Shear-induced lift force on spheres in a viscous linear shear flow at finite volume fractions

Abstract

Several studies have shown a significant increase in drag on a distribution of solid spherical particles within a fluid with increasing particle volume fraction. As a result, many empirical drag laws accounting for the dependence on the Reynolds number and volume fraction can be found in the literature. This study investigates the possibility of a similar effect of the particle volume fraction on the mean hydrodynamic lift force on randomly distributed spherical particles in a linear shear flow. Particle-resolved direct numerical simulations are performed to evaluate the mean lift force, and the results are compared with the case of an isolated particle in a linear shear flow for the same Reynolds number and shear rate. The mean lift force acting on the particles appears to remain nearly the same as that on an isolated particle. However, due to the influence of neighboring particles, there is a substantial force variation in transverse directions on each individual particle, whose magnitude is comparable to the mean drag force. The distribution of drag force in a linear shear flow is shown to be nearly the same as in a uniform flow at the same volume fraction and Reynolds number. A simple stochastic model based on a Gaussian distribution is presented for the lift force variation, and its performance is compared to the prediction of the deterministic pairwise interaction extended point-particle model.