Shear-induced Particle Migration: Predictions from Experimental Evaluation of the Particle Stress Tensor
Résumé
This paper addresses the modeling of the phenomenon of particle migration in the flow of monodispersed non-colloidal suspensions at neglected inertia using the Suspension Balance Model (SBM). The SBM describes the migration flux of particles as the divergence of the particle stress tensor. It is selected in this work because of its parameters that can be measured experimentally and its capability to quantify well the shear-induced migration phenomenon. A recent experiment [Dbouk et al. 2012] reported measurements of the different parameters in the SBM, which are used in this work to study their effects on the prediction of the particle migration phenomenon. For that purpose, a two-dimensional solver capable of solving the set of conservation equations of the SBM using the finite volume method is developed within the "OpenFOAM®" CFD toolbox. The code is validated by simulating the suspension flows in a channel of rectangular cross-section, and in a wide gap Couette cell. Solutions are generated using the newly measured SBM parameters, and results are compared to similar ones obtained using the old SBM parameters. It is found that the new measured parameters have no significant influence on prediction of particle migration as compared to those proposed in the literature. Finally, the SBM is extended to general two-dimensional flows through a frame-invariant formulation that takes into account the local kinematics of the suspension including buoyancy effects. The frame-invariant model is applied to the resuspension and mixing of a monodispersed suspension in a horizontal Couette cell. The predicted results are found to be in good agreement with experimental measurements.