MODELING OF CONCENTRATED SUSPENSIONS USING A CONTINUUM CONSTITUTIVE EQUATION

We simulate the behaviour of suspensions of large-particle, non-Browni an, neutrally-buoyant spheres in a Newtonian liquid with a Galerkin, f inite element, Navier-Stokes solver into which is incorporated a conti nuum constitutive relationship described by Phillips et al. (1992). Th is constitutive description couples a Newtonian stress/shear-rate rela tionship (where the local viscosity of the suspension is dependent on the local volume fraction of solids) with a shear-induced migration mo del of the suspended particles. The two-dimensional and three-dimensio nal (axisymmetric) model is benchmarked with a variety of single-phase and two-phase analytic solutions and experimental results. We describ e new experimental results using nuclear magnetic resonance imaging to determine non-invasively the evolution of the solids-concentration pr ofiles of initially well-mixed suspensions as they separate when subje cted to slow flow between counter-rotating eccentric cylinders and to piston-driven flow in a pipe. We show good qualitative and quantitativ e agreement of the numerical predictions and the experimental measurem ents. These flows result in complex final distributions of the solids, causing rheological behaviour that cannot be accurately described wit h typical single-phase constitutive equations.