Electrolyte droplet spraying in H_2 bubbles during water electrolysis under normal and microgravity conditions

Domain: earth_science
Published: 2025-05-16
Editorial outcome: minor_revision

Abstract
Electrolytically generated gas bubbles can significantly hamper the overall electrolysis efficiency. Therefore it is crucial to understand their dynamics in order to optimise water electrolyzer systems. Herein, we elucidate a distinct transport mechanism whereby electrolyte droplets are sprayed into H2 bubbles. These droplets arise from the fragmentation of the Worthington jet, which is engendered by the coalescence with microbubbles. The robustness of this phenomenon is corroborated under both normal and microgravity conditions. Reminiscent of bursting bubbles on a liquid-gas interface, electrolyte spraying results in a flow inside the bubble. This flow couples, in an intriguing way, with the thermocapillary convection at the bubble’s surface, clearly underlining the high interfacial mobility. In the case of electrode-attached bubbles, the sprayed droplets form electrolyte puddles affecting the dynamics near the three-phase contact line and favoring bubble detachment from the electrode. The results of this work unravel important insights into the physico-chemical aspects of electrolytic gas bubbles, integral for optimizing gas-evolving electrochemical systems.

Introduction
The growth of gas bubbles abounds in nature and has various engineering applications and is reflected in natural phenomena. Some of them, featuring rapid dynamics, are sonochemistry and sonoluminescence, cavitation, the evolution of CO2 bubbles in sparkling drinks, and the bursting bubbles at the oceans surface. The latter contributes significantly to atmospheric aerosol generation via two different mechanisms: the disintegration of a thin liquid film between the bubble and gas interface at the onset of bursting, and by an inertia-driven liquid jet–referred to as Worthington jet fragmenting into multiple droplets, where the mechanism is either end-pinching or Rayleigh–Plateau instability. Beyond aerosol generation, these jets are responsible for contaminant dispersion. Additionally, they result in surface erosion and deformation through the impact of droplets on solid and liquid surfaces, respectively. A related problem also occurs in electrolysis, where the coalescence of hydrogen or oxygen bubbles can be approximated to bursting events at a liquid-gas interface. This is a particularly interesting problem of high practical relevance due to the prominent role of hydrogen produced via water electrolysis as an energy carrier, fuel, and feedstock for chemical and steel industries. Alkaline water electrolysis is still the most mature technology, albeit suffering from inadequate efficiency when operated at high current densities. A considerable part of the losses can be attributed to the formation of H2 and O2 bubbles, present at the electrodes and in the bulk. These bubbles mask the active area of the electrodes, reduce the number of nucleation sites, and raise ohmic cell resistance. Thus, enhanced removal of gas bubbles, inherently requiring a better understanding of their growth and departure, will promote continuous catalytic activity and benefit further optimization of the system’s energy efficiency.

The dynamics of electrolytic bubbles have been extensively studied in the last few decades to uncover the growth laws controlled by either the diffusion of dissolved hydrogen or direct injection of the gas at the bubble foot; mass transfer and associated limitations; interactions between neighboring bubbles; the impact of the electrolyte composition, also in the presence of surfactants; the force balance governing the bubble departure and finally the impact of bubbles on the cell overpotentials. Only recently, the soluto- and thermocapillary Marangoni force and an electric force caused by charge adsorption, which had not been considered before, have been uncovered and quantified. Furthermore, it has been discovered that H2 bubbles on microelectrodes do not necessarily adhere to the surface. Instead, they might reside atop a “carpet” of microbubbles and grow via intensive coalescence with this bed of tiny precursors. However, the full implications of such rapid coalescence events in water electrolysis remain elusive – an area ripe for further inquiry. Several lingering questions are yet to be addressed: What are the main features of the coalescence in the confined geometry, set by H2 bubble, carpet and electrode, and how do they interact with the Marangoni flow at the bubble surface? Under what conditions does electrolytic bubble coalescence lead to droplet and spray formation? Does this affect the contact line and potentially the detachment of the electrode-attached bubble?

In the present work, we address these open questions by combining experiments on the coalescence-driven dynamics of H2 bubbles, focusing on the interior of the bubbles under both terrestrial and microgravity environments, alongside tailored direct numerical simulations.

Results
Electrolyte spraying
The main phenomenon under study, spray formation inside a H2 bubble during water electrolysis, is presented in Fig. 1. This observation was made under microgravity conditions provided by parabolic flights of an Airbus A310. The snapshot at t=0 shown in Fig. 1a documents the time instant when the bubble sits at the electrode surface, blocking most of its active area, hindering the reaction and hydrogen production rates. Figure 1b, c zooms into the central and lower segments of the bubble, respectively, at various time points leading up to its departure. Soonafter t=0, the bubble begins a lateral shift to the right driven by residual gravitational forces releasing the electrode and enabling the formation of a dense carpet of microbubbles. As a result, the primary bubble continuously coalescences with these microbubbles emerging on a timescale of O(μs). The successive images document an emerging flow consisting of electrolyte droplets, which is initiated soon after the onset of coalescence events and ascends from the base of the bubble toward its apex. These droplets become noticeable at t=0.16 s, with their population density peaking at t=1.08 s and declining by t=2.92 s. The gradual widening of the gap between electrode and bubble interface over time has two different effects: (i) It enhances the electrochemical reaction (by increasing the electric current, see Supplementary Fig. 1), thereby elevating H2 production and bubble–carpet coalescence rates, and (ii) it leads to the generation of larger pre-coalescence bubbles, in turn decreasing the frequency of the coalescence events and, subsequently, droplet injections into the main bubble. The competition between these two effects establishes an optimal carpet thickness at which the coalescence rate has its maximum. Beyond this distance, the droplet population significantly reduces, as evidenced at t=2.92 s. The droplet radii remain approximately constant at 1.8 ± 0.8 μm during most of the coalescence phase, increasing to about 3.1 ± 1.3 μm only just before bubble departure, when the gap between bubble interface and the electrode is at its maximum.

