Residence times of polydisperse dilute suspensions in sheared and extensional flows

Abstract

The residence time distribution (RTD) of tiny particles advected in flows primarily depends on the flow characteristics and is often approximated by the RTD of the carrying fluid itself. However, when particles have a finite response time, their residence times can significