To jump or not to jump: Adhesion and viscous dissipation dictate the detachment of coalescing wall-attached bubbles

TL;DR

This work addresses how wall-attached bubbles detach after coalescence, a process relevant to improving gas-evolving electrochemical systems. It combines transparent-electrode experiments with volume-of-fluid DNS to quantify how released surface energy, adhesion energy, and viscous dissipation determine jumping versus sticking, uncovering a robust detachment criterion $\alpha_1 W^*_{a,\mathrm{tot}} + \alpha_2 W^*_{\mu} = 1$ that holds across a wide parameter range. A key finding is that, in low effective Ohnesorge conditions, detachment occurs when $W^*_{a,\mathrm{tot}} \approx 0.15$, while dissipation-dominated regimes align with $W^*_{\mu} \approx 0.00233$, with an effective Ohnesorge number $W^*_{\mu} = (\mu_{gas}/\mu) \; Oh \; f(x)$ that accounts for asymmetry. The results offer a predictive framework for tailoring surface properties to promote bubble removal in electrochemical devices, potentially boosting efficiency in processes like water electrolysis, by guiding electrode-texture and wettability design.

Abstract

Bubble coalescence can promote bubble departure at much smaller sizes compared to buoyancy. This can critically enhance the efficiency of gas-evolving electrochemical processes, such as water electrolysis. In this study, we integrate high-speed imaging experiments and direct numerical simulations to dissect how and under which conditions bubble coalescence on surfaces leads to detachment. Our transparent electrode experiments provide new insights into contact line dynamics, demonstrating that the bubble neck generally does not contact the surface during coalescence. We reveal that whether coalescence leads to bubble departure or not is determined by the balance between surface energy, adhesion forces, and viscous dissipation. For the previously unexplored regime at low effective Ohnesorge number, a measure of viscosity that incorporates the effect of asymmetry between the coalescing bubbles, we identify a critical dimensionless adhesion energy threshold of $\approx$15% of the released surface energy, below which bubbles typically detach. We develop a global energy balance model that successfully predicts coalescence outcomes across diverse experimental conditions.

Figures (9)

• Figure 1: (a) Schematic of the shadowgraphy setup for observing the coalescence of wall-attached bubbles. (b) Typical experimental image of coalescing bubbles, used to determine $R_{cont}$ and $R_e$ (indicated by half-circles). (c) Reconstructed bubble shape based on the Young-Laplace equation and the measured values of $R_{cont}$ and $R_e$.
• Figure 2: Shape and contact line evolution of two coalescing bubbles on a surface comparing experiment and simulations. Each pair shows: (left) experimental bottom view (grayscale) overlaid with numerical simulation contour (orange), and (right) 3D rendering from numerical simulation. In the experiments: $R_l \approx 323µm, R_s \approx 321µm$, $R_{\text{cont},l} = 59µm$ and $R_{\text{cont},s} = 72µm$. In the simulations: $R = 322µm$ and $R_{\text{cont}} = 59µm$. $Oh = 0.0066$, $Bo = 0.016$, and $W^*_{a,\text{tot}} \approx 0.07$. See the full movie in Suppl. Mat.
• Figure 3: Coalescence outcomes for similarly sized bubbles ($x < 1.2$ and $\mathrm{R_{cont,l}/R_{cont,s} < 1.2}$) in the experiments (red), and identical ones the simulations (orange) across the Bond number $Bo$ vs. dimensionless adhesion energy $W^*_{a, \text{tot}}$ phase space. Open and filled markers denote jumping and sticking cases, respectively. Gray shading marks the jumping-sticking transition region.
• Figure 4: Sticking (filled) and jumping (open markers) as a function of the dimensionless adhesion energies of the larger ($W_{a,l}^*$) and smaller ($W_{a,s}^*$) bubbles. The diagonal line represents $W_{a,l}^* = W_{a,s}^*$, dashed lines are isocontours of the total dimensionless adhesion energy $W_{a,\text{tot}}^*$.
• Figure 5: Generalized detachment prediction model for coalescing wall-attached bubbles. Data from two different experimental setups are included: small bubbles (up to $\approx$150 ${\mu}m$) with pinned contact line (upper left part, taken from Ref. lv2021self) and larger bubbles (up to $\approx$1250 ${\mu}m$) with spreading contact line (lower right part, our experiments). Simulation results correspond to those in Fig. \ref{['fig:2_Bo_Wa']}. The black curve depicts the best fit threshold curve base on Eq. \ref{['eq:energy_bal_nonDim_star']}. The asymptote values, $W_{a,\text{tot}}^* \approx 0.150$ and $W_{\mu}^* \approx 0.00233$ are shown as vertical and horizontal dashed lines, respectively. See section S4 of supplMaterial for the details of parameters investigated in the plot.