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 number Pec 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 is 0 (10(-2)) to 0 (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, Pec2 dependence is again found, but with a proportionality constant dependent upon the power law exponent n.(ABSTRACT TRUNCATED AT 250 WORDS)

Unsteady Convective Diffusion with Interphase Mass Transfer in Casson Liquid

“…Sukla [21] investigated the first-order chemical reaction of solute in non-Newtonian fluids flowing through parallel plates and circular tubes by considering the following models: (i) Power law model, (ii) Bingham model, (iii) Casson model. Sharp [22] analyzed the dispersion in nonNewtonian fluids (Casson, Bingham plastic and power law fluids) through conduits using Taylor-Aris dispersion theory which is valid after a large time. This study was extended by Dash et al [23] for Casson fluids using the generalized dispersion model and they discussed the application of their study in blood flow analysis.…”

Mathematical analysis for unsteady dispersion of solute with chemical reaction in blood flow

“…The study of solute dispersion for steady dispersion in non-Newtonian fluids such as Casson, power-law and Bingham fluids through pipe and channel was analyzed by Sharp [10] using Taylor-Aris's theory. Dash et al [11] investigated the unsteady dispersion of solute in Casson fluid through pipe and channel using GDM.…”

Time dependent dispersion of nanoparticles in blood vessels

“…In particular, as  (or, equivalently, ) goes to zero (impermeable capillary) Eq.34 coincides with the relation given in [5], whereas as the rheological parameter  c goes to zero the result given by [8] is recovered. The classical solution of Taylor and Aris [1,2] is found when both () and  c are null.…”

“…nanoparticles). In 1993, Sharp derived explicit expressions for the constant steady state coefficient D eff for a non-Newtonian fluid considering, in particular, a Casson-like fluid [5]. Dash et al [6] and Nagarani et al [7] combined the model of Sharp and the GDM to obtain the unsteady dispersion in a Casson-like fluid, introducing solute adsorption to the walls.…”