Impact of Marangoni convection on internal flow structure
In the following, we demonstrate how the phenomenon manifests itself under normal gravity conditions. Figure 2 illustrates (a) the electric current I at −3 and −7 V, and shadowgraphs along bubble evolution at −3 V in 0.1 mol L−1 H2SO4. In detail, a single primary bubble forms via coalescence shortly after nucleation at t/T=0 from many nano- and micrometer bubbles. It continues to grow through rapid O(μs) coalescence with the carpet of microbubbles beneath. The evolution ends with the bubble departure at t/T=1 when buoyancy overcomes downward forces. T is the bubble lifetime. I(t) reflects variations in ohmic resistance due to bubble size and position relative to the electrode, peaking between the departure and nucleation of the next bubble.

In analogy to Fig. 1, numerous electrolyte droplets are injected during the coalescence events, as seen in the last image of Fig. 2a, which focuses on the central segment of the bubble at t/T=0.8. The snapshots in (b, c) highlight the streaklines of the droplets over Δt=25 ms, emerging at the bubble-carpet interface and moving towards the bubble apex with the velocities plotted in (d, e).

The flow in Fig. 2b–e develops continuously throughout the bubble evolution, along with and in response to the growing carpet thickness and hence elevated current, reaching velocities of up to 14 mm s−1 at t/T=1.0. High-speed recordings at 600 and 720 kHz (Supplementary Note 3 and Supplementary Fig. 4) reveal that some droplets are injected at velocities up to 15.8 m s−1, i.e. three orders of magnitude higher. These rare events, resulting in larger droplets, occur around the bubble’s departure when the carpet thickness is at its maximum, approximately between δ=16 μm and δ=43 μm (see Fig. 2a), but are not observed during the earlier stages of the bubble’s evolution when δ < 16 μm.

At a substantially larger electric current (see Fig. 2a), the flow is altered by the presence of a vortical structure, see a transition from a fireworks-like shape (b, d) at −3 V to a vortex-like shape at −7 V (c, e). Meanwhile, the flow at the base of the injection remains similar. At lower potential, the flow expands away from the injection source, while at higher potential, the droplets are carried away from the injection area and ascend along the bubble-electrolyte interface. In the latter, some droplets enclosing the vortex are carried back toward the electrode. In both cases, the velocity gradually decays with distance. Indeed, the velocity of injected droplets is expected to decay exponentially over time due to viscous drag: vd(t)=vd,0 exp(−t/τd), where τd = ρd Rd2 / 18μH2 and the initial velocity of the rising bubbles. This demonstrates that Marangoni convection at the electrolyte-gas interface drives internal flow in electrogenerated gas bubbles, directing and accelerating injected microdroplets. This also indicates that the gas-electrolyte interface is mobile, though the mechanism behind preferential ion adsorption and its effects remain unclear.

Electrolyte puddles at the bubble-electrode interface
Another intriguing outcome of the spraying, shown in Fig. 3, is the formation of electrolyte fractions within an electrode-attached and growing H2 bubble, specifically at the contact area with the electrode surface. Figure 3a, b, d documents the views from below a transparent planar electrode (20 nm of Pt). The snapshots in Fig. 3b zoom in on the contact patch (area marked by the red rectangle in Fig. 3a), which is seen to feature sessile electrolyte droplets inside the gas phase, that expand throughout the bubble evolution. The bubble grows mainly due to diffusion of the dissolved gas but also via coalescence with the neighboring bubbles. Here, the smaller bubbles nucleate below the equator of the primary bubble and quickly detach, see a plume of out-of-focus small bubbles in Fig. 3a, likely due to the altered morphology/wettability of a tiny cavity they nucleated at. Consequently, upon reaching the gas-liquid interface of the larger bubble, coalescence occurs between the two, see schematic in Fig. 3c.

Figure 3d details the injection of at least two microdroplets, marked by red and blue arrows, following the coalescence event between the primary and smaller bubble (black arrow at t=0). The first droplet (red arrow) moves with a much faster velocity, likely shooting through the gas-electrolyte interface on the opposite side. In contrast, the second droplet, about r=4 μm (blue arrow), slows down quickly due to Stokes’s drag (Supplementary Note 4 and Supplementary Fig. 5) and falls, presumably at terminal velocity, to the contact patch at t=86.67 ms, merging with another droplet. In detail, it moves with an average velocity of about vd=0.26 m s−1 within the first 1.33 ms and about vd=6 mm s−1 between 1.33 ms and 86.67 ms, assuming the traveled distance S equals the bubble radius Rb=509 μm. The latter correlates well with the terminal velocity of the droplet vt=4.1 mm s−1 in the Stokes regime (Supplementary Note 4). The process repeats during numerous coalescence events, resulting in the gradual formation of electrolyte puddles, as shown in Fig. 3b. These puddles grow in size throughout the bubble evolution, as more electrolyte droplets are injected, wetting larger areas of the electrode. Once any of the puddles reaches the gas-electrolyte interface, it rapidly merges with the electrolyte bulk, thereby moving the contact line and effectively reducing the bubble-electrode contact area (see frames at 47.783 s and 64.650 s).

