Studying effects of nonuniform particle laden flows from uniform particle suspensions

Most practical particle laden flows are non-uniform, while the drag models used in our calculations are obtained from studies of uniform flows. Performing particle resolved direct numerical simulations (PRDNS) in a nonuniform particle distribution encounters many theoretical and practical difficulties. In this talk we show how to process the expensive and valuable PRDNS results obtained from uniform flows to infer drag models for nonuniform cases. We show that the drag force in a non-uniform disperse multiphase flow can be decomposed into three terms. For steady flows, these terms are the drag force, the diffusion stress, and the particle-fluid--particle (PFP) stress. Models for these terms can be studied using PRDNS results performed in statistically uniform particle distributions. Within an error proportional to the square of the ratio between the mean particle distance to the macroscopic length scale, such obtained force models are applicable to systems with non-uniform particle distributions. The force decomposition was first derived using the nearest particle statistics (Zhang, 2021, J. Fluid Mech., 910, A16, Wang et al., 2024, Phys. Rev. Fluids, 9, 2024, 104301). This talk provides an independent alternative derivation.