Theory of Extremely Low Reynolds number Flows in Microscopic Tapered-tube

Abstract

This paper aims to investigate flows in a model of microscopic lymphatic vessels of mice for developing noninvasive cancer treatments. The model consists of an axisymmetric tube with its diameter changing linearly along the axis, called a tapered tube. Reynolds number of the flow is assumed to be much smaller than unity because the tube diameter and the flow velocity are small. Continuity equation and Navier-Stokes equations are solved in an analytical manner based on the Stokes approximation. Solutions of the velocity and pressure are represented in nondimensional forms. The friction coefficient of the flow is expressed in a simple form for convenience of applications.