This process thus plays a key role for the bubble detachment. The detachment size of an electrode-attached bubble is primarily governed by the surface tension force Fs, which depends on the length of the contact line (Lc). Comparing the snapshots at 47.783 s and 64.650 s, the length of the contact line can either increase or decrease after the puddle merges into the electrolyte bulk. A sudden reduction in Lc, provided there is sufficient buoyancy, causes an earlier detachment from the electrode surface, as illustrated in the snapshot at 64.667 s.

Worthington jet: electrolyte injection
Figure 4a shows a sequence of shadowgraphs detailing the mechanism of droplet injection characterized by the formation of an internal jet that entrains a volume of electrolyte, known in the fluid mechanics and physical oceanography communities as the Worthington jet. The process is demonstrated by two coalescing H2 bubbles with sizes Rb=400 μm and Rs=205 μm, respectively. The results are corroborated by direct numerical simulations (DNS) shown in Fig. 4b. In detail, when a smaller bubble touches a larger one, the liquid film that separates the bubbles gradually drains, forming a neck connecting the two (t=33.3 μs). Growth of this neck follows a Taylor–Culick-type mechanism exciting capillary waves that propagate along the bubble interface, see t=66.7 μs–183.3 μs. Viscous forces damp the motion of these capillary waves, except for the strongest ones, which have the highest curvature. These waves concentrate at the bottom and induce a region of high curvature, see t=191.7 μs–208.3 μs. This inertial flow focusing creates an upward jet (t=216.7 μs–241.7 μs) propagating inside of the merging H2 bubbles. Consequently, this process is controlled by the dimensionless viscosity of the electrolyte given by the Ohnesorge number (Oh) Oh = μel / sqrt(ρel γ Rs), where μ represents the dynamic viscosity, ρ the density of the electrolyte, γ the surface tension, and Rs the initial radius of the smaller bubble. Eventually, the jet breaks into two droplets due to the end-pinching mechanism, for Oh < Oh*. Here, Oh* ≈ 0.035 is the critical Ohnesorge number for the transition from drop ejection to no-drop ejection for bursting of a jet at a free liquid-gas interface. The jet fragmentation results from the competition between the pressure-driven flow from the cylindrical jet toward the tip of the jet, and the capillary retraction of the jet tip. As a result of the latter, the tip is converted into a bulbous end, followed by a localized necking near the bulbous end, creating a blob. This blob at the jet tip detaches to form one droplet at a time. This pinching-off mechanism is consistent with the framework established previously for filament breakup. Beyond the critical Ohnesorge number, viscous dissipation starts to dominate, ceasing the end-pinching of drops. We stress that in this regime, the jet could still break-up following the Rayleigh–Plateau mechanism. On further increasing the Ohnesorge number (Oh > 0.1), the Worthington jet does not form, and there are no droplets.

The DNS results in Fig. 4b accurately reproduce key features and timescales of the phenomenon, such as neck formation, capillary wave propagation, formation, and breakup of the jet. In the experiments, the first droplet with a radius of rd=13 μm is observed at t=250.0 μs and ejects with a velocity of approximately vd=7.2 m s−1. In close qualitative and quantitative agreement, the simulation demonstrates the first droplet (radius rd=15 μm) pinching off at t=260 μs with vd=4.3 m s−1. Minor quantitative discrepancies arise from several factors. Experimental estimates of droplet size and velocity may be compromised due to the bubble curvature, which could be analytically corrected for aspherical shape. However, the significant deformations during the coalescence process complicate precise measurements. We stress that the breakup process is a finite-time singularity—so whether or not the jet breaks into droplets can be precisely reproduced in the simulations—however, the time to breakup and the velocity of the ejected drop are sensitive to the discrete nature of simulation method, experimental noise, and the measurement technique. Additionally, the jet velocity, which determines the droplet post-ejection velocity, varies over time; small variations in sampling time can thus explain discrepancies. Factors such as an inaccurate gas-liquid viscosity ratio and the sensitivity of velocity to the Ohnesorge number and size ratio also contribute to the differences between experimental and simulation results. Given these error sources, the observed discrepancies are reasonable.

It is important to note that the injection demonstrated at Oh=0.008 in Fig. 4 represents a relatively isolated but conventional case, with the smaller bubble being located far from the electrode. In contrast, the bursting events in Figs. 1 and 2 taking place in a highly confined configuration near the Pt electrode feature high coalescence rates and involves smaller bubbles (up to about Rs=δ/2=8 μm). Despite the higher Ohnesorge number (Oh=0.042), injections still occur, exceeding the critical Oh* found for an unconfined isolated bubble. This observation suggests that a nearby wall and high coalescence rates can significantly influence the injection mechanism. In agreement with this, Lee et al. (2011) identified a higher critical value Oh*=0.052, specifically for smaller bubbles (with Bond number Bo= ρel g Rs2 / γ < 10−3) bursting near a solid boundary. Lee et al. (2011) also studied a bubble with a relatively small Rs=26.5 μm adjacent to a Pt substrate using ultrafast X-ray imaging, finding daughter aerosol droplets (2 μm to 4 μm radii) with velocities around 0.3 m s−1. Consequently, we can classify the bursting events in order of increasing droplet speed: (i) carpet bubbles (Rs=8 μm) bursting near a solid wall with a velocity of vd ~ 10−2 m s−1, (ii) a bubble with Rs=26.5 μm bursting near the solid wall, resulting in a droplet velocity of vd ~ 10−1 m s−1, and (iii) the bubble with Rs=205 μm bursting away from the wall (as detailed in Fig. 4), which results in a droplet velocity in the range of vd ~ 100 m s−1 to 101 m s−1. Further deceleration likely comes from viscous drag within the surrounding H2 gas, as described by the Oseen approximation to the Stokes flow. Finally, a high coalescence rate, as seen in Figs. 1 and 2, could disrupt the symmetry of coalescence, affecting the propagation of capillary waves in each event and potentially significantly reducing the velocity of the ejected droplets to vd ~ 10−2 m s−1. Therefore, the small initial size of the bursting bubble (i.e., large Oh), proximity to a wall, higher viscosity of the gas bubbles, and potentially high coalescence rates can substantially reduce the injection velocity.

