Stokes flow through a permeable tube

摘要

Pressure-driven Stokes flow theihrough a circular tube with a permeable wall is considered as a model of blood flow through a capillary vessel. Fluid penetrates the tube wall over a test section according to Starling law relating the normal fluid velocity to the transmural pressure defined as the difference between the wall and the uniform ambient pressure. The problem is formulated using the integral representation for Stokes flow, and the solution is computed with high accuracy using a boundary-element method for specified values of the wall permeability and percentage of fluid escaping through the walls. The results illustrate the structure of the flow and validate the predictions of a model based on the assumption of locally unidirectional flow for sufficiently small permeability.