Moment analysis of unsteady bi-component species (drug) transport with coupled chemical reaction in non-Newtonian blood flow

Abstract

Motivated by exploring the fluid dynamics of dual drug delivery systems in biomedicine, a mathematical analysis of the bi-component species transport (convective-diffusion) in rheological blood flow with bulk chemical reaction through a two-dimensional rigid vessel is presented. Two different bulk degradation reaction rates are included for the dual species (pharmacological agents, A, B). An analytical expression for axial velocity is derived using a perturbation method. The decoupled convection-diffusion equations are then analyzed with the Aris – Barton approach. The mean concentration of the species is estimated using the first five concentration moments with the aid of fourth order Hermite polynomials. A finite difference technique based on the Crank Nicholson implicit scheme is employed to handle the pth order moment of the general concentration. The analysis reveals that increasing reversible transfer rate and irreversible bulk degradation result in a reduction in the total mass of the species over time. The mass of both species decreases with an increase in reversible transfer rate, even though the mass of species A depletes faster than the mass of species B. The skewness of the concentration distribution decreases as yield stress increases and the distributions in all scenarios are positively skewed and tend to zero over time, implying that the distribution tends to symmetry over time. The kurtosis decreases over time from positive to negative values and eventually approaches zero. Mean concentration peaks for both species A and B are elevated with increasing yield stress, although magnitudes are significantly higher for species A. With increasing values of the distribution coefficient between two species, mean concentration peaks are elevated for species (component) A whereas they are depleted for species B, although substantially greater magnitudes are computed for species B. Good correlation of the skewness with earlier Newtonian results is achieved. The results provide some useful insight into the bi-component drug transport in smaller vessel pharmacodynamics where hemorheology is important.