Peristaltic Transport of a Couple Stress Fluid: Some Applications to Hemodynamics

TL;DR

This paper theoretically investigates peristaltic flow of a couple stress fluid in porous channels, relevant to blood flow in micro-circulatory systems, analyzing effects of physical parameters on flow characteristics and trapping phenomena.

Contribution

It introduces a novel analysis of peristaltic transport considering couple stress effects and porosity, extending prior models to better understand physiological blood flow in micro-circulatory systems.

Findings

Flow reversal can be controlled by couple stress and permeability parameters.

Reducing permeability can prevent trapping phenomena.

Results align with previous non-porous, no-couple-stress studies.

Abstract

The present paper deals with a theoretical investigation of the peristaltic transport of a couple stress fluid in a porous channel. The study is motivated towards the physiological flow of blood in the micro-circulatory system, by taking account of the particle size effect. The velocity, pressure gradient, stream function and frictional force of blood are investigated, when the Reynolds number is small and the wavelength is large, by using appropriate analytical and numerical methods. Effects of different physical parameters reflecting porosity, Darcy number, couple stress parameter as well as amplitude ratio on velocity profiles, pumping action and frictional force, streamlines pattern and trapping of blood are studied with particular emphasis. The computational results are presented in graphical form. The results are found to be in good agreement with those of Shapiro et. al \cite{r25} that was carried out for a non-porous channel in the absence of couple stress effect. The present study puts forward an important observation that for peristaltic transport of a couple stress fluid during free pumping when the couple stress effect of the fluid/Darcy permeability of the medium, flow reversal can be controlled to a considerable extent. Also by reducing the permeability it is possible to avoid the occurrence of trapping phenomenon.