Expansion of a two-dimensional foam

Abstract

Numerical simulations are presented to illustrate the transient and asymptotic structure of a foam generated by the expansion of an ordered doubly periodic array of inviscid gas bubbles with uniform interfacial tension arranged on a square or hexagonal lattice, subject to a constant rate of expansion. The flow of the liquid between the bubbles is computed by solving the equations of Stokes flow using a boundary-integral method that employs the doubly periodic Green's function. It is found that the radius of curvature of the developing Plateau borders and the amount of liquid distributed inside them strongly depend on the nominal capillary, defined as the instantaneous capillary number evaluated at the time when non-deforming circular bubbles arranged on a square or hexagonal lattice touch during the expansion. The thickness of the thin films developing between adjacent bubbles is found to decrease at an algebraic rate in time, and film rupture in the absence of destabilizing intermolecular forces occurs after an infinite evolution time.