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<inf>1</inf>(Γ), which shows the effect of the added viscosity coefficient Γ on the convective coefficient. It is seen that the value of the K<inf>1</inf>(Γ) for Γ ≠ 0 is always smaller than the corresponding value for a Newtonian fluid. Also, the effect of the added viscosity coefficient on the K<inf>2</inf>(t,Γ) (which is a measure of the longitudinal dispersion coefficient of the solute) is explored numerically. Finally, the axial distribution of the average concentration C<inf>m</inf> 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. © 2002 Elsevier Science Ltd. All rights reserved.