Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Peristaltic transport of a Herschel-Bulkley fluid in contact with a Newtonian fluid

Authors: K. Vajravelu, S. Sreenadh and V. Ramesh Babu
Journal: Quart. Appl. Math. 64 (2006), 593-604
MSC (2000): Primary 34B15, 92C10
DOI: https://doi.org/10.1090/S0033-569X-06-01020-9
Published electronically: September 11, 2006
MathSciNet review: 2284461
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Abstract: Peristaltic transport of Herschel-Bulkley fluid in contact with a Newtonian fluid in a channel is investigated for its various applications to flows with physiological fluids (blood, chyme, intrauterine fluid, etc.). The primary application is when blood flows through small vessels; blood has a peripheral layer of plasma and a core region of suspension of all the erythrocytes. That is, in the modeling of blood flow, one needs to consider the core region consisting of a yield stress fluid and the peripheral region consisting of a Newtonian fluid. Peristaltic pumping of a yield stress fluid in contact with a Newtonian fluid has not previously been studied in detail. Our goal is to initiate such a study. The Herschel-Bulkley fluid model considered here reduces to the power law model in the absence of yield stress.

The stream function, the velocity field, and the equation of the interface are obtained and discussed. When the yield stress $ \tau_0\to 0$ and when the index $ n=1$, our results agree with those of Brasseur et al. (J. Fluid Mech. 174 (1987), 495) for peristaltic transport of the Newtonian fluid. It is observed that for a given flux $ \overline Q$ the pressure rise $ \Delta p$ increases with an increase in the amplitude ratio $ \phi$. Furthermore, the results obtained for the flow characteristics reveal many interesting behaviors that warrant further study of the peristaltic transport models with two immiscible physiological fluids.

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Additional Information

K. Vajravelu
Affiliation: Department of Mathematics, University of Central Florida, Orlando, Florida 32816

S. Sreenadh
Affiliation: Department of Mathematics, Sri Venkateswara University, Tirupati 517502, India

V. Ramesh Babu
Affiliation: Department of Mathematics, S. V. Arts College, Tirupati, India

DOI: https://doi.org/10.1090/S0033-569X-06-01020-9
Keywords: Peristaltic transport, Herschel-Bulkley fluid, Newtonian fluid, volume flow rate
Received by editor(s): June 21, 2004
Published electronically: September 11, 2006
Article copyright: © Copyright 2006 Brown University

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