On the role played by extensional viscosity in peristaltic transport of circular solid particles suspended in Oldroyd-B liquids

Abstract

The efficiency of the peristalsis mechanism is numerically investigated for the transport of circular solid particles suspended in viscoelastic liquids obeying the Oldroyd-B model. Having modeled the solid particle as a viscoplastic droplet obeying the bi-viscous model, we have relied on the finite-element method for solving the equations of motion (at low Reynolds numbers) for the carrier liquid and the viscoplastic droplet. Viscoelasticity of the carrier liquid is predicted to impede the particle's peristaltic transport with its severity depending on the Deborah number, the size of the particle, and the wave parameters. The obtained numerical results suggest that, when suspended in viscoelastic liquids, smaller-sized particles are more suitable for peristaltic drive. It is also predicted that at a critical Deborah number around unity, particles that are too large might exhibit a sudden drop in their transport velocity. We have interpreted the hampering effect of elasticity in terms of the extensional viscosity and the strain-hardening behavior of the carrier liquid, which is shown to be controlled by the Deborah number, the size of the particle, and the wave parameters.