Peristaltic Pumping of Solid Particles Immersed in a Viscoelastic Fluid

¹ Department of Mathematics, Tulane University, New Orleans, Louisiana 70118, USA
² Center for Computational Science, Tulane University, New Orleans, Louisiana 70118, USA

^⋆ Corresponding author. E-mail: jchrispe@tulane.edu

Abstract

Peristaltic pumping of fluid is a fundamental method of transport in many biological processes. In some instances, particles of appreciable size are transported along with the fluid, such as ovum transport in the oviduct or kidney stones in the ureter. In some of these biological settings, the fluid may be viscoelastic. In such a case, a nonlinear constitutive equation to describe the evolution of the viscoelastic contribution to the stress tensor must be included in the governing equations. Here we use an immersed boundary framework to study peristaltic transport of a macroscopic solid particle in a viscoelastic fluid governed by a Navier-Stokes/Oldroyd-B model. Numerical simulations of peristaltic pumping as a function of Weissenberg number are presented. We examine the spatial and temporal evolution of the polymer stress field, and also find that the viscoelasticity of the fluid does hamper the overall transport of the particle in the direction of the wave.