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 in a suspended 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.

Gravitational dispersion of solid particles in a liquid-filled channel can be seen in various engineering processes. However, it is known that the dispersion behavior is greatly influenced by properties of suspension and channel geometry. In this study, the gravitational dispersion behaviors of solid particles into a liquid-filled complex channel are examined experimentally. Particularly we focus on the dispersion of particles during the collective settling which occurs when the particle size is small and the concentration is large. In such conditions, the suspended particles form a finger-like blob and they behave as a continuum which is immiscible to surrounding fluid. We experimentally observed the collective settling in a fractal-shaped transparent channel. We also developed a scale-independent model on temporal change of the occupancy ratio of suspended particles in channels having fractal characteristics.