Solute dispersion in unsteady and viscous flow regimes of a non-Newtonian fluid flow with periodic body acceleration/deceleration

This study seeks to analyze unsteady solute dispersion in the pulsatile flow of a non-Newtonian Ellis fluid within a tube, influenced by periodic body acceleration and deceleration, across three distinct flow and dispersion regimes: viscous flow with diffusive dispersion, viscous flow with unsteady dispersion, and unsteady flow with unsteady dispersion. These are characterized by the interplay between the values of the Péclet number Pe, the Womersley frequency parameter α, which is associated with the pressure pulsation, and the oscillatory Péclet number P which has inherently the Schmidt number Sc. The fluid velocity is computed for all α, then Aris' method of moments is employed to solve the convection–diffusion equation considering the higher order moments. Impact of the body acceleration/deceleration parameter M, wall absorption parameter β, degree of shear thinning behavior index a, shear stress τ1/2, α, and the fluctuating pressure parameter e on the mean solute concentration Cm is investigated. The value of the dispersion coefficient decreased monotonically in the viscous flow with the diffusive dispersion region, while the skewness and kurtosis both have shown significant variations in the unsteady dispersion regime, which lead to the significant variation in the axial mean concentration. Graphical analysis reveals a leftward shift and a diminished peak in the mean concentration, resulting in non-Gaussian behavior under body acceleration/deceleration conditions. As τ1/2→∞, this Ellis fluid behaves like the Newtonian fluid, these results agree with those results for Newtonian fluid flow case.