On the dispersion of a solute in Poiseuille flow of a third-grade fluid in a channel

Abstract

Gill and Sankarasubramanian's analysis of the dispersion of Newtonian fluids in laminar flow between two parallel walls are extended to the flow of non-Newtonian viscoelastic fluid (known as third-grade fluid) using a generalized dispersion model which is valid for all times after the solute injection. The exact expression is obtained for longitudinal convective coefficient K-1(Gamma), which shows the effect of the added viscosity coefficient Gamma on the convective coefficient. It is seen that the value of the K-1(Gamma) for Gamma not equal 0 is always smaller than the corresponding value for a Newtonian fluid. Also, the effect of the added viscosity coefficient on the K-2(t, Gamma) (which is a measure of the longitudinal dispersion coefficient of the solute) is explored numerically. Finally, the axial distribution of the average concentration C-m of the solute over the channel cross-section is determined at a fixed instant after the solute injection for several values of the added viscosity coefficient. (C) 2002 Elsevier Science Ltd. All rights reserved.