Cross-border gas diffusion in aqueous foams

A liquid foam consists of gas bubbles immersed in a continuous liquid, with applications ranging from fire-fighting, carbon capture and soil remediation to precursors for foodstuffs such as meringues and bread. Our aim is to predict how foams decay in time due to inter-bubble gas diffusion, to improve predictions of foam lifetime and hence their usefulness in applications. The rate at which gas diffuses between bubbles depends on the foam's liquid content. Predicting the rate of gas transfer between bubbles in a wet foam is complicated by the local geometric structure. The liquid in the foam is found in thin films, in a network of Plateau borders, the small regions of liquid where three or more bubbles meet, and in nodes where four or more Plateau borders meet. The concentration of dissolved gas in the liquid satisfies Laplace's equation. On the interface of a bubble the boundary condition is given by Henry's law. This project will develop accurate solutions of Laplace's equation in these complex geometries to improve analytic and numerical approximations to the gas flow through Plateau borders and nodes. These approximations will be used to generate improved mathematical models for foam coarsening, validated against experiments on the International Space Station, which predict how bubbles grow or shrink depending on their local environment, and hence predict the stability of the foam as a whole.