SHEAR-AUGMENTED DISPERSION IN NON-NEWTONIAN FLUIDS

The rate of spread of a passive species is modified by the superpositi on of a velocity gradient on the concentration field. Taylor (18) solv ed for the rate of axial dispersion in fully developed steady Newtonia n flow in a straight pipe under the conditions that the dispersion be relatively steady and that longitudinal transport be controlled by con vection rather than diffusion. He found that the resulting effective a xial diffusivity was proportional to the square of the Peclet number P ec and inversely proportional to the molecular diffusivity. This artic le shows that under similar conditions in Casson and power law fluids, both simplified models for blood, and in Bingham fluids the same prop ortionalities are found. Solutions are presented for fully developed s teady flow in a straight tube and between flat plates. The proportiona lity factor, however, is dependent upon the specific rheology of the f luid. For Bingham and Casson fluids, the controlling parameter is the radius of the constant-velocity core in which the shear stress does no t 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 flu ids is reduced to approximately 0.78 times that in a Newtonian fluid a t the same flow. Using average flow conditions, it is found that the c ore radius/tube radius ratio is o(10(-2)) to o(10(-1)) in canine arter ies and veins. Even at these small values, the effective diffusivity i s diminished by 5% to 18%. For power law fluids, Pec2 dependence is ag ain found, but with a proportionality constant dependent upon the powe r law exponent n. The effective diffusivity in a power law fluid relat ive to that in a Newtonian fluid is roughly linearly dependent on n fo r 0 < n < 1. For n = 0.785, representative of human blood, the effecti ve diffusivity reduction is 10% in a circular tube.