Peristaltic Transport of a Particle–Fluid Suspension through a Uniform and Non‐Uniform Annulus

K S Mekheimer,Y Abd Elmaboud

doi:10.1080/11762320802376183

Abstract

This study looks at the influence of an endoscope on the peristaltic flow of a particle–fluid suspension (as blood model) through tubes. A long wavelength approximation through a uniform and non‐uniform infinite annulus filled with an incompressible viscous and Newtonian fluid mixed with rigid spherical particles of identical size is investigated theoretically. The inner tube is uniform, rigid and moving with a constant velocity V0, whereas the outer non‐uniform tube has a sinusoidal wave travelling down its wall. The axial velocity of the fluid phase uf, particulate phase up and the pressure gradients have been obtained in terms of the dimensionless flow rate Q, the amplitude ratio ɸ, particle concentration C, the velocity constant V0 and the radius ratio ϵ (the ratio between the radius of the inner tube and the radius of the outer one at the inlet). Numerical calculations for various values of the physical parameters of interest are carried out for the pressure rise and the friction force on the inner and the outer tubes.

Highlights

Peristaltic pumping is a form of fluid transport that occurs when a progressive wave of area contraction or expansion propagates along the length of distensible duct containing liquid or mixture
For a non-uniform tube, the average pressure rise is plotted versus the mean flow rate for different values of C, V0 and in Figure 7; it is noticed that a linear relation between them and an increase in the flow rate reduce the pressure rise, and the maximum flow rate is achieved at zero pressure rise, and maximum pressure occurs at zero flow rate
The problem of peristaltic flow through a uniform and nonuniform annulus filled with an incompressible viscous and Newtonian fluid mixed with rigid spherical particles of identical size is investigated theoretically

Summary

Introduction

Peristaltic pumping is a form of fluid transport that occurs when a progressive wave of area contraction or expansion propagates along the length of distensible duct containing liquid or mixture. The effect of an endoscope on peristaltic motion of a fluid with suspended particles is very important for medical diagnosis, and it has many clinical applications. When there is some obstruction in the ureter or in the ureter–bladder junction, the upstream ureter dilates In such hydroureter cases, peristaltic motion becomes a travelling wave of relatively small amplitude over a cylindrical tapered tube. The continuum theory of mixtures is applicable to hydrodynamics of biological systems, because it provides an improved understanding of diverse subjects such as diffusion of proteins, the rheology of blood, swimming of microorganisms and particle deposition in the respiratory tract (Srivastava and Srivastava 1989, 1997; Misra and Pandey 1994; Srivastava and Saxena 1997), etc. A motivation of the present analysis is the hope that such a problem will be applicable in many clinical applications such as the endoscope problem

Formulation of the problem

Numerical results and discussion

Conclusion