Solving the inertial particle equation with memory

Abstract

The dynamics of spherical particles in a fluid flow is governed by the well-accepted Maxey–Riley equation. This equation of motion simply represents Newton’s second law, equating the rate of change of the linear momentum with all forces acting on the particle. One of these forces, the Basset–Boussinesq memory term, however, is notoriously difficult to handle, which prompts most studies to ignore this term despite ample numerical and experimental evidence of its significance. This practice may well change now due to a clever reformulation of the particle equation of motion by Prasath, Vasan & Govindarajan (J. Fluid Mech., vol. 868, 2019, pp. 428–460), who convert the Maxey–Riley equation into a one-dimensional heat equation with non-trivial boundary conditions. Remarkably, this reformulation confirms earlier estimates on particle asymptotics, yields previously unknown analytic solutions and leads to an efficient numerical scheme for more complex flow fields.