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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.

In an unsteady pulsatile non-Newtonian fluid past a tube with a thin wall layer, the dispersion of a narrow uniform slug of injected solute over a cross-section is examined. At the interface between the mobile fluid phase and the immobile wall phase, both irreversible and reversible reactions have been adopted. The Carreau–Yasuda model is used to describe the fluid’s rheology. The impacts of fluid rheology and reaction parameters on the concentration profiles in the fluid- and wall-phases and the three transport coefficients, viz , the depletion coefficient ( K 0 ) , the convection coefficient ( K 1 ) , the dispersion coefficient ( K 2 ) in the fluid phase are predicted numerically. A considerable shift in the behaviour of K 1 and K 2 with a higher reaction rate may be observed in the transient stage. The axial dispersion of mobile-phase concentration in the unsteady Carreau–Yasuda II fluid model is significantly larger than in Poiseuille and steady Carreau–Yasuda II fluid models, and flow pulsatility on the immobile-phase concentration is prominent upstream at a longer time. In addition, the peak value of the mobile-phase section-mean concentration is consistently lower than in other fluid models. This study could help researchers to understand the drug delivery in blood vessels and pulmonary mechanical ventilation.

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