Heterogeneous multiscale simulations of suspension flow

Abstract

The macroscopically emergent rheology of suspensions is dictated by details of fluid-particle and particle-particle interactions. For systems where the typical spatial scale on the particle level is much smaller than that of macroscopic properties, the scales can be split. We present a heterogeneous multiscale method (HMM) approach to modeling suspension flow in which at the macroscale the suspension is treated as a non-Newtonian fluid. The local shear-rate and particle volume fraction are input to a simulation of fully resolved suspension microdynamics. With the help of these simulations, the apparent viscosity and shear-induced diffusivities can be computed for a given shear-rate and volume fraction, and are then used to complete the information needed in the constitutional relations on the macroscopic level. On both levels, the lattice-Boltzmann method (LBM) is applied to model the fluid phase and coupled to a Lagrangian model for the advection-diffusion of the solid phase. Down and upward mapping of viscosity and diffusivity related quantities will be discussed, as well as information exchanged between the phases on both scales. Temporal scale splitting between viscous and diffusive dynamics has also been exploited to accelerate the macroscopic equilibration dynamics. Additionionally, Galileian and rotational symmetries allow us to make very efficient use of a database where the results of previous simulations can be stored, again reducing the computational effort by factors of several orders of magnitude. The HMM suspension model is applied to the simulation of a 2-dimensional flow through a straight channel of macroscopic width. The equilibration dynamics of flow and volume fraction profiles and equilibrium profiles of volume fraction, diffusivity, velocity, shear-rate, and viscosity are discussed. We show that the proposed HMM model not only reproduces experimental findings for low Reynolds numbers but also predicts additional dependencies introduced by shear-thickening effects not covered by existing macroscopic suspension flow models. © 2011 Society for Industrial and Applied Mathematics.