Dispersion of a solute in a Poiseuille flow of a viscoelastic fluid

Abstract

Gill and Sankarasubramanian's analysis of the dispersion of Newtonian fluids in laminar flow between two parallel walls is extended to the flow of non-Newtonian viscoelastic fluids (known as Phan–Thein–Tanner (PTT)). Using a generalized dispersion model which is valid for all times after the solute injection, the diffusion coefficient K i ( t) is obtained exactly and numerically for linearized and exponential forms of the PTT fluids, respectively. The analysis leads to the novel result for K 1 and K 2( t) (which is a measure of the longitudinal dispersion coefficient of the solute). It is found that the value of K 2( t) depends on the value of Deborah number ( De=a measure of the level of elasticity in the fluid) whereas the value of K 1 is constant in both cases. Finally, the effect of the Deborah number on the axial distribution of the mean concentration θ m is investigated in detail.