Physics of Granular Flows

Title

Phase transition in peristaltic transport of granular particles

Abstract

Peristalsis is a progressive wave of area contraction and expansion in a tube. Transport due to the peristaltic motion of a tube is one of the main transport mechanisms in biological systems such as the esophagus, small intensine, ureter, and so forth [1]. Peristaltic transport is also found in the pumping of fluids, known as peristaltic pumps. While the study of peristaltic transport of fluids has a long history [1], there are few studies on the peristaltic transport of particles [2, 3]. Especially, the peristaltic transport of dense particles has never been studied.
We study flows of dissipative particles driven by the peristaltic motion of a tube using the discrete element methods [4]. A transition from a slow "unjammed" flow to a fast "jammed" flow is found through the observation of the flow rate at a critical width of the bottleneck of a peristaltic tube. In order to determine the value of the critical width, we observe the time when the flow profile transits from unstable unjammed flow to stable jammed flow. It is found that the average and fluctuation of the transition time, and the peak value of the second moment of the flow rate exhibit power-law divergence near the critical point and that these variables satisfy scaling relationships near the critical point. The dependence of the critical width and exponents on the peristaltic speed and the density is also discussed.

1. M. Y. Jaffrin and A. H. Shapiro, Annu. Rev. Fluid Mech. 3, 13 (1971).
2. T.-K. Hung and T. D. Brown, J. Fluid Mech. 73, 77 (1976).
3. J. Jiménez-Lozano, M. Sen, and P. F. Dunn, Phys. Rev. E 79, 041901 (2009).
4. N. Yoshioka and H. Hayakawa, Phys. Rev. E 85, 031302 (2012).