Shear-augmented dispersion in non-Newtonian fluids

Area of Science:

• Fluid Dynamics
• Transport Phenomena
• Biomedical Engineering

Background:

• Species spread is influenced by fluid flow, particularly velocity gradients.
• Taylor's work established axial dispersion in Newtonian fluids, dependent on Peclet number (Pec).
• Blood flow exhibits non-Newtonian characteristics, necessitating study in models like Casson, Bingham, and power law fluids.

Purpose of the Study:

• To investigate axial dispersion in non-Newtonian fluids (Bingham, Casson, power law).
• To compare dispersion rates in these fluids with Newtonian fluids.
• To determine the impact of fluid rheology on the proportionality factor of effective axial diffusivity.

Main Methods:

• Analytical solutions for fully developed steady flow in tubes and between flat plates.
• Analysis of dispersion under conditions where convection dominates diffusion.
• Examination of the role of the constant-velocity core in Bingham and Casson fluids.

Main Results:

• Bingham, Casson, and power law fluids exhibit the same Peclet number squared (Pec²) dependence for axial dispersion as Newtonian fluids.
• The proportionality factor for effective axial diffusivity is rheology-dependent.
• For Casson fluids with a core radius of 0.1, diffusivity is reduced to ~0.78 times that of Newtonian fluids.
• In canine arteries and veins, small core radii lead to 5%-18% diminished effective diffusivity.
• Power law fluid proportionality depends on the power law exponent (n).

Conclusions:

• Non-Newtonian fluid rheology significantly modifies axial dispersion rates.
• The constant-velocity core in Bingham and Casson fluids is a key factor in reducing diffusivity.
• Findings are relevant for understanding solute transport in biological systems like blood vessels.