Viscous instabilities in flowing foams: a Cellular Potts Model approach

Abstract

The Cellular Potts Model (CPM) successfully simulates drainage and shear in foams. Here we use the CPM to investigate instabilities due to the flow of a single large bubble in a dry, monodisperse two-dimensional flowing foam. As in experiments in a Hele-Shaw cell, above a threshold velocity the large bubble moves faster than the mean flow. Our simulations reproduce analytical and experimental predictions for the velocity threshold and the relative velocity of the large bubble, demonstrating the utility of the CPM in foam rheology studies.

Figure 1

Detail of a CPM simulation of a quasi-stationary flowing foam with a large bubble. The shading denotes bubble pressures, with darker shades denoting lower pressures.

Figure 2

(a) Equilibration of the stored surface energy of a simulated flowing foam containing a large bubble with small bubbles nucleating every 50 MCS. (b) Equilibration of bubble velocities in a simulated flowing foam: large bubble—dashed lines, small bubbles—solid lines. The three pairs of curves are for different nucleation sizes of the small bubbles. The lowest curve corresponds to an initial nucleation size of 481 pixels and the higher curves to nucleation sizes of 156 and 25 pixels respectively.

Figure 3

Difference between large-bubble velocity υ_L and average foam velocity, rescaled by rυ_f, versus υ_f for different large-bubble sizes, on a semilog scale. The symbols on the graph correspond to different values of r.