Flow of deformable droplets: discontinuous shear thinning and velocity oscillations

We study the rheology of a suspension of soft deformable droplets subjected to a pressure-driven flow. Through computer simulations, we measure the apparent viscosity as a function of droplet concentration and pressure gradient, and provide evidence of a discontinuous shear thinning behaviour, which occurs at a concentration-dependent value of the forcing. We further show that this response is associated with a nonequilibrium transition between a `hard' (or less deformable) phase, which is nearly jammed and flows very slowly, and a `soft' (or more deformable) phase, which flows much more easily. The soft phase is characterised by flow-induced time dependent shape deformations and internal currents, which are virtually absent in the hard phase. Close to the transition, we find sustained oscillations in both the droplet and fluid velocities. Polydisperse systems show similar phenomenology but with a smoother transition, and less regular oscillations.