A Jeffrey Fluid Model for a Porous-walled Channel: Application to Flat Plate Dialyzer

M Kahshan,A M Siddiqui,D Lu

doi:10.1038/s41598-019-52346-8

Abstract

Creeping motion of a Jeffrey fluid in a small width porous-walled channel is presented with an application to flow in flat plate hemodialyzer. Darcy’s law is used to characterize the fluid leakage through channel walls. Using suitable physical approximations, approximate analytical solution of equations of motion is obtained by employing perturbation method. Expressions for velocity field and the hydrostatic pressure are obtained. Effects of filtration coefficient, the inlet pressure and Jeffrey fluid parameters on the flow characteristics are discussed graphically. The derived results are used to study the flow of filtrate in a flat plat hemodialyzer. Using the derived solutions, theoretical values of the filtration rate and the mean pressure difference in the hemodialyzer are calculated. On comparing the computed results with the available experimental data, a reasonable agreement between the two is found. It is concluded that the presented model can be used to study the hydrodynamical aspects of the fluid flow in a flat plate hemodialyzer.

Highlights

The study of hydrodynamics of fluid flow in porous-walled channels and tubes have been remained a subject of interest for researchers since decades
Flow of a viscous fluid in a porous-walled channel was studied by Marshall et al.5 who assumed that the fluid leakage across the channel walls is proportional to the pressure differences across the walls
The Jeffrey fluid model is capable of describing the stress relaxation property of non-Newtonian fluids, which the usual viscous fluid model cannot describe

Summary

Introduction

The study of hydrodynamics of fluid flow in porous-walled channels and tubes have been remained a subject of interest for researchers since decades. The fluid loss at the wall is taken as function of the wall permeability, the flow rate determined can be found to decay linearly or exponentially along the channel wall as special case in our study. In these equations p i is the mean pressure and Q i is the flow rate at the inlet of the channel at x = 0.

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