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Applied Bionics and Biomechanics
Volume 2015, Article ID 703574, 14 pages
http://dx.doi.org/10.1155/2015/703574
Research Article

Slip Effects on Peristaltic Transport of a Particle-Fluid Suspension in a Planar Channel

1Department of Engineering Mathematics and Physics, Faculty of Engineering, Cairo University, Giza, Egypt
2Department of Basic Engineering Sciences, Faculty of Engineering, Menoufia University, Shebin El-Kom, Egypt

Received 1 August 2014; Revised 16 March 2015; Accepted 16 April 2015

Academic Editor: Agnès Drochon

Copyright © 2015 Mohammed H. Kamel et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Peristaltic pumping induced by a sinusoidal traveling wave in the walls of a two-dimensional channel filled with a viscous incompressible fluid mixed with rigid spherical particles is investigated theoretically taking the slip effect on the wall into account. A perturbation solution is obtained which satisfies the momentum equations for the case in which amplitude ratio (wave amplitude/channel half width) is small. The analysis has been carried out by duly accounting for the nonlinear convective acceleration terms and the slip condition for the fluid part on the wavy wall. The governing equations are developed up to the second order of the amplitude ratio. The zeroth-order terms yield the Poiseuille flow and the first-order terms give the Orr-Sommerfeld equation. The results show that the slip conditions have significant effect within certain range of concentration. The phenomenon of reflux (the mean flow reversal) is discussed under slip conditions. It is found that the critical reflux pressure is lower for the particle-fluid suspension than for the particle-free fluid and is affected by slip condition. A motivation of the present analysis has been the hope that such theory of two-phase flow process under slip condition is very useful in understanding the role of peristaltic muscular contraction in transporting biofluid behaving like a particle-fluid mixture. Also the theory is important to the engineering applications of pumping solid-fluid mixture by peristalsis.