Rheology of deformable droplet suspensions: a lattice Boltzmann study

We study the rheology of a two dimensional 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 phase, which is nearly jammed and flows very
slowly, and a soft 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.

In the second part of this project, we focus on the properties of
reversibility of our suspension. In particular, we perform simulations
applying a periodic oscillatory shear to our system. This allows us to
compare the droplets positions after each period of the imposed oscillations
and observe if our droplets undergo a reversible motion.  A similar kind of
analysis is performed on a system where a selected droplet sees a periodic
increase of its volume, therefore forcing its neighbours to rearrange their
position.