I ($I_{I}$) and mode
II ($I_{II}$). (d) Snapshots throughout the bubble evolution at -2.8 V and
$H=270$ $\mu$m. $t_{0}=0$ 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.

To quantify the performance gain and to compensate for the $\phi$ dependence
of the current, we normalise the current on the dual electrode by
$\overline{I}_{s}$. This also accounts for small differences in
$\overline{I}_{s}$ between the different electrodes used in this study (see
Supporting Information). In figure 7a, the ratio
$\overline{I}_{I}/\overline{I}_{s}$ is plotted for different $H$ as a function
of $\phi$. As the figure shows, the interference effects at low overpotentials
already discussed in the context of figure 3, cause $\overline{I}_{I}$ to even
fall below $\overline{I}_{s}$ for $\phi\gtrapprox-0.5$ 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 $\overline{I}_{I}/\overline{I}_{s}>1$ which also
consistently increases with increased overpotential exceeding a value of 2 at
$\phi=-2.8$ V. Approximately the same values are also encountered for this
potential for the ratio $\overline{I}_{II}/\overline{I}_{s}$ 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 $\overline{I}_{II}/\overline{I}_{s}$ increases approximately
linearly with $H$ at constant potential.

Finally, figure 7c shows how the resulting effective current on the dual
electrode $\overline{I}_{d}$ changes relative to $\overline{I}_{s}$. In
addition to variations in $I_{I}$ and $I_{II}$, this quantity is also
influenced by the probability $P(H,\phi)$ of bubble return (mode II). Given
the results in figure 5a, the ratio $\overline{I}_{d}/\overline{I}_{s}$ 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 $|\phi|$ 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 $H=242\>\mu$m and $H=270\>\mu$m (see inset of figure 7c). For these
cases, the mode transition is therefore even beneficial.

Figure 7d shows snapshots for the parameter combination $H=270\>\mu$m and
$\phi=-2.8$ V for which the highest ratio
$\overline{I}_{d}/\overline{I}_{s}=2.4$ 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.70, 31

###  4.4 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.

##  5 Conflicts of interest

There are no conflicts to declare.

##  6 Acknowledgements

This research received funding from the Dutch Research Council (NWO) with a
co-funding acquired from Nobian and Helmholtz-Zentrum Dresden-Rossendorf
(HZDR) in the framework of ElectroChemical Conversion and Materials (ECCM)
KICkstart DE-NL (KICH1.ED04.20.009). S.P. acknowledges the support by Basic
Science Research Program through the National Research Foundation of Korea
(NRF) funded by the Ministry of Education (2021R1A6A3A14039678). D.K., D.L.
and M.T.M.K. received funding from the European Research Council (ERC) (BU-
PACT grant agreement number 950111, ERC Advanced grant number 740479-DDD and
ERC Advanced Grant ‘FRUMKIN’ number 101019998, respectively). We thank V.
Sanjay for insightful discussions on the subject.

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