Peristaltic transport of a power-law fluid induced by a single wave: A numerical analysis using the cumulant lattice Boltzmann method

Abstract

Peristaltic pumping is the primary mechanism of food transport in the human intestine. Intestinal contents are often modeled as power-law fluids with low-behavior indices ( n < 1). Peristaltic flows were studied for periodic contraction waves ([Formula: see text]) with infinitely long wavelengths ([Formula: see text]) in the Stokes flow regime ([Formula: see text]). However, the peristaltic flow generated by an isolated contraction wave with a short wavelength at nonzero Reynolds numbers is more relevant to physiological conditions. In this study, we investigated the peristaltic transport of a power-law fluid with a low behavior index of n = 0.21 at nonzero Reynolds numbers up to Re = 10, generated by a single short contraction wave. First, we investigated the analytical solution for the peristaltic transport of the power-law fluid for [Formula: see text] and [Formula: see text]. The analytical solution shows that the discharge flow rate of a power-law fluid generated by a single contraction wave is much smaller than that of a Newtonian fluid ( n = 1). Next, we investigated the peristaltic transport for [Formula: see text] 10 using the cumulant lattice Boltzmann method. The numerical results demonstrate that the discharge flow rate for the power-law fluid sharply increased owing to the inertia effect. The power-law fluid induces an asymmetric flow field with respect to the contraction wave at smaller Reynolds numbers than Newtonian fluids. The inertia effect was increased by the sharpness of the contraction wave. These results suggest that intestinal contents can be transported more quickly by an isolated contraction wave with a shorter wavelength when the contents have low consistency indices or when the contraction wave has a large propagation velocity.