  Dense suspensions of soft colloidal particles display a broad range of
physical and rheological properties which are still far from being fully
understood. To elucidate the role of deformability on colloidal flow, we employ
computer simulations to measure the apparent viscosity of a system of droplets
of variable surface tension subjected to a pressure-driven flow. We confirm
that our suspension generically undergoes discontinuous shear thinning, and
determine the dependence of the onset of the discontinuity on surface tension.
We find that the effective viscosity of the suspension is mainly determined by
a capillary number. We present active microrheology simulations, where a single
droplet is dragged through the suspension. These also show a dynamical phase
transition, analogous to the one associated with discontinuous shear thinning
in our interpretation. Such a transition is signalled by a discontinuity in the
droplet velocity versus applied force.
