Numerical Study on Statistical Behaviors of Two-Dimensional Dry Foam

Abstract

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 µ 2 , 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.

Experimentally Testing a Generalized Coarsening Model for Individual Bubbles in Quasi-Two-Dimensional Wet Foams

“…These are true for any foam in a "dry limit" where it can be considered that the films contain zero liquid and all the liquid phase can be decorated on the vertices [7]. Bubble coarsening in 2d dry foams has been studied in both experiment [8][9][10][11] and simulation [12][13][14][15][16][17] and general agreement with Eq. 1 is observed.…”