Discrete modelling of two-dimensional liquid foams

Abstract

Liquid foam is a dense random packing of gas or liquid bubbles in a small amount of immiscible liquid containing surfactants. The liquid within the Plateau borders, although small in volume, causes considerable difficulties to the investigation of the spatial structure and physical properties of foams, and the situation becomes even more complicated as the fluid flows. To solve these problems, a discrete model of two-dimensional liquid foams on the bubble scale is proposed in this work. The bubble surface is represented with finite number of nodes, and the liquid within Plateau borders is discretized into lattice particles. The gas in bubbles is treated as ideal gas at constant temperatures. This model is tested by choosing an arbitrary shape bubble as the initial condition. This then automatically evolves into a circular shape, which indicates that the surface energy minimum routine is obeyed without calling external controlling conditions. Without inserting liquid particle among the bubble channels, periodic ordered and disordered dry foams are both simulated, and the fine foam structures are developed. Wet foams are also simulated by inserting fluid among bubble channels. The calculated coordination number, as a function of liquid fractions, agrees well with the standard values.