Inertial forces in the Maxey–Riley equation in nonuniform flows

Abstract

Here, inertial forces on particles in nonuniform ambient flows, previously missing from the Maxey---Riley formulation of inertial particle dynamics, are identified. These forces involve both local and convective fluid inertia and depend on the curvature of the ambient flow. These new terms provide quantitative corrections and qualitative additions to the Maxey---Riley equation and are relevant when the particle size is appreciable relative to the characteristic length scale of the ambient flow.