Viscous Froth Simulations with Surfactant Mass Transfer and Marangoni Effects: Deviations from Plateau's Rules

The viscous froth model is a rheological model for dry, “two-dimensional” foams, such as a monolayer of bubbles confined between two glass plates. The model is typically out of mechanical equilibrium due to viscous dissipation by drag along the confining plates. By introducing variable local surfactant coverages and variable local surface tensions, we modify the model such that, in addition to being out of mechanical equilibrium, foam structures can also be out of physicochemical equilibrium. We include effects accounting for spatially and temporally varying Marangoni forces and surfactant transport, and we investigate the effects on a simple, periodic honeycomb lattice under shear. It is found that surfactant coverage can vary substantially between and within films, with surfactant becoming highly depleted on film edges that are subjected to rapid direct shear. Moreover substantial deviations from Plateau's laws occur at flowing three-fold vertices an effect previously noted in experiments but without any definitive explanation in theory or models. For large enough values of the governing dimensionless groups (capillary, Deborah, and Marangoni numbers), angles may locally vary from 120° by 10° or more. Correspondingly, the change in surface tensions at a three-fold vertex leads to a change in the time required to induce a topological rearrangement (T1) in a sheared foam sample. In this sense, variable surfactant coverage effects help to preserve the structure of a flowing foam, but also lead to an increase in energy storage within the foam.