Elastic membranes in viscous shear flow

Liquid capsules with an elastic membrane surface in simple shear flow are considered beyond the regime of small deformations. A simple model is introduced to give a mathematical description of an elastic membrane in viscous flow. The question of whether there is a steady state of a system of a single membrane in external shear flow is studied. It is found by analytical considerations that the possible steady-state flows are restricted by symmetry. The evolution of the membrane in time is found by numerical calculations. For a single spherically symmetric membrane, I find by numerical simulations, a steady-state shape and its dependence on the shear strength. For nonspherically symmetric membranes we see that there is no steady-state shape in general, but by numerical simulations I find that the shape changes can become periodic. This leads to a new alternative explanation of previous experimental results. The stress tensor of the membranes and the effective viscosity of a dilute system of elastic membranes immersed in a liquid is calculated. I find an agreement with former analytical calculations for small shear, and obtain shear thinning behavior when the shear rate is increased.