Methods
The hydrogen gas bubbles were produced using both micro- and planar electrodes during water electrolysis. Part of the results (see Fig. 1) were obtained in a microgravity environment achieved during the 34th DLR Parabolic Flight Campaign in September 2019 (see Bashkatov et al.).

Materials
All chemicals were used without further purification process. The electrolytes were prepared from 1 mol L−1 H2SO4 (Carl Roth GmbH & Co) and 1 mol L−1 HClO4 (Carl Roth GmbH & Co), and Milli-Q water (≥18.2 MΩ cm).

Microelectrode system
Single hydrogen gas bubbles growing on the carpet of microbubbles were produced using a three-electrode electrochemical cell filled with sulfuric acid of either 0.1 mol L−1 or 0.5 mol L−1 concentration, see Fig. 5a. The cell used here closely resembles that used in earlier studies. It comprises a cathode (Pt microelectrode, 99.99%, ⌀100 μm, ALS Co., Ltd) inserted horizontally facing upward in the base of a transparent cuboid glass cuvette (Hellma) with dimensions of 10×10×40 mm3, anode (⌀0.5 mm Pt wire, 99.99%, ALS Co., Ltd) and the Ag/AgCl reference electrode (BASi, Inc.) both inserted from the top. The experiments in a microgravity environment were done using a pseudo-reference electrode (identical to the anode). The electrochemical cell was fixed inside an outer housing featuring two optically accessible observation windows. Before the measurements, the microelectrode surface underwent mechanical polishing with sandpaper (2000 grit), sonication, and rinsing with ultrapure water (≥18.2 MΩ cm). For microgravity experiments, it was polished by diamond (1 μm) and alumina (0.05 μm) suspensions (ALS Co., Ltd) instead. The cell was connected to an electrochemical workstation (CHI660E, Autolabor Biologic VSP-300) and operated at a constant potential of either −3, −4, or −7 V.

The experiments using a blunt needle in Fig. 4 were performed as follows: A larger H2 bubble (≈400 μm radius) was generated up front at the microelectrode and detached upon potential interruption. As it ascended, it adhered to a blunt needle positioned above the microelectrode, with surface tension keeping the bubble attached. A second, smaller bubble (≈205 μm radius) was produced in the same manner, with the smaller size achieved by applying a shorter pulse of potential. As the smaller bubble rose, it contacted the larger bubble, initiating the coalescence process. The time t0 marks the moment just before coalescence begins.

Planar electrode system
The electrode-attached hydrogen gas bubbles were produced at the surface of a ⌀50 mm disc-like planar electrode (cathode) inserted horizontally facing upward in the base of the cylindrical PTFE (polytetrafluoroethylene) compartment with an inner ⌀ of 40 mm and a height of 50 mm filled with 0.1 mol L−1 HClO4. The cathode was fabricated by sputtering a 20 nm thin film of platinum onto a glass slide, with a 3 nm tantalum layer applied for improved adhesion. The thin layer of platinum ensured the transparency of the cathode and allowed visualization from the bottom of the cell. The cell was completed by a platinized titanium mesh (anode) and the Ag/AgCl reference electrode (BASi, Inc.), both inserted from the top. The system was controlled by the electrochemical workstation (Biologic VSP-300) maintaining a constant current density of −50 Am−2. The relatively low current density and smooth surface of the cathode allowed only a limited number of active nucleation sites, making the study of the contact line and electrolyte puddles dynamics possible. For details, we refer to Demirkır et al.

Shadowgraphy system
The visualization of the bubble dynamics is performed using a conventional shadowgraphy system, shown schematically for a microelectrode system in Fig. 5a. It consists of a high-speed camera connected to the microscope and LED illumination. The shadowgraphs in Figs. 1 and 2a were recorded using an IDT camera (NX4-S1 and Os7-S3) with spatial resolutions of 678 and 1391 pixels mm−1, respectively. In Figs. 3 and 4a, a Photron camera (FASTCAM NOVA S16) was used, with spatial resolutions of 530 and 496 pixels mm−1, respectively. To achieve the bottom view (planar electrode system), the optical path of a horizontally installed camera is redirected vertically through the transparent cathode using a 45° mirror mounted below the electrode. The light intensity is adjusted to ensure the contrast of the bubble and the electrolyte droplets.

Particle tracking velocimetry (PTV)
The evolution of H2 bubbles at microelectrodes is featured by the intensive coalescence with the carpet of microbubbles sandwiched between the bubble bottom and electrode (Fig. 5b) on a timescale of μs. Owing to these coalescence events, multiple electrolyte droplets are injected into the bubble. The velocity measurement of these electrolyte droplets is performed using a particle tracking velocimetry (PTV) system, schematically shown in Fig. 5c.

