Unsteady solute dispersion in pulsatile Luo and Kuang blood flow (K- L Model) in a tube with wall reactive absorption

Unsteady solute dispersion in pulsatile non-Newtonian flow in a circular tube has been investigated considering higher order moments using the Aris's method of moments. The Luo and Kuang (1992) (K -L Model) constitutive relation is used for the non-Newtonian fluid. The axial mean concentration of solute is estimated by considering exchange, convective, dispersion coefficients. In addition, considering the 3rd and 4th central moments, the skewness, and kurtosis in the mean concentration is examined. Variations of these five moments against the reactive absorption parameter, K-L fluid parameters, and Womersley frequency parameter are thoroughly investigated. The increase in the Womersley frequency parameter led to the occurrence of a double frequency period for the dispersion coefficient, which influenced the skewness and kurtosis coefficients that led to the deviation from usual normal distribution of the mean concentration distribution at the starting of the dispersion process. The concentration distribution is skewed towards the central region of the tube. The concentration contours also reveal that the solute convection is more in the central region of the tube. The results for Newtonian, Bingham, and Casson fluid models are retrieved as special cases. The mean concentration has the highest peak for the K-L model and the lowest for the Newtonian fluid model. It is scattered axially more for the Bingham fluid than the Casson fluid. This investigation emphasizes that higher moments provide precise information about the solute dispersion in the flow field and its deviation from the normal distribution at small time scales.