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Research Papers

Peristaltic Pumping of Blood Through Small Vessels of Varying Cross-Section

[+] Author and Article Information
J. C. Misra

Department of Mathematics, Institute of Technical Education and Research,  Siksha O Anusandhan University, Bhubaneswar 751030, Indiamisrajc@rediffmail.com

S. Maiti

School of Medical Science and Technology, and Center for Theoretical Studies, Indian Institute of Technology, Kharagpur 721302, Indiasomnathm@cts.iitkgp.ernet.in

J. Appl. Mech 79(6), 061003 (Sep 13, 2012) (19 pages) doi:10.1115/1.4006635 History: Received June 08, 2010; Revised March 22, 2012; Posted April 18, 2012; Published September 13, 2012; Online September 13, 2012

The paper is devoted to a study of the peristaltic motion of blood in the micro-circulatory system. The vessel is considered to be of varying cross-section. The progressive peristaltic waves are taken to be of sinusoidal nature. Blood is considered to be a Herschel-Bulkley fluid. Of particular concern here is to investigate the effects of amplitude ratio, mean pressure gradient, yield stress, and the power law index on the velocity distribution, streamline pattern, and wall shear stress. On the basis of the derived analytical expressions, extensive numerical calculations have been made. The study reveals that velocity of blood and wall shear stress are appreciably affected due to the nonuniform geometry of blood vessels. They are also highly sensitive to the magnitude of the amplitude ratio and the value of the fluid index.

Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 4

Axial velocity contour at different time when φ = 0.1, n = 1, Λ=0, τ = 0, Q = 0

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Figure 7

Pressure rise versus flow rate

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Figure 9

Streamline patterns for peristaltic flow of a Newtonian fluid at different instants of time (Q=0, Λ=0, τ=0, φ=0.5)

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Figure 10

Streamline patterns in the case of peristaltic flow for different values of φ when n = 1, t = 0.25, τ=0, Λ=0, Q = 0

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Figure 12

Streamline patterns in the case of peristaltic flow for different values of n when Q = 0, t = 0.25, τ=0.1, Λ=0, φ=0.5

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Figure 13

Streamline patterns for the peristaltic flow of a shear thinning fluid (n = 2/3) for different values of Q when t = 0.25, τ=0.1,Λ=0,φ=0.5

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Figure 14

Streamline patterns for the peristaltic flow of a shear thickening fluid (n = 4/3) for different values of Q when t = 0.25, τ=0.1,Λ=0,φ=0.5

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Figure 15

Trajectories of massless particles for Newtonian/non-Newtonian fluids at different locations (Q=0, φ=0.5, τ=0, Λ=0); —— for Q = 0; … for Q=3φ2/(2+φ2); • initial locations; □ at the end of one wave period if Q=0; Δ at the end of one wave period if Q=3φ2/(2+φ2); ° at the end of one particle period if Q = 0; * at the end of one particle period if Q=3φ2/(2+φ2). In part (a), ■ stands for the corresponding results reported by Shapiro [15].

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Figure 5

Velocity distribution at different instants of time

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Figure 11

Streamline patterns in the case of peristaltic flow of rheological fluid for different values of τ when Q=0, t=0.25, Λ=0, φ=0.5

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Figure 3

Aerial view of the velocity distribution at different instants of time (n=1,Λ=0,ΔP=0,τ=0,φ=0.5)

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Figure 2

Variation of axial velocity in the vertical direction (a) at x = 0.5, t = 0.25 (Λ=0,φ=0.5,τ=0, n=1,ΔP=0), (b) for different values of φ at wave crest when Λ=0, n=1, τ=0, Q=0, and (c) for different values of φ at wave trough when Λ=0, n=1, τ=0, Q=0

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Figure 1

A physical sketch of the problem for a tapered channel

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