Effect of pillars on the mixing efficiency of a peristaltically-driven Bingham fluid within a closed channel: A LBM simulation

Abstract

We have numerically studied the effect of a fluid’s yield stress on the performance of a peristaltic mixer reinforced by cylindrical pillars, typical of those used in microfluidic systems. A multiple-relaxation-time, Lattice Boltzmann code was used to investigate the effect of a fluid’s yield stress on mixing efficiency for a viscoplastic fluid obeying the bi-viscous model. A Lagrangian particle-tracking method called “boxcounting” has been utilized for evaluating the mixing performance of the channel through introducing a stirring index parameter. Numerical results indicate that for both Newtonian and Bingham fluids, wave amplitude is the most potent tool for controlling the mixing performance of the mixer. It is shown that while for Newtonian fluids the mixing index is dropped if the channel is equipped with circular pillars, for Bingham fluids pillars can play a slightly positive role in enhancing the mixing efficiency of the mixer, and this is particularly so when the confinement ratio is sufficiently large. A more dramatic increase in the mixing efficiency can be attained when only one of the membranes is vibrating (i.e., the asymmetric case).