The setup employs a light sheet optical configuration comprising a laser (OBIS 488LX, 150 mW, Coherent Inc.) that was spatially enlarged using a telescope (L1 & L2). To minimize reflection at the bubble surface, a λ/2-waveplate is employed to rotate the polarization. Subsequently, the beam is vertically expanded using a cylindrical lens (L3) before being focused inside the bubble by another lens (L4) with a focal length f=19 mm. For imaging purposes, a microscope objective (PLN 10×, Olympus) is positioned such that the bubble resides within the working distance. Finally, the bubble is imaged onto the camera (EoSens 3CXP, Mikrotron) using a lens (L5) with a focal length f=160 mm. To resolve the contours of the bubble, the system additionally possesses a background LED illumination. A series of images from Fig. 2b, c is collected at 1 kHz, having a spatial resolution of 1140 pixels mm−1. Before velocity calculations, optical distortions (aberration) caused by the curvature of the bubble are analytically corrected (see next subsection). The resulting series of images were processed by the software DaViS 10, which employs a PTV algorithm to track each particle (droplet) over 25 ms at t/T=0.6, 0.8 and 1.0. Due to the limited number of droplets, the resulting tracks were collected over several bubbles. Subsequently, the tracks were converted into a vector field using a binning function that interpolates local tracks on a specified fine grid. Finally, the vector fields are used to plot the streamlines of the averaged drop velocity field shown in Fig. 2.

Analytical aberration correction
Aberrations (optical distortions) caused by light refraction at the curved gas-liquid interface of the bubble lead to a significant systematic measurement deviation. As the bubbles are of sub-millimeter size, the correction using an optical element is challenging. However, for object-space telecentric lenses, like the microscope objective used for the measurements here, the aberrations can be corrected analytically, which has already been done for the flows inside the droplets. In the present study, the entrance pupil of the system is at infinity, resulting in chief rays parallel to the optical axis in the object space. When back-propagating the rays through the optical system, the intersection of the back-propagated ray and the light sheet (positioned in the middle of the bubble), can be calculated with and without the bubble in the system.

Supplementary Fig. 2a documents a schematic of the chief rays passing through the bubble surface. The solid lines mark the real path of the light scattered at the injected electrolyte droplets, whereas the dashed lines indicate the path recorded by the camera. Supplementary Fig. 2b demonstrates a single ray passing through the bubble-electrolyte interface with the relevant geometry used in further calculations of the corrected position for each detected droplet. Since the bubble is assumed to be axisymmetric, the position of the droplet is defined by the radial distance from the bubble center in the plane of the laser sheet. The measured and real (corrected) positions of the injected droplet are therefore defined as rmeas and rcorr. The corrected position for each of the detected droplets can be calculated as rcorr = rmeas + Δr using

Δr = tan(sin−1(n sin(tan−1(sqrt(Rb2 − rmeas2) / rmeas)))) * sqrt(Rb2 − rmeas2) - rmeas

where n is the refractive index of the electrolyte and Rb is the radius of the bubble. The results of the analytical aberration correction and further details can be found in Supplementary Note 2 and Supplementary Fig. 3.

