Scale-independent model of gravitational settling of particulate suspension in a fractal channel

Abstract

Gravitational settling of solid particles into a fractal-shaped channel was investigated experimentally and theoretically. Previous studies have reported that the settling behavior of particles in liquid-filled channels depends strongly on particle properties and suspension conditions. At small particle size and high concentration, particles settle collectively like an immiscible fluid with respect to the surrounding one. In this study, we examined the gravitational dispersion behavior of solid particles in a three-dimensional fractal-shaped channel under various collective conditions. The experimental results showed that the settling behavior varies with the collectivity of suspended particles. In the case of high collectivity conditions, settling velocity is enhanced by a density-driven instability, which depends not only on the physical properties of the particles and fluid but also on channel geometry. We developed a model of temporal change in the volumetric occupancy ratio of the suspended particles region. This model describes the invasion of particles into a fractal channel. Our model comprises only the fractal characteristics of the channel, such as a homothetic ratio and a bifurcation number. Consequently, This model could provide a rough prediction of the gravity-induced invasion behavior of particles into any fractal-shaped channel.