Direct numerical simulation of two-phase flow: Effective rheology and flow patterns of particle suspensions

We analyze the mechanical behavior of a two-phase system consisting of rigid grains and an interconnected pore fluid. For this purpose we use 2D direct numerical simulations on the spatial scale of individual grains for Newtonian and non-Newtonian fluid rheology. By using the stress–strain rate relation we derive scaling laws for effective viscosity of two-phase particle suspensions. We demonstrate that the effective rheology of the assemblage is non-Newtonian only if the fluid has a non-Newtonian rheology. At small fluid fraction, inter-granular strain rates are up to 3 orders of magnitude higher than the applied background strain rate. We suggest that this effect explains the experimentally observed change at higher strain rates in rheology, from Newtonian to non-Newtonian aggregate rheology.To establish the conditions at which the fluid–solid aggregate deforms coherently as a consequence of Rayleigh–Taylor instabilities we studied flow patterns of particle suspensions and characterized them as a function of fluid fraction, viscosity, density, shape and size of the grains. From initial conditions with homogeneously distributed grains and interstitial fluid above a layer of pure fluid, our results show that the Rayleigh–Taylor instability dominates for moderate to large fluid fractions. At large fluid fractions, we observed a transition to a Stokes suspension mode, in which grains do not interact but sink independently. An analytical expression is derived that predicts the transition from Rayleigh–Taylor instability to Stokes suspension mode. The transition is a function of fluid fraction, radius of the grains, height of the interface and initial amplitude. Systematic numerical simulations are in good agreement with the analytical predictions.