Shear-augmented dispersion in non-Newtonian fluids

Abstract

The rate of spread of a passive species is modified by the superposition of a velocity gradient on the concentration field. Taylor (18) solved for the rate of axial dispersion in fully developed steady Newtonian flow in a straight pipe under the conditions that the dispersion be relatively steady and that longitudinal transport be controlled by convection rather than diffusion. He found that the resulting effective axial diffusivity was proportional to the square of the Peclet numberPec and inversely proportional to the molecular diffusivity. This article shows that under similar conditions in Casson and power law fluids, both simplified models for blood, and in Bingham fluids the same proportionalities are found. Solutions are presented for fully developed steady flow in a straight tube and between flat plates. The proportionality factor, however, is dependent upon the specific rheology of the fluid. For Bingham and Casson fluids, the controlling parameter is the radius of the constant-velocity core in which the shear stress does not exceed the yield stress of the fluid. For a core radius of one-tenth the radius of the tube, the effective axial diffusivity in Casson fluids is reduced to approximately 0.78 times that in a Newtonian fluid at the same flow. Using average flow conditions, it is found that the core radius/tube radius ratio iso(10⁻²) too(10⁻¹) in canine arteries and veins. Even at these small values, the effective diffusivity is diminished by 5% to 18%. for power law fluids,Pec ² dependence is again found, but with a proportionality constant dependent upon the power law exponentn. The effective diffusivity in a power law fluid relative to that in a Newtonian fluid is roughly linearly dependent onn for 0<n<1. Forn=0.785, representative of human blood, the effective diffusivity reduction is 10% in a circular tube.