Effect of Vibration on the Settling Dynamics of Particles Stuck in Yield Stress Liquids: A Numerical Study

In the present study, the effect of a vessel’s vibration is numerically investigated on the settling dynamics of a single two-dimensional circular solid particle immersed in a viscoplastic fluid obeying the Bingham-Papanastasiou (BP) model. We have investigated the effect of different parameters on the response of a particle initially stuck in the BP fluid using the finite element method. Based on the obtained numerical results, the stuck particle can be excited to sediment in the BP liquid by vibrating the vessel in the vertical direction provided that the angular frequency and/or the amplitude of the forced oscillation are properly chosen. As a general rule, our numerical results demonstrate that by an increase in the angular frequency, the amplitude needed to unsettle a particle is reduced. The marginal frequency/amplitude combination needed to unsettle a stuck particle is predicted to decrease the larger the particle or the larger its density. Our numerical results show that sinusoidal waves are more effective than sawtooth waves to unsettle stuck particles. For a particle which is already settling in the BP material, it is predicted that vertical vibration is more effective than horizontal vibration to force sedimentation.