Suspensions of deformable particles in a Couette flow

We consider suspensions of deformable particles in a Newtonian fluid by means of fully Eulerian numerical simulations with a one-continuum formulation. We study the rheology of the visco-elastic suspension in plane Couette flow in the limit of vanishing inertia and examine the dependency of the effective viscosity mu on the solid volume-fraction Phi, the capillary number Ca, and the solid to fluid viscosity ratio K. The suspension viscosity decreases with deformation and applied shear (shear-thinning) while still increasing with volume fraction. We show that mu collapses to an universal function, mu(Phi(e)), with an effective volume fraction Phi(e), lower than the nominal one owing to the particle deformation. This universal function is well described by the Eilers fit, which well approximate the rheology of suspension of rigid spheres at all O. We provide a closure for the effective volume fraction Phi(e) as function of volume fraction Phi and capillary number Ca and demonstrate it also applies to data in literature for suspensions of capsules and red-blood cells. In addition, we show that the normal stress differences exhibit a non-linear behavior, with a similar trend as in polymer and filament suspensions. The total stress budgets reveals that the particle-induced stress contribution increases with the volume fraction Phi and decreases with deformability.