Numerical method
In this work, the direct numerical simulation, using open source language Basilisk C, is employed to simulate the coalescence of two bubbles. A two-fluid model, combined with a Navier Stokes solver, is employed. The interface of the liquid and gas is tracked with the Volume of Fluid (VoF) method. The liquid phase is water with a density and dynamic viscosity of 1000 kg m−3 and 0.00105 Pa s, respectively. The gas phase is air, with a density and dynamic viscosity of 1.41 kg m−3 and 1.86 · 10−5 Pa s. The surface tension on the interface of liquid and gas is 0.072 N m−1. The initial radius of bubble 1 is Rb=400 μm and bubble 2 is Rs=200 μm. Figure 6 demonstrates a sketch of the simulation model. Spatial discretization is performed using a quad-tree method in a 2D axisymmetric calculation domain of 1.5 · 10−3 m × 1.5 · 10−3 m. The adaptative Mesh Refinement algorithm was used to increase the calculation accuracy and reduce the hardware requirement. The maximum refinement level and the minimum level are 9 and 5, respectively. The calculation time step size is set to 1 · 10−8 s. We emphasize that while present simulations assume axisymmetric bubbles as previous simulation work has done, real bursting events may demonstrate slight asymmetry, leading to the deviations in the jet/droplet bursting velocity and droplet radius.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In this article, a distinct transport mechanism whereby electrolyte droplets are sprayed into H2 bubbles is evidenced, both experimentally and numerically. These droplets arise from the fragmentation of the so-called \"Worthington jet\", which is engendered by the coalescence with microbubbles.\nAuthors conclude that H2 bubbles are therefore not only composed of hydrogen gas and water vapor but also include electrolyte fractions given the coalescence with nearby bubbles. Moreover, author evidenced that the microdroplets formed in the bubble through this process play an important role for the bubble detachment, once they merge with the surrounding electrolyte at the contact line.\nUndoubtedly, this study has been properly carried out through high-speed imaging, but also concerning the digital modeling part of the article, thus bringing new insights into the physicochemical aspects of electrolytic gas bubbles.\nI recommend publication of this article in Nat Communications, but I nevertheless highlight a little technical point to correct/clarify in the introduction about the mechanisms responsible for the fragmentation into mulitple droplets of the so-called Worthington jet.\nIndeed, to the best of my knowledge, the breakup of this very small jet is not a consequence of the Rayleigh-Plateau instability. Instead, the breakup takes place only at the jet tip, and detaches one droplet at a time.This mechanisms, rather called \"the end-pinching\" mechanism, is a consequence of a competition between the capillary retraction of the jet tip (shaping a blob) and a pressure driven flow from the cylindrical jet toward the bulbous end (Keller et al, Phys Fluids (1995)).\nThis leads to the development of a neck, clearly seen on the snaphots, where the jet joins the blob, and thus force the drop detachment via a capillary pinch-off process.\nTo the best of my knowledge, this mechanism has first been described in the context of a stronlgy deformed viscous drop (Stone et al, J. Fluid Mech (1989)), and later for a free liquid filament of arbitrary viscosity (Castrejon-Pita et al, Phys Rev Lett (2012)).", "reviewer_2": "The work deals with the study of the formation of bubbles and the role of the electrolyte in the formation of these bubbles. I find the topic exciting and with a significant relevance in our understanding of the electrochemical systems. However, with this detailed data the support and development of computational methodologies to introduce all these aspects seems crucial to me. I understand that this might not be the area of expertise of the authors, but at least a discussion on the data generated or needed to inform the computational models could activate the work in this area."}, "author_response": "Response to the reviewers\nWe are very thankful to the reviewers for their critical reading of the manuscript and helpful\ncomments and suggestions. All the changes incorporated in the manuscript are made in pink.\nBelow, we have addressed the raised questions point-by-point:\nReviewer 1\nInthisarticle,adistincttransportmechanismwherebyelectrolytedropletsaresprayedintoH bub-\n2\nblesisevidenced,bothexperimentallyandnumerically. Thesedropletsarisefromthefragmentation\nof the so-called ”Worthington jet”, which is engendered by the coalescence with microbubbles. Au-\nthors conclude that H bubbles are therefore not only composed of hydrogen gas and water vapor\n2\nbut also include electrolyte fractions given the coalescence with nearby bubbles. Moreover, author\nevidenced that the microdroplets formed in the bubble through this process play an important role\nfor the bubble detachment, once they merge with the surrounding electrolyte at the contact line.\nUndoubtedly, this study has been properly carried out through high-speed imaging, but also con-\ncerning the digital modeling part of the article, thus bringing new insights into the physicochemical\naspectsofelectrolyticgasbubbles. IrecommendpublicationofthisarticleinNatCommunications,\nbut I nevertheless highlight a little technical point to correct/clarify in the introduction about the\nmechanisms responsible for the fragmentation into multiple droplets of the so-called Worthington\njet.\nPoint 1.1 — Indeed, to the best of my knowledge, the breakup of this very small jet is not a\nconsequenceoftheRayleigh-Plateauinstability. Instead,thebreakuptakesplaceonlyatthejettip,\nanddetachesonedropletatatime. Thismechanisms, rathercalled”theend-pinching”mechanism,\nis a consequence of a competition between the capillary retraction of the jet tip (shaping a blob)\nand a pressure driven flow from the cylindrical jet toward the bulbous end (Keller et al. (1995)).\nThis leads to the development of a neck, clearly seen on the snapshots, where the jet joins the blob,\nand thus force the drop detachment via a capillary pinch-off process. To the best of my knowledge,\nthis mechanism has first been described in the context of a strongly deformed viscous drop (Stone\nand Leal (1989)), and later for a free liquid filament of arbitrary viscosity (Castrej´on-Pita et al.