Viscous froth model for a bubble staircase structure under rapid applied shear: An analysis of fast flowing foam

Abstract

The viscous froth model is applied to the rapid shear of ‘2-dimensional’, dry foams for bubbles confined in a monolayer and arranged in an ordered staircase configuration that forms part of a hexagonal honeycomb structure. High system energies are attained as particular films in the staircase become highly elongated under shear. Topological transformations during which bubbles exchange neighbours can relax the staircase energy, but their onset is postponed at high shear rates. Moreover as the imposed shear rate increases, the rate at which topological transformations subsequently occur cannot keep pace with the imposed shear, and secular film stretching onsets. A critical capillary number (a dimensionless measure of shear rate) separates a regime where film lengths are periodic functions of imposed strain from a regime of secular growth.