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Peristaltic Pumping of Solid Particles Immersed in aViscoelastic Fluid

Published online by Cambridge University Press:  10 August 2011

J. Chrispell  and
L. Fauci
J. Chrispell*
Affiliation:
Department of Mathematics, Tulane University, New Orleans, Louisiana 70118, USA Center for Computational Science, Tulane University, New Orleans, Louisiana 70118, USA
L. Fauci
Affiliation:
Department of Mathematics, Tulane University, New Orleans, Louisiana 70118, USA Center for Computational Science, Tulane University, New Orleans, Louisiana 70118, USA
*
⋆ Corresponding author. E-mail: [email protected]
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Abstract

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

Keywords

viscoelastic fluidperistaltic pumpingOldroyd-B
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 6 , Issue 5: Complex Fluids , 2011 , pp. 67 - 83
Copyright
© EDP Sciences, 2011

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