Rheology of concentrated suspensions of viscoelastic particles

Abstract

The viscoelastic properties of particles strongly influence the rheology of many concentrated industrial or biological dispersions (emulsions, paints or blood). The deformation-orientation of interacting particles under flow enhances the maximum packing fraction of particles and leads to a non-linear rheological behaviour. We first present a Kelvin Voigt model to describe the deformation and stable orientation of a viscoelastic particle in a simple shear field. We then use a viscosity law for concentrated suspensions of hard particles in purely hydrodynamic interactions and relate the maximum packing concentration to the component of the particle deformation tensor in the direction of the flow. In the range of small deformations and diluted suspensions, the model gives a viscosity law similar to the relation obtained by Lhuillier [Phenomenology of hydrodynamic interactions in suspensions of weakly deformable particles, J. de Phys. 48 (1987) 1887–1902]. In concentrated suspensions, a self-consistent theory based on an effective medium approximation yields a non-linear equation for the relative shear viscosity. The rheological law describes the viscosity of concentrated suspensions of viscoelastic particles such as red cells in saline solution and allows information about the non-linear viscoelastic properties of the cell membrane.