Falling clouds of particles with finite inertia in viscous flows

Abstract

When sedimenting in a viscous fluid under gravity, a cloud of particles undergoes a complex shape evolution due to the hydrodynamic interactions. In this work, Lagrange particle dynamic simulation, which combines the Oseen solution for flow around a particle and a Gauss–Seidel iterative procedure, is adopted to investigate the effects of the particle inertia and the hydrodynamic interactions on the cloud's sedimentation behavior. It is found that, with a small Stokes number (St), the cloud evolves into a torus and then breaks up into secondary clouds. In contrast, the cloud with a finite Stokes number becomes compact in the horizontal direction and is elongated along the vertical direction. The critical St value that separates the breakup mode and the vertical elongation mode is around 0.2. The cloud response time (t̂r) and the maximum settling velocity (V̂max) are measured at different Stokes numbers, particle Reynolds numbers, and particle volume fractions. A linear relationship, t̂r=aSt, is found between t̂r and the Stokes number and the correlation between V̂max and St can be well described by an exponential function V̂max=b1exp−b2St+b3. At last, the chaotic dynamics of the sedimentation system are discussed. A small difference between the initial configurations diverges exponentially. The sedimentation system containing particles with larger inertia has a lower divergence rate.