Abstract: We present recent interface-resolved numerical simulations of the rheological behavior of suspensions in the presence of elastic effects. In particular, we will consider hyper-elastic spheres, flexible filaments and the flow of a suspension over elastic walls. In all cases, elasticity is found to decrease the system effective viscosity.
First, we shall consider viscous hyper-elastic particles in shear flow. We study suspensions of deformable (viscoelastic) spheres in a Newtonian solvent in plane Couette geometry. We find that in the limit of vanishing inertia, the effective viscosity of the suspension increases as the volume fraction occupied by the spheres increases and decreases as the elastic modulus of the spheres G decreases; thus the system is shear thinning with respect to deformability. We shall also present a numerical study on the rheology of semi-dilute and concentrated filament suspensions for different bending stiffness and Reynolds number, with the immersed boundary method used for the coupling between fluid and solid. The filaments are considered as one-dimensional inextensible slender bodies with fixed aspect ratio, obeying the Euler-Bernoulli beam equation. At last, we study suspensions of rigid particles in a plane Couette flow with deformable elastic walls and find that, in the limit of vanishing inertia, the elastic walls induce shear thinning of the suspension flow such that the effective viscosity decreases as the wall deformability increases. This shear-thinning behavior originates from the interactions between rigid particles, soft wall and carrier fluid; an asymmetric wall deformation induces a net lift force acting on the particles which therefore migrate towards the bulk of the channel.