Peristaltic transport of two immiscible viscous fluids in a circular tube

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.

Thermodynamic Analysis for the MHD Flow of Two Immiscible Micropolar Fluids Between Two Parallel Plates

“…Blood flow in arteries has been studied by many researchers considering the flow of blood as a two phase flow. Several investigations of multi-phase flows are reported by various researchers (e.g., Bird et al, 1960;Kapur, 1964;Bhattacharya, 1968;Chaturani and Samy, 1985;Rao and Usha, 1979;Bakhtiyarov and Siginer, 1997). The flow and heat transfer in immiscible fluids are of special importance in the petroleum extraction and transport problem.…”

Peristaltic motion of a Bingham fluid in contact with a Newtonian fluid in a vertical channel

“…Brasseur et al [4] made a significant contribution on the peristaltic motion of two immiscible fluids in a channel using flexible walls and have demonstrated the deficiency of the examination specified above in the limit of vast peripheral layer thickness. This problem is solved for axisymmetric case by Ramachandra Rao and Usha et al [5]. Usha and Ramachandra Rao [6] discussed the peristaltic pumping of two layered power-law fluids in an axisymmetric tube.…”

Peristaltic Pumping of Williamson fluid through a porous medium in a horizontal channel with heat transfer

“…In industrial applications, these flows occur in blood pumps in heart-lung machine, in sanitary fluid transport and transport of corrosive fluids. Since, the pioneering works of Latham [10] and Shapiro et al [17] a number of analytical, numerical and experimental (Fung and Yih, [6]; Jaffrin, [9]; Ramachandra Rao and Usha, [16]; Siddiqui and Schwarz, [20]; Subba Reddy et al, [22]; Brown and Hung, [2]; Takabatake and Ayukawa, [25]; Takabatake et al, [26]; Weinberg et al, [28] ) studies of peristaltic flows of different fluids have been reported under different conditions with reference to physiological and mechanical situations. Several researchers considered the fluid to behave like a Newtonian fluid for physiological peristalsis including the flow of blood in arterioles.…”