The Basset–Boussinesq history force: its neglect, validity, and recent numerical developments

Abstract

Particle-laden flows are ubiquitous, ranging across systems such as platelets in blood, dust storms, marine snow, and cloud droplets. The dynamics of a small particle in such non-uniform flows, under the idealization of being rigid and spherical, is described by the Maxey–Riley–Gatignol equation, which includes the Basset–Boussinesq history force among other better-understood forces. The history force, which is an integral over time with a weakly singular kernel, is often neglected, not because such neglect is known to be justified, but because it is difficult to be included in general scenarios. It is becoming increasingly evident that there are situations where neglecting this force might not be valid. In this review, after introducing classical knowledge about the history force, we outline recent studies that suggest alternative forms for it and discuss the range of validity of each, and describe recent numerical methods that have been developed to efficiently compute the history force. The question of whether the history force matters requires careful consideration and can be settled only with its accurate inclusion. We hope this review will help researchers addressing the multitude of open questions related to particulate flows to account for this effect.