Settling dynamics of circular particles in vibrating tanks filled with a yield-stress liquid

Abstract

The effect of sinusoidal vibration is numerically investigated on the settling dynamics of a heavy particle of circular shape immersed in a viscoplastic fluid obeying the regularized Bingham–Papanastasiou (BP) model. Having modeled the solid particle as a highly viscous Newtonian droplet, we have relied on the finite element method for solving the equations of motion for the particle and the surrounding fluid. Our numerical results could closely recover the theoretical critical Bingham number of 0.0658 for circular particles settling in Bingham materials. Using a very small threshold velocity to decide whether a particle is stuck or unstuck, it is shown that stuck particles can be excited to fall in the BP liquid provided that, for any given frequency, the amplitude is larger than a minimum value. An increase in the size of the particle or its density is predicted to reduce the threshold amplitude. In general, vibration is found to have an accelerating effect on particle settling in the BP liquid although the effect is non-monotonic. The accelerative effect of vibration is attributed to the enlarged size of the yielded zone, while the non-monotonic behavior is attributed to the effect of the sidewalls. At high density ratios, a phase lag is predicted to arise between the particle and the vessel. A comparison between the obtained numerical results with published experimental data for spherical particles suggests that, in settling flows, circular particles can be used as a good paradigm for spherical particles.