Micro-mechanical prediction of the effect of surfactant concentration and external friction on the visco-elasto-plastic response of an aqueous foam.

We apply a combination of the Viscous Froth model and a surfactant transfer model [Zaccagnino et al., Phys. Rev. E, 2018, 98, 022801] to predict the rheological response of a two-dimensional dry aqueous foam. The model includes both the effect of friction between the foam and the boundaries of the container and also the dissipative effects on the film interfaces caused by surfactant motion. These dynamics are characterized by two free parameters: the Gibbs elasticity, relating surfactant concentration to interfacial tension, and the mobility of the surfactant molecules on the interfaces. We employ numerical simulations to evaluate the static shear modulus, yield stress and the storage and loss moduli of a foam and investigate the effect of our free parameters on these rheological properties.