Numerical Study on Statistical Behaviors of Two-Dimensional Dry Foam (Communications in Computational Physics, 2018)
We investigate the statistical behaviors of two-dimensional dry foam using numerical simulations based on the immersed boundary (IB) method. We model the liquid phase of a foam as a thin elastic boundary with surface tension and the gas phase as a viscous incompressible fluid which can go through the liquid boundary. We present evidence of the existence of a limiting scaling state of the dry foam dynamics in which the asymptotic value of µ2, the second moment of the distribution of the numbers of cell sides, lies in the range of 1.3±0.3. We also numerically verify some well-known formulas derived in the dynamics of two-dimensional dry foam such as von Neumann relation, Lewis law, and Aboav-Weaire law. Our simulation results are comparable to those of soap froth experiments and Potts model simulations. Furthermore, we investigate the statistical behaviors of two-dimensional dry foam in an oscillatory shear flow to show the applicability of our method to more general flow conditions.
Keywords: Foam dynamics; immersed boundary method; scaling state; von Neumann relation; Lewis law; Aboav-Weaire law.