Mathematical modelling of unsteady solute dispersion in two-fluid (micropolar-Newtonian) blood flow with bulk reaction

Abstract

A mathematical model is developed for hemodynamic transport of a reactive diffusing species e.g., oxygen in a rigid artery under constant axial pressure gradient and undergoing a first-order chemical reaction with streaming blood. A two-fluid model is deployed where the core region is simulated as an Eringen micropolar fluid, and the plasma layer engulfing the core, i.e., near the boundary, is analyzed as Newtonian viscous fluid. Closed-form solutions are presented for the velocity and micro-rotation profiles, and a Gill decomposition method is deployed for the concentration field. Expressions are derived for the dispersion coefficient, mean and transverse concentration. Transverse concentration is observed to be enhanced with increasing micropolar coupling number (N) and reaction rate (β); however, it is reduced with greater micropolar material parameter (s) and viscosity ratio (λ). Axial mean concentration peaks are reduced in magnitude and displaced further along with the arterial geometry with greater micropolar material parameter values, whereas the opposite effect is induced with greater micropolar coupling number. The study is relevant to hemorheology, diseased arteries and coagulating hemodynamics and may help physiologists in furnishing a more refined understanding of diffusion processes in cardiovascular hydrodynamics.