Solute dispersion in transient Casson fluid flow through stenotic tube with exchange between phases

Abstract

A mathematical study on solute dispersion has been carried out in a stenotic tube having an absorptive wall—a study relevant to arterial pharmacokinetics. The rheology of blood is represented by Casson model and the solute is introduced at a point that is uniformly distributed over the cross section. The two-dimensional fluid flow is considered in this study. The governing equations of motion for the flow of Casson fluid, for the transport of solute in the lumen as well as in the tissue along with appropriate initial and boundary conditions, are numerically solved by leveraging the Marker and Cell method and the immersed boundary method in staggered grids formulation. Following the introduction of solute, we provide a comprehensive investigation of the influence of the wall absorption parameter (κ), yield stress (τy), and the severity of the stenosis (ξ) on the three transport coefficients, namely, the fraction of solute remaining in the fluid phase, the apparent convection velocity, and the dispersion coefficient. Simulated results predict the diminishing magnitudes of the transport coefficients with the increase in the values of yield stress and absorption parameter. Moreover, the transport coefficients and the axial mean concentration get significantly perturbed by the severity of the stenosis. Obtained results presented graphically concur with existing steady-state results in the literature. The present study would certainly be of some use in the case of targeted drug delivery and in treatment related to microvascular disease.