Mathematical analysis of unsteady solute dispersion in Herschel-Bulkley fluid with interphase mass transfer.

This investigation involves an examination of the miscible dispersion theory in a circular, straight pipe. The analysis takes into account the interphase mass transfer resulting from an irreversible first-order reaction located at the annulus's outer wall. Small molecules such as oxygen, nutrients, and drug molecules can be absorbed irreversibly into the wall tissues due to molecular diffusion and convection. This study focuses on investigating a non-Newtonian mathematical model of blood flow known as the Herschel-Bulkley (H-B) fluid model in a catheterised stenosed artery. Plus, the investigation also takes into consideration the wall absorption effect. The transport of solute is determined by the convective-diffusion equation describing the dispersion process. An exact method called the Generalised Dispersion Model (GDM) solves the transport equation to obtain three efficient transport coefficients, which are exchange, K0, convection, K1 as well as diffusion, K2. Resultantly, the asymptotic value of both K1 as well as K2 reduces caused by an increment in the yield stress, θ, together with the power-law index, n. Here, provided that the wall absorption parameter rises, the asymptotic value of K0 and K1 increases, while K2 decreases. In brief, this research finds an application of drug transportation in blood flow through blood vessels with stenosis. [ABSTRACT FROM AUTHOR]