Gibbs elasticity effect in foam shear flows: a non quasi-static 2D numerical simulation

The origin of the dissipation in liquid foams is not fully understood, especially in the large deformation, large velocity regime. Numerical simulations, now very accurate in the quasi static regime, are still sparse in the dissipative regime, and are all based on restrictive assumptions or very small bubble numbers. Here we present the results obtained with 2D numerical simulations involving 500 bubbles under simple shear, in a non-quasi static regime. The bubble description is kept as simple as possible and the dissipation is assumed to arise from surface tension variations induced by film area variations. This model leads to a steady state stress under simple shear that is well fitted by a Herschel-Bulkley law with an exponent 0.6. We show that small tension dynamical inhomogeneities induce foam structure modifications responsible for the largest part of the stress increase.