\n(2012)).\nReply: We are very grateful to the reviewer for his/her excellent comment which has stimulated us to\nconduct new proof-of-concept simulations. Here we could show that the Worthington jet in our experi-\nment indeed exhibits the end-pinching route, forecasted by the reviewer, rather than a Rayleigh–Plateau\ninstability. The present pinching-off mechanism is consistent with the framework established previously\nfor filament breakup (Stone and Leal, 1989; Keller et al., 1995; Castrej´on-Pita et al., 2012; Anthony\net al., 2019).\nWe have updated the text accordingly and cited the relevant references. We also note that depend-\ning on the viscosity ratio, jet geometry, and the timescale of bubble coalescence, other fragmentation\npathways (e.g., Rayleigh—Plateau-like modes or film rupture mechanisms) could in principle operate in\nrelated setups such as coalescence of bulk bubbles as discussed recently in Jiang et al. (2024). In our\npresent study, however, end-pinching is the dominant route for droplet formation within the confined\nbubble–carpet coalescence environment of the growing H bubble. The main conclusion—that elec-\n2\ntrolyte droplets are driven inside the main H bubble and eventually facilitate its detachment—remains\n2\n1\nrobust regardless of the fragmentation mechanism. We appreciate the reviewer’s suggestion and have\nemphasized that end-pinching is the primary mode in our case.\nWe incorporated the above discussion in the revised manuscript as follows:\nIn Introduction:\n“... where the mechanism is either end-pinching (Stone and Leal (1989); Keller et al. (1995); Cas-\ntrej´on-Pita et al. (2012); Anthony et al. (2019)) or Rayleigh–Plateau instability (Blanco-Rodr´ıguez\nand Gordillo (2020); Dixit et al. (2024)).”\nIn sec: Worthington jet: electrolyte injection:\n“Eventually, the jet breaks into two droplets due to the end-pinching mechanism (Sanjay et al.\n(2021); Walls et al. (2015)), for Oh < Oh∗. Here, Oh∗ ≈ 0.035 is the critical Ohnesorge num-\nber for the transition from drops ejection to no-drops ejection (Sanjay et al. (2021); Walls et al.\n(2015)) for bursting of a jet at a free liquid-gas interface. The jet fragmentation results from the\ncompetition between the pressure-driven flow from the cylindrical jet toward the tip of the jet,\nand the capillary retraction of the jet tip. As a result of the latter, the tip is converted into a\nbulbous end, followed by a localized necking near the bulbous end, creating a blob. This blob at\nthe jet tip detaches to form one droplet at a time. This pinching-off mechanism is consistent with\nthe framework established previously for filament breakup (Stone and Leal, 1989; Keller et al.,\n1995; Castrej´on-Pita et al., 2012; Anthony et al., 2019).Beyond the critical Ohnesorge number,\nviscous dissipation starts to dominate, ceasing the end-pinching of drops. We stress that in this\nregime the jet could still break-up following Rayleigh–Plateau mechanism (Blanco-Rodr´ıguez and\nGordillo (2020); Dixit et al. (2024)). On further increasing the Ohnesorge number (Oh > 0.1), the\nWorthington jet does not form and there are no droplets(Walls et al. (2015); Sanjay et al. (2021)).”\nThe work deals with the study of the formation of bubbles and the role of the electrolyte in\nthe formation of these bubbles. I find the topic exciting and with a significant relevance in our\nunderstanding of the electrochemical systems.\nPoint 2.1 — However, with this detailed data the support and development of computational\nmethodologies to introduce all these aspects seems crucial to me. I understand that this might not\nbe the area of expertise of the authors, but at least a discussion on the data generated or needed\nto inform the computational models could activate the work in this area.\nReply:\nWe thank the reviewer for this comment. The main thrust of our article has been on experimentally\nuncovering the electrolyte-spraying mechanism, and its implications, in connection with the numerical\nsimulations to reveal the underlying mechanism. However, our data indeed serve as a foundation for the\ncomputationalcommunitytoincorporatethesefeaturesintonext-generationmultiphaseelectrochemical\nflow solvers. In the revised manuscript, we highlight which particular datasets—such as droplet veloc-\nity fields, bubble interface topologies, and boundary conditions—are essential for refining multiphase\nelectrochemical flow solvers.\nParticularly, as computing power continues to improve significantly, direct numerical simulation\n(DNS) becomes viable for the research of fluid dynamics. With a well-suited adaptive mesh refinement\nmethod (Popinet, 2003, 2009, 2015; Beetham et al., 2016), the open-source partial differential equation\nsolver Basilisk becomes well suited for resolving the multiphase flow problems such as bubble dynamics\n(Sanjay et al., 2021), bubble-related jetting (Deike et al., 2018; Yang et al., 2023) and droplet break-up\n(Brasz et al., 2018). Here, we use the open-source language Basilisk C to simulate the coalescence of\ntwo bubbles, the induced jet and the resulting droplet. The interface of the liquid and gas is tracked\nusing the Volume of Fluid (VoF) method in the code. The liquid phase is water with a density and\ndynamic viscosity of 1000 kg/m3 and 0.00105 Pa·s, respectively. The gas phase is air, with a density\nand dynamic viscosity of 1.41 kg·m³ and 1.46 · 10−5 Pa·s. The surface tension on the interface of liquid\nand gas is 0.072 N/m. The initial radii of bubble 1 and bubble 2 are 400 µm and 200 µm, respectively.\nFigure 6 demonstrates a sketch of the simulation model. Spatial discretization is performed using a\nquad-tree method in a 2D axisymmetric calculation domain of and 1.5·10−3 m ×1.5·10−3 m.\nThe maximum refinement level and minimum level are set at 9 and 5 respectively based on our convergence\ntests and previous works (Yang et al., 2023). The calculation timestep size is set to 1·10−8 s. The\nnumerical simulations had a good agreement compared with experiments regarding the wave excitation,\npropagating, and jet/droplet formation as shown in Fig. 4. In addition, the present simulations assumed\naxisymmetric distributed bubbles as most previous simulation work has done (Sanjay et al., 2021),\nbut jet/droplet bursting in reality might show slightly asymmetry which may offer a deviation on the\njet/droplet bursting velocity and radius. In the spirit of open-source code development and reproducible\nopen science, we have made the entire code base available on GitHub: https://github.com/wding-\nhzdr/CoBub.\nWe emphasize that capturing coalescence in real electrochemical environments will eventually re-\nquire coupling potential fields, mass transfer of dissolved gas, and surface tension gradients arising\nfrom reactant depletion or thermal effects. Ongoing work seeks to incorporate these electrochemical\nboundary conditions, including local current densities and temperature fields, into multiphase solvers.\nproperties, can serve as validation benchmarks.\nTo address the point raised by the reviewer and to further highlight the origin of the minor quantitative\ndifferences between simulations and experiments, we have incorporated the following revisions into the\nmanuscript:\nIn sec: Worthington jet: electrolyte injection:\n“Minor quantitative discrepancies arise from several factors. Experimental estimates of droplet\nsize and velocity may be compromised due to the bubble curvature, which could be analytically\ncorrectedforasphericalshape. However,thesignificantdeformationsduringthecoalescenceprocess\ncomplicate precise measurements. We stress that the breakup process is a finite-time singularity\n(Zeff et al. (2000)) – so whether or not the jet breaks into droplets can be precisely reproduced\nin the simulations (Dixit et al. (2024)) – however, the time to break up and the velocity of the\nejected drop are sensitive to the discrete nature of simulation method, experimental noise, and\nmeasurement technique (Eggers et al. (2024)). Additionally, the jet velocity, which determines\nthe droplet post-ejection velocity, varies over time (Deike et al. (2018); Sanjay et al. (2021)); small\nvariations in sampling time can thus explain discrepancies. Factors such as an inaccurate gas-liquid\nviscosityratioandthesensitivityofvelocitytotheOhnesorgenumberandsizeratioalsocontribute\nto the differences between experimental and simulation results (Walls et al. (2015)). Given these\nerrorsources,theobserveddiscrepanciesarereasonable. Furtherdetailsonthecomparisonbetween\nthe experiments and simulations are provided in Supplementary Section 5.”\nIn Conclusions:\n“Additionally, our findings will be valuable for validating and tailoring numerical and theoretical\nmodels. In particular the droplet radii, injection speeds and trajectories in various configurations,\nsee the bubble-carpet system in Fig. 1 and 2, the surface-attached bubble system in Fig. 3 and the\nmodel experiment in Fig. 4, can serve as validation benchmarks. ”\nIn Methods: Numerical method\n“The calculation time step size is set to 1·10−8 s. We emphasize that while present simulations\nassume axisymmetric bubbles as previous simulation work has done (Sanjay et al., 2021), real\nbursting events may demonstrate slight asymmetry leading to the deviations in the jet/droplet\nbursting velocity and droplet radius.”\nReferences\nC. R. Anthony, P. M. Kamat, M. T. Harris, and O. A. Basaran. Dynamics of contracting filaments.\nPhys. Rev. Fluids, 4(9):093601, 2019.\nE. Beetham, P. S. Kench, J. O’Callaghan, and S. Popinet. Wave transformation and shoreline\nwater level on f unafuti a toll, t uvalu. Journal of Geophysical Research: Oceans, 121(1):311–326,\n2016.\nF.J.Blanco-Rodr´ıguezandJ.M.Gordillo. Ontheseasprayaerosoloriginatedfrombubblebursting\njets. J. Fluid Mech., 886:R2, 2020. doi: 10.1017/jfm.2019.1061.\nC. F. Brasz, A. Berny, and J. C. Bird. Threshold for discretely self-similar satellite drop formation\nfrom a retracting liquid cone. Physical Review Fluids, 3(10):104002, 2018.\nreview letters, 108(7):074506, 2012.\nL. Deike, E. Ghabache, G. Liger-Belair, A. K. Das, S. Zaleski, S. Popinet, and T. S´eon. Dynamics\nof jets produced by bursting bubbles. Physical Review Fluids, 3(1):013603, 2018.\nA.K.Dixit,A.Oratis,K.Zinelis,D.Lohse,andV.Sanjay. Viscoelasticworthingtonjets\\&droplets\nproduced by bursting bubbles. arXiv preprint arXiv:2408.05089, 2024.\nJ. Eggers, J. E. Sprittles, and J. H. Snoeijer. Coalescence dynamics. Annual Review of Fluid\nMechanics, 57, 2024. doi: 10.1146/annurev-fluid-121021-044919.\nX.Jiang,L.Rotily,E.Villermaux,andX.Wang. Abyssaerosols: Dropproductionfromunderwater\nbubble collisions. Phys. Rev. Lett., 133(2):024001, 2024.\nJ. B. Keller, A. King, and L. Ting. Blob formation. Phys. Fluids, 7(1):226–228, 1995.\nS. Popinet. Gerris: a tree-based adaptive solver for the incompressible euler equations in complex\ngeometries. Journal of computational physics, 190(2):572–600, 2003.\nS. Popinet. An accurate adaptive solver for surface-tension-driven interfacial flows. Journal of\nComputational Physics, 228(16):5838–5866, 2009.\nS. Popinet. A quadtree-adaptive multigrid solver for the serre–green–naghdi equations. Journal of\nComputational Physics, 302:336–358, 2015.\nV. Sanjay, D. Lohse, and M. Jalaal. Bursting bubble in a viscoplastic medium. J. Fluid Mech.,\n922:A2, 2021. doi: 10.1017/jfm.2021.489.\nH. A. Stone and L. G. Leal. The influence of initial deformation on drop breakup in subcritical\ntime-dependent flows at low reynolds numbers. J. Fluid Mech., 206:223–263, 1989.\nP. L. Walls, L. Henaux, and J. C. Bird. Jet drops from bursting bubbles: How gravity and viscosity\ncouple to inhibit droplet production. Physical Review E, 92(2):021002, 2015.\nZ. Yang, B. Ji, J. T. Ault, and J. Feng. Enhanced singular jet formation in oil-coated bubble\nbursting. Nature Physics, 19(6):884–890, 2023.\nB. W. Zeff, B. Kleber, J. Fineberg, and D. P. Lathrop. Singularity dynamics in curvature collapse\nand jet eruption on a fluid surface. Nature, 403(6768):401–404, 2000. doi: 10.1038/35000151.\n5"}, {"round": 2, "reviewer_comments": {"reviewer_1": "My comments were carefully taken into account, I therefore recommend the publication of this paper in its present form", "reviewer_2": "The authors have successfully answered all the questions I raised to the previous version of the manuscript. Therefore, I warmly recommend the work for publication."}, "author_response": ""}]

Decision letter