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# The Influence of Slip Boundary Conditions on Peristaltic Pumping in a Rectangular Channel

[+] Author and Article Information
X. Mandviwalla, R. Archer

Department of Engineering Science, The University of Auckland, Private Bag 92019, Auckland 1001, New Zealand

$ϕ=b/a$, where $b$ is the amplitude of the peristaltic wave and $a$ is the height of the channel.

$β=a/d$ where $a$ is the height of the channel and $d$ is half the width of the channel.

J. Fluids Eng 130(12), 124501 (Oct 24, 2008) (5 pages) doi:10.1115/1.3001107 History: Received April 02, 2008; Revised September 16, 2008; Published October 24, 2008

## Abstract

The flow of an incompressible fluid is modeled in a channel of a rectangular cross section with two symmetric peristaltic waves propagating on the top and bottom. A low Reynolds number and a long wavelength are assumed. The effect on pumping of the inclusion of slip boundary conditions on the side walls is investigated.

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## Figures

Figure 1

An illustration of the model geometry

Figure 2

(a) Shows a solution involving a nondimensional slip length of 0.5 for the side walls and (b) shows a no-slip solution. ϕ=0.6 and β=1 for both solutions.

Figure 3

Plots (a)–(c) relate the pressure drop (Δp) and the average flux (Q) for varying nondimensional slip lengths (lSlip=0,0.2,0.4,0.6). All plots solve for a channel with a square cross section in x-z(β=1). (a) Plots ϕ=0, which result in a Poiseuille flow as no peristaltic wave is present, (b) plot results with ϕ=0.4, and (c) plot results with ϕ=0.8.

Figure 4

A blow-up of the intercept for the solution ϕ=0.2 and β=1

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