Viscous growth and rebound of a bubble near a rigid surface

TL;DR

This paper theoretically investigates how bubbles grow and rebound near a rigid surface in viscous flow, revealing conditions for bouncing and the influence of slip length on drainage dynamics.

Contribution

It introduces a unified analytical framework for bubble growth near surfaces considering slip length, explaining bouncing behavior and universal drainage scaling.

Findings

Bubbles with finite slip lengths can bounce off surfaces before draining.

Clean bubbles always monotonically repel from the surface.

Final drainage follows a universal algebraic scaling law.

Abstract

Motivated by the dynamics of microbubbles near catalytic surfaces in bubble-powered microrockets, we consider theoretically the growth of a free spherical bubble near a flat no-slip surface in a Stokes flow. The flow at the bubble surface is characterised by a constant slip length allowing to tune the hydrodynamic mobility of its surface and tackle in one formulation both clean and contaminated bubbles as well as rigid shells. Starting with a bubble of infinitesimal size, the fluid flow and hydrodynamic forces on the growing bubble are obtained analytically. We demonstrate that, depending on the value of the bubble slip length relative to the initial distance to the wall, the bubble will either monotonically drain the fluid separating it from the wall, which will exponentially thin, or it will bounce off the surface once before eventually draining the thin film. Clean bubbles are shown to be a singular limit who always monotonically get repelled from the surface. The bouncing events for bubbles with finite slip lengths are further analysed in detail in the lubrication limit. In particular, we identify the origin of the reversal of the hydrodynamic force direction as due to the change in the flow pattern in the film between the bubble and the surface and to the associated lubrication pressure. Finally, the final drainage dynamics of the film is observed to follow a universal algebraic scaling for all finite slip lengths.