Bubble dynamics and rheology in sheared two-dimensional foams

Abstract

The flow of foams and emulsions is characterized by a nonlinear relation between stress and strain rate. In simulations of linearly sheared, two-dimensional foam flows we observe two distinct regimes with qualitatively different bubble dynamics: at low shear rates there is strongly non-affine bubble motion while at higher shear rates the bubbles are confined to lanes. The transition between these two regimes is smooth and stretches over one decade in strain rate. We measure the fluctuations in the non-affine bubble motion over a wide range of strain rates in order to elucidate the nature of this transition and connect the bubble dynamics to the bulk rheology. While the first regime is well described by a deformation-relaxation model, the second regime is consistent with a flow model where the shear stress follows directly from the viscous drag between the bubbles.