Bubble-Scale Simulations of Coarsening Wet Foams

Abstract

Liquid foams are composed of gas bubbles packed inside a liquid. They have applications in industry, such as ore separation and fire suppression, but are subject to several instabilities. These include coarsening, whereby gas diffuses from small to large bubbles, causing small bubbles to shrink and eventually vanish, while the average bubble size increases. Hence, the number of bubbles decreases, and the foam degrades. In wet foams, with moderately-large liquid content, there are few tested predictions of the foam's evolution with coarsening, nor of individual bubble growth rates, primarily due to difficulty in suppressing liquid drainage during experiments.

In this thesis, we develop bubble-scale simulations of wet foams in two and three dimensions to study bubble properties related to coarsening, including gas pressure and the size of contact films, along with bubble growth rates. In two dimensions, the foams contain 256 or 1024 bubbles, and they contain 64 bubbles in three dimensions. Our simulations allow finite contact angles between films and bulk-liquid interfaces, and thus model adhesion between bubbles. We study contact angles up to 10°, in addition to foams without adhesion. We also incorporate approximations for gas transfer through contact films and bulk liquid, and we investigate the relative contributions of these mechanisms to bubble growth rates in two dimensions. In three dimensions, we develop an approximate expression for bubble pressures in terms of properties measurable in experiments.

We also derive simple approximations for coarsening-related bubble properties such as pressure, film size, and growth rate in two and three dimensions, expressed in terms of bubble size only, which we find are typically in good agreement with averaged simulation data. These approximations may be useful as ingredients of large-scale coarsening models, in which detail is sacrificed to allow the study of foams with large numbers of bubbles, and thus over long times. We perform preliminary work of this type by deriving the late-time bubble-size distribution predicted by the mean-field growth rate approximation we propose, and we compare the result with recent coarsening experiments on the International Space Station.

Date of Award	2025
Original language	English
Awarding Institution	Aberystwyth University
Supervisor	Simon Cox (Supervisor) & Tudur Davies (Supervisor)