A correlation for the lift-off of many particles in plane Poiseuille flows of Newtonian fluids

Choi and Joseph (2001) reported a two-dimensional numerical investigation of the lift-off of 300 circular particles in plane Poiseuille flows of Newtonian fluids. We perform similar simulations. Particles heavier than the fluid are initially placed in a closely packed ordered configuration at the bottom of a periodic channel. The fluid-particle mixture is driven by an external pressure gradient. The particles are suspended or fluidized by lift forces that balance the buoyant weight perpendicular to the flow. Pressure waves corresponding to the waves at the fluid-mixture interface are observed. During the initial transient, these waves grow, resulting in bed erosion. At sufficiently large shear Reynolds numbers the particles occupy the entire channel width during the transient. The particle bed eventually settles to an equilibrium height which increases as the shear Reynolds number is increased. Heavier particles are lifted to a smaller equilibrium height at the same Reynolds number. A correlation for the lift-off of many particles is obtained from the numerical data. The correlation is used to estimate the critical shear Reynolds number for lift-off of many particles. The critical shear Reynolds number for lift-off of a single particle is found to be greater than that for many particles. The procedures used here to obtain correlations from direct simulations in two dimensions and the type of correlations that emerge should generalize to three-dimensional simulations at present underway.