Unsteady solute dispersion in the presence of reversible and irreversible reactions

Abstract

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.