Dispersion phenomena of reactive solute in a pulsatile flow of three-layer liquids

Article Type

Research Article

Publication Title

Physics of Fluids


This study aims at investigating the dispersion process in an oscillatory flow of a layered liquid. The liquid is considered as a three-layer liquid where the center region is the Casson liquid surrounded by a Newtonian liquid layer flowing through a narrow pipe under the wall reaction. The perturbation technique has been used for solving the momentum equations. In order to assist the analysis of solute transport behavior, Aris-Barton's method of moments has been utilized, where different molecular diffusivities were assumed for different respective regions, yet to be constant. The effects of finite yield stress, viscosity ratio, density ratio, peripheral layer thickness, and irreversible absorption at the tube wall on dispersion are investigated in detail. In the cases of steady, unsteady, and combined flow situations, dispersion coefficient is found to be diminished by absorption parameter, viscosity ratio, and yield stress, respectively. In the case of a steady flow and unsteady convective diffusion of a reactive solute, dispersion coefficient is independent of density ratio. For both the unsteady and combined flows, density ratio provides a pulsatile behaviour of the dispersion process though an increase in the density ratio may faster the dispersion process. Dispersion at early times is not affected by absorption though a considerable effect is observed for large time. The presence of a peripheral layer enhances the value of the dispersion coefficient and is higher than the single layer Casson liquid flow. As strong as the non-Newtonian effect is considered, the dispersion process becomes slower. Larger values of molecular diffusivity at different layers are the reason for less dispersion coefficient. This study may be useful for understanding the dispersion process in the blood-like liquid flowanalysis for microcirculation.



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