The Invisible Anchor: How a Cascade of Coalescence Holds a Bubble at the Electrode ✛

Original: "Cascade coalescence dynamically sustains bubble retention near gas-evolving surfaces"
arXiv:2609.03387v1 · 2026-09-03 · CC BY 4.0 · 2 min
A large bubble doesn't rise because each merger with a small bubble gives a brief downward jolt, and thousands of such jolts add up to a steady holding force.

A hydrogen bubble on a platinum electrode behaves like a swimmer trying to surface, but every time it almost breaks free, something below grabs its legs. In the lab, high-speed cameras captured this behavior: a millimeter-sized bubble hangs near the surface, even though buoyancy pulls it upward with a force thousands of times stronger than surface tension can hold.

The secret lies in the tiny bubbles continuously born on the electrode. As the large bubble rises, it collides with these little ones and merges with them. After each merger, the combined bubble abruptly flips and moves downward at speeds up to 13 centimeters per second. That's a hundred times faster than its upward motion before the collision.

A single downward jolt lasts less than a millisecond, but there can be up to a hundred thousand such jolts before the bubble grows to a millimeter.

To understand the origin of the jolt, the authors built a computer model of the coalescence. They found that when two bubbles of different sizes merge, the interface contracts unevenly: most of the energy goes into decelerating the liquid near the smaller bubble. This asymmetry creates a viscous impulse directed toward the electrode. The impulse magnitude grows with the size difference between the bubbles.

With repeated mergers, the impulses add up like strikes from many tiny hammers. The total force reaches about one millionth of a newton, comparable to the buoyancy force on a bubble with a radius of half a millimeter. Electrostatic forces and Marangoni effects, previously considered possible candidates, turned out to be an order of magnitude weaker.

The frequency of coalescence is set by the current: the higher the current, the faster microbubbles are born and the more often the large bubble receives downward jolts.

This discovery changes the game for electrolyzers, where bubbles shield electrodes and reduce efficiency. If engineers can control the coalescence frequency, they could make bubbles detach earlier or, conversely, hold them longer. That can be done simply by adjusting the current, surface texture, or electrolyte composition. Thus, an invisible anchor made of thousands of tiny jolts becomes a tool in the hands of engineers.

A millimeter-sized bubble held at the electrode can result from up to one hundred thousand coalescence events with microbubbles, each lasting less than a millisecond.

Controlling bubbles through cascade coalescence resembles science-fiction technologies where microscopic robots collectively hold macroscopic objects, though here the bubbles themselves play the role of the robots.

v_{m,0} = -\frac{3C_j}{2\pi}\frac{\mu}{\rho_l}\frac{R_s^2}{R_l^3}A(\lambda)
The initial velocity is directed toward the electrode and increases with the size asymmetry of the parent bubbles
F_{ret,coal} = J_v f_c \approx \chi \frac{3C_j \mu |I| R_g T_g}{8\pi F P_g R_s} A(\lambda)
The force is proportional to the current and inversely proportional to the microbubble radius
Concepts
energy cascade turbulent coagulation convection cosmic bubble nucleation surface tension bubble collision eddy evaporation fluid dynamics in porous media drag dust dynamics liquid turbulent mixing condensation elastic scattering carbon cycle gas accretion energy conservation cascade fluid flow