Journal of Fluid Mechanics

Peristaltic transport of two immiscible viscous fluids in a circular tube

Adabala Ramachandra  Rao a1 and Srinivasan  Usha a1
a1 Department of Mathematics, Indian Institute of Science, Bangalore, India

Article author query
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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.

(Published Online April 26 2006)
(Received December 15 1994)
(Revised March 30 1995)