Peristaltic transport of solid particles suspended in a viscoplastic fluid: A numerical study

Peristaltic transport of circular rigid particle(s) suspended in a viscoplastic fluid is numerically investigated in a planar two-dimensional channel using the lattice Boltzmann method (LBM) coupled with the smoothed profile method (SPM). Numerical results could be obtained at non-zero Reynolds numbers for a wide range of the propagating wave's parameters. Our numerical results reveal that a fluid's yield stress has a dramatic effect on the peristaltic transport of solid particles. For a single particle suspended in a viscoplastic fluid, which obeys the bi-viscosity (Bingham) model as its constitutive equation, it is found that there exists a threshold wave number below which the yield stress slows down the particle's transport but above which it has an accelerating effect. A fluid's yield stress is also predicted to lower the average velocity of an initially-centered single particle at any given confinement ratio. For a given Bingham number, particle's velocity is predicted to increase by an increase in the confinement ratio provided that it is larger than a critical value. An increase in the Reynolds number may increase or decrease the particle's average velocity depending on the Bingham number. For the two-particle and four-particle scenarios, our numerical results show that the initial positioning of the particles in the channel has a decisive role in their eventual fate.