Solute dispersion in non-Newtonian fluids flow through small blood vessels: A varying viscosity approach

Abstract

Present work concerns the combined effect of Jeffrey fluid parameter and varying nature of viscosity on the solute dispersion in non-Newtonian fluids flow through small blood vessels. The generalized dispersion model of Sankarasubramanian and Gill (1973) has been considered. The objective of the present work is to understand the solute dispersion in non-Newtonian fluids flow through microvessels with absorbing walls under varying viscosity assumption. For more realistic modeling of blood flow in microvessels, Jeffrey and Herschel–Bulkley fluids model have been considered for a comparative study due to its low shear rate flow in small blood vessels such as arterioles, venules and capillaries. The whole solute dispersion analysis has been done for two alternative non-Newtonian fluids (Herschel–Bulkley and Jeffrey fluids) owing to their physiological importance. The present model has been validated by reducing it to previously studied specific cases of Newtonian, Bingham-plastic and Power-law fluids with constant/varying viscosities. It is perceived that the mean concentration, convection and axial dispersion coefficients are significantly affected by varying viscosity and Jeffrey fluid parameters. A noteworthy observation is that an increase in ratio of relaxation to retardation times (Jeffrey fluid parameter) enhanced the values of the transport coefficients. The outcome of the present study shows the diffusion of drugs to the physiological system through small blood vessels is significantly affected by the varying nature of viscosity and Jeffrey fluid parameters.