Coarsening of two-dimensional disordered wet foams in simulations with accurate bubble geometries #

Jacob Morgan, Simon Cox

11:30 Tuesday in 3E11.

Part of the Liquid crystals and transport models session.

Abstract #

Aqueous foams can be found in applications such as fire suppression, soil treatment, foods, and cleaning products. Differences in bubble pressures cause gas diffusion through their liquid component, primarily via the thin films separating the bubbles. This results in coarsening, one of several foam instabilities, whereby the mean size of the bubbles increases and their total number decreases. Predictions of the bubble growth rates are mainly limited to foams with very small or large liquid volume fractions, partly due to the difficulty, in experiments, of suppressing liquid drainage from foams with intermediate values. Furthermore, the influence of bubble attraction, determined by the surfactant used to stabilise the films, remains unclear.

We present simulation results concerning coarsening in two-dimensional, disordered, wet foams, at intermediate liquid fractions from 2% to beyond 20%, and for various strengths of bubble attraction. We use a quasi-static, finite-element approach for the foam structure, adapted from the work of [Kähärä et al. Phys Rev E. 2014; 90: 032307], which allows the bubble geometry to be accurately captured. Nearby liquid/gas interfaces are repelled by a disjoining pressure, the form of which sets the degree of bubble attraction. We approximate the gas diffusion between bubbles using an approach similar to that of [Schimming et al. Phys Rev E. 2017; 96: 032805], allowing contributions from the liquid Plateau borders adjoining the films, in addition to the films themselves. Our model is implemented using the Surface Evolver [Brakke. Exp Math. 1992; 1: 141-165].

Our simulations indicate that, when films exist between the foam’s bubbles, the effective number of neighbours of a bubble [Fortuna et al. Phys Rev Lett. 2012; 108: 248301] is highly correlated with its growth rate. These films may be due either to compression of the foam, or to bubble attraction. We also find that attractive bubble interactions result in root-mean-square growth rates that are approximately independent of liquid fraction beyond about 17%. Our results may find application in refining the assumptions used in future simulations of large systems, which use simpler bubble-scale models in order to have access to reliable statistics.