Strain and liquid content of sheared, stretching foams: A model for dynamic dilatancy

In drainage experiments for liquid–gas foams, a sufficiently large liquid flow rate results in a downwards convection of bubbles. This ‘wet’, downwards-convecting region of foam can coexist with stationary ‘dry’ regions or with ‘dry’ regions that convect upwards. A possible explanation of this phenomenon is dilatancy. We introduce and develop a model that considers the dynamic dilatancy of a foam via force balances on a continuously sheared sample with a finite liquid fraction. Using microstructural information for the strain of typical foam structures (e.g. Kelvin and Weaire–Phelan foams) and the notion of stretching Plateau borders (i.e. foam channels) within a non-uniform bubble velocity field, the model can estimate the liquid content within a convective roll. Alternatively liquid content can be obtained via previously established relations between applied shear rate and foam osmotic pressure. The continuously sheared, downwards-convecting portion of foam is predicted to subsist at higher liquid content than an adjacent, unyielded, upwards-convecting portion of foam. Sustainable liquid content variations in the dynamic dilatancy model are comparable to or greater than those associated with static foam dilatancy.