Peristaltic flow of Bingham fluids at large Reynolds numbers: A numerical study

Abstract

Peristaltic flow of a viscoplastic fluid which obeys the bi-viscous (Bingham) model as its constitutive equation is numerically studied in a planar two-dimensional channel using the multiple-relaxation-time lattice Boltzmann method (MRT-LBM). Numerical results could be obtained at large Reynolds numbers for arbitrary set of wavelength and amplitude ratios of the peristaltic wave. It is shown that depending on the Reynolds number, a fluid's yield stress may increase or decrease the time-mean flow rate of peristaltic pumps. Our numerical results also show that for yield-stress fluids there exists a threshold wave number above which the yield stress can accelerate fluid transport whereas below which it can have a decelerating effect. The yield stress is also predicted to diminish the size of the fluid bolus in the “trap” phenomenon for certain set of parameters.