Flow enhancement produced by a pulsatile flow of shear-thinning fluids in circular and concentric annular tubes

Abstract

Although the analysis of the flow enhancement of non-Newtonian fluids produced by pulsatile flows through tubes is common in the literature, the case of Carreau fluid has not been analyzed, which is the aim of this work. This study determines the flow enhancement caused by the pulsatile fluid flow through (a) a circular tube and (b) a concentric annular tube. We show that the flow rate enhancement of the shear-thinning fluid is controlled by the Carreau number $Cu$, the Womersley number $Wo$, the fluid power-law index $n$, the ratio between the outer and inner radii $\kappa$, a parameter $\beta$ that represents the ratio between the infinite and zero-shear viscosities, and the amplitude of the oscillatory signal $\varepsilon$. In both cases (a) and (b), a numerical solution of the start-up of the hydrodynamic is evaluated. With the aid of the velocity solution, the volumetric flow rate is determined under periodic conditions after the initial transient has vanished. Then, the fractional increase in the mean flow rate $I$ due to the pulsatile pressure gradient is calculated. Furthermore, an asymptotic solution for small, intermediate, and very large values of the Carreau number is performed to provide physical insight into flow enhancement.