Influence of the oscillatory Péclet number and periodic body acceleration on the unsteady Taylor dispersion in a non Newtonian fluid flow in a microvessel

In this study, we investigate unsteady solute dispersion in the pulsatile flow of a non-Newtonian Herschel–Bulkley fluid through a circular tube under the influence of periodic body acceleration/deceleration. A new nondimensional time scaling, $t=t^{\prime }\omega$ ($\omega$ is the frequency of body acceleration) (Singh and Murthy, J. Fluid Mech., vol. 962, 2023, A42), is employed to capture unsteady effects more effectively, in contrast to the classical scaling $t_1=D_m{t}^{\prime }/R^2$ (with $D_m$ as molecular diffusivity and $R$ as the tube radius) used in earlier works (Rana and Murthy, J. Fluid Mech., vol. 793, 2016, pp. 877–914). This new framework simplifies the governing equations by preserving the sinusoidal form of the oscillatory pressure gradient, $p\left(t\right)=2(1+e\sin (t\left)\right)$, and connects with the classical scaling through the relation $t={\alpha }^2\times Sc\times t_1$, where $e$ is the pressure pulsation gradient, $\alpha$ is the Womersley frequency parameter, and $Sc$ is the Schmidt number. Velocity profiles are obtained for all values of Womersley frequency parameters. Solute transport is analyzed using Aris’ method of moments, considering higher-order measures such as skewness and kurtosis that lead to non-Gaussian concentration profiles. Three solute dispersion regimes are investigated, which are governed by the Péclet number ($Pe$), Womersley frequency parameters ($\alpha$), and the oscillatory Péclet number ($P^2$). The oscillatory Péclet number strongly affects the exchange coefficient $K_0\left(t\right)$, and the effect of body acceleration ($M$), wall absorption ($\beta$), and other parameters on the convection, dispersion, skewness, and kurtosis coefficients ($K_1\left(t\right)$–$K_4\left(t\right)$) are systematically.