Peristaltic transport of a particle-fluid suspension in a cylindrical tube

Abstract

Peristaltic pumping induced by a sinusoidal travelling wave of moderate amplitude is analysed in the axisymmetrical case for a viscous incompressible and Newtonian fluid mixed with rigid spherical particles which are of identical size. A perturbation method has been employed to find the solution of the problem, choosing the amplitude ratio (i.e., wave amplitude/tube radius) as a parameter. The analysis has been carried out by duly accounting for the nonlinear convective acceleration terms, and the nonslip condition for the fluid part on the wavy wall. The governing equations are developed up to the second order of the amplitude ratio. The zeroth order terms yield the Poiseuille flow and the first order terms give the Orr-Sommerfeld equation. In the absence of the pressure gradient and the wall motion, the mean flows (for the fluid and the solid particles) and the mean pressure gradient (averaged over time) are all found to be proportional to the square of the amplitude ratio. Numerical results are obtained for this simple case by approximating complicated groups of the products of Bessel functions by polynomials. It is observed that a reversal of flow occurs when the pressure gradient exceeds the critical value; this is favoured by the presence of the solid particles. The reversal of flow may take place near the boundaries also.