Homogeneous reactive mass transport in a four layer model of KL-Newtonian fluids flowing through biporous layered microvessels

The present work is an effort to investigate the dispersion process of reactive mass transport in human blood vessels for varying viscosity and permeability. Considering a four-layer model of Luo and Kuang (KL)-Newtonian fluids flowing through a biporous layered microvessel, the current research focuses on unsteady mass transport under the first-order chemical reaction. A two-fluid model is adopted where the core region contains the KL fluid, depicting the flow of blood cells, and the coaxial peripheral region represents the plasma region. The outer plasma layer containing Newtonian fluid is segregated into three sublayers, where adjacent to the KL fluid is the non-porous plasma region. The outer two regions, the Brinkman and the Brinkman-Forchheimer regions exhibit radially varying permeability and viscosity characteristics. Analyzing the impact of the Froude number on the solute dispersion process necessitates incorporating an additional body force into the analysis. The porous medium equations are solved using regular and singular perturbation techniques to obtain closed-form solutions. Nevertheless, analytical solutions for the KL fluid and non-porous plasma layer have been derived. The analytical solution of mass distribution due to advection and diffusion is obtained through the Gill and Sankarasubramanian (1970) approach with the aid of Hankel transformation. The effect of various parameters such as Darcy's number, Forchheimer number, Reynolds number, Froude number, permeability parameters (epsilon(1), epsilon(2)), and viscosity parameters (alpha(1), alpha(2)) on the transport coefficients and mean concentration are discussed graphically. Higher Froude numbers caused weaker dispersion, while the parameters of the Brinkman-Forchheimer region have a significant effect on mass transport compared to the parameters of the Brinkman region. The findings of the current study may assist physiologists in developing a more nuanced understanding of these complex processes, ultimately leading to improved clinical outcomes.