The laminar viscous resuspension of sphere particles in two-dimensional channel with gravity and electrostatic effects is studied numerically. The constitutive equation for particles include the shear-induced diffusion flux, gravitational sedimentation flux and electro-static diffusion flux. In addition the continuity equation and the momentum equations for incompressible flow are solved for developing flow using finite element method.

The parameters in this study are ratio of particle diameter to channel height d/h, Reynolds number Re, Froude number Fr, uniform inlet particle volume fraction Φ₀, and electrostatic parameter Q. The numerical simulation included d/h from 0.03 to 0.12, Re from 5 to 46, Fr from 0.048 to 0.38, Φ₀ from 0.20 to 0.35 and Q from 0 to 0.005.

It was found that there may exist three maximum particle concentrations; between the channel centerline and the top channel wall, along the centerline and between the centerline and the bottom channel wall. However due to gravity effect the highest particle concentration is at the bottom wall. The maximum concentration near the top wall increases with increasing Φ₀ for 0.3>Φ₀>0.20. At d/H=0.03 and Φ₀=0.30 this maximum is Φ/Φ₀, = 1.40. This maximum concentration also increases with decreasing d/H ratio.

The electrostatic force tends to diminish the maximum concentration near the top wall but enhance the maximum near the centerline. It was found that the electrostatic effect may be neglected when Q<O. 000 1 and may become significant when Q>O. 00 1.The velocity profile of the fluid deviates from the Poiseuille flow (parabolic) profile in the top portion of the channel. At the midway between the centerline and the top wall the velocity is about I I % higher than that of parabolic profile.Comparison with some experimental results for flow in a circular tube gives qualitatively good agreement.