Effect of the volume fraction gradient on the phase interaction force model for disperse two-phase flows

Particle-resolved numerical simulations with a macroscopic gradient in the particle concentration are performed. The velocity contours for flows along (left) and against (right) the particle concentration gradient suggest different average particle-fluid interaction forces in these flows. We show that the average forces can be decomposed into the drag force, which is independent of the particle concentration gradient, and two terms related to the particle-fluid-particle (PFP) stress and the diffusion stress. The effect of the concentration gradient is accounted by the two stress related terms. These stresses can be studied in statistically uniform flows.