Macroscopic characteristics of heavy particle resuspension obtained from direct numerical simulations of pressure driven channel flow

Three-dimensional direct numerical simulations are presented of the flow of fluid containing heavy spherical particles in a channel. The simulations resolve the motion of individual particles and the details of the flow at the particle level. They are based on the finite element method and the Distributed Lagrange Multiplier/ Fictitious Domain Method. The problem is characterized by four parameters, namely a Reynolds and an Archimedes number, a density ratio and a dimensionless particle size. The last three are fixed and the effects of the Reynolds number are studied over a range covering the onset of particle resuspension and the transition of flow to significant unsteadiness. Encouraging estimates for the onset of resuspension and the particle flux as a function of the excess Shields number are found. The results are analyzed in terms of the vertical distribution of horizontally averaged macroscopic quantities, obtained by applying integral momentum balances. On the basis of such balances, particle stresses and interfacial forces between the fluid and particle phases are estimated and compared to existing models, developed mainly for Stokes flow conditions. The qualitative agreement is encouraging but points to the need for taking into account several effects, notwithstanding those of finite particle Reynolds numbers. Provided that such information becomes available the set of four equations derived from the suspension and particle phase momentum equations could describe the average equilibrium distribution, the flow of both phases and the pressure in the fluid.