Falling plumes of point particles in viscous fluid

Abstract

The growth of radial bulges on the conduit of a falling viscous plume of particles, reported by Pignatel et al. for a finite starting plume [F. Pignatel, M. Nicolas, E. Guazzelli, and D. Saintillan, “Falling jets of particles in viscous fluids,” Phys. Fluids 21, 123303 (2009)10.1063/1.3276235], is investigated both numerically and analytically. As a model for the plume conduit, an infinite vertical cylinder of identical non-Brownian point particles falling under gravity in Stokes flow is considered. Numerically, this is implemented with periodic boundary conditions of a large, but finite, period. The quasi-periodic numerical simulations exhibit qualitatively similar behaviour to that previously observed for the finite plume, demonstrating that neither the plume head nor the plume source play a role in the growth of the radial bulges. This growth is instead shown to be due to fluctuations in the average number density of particles along the plume about its mean value n, which leads to an initial growth rat...