Analysis of Stokes flow through periodic permeable tubules

Abstract

This article reports the detailed analysis of the Stokes flow through permeable tubes. The objective of this investigation was to search for exact solutions to the Stokes flow and thereby observe the effects on radial flow component, provided the permeability on the tubular surface is an elementary trigonometric function. Mathematical expressions for the pressure distribution, velocity components, volume flux, average wall shear stress and leakage flux are presented explicitly. Graphical analysis of the fluid flow is presented for a set of parametric values. Important conclusions are drawn for Stokes flow through tubes with low as well as high permeability. The classical Poiseuille flow is presented as a limiting case of this immense study of Stokes flow.

Keywords

• Stokes flow
• Permeable tube
• Periodic penetration
• Bessel function