An Eulerian-Eulerian formulation of suspension rheology using the finite volume method

We have adapted a well-known constitutive model formulated by Morris and Boulay (1999) that describes the stress tensor for a mixture of particles in a Newtonian liquid into a two-phase finite-volume solver. The two-phase model treats each phase with a separate continuity and momentum equation that splits the stress of the constitutive model between the two phases, with the particle pressure applied only to the particle phase in addition to source terms related to the drag of particles in the fluid. We compare the resulting model using a variety of NMR experiments, considering the flow of neutrally buoyant monodisperse particles at low Reynolds number in the following geometries: 2D simple shear flow in a Couette device, axisymmetric and 3D pressure driven flow down a pipe and in a 2D and 3D asymmetric channel bifurcation. We find excellent agreement with velocity and volume fraction profiles in all of the comparisons with experimental data without much further numerical fitting beyond the original suspension stress model.