Calculation of non-Newtonian flow of colloidal dispersions: Finite elements and Brownian dynamics

Abstract

We present a novel method for the numerical calculation of the flow of particulate fluid systems and apply it to the flow of a colloidal dispersion. This method is based on the CONNFFESSIT (Calculation Of Non-Newtonian Flow: Finite Element and Stochastic Simulation Technique) [Laso and Ottinger, J. Non-Newtonian Fluid Mech., 47 (1993) 1]. It couples microscopic dynamic simulations (Brownian Dynamics, BD) with macroscopic Finite Element (FE) methods as traditionally used in the calculation of viscoelastic flow. The standard continuum-mechanical form of the momentum transport equation is closed by microscopic BD simulations. The coupling between the macroscopic FE formulation for the velocity field and the microscopic simulation is effected through the stress tensor, which is obtained as an ensemble average over BD trajectories. This combination of microscopic simulations with macroscopic FE methods obviates the need for a rheological constitutive equation (strain history-stress relationship) to describe the fluid system. It is therefore possible to solve flow problems for very general fluid systems, for which no exact constitutive equation can be derived.