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

Choi & Joseph (2001) reported a two-dimensional numerical investigation of the lift-off of 300 circular particles in plane Poiseuille flows of Newtoni an fluids. We perform similar simulations. Particles heavier than the fluid are initially placed in a closely packed ordered configuration at the bott om of a periodic channel. The fluid-particle mixture is driven by an extern al pressure gradient. The particles are suspended or fluidized by lift forc es that balance the buoyant weight perpendicular to the flow. Pressure wave s corresponding to the waves at the fluid-mixture interface are observed. D uring 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 incre ased. Heavier particles are lifted to a smaller equilibrium height at the s ame Reynolds number. A correlation for the lift-off of many particles is ob tained from the numerical data. The correlation is used to estimate the cri tical shear Reynolds number for lift-off of many particles. The critical sh ear Reynolds number for lift-off of a single particle is found to be greate r than that for many particles. The procedures used here to obtain correlat ions from direct simulations in two dimensions and the type of correlations that emerge should generalize to three-dimensional simulations at present underway.