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Peristaltic transport of two immiscible viscous fluids in a circular tube

Published online by Cambridge University Press:  26 April 2006

Adabala Ramachandra Rao  and
Srinivasan Usha
Adabala Ramachandra Rao
Affiliation:
Department of Mathematics, Indian Institute of Science, Bangalore, India
Srinivasan Usha
Affiliation:
Department of Mathematics, Indian Institute of Science, Bangalore, India
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Abstract

Peristaltic motion of two immiscible viscous incompressible fluids in a circular tube is studied in pumping and copumping ranges under long-wavelength and low-Reynoldsnumber assumptions. The effect of the peripheral-layer viscosity on the time-averaged flux and the mechanical efficiency is studied. The formation and growth of the trapping zone in the core and the peripheral layer are explained. It is observed that the bolus volume in the peripheral layer increases with an increase in the viscosity ratio. The limits of the time-averaged flux $\bar{Q}$ for trapping in the core are obtained. The trapping observed in the peripheral layer decreases in size with an increase in $\bar{Q}$ but never disappears. The development of the complete trapping of the core fluid by the peripheral-layer fluid with an increase in the time-averaged flux is demonstrated. The effect of peripheral-layer viscosity on the reflux layer is investigated. It is also observed that the reflux occurs in the entire pumping range for all viscosity ratios and it is absent in the entire range of copumping.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 298 , 10 September 1995 , pp. 271 - 285
Copyright
© 1995 Cambridge University Press

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