Effects of curvature and inertia on the peristaltic transport in a two-fluid system

Abstract

The peristaltic pumping of a biofluid consisting of two immiscible fluids of different viscosities, one occupying the core and the other the peripheral layers on either side, in a two-dimensional channel is investigated including the effects of curvature and inertia. The flow is proved to be steady in a wave frame provided that the interface and the peristaltic wave have the same period. An asymptotic solution for the low Reynolds number flow is presented in powers of a geometric parameter which is the ratio of the channel width to the wavelength. Velocity and stress balance at the interface at different orders are reduced and transferred to the known zeroth order interface. An expression for the jump in the first order pressure across the interface is obtained through the balance of the normal stress and the solutions are presented up to first order. For some non-zero wall curvature, the trapping in the core splits into three eddies, a larger bolus with two small boluses on either side, for μ>1, where μ is the ratio of the viscosity of the peripheral layer fluid to that of the core. The trapped bolus volume decreases with an increase in curvature for all μ. The inertia force mainly causes asymmetry in the streamline structure as pointed out by the earlier authors. However, the trapped bolus being pushed forward for μ<1 is a new phenomenon. Another interesting feature for a single fluid in copumping range is the displacement of the trapped bolus near the wall to the downstream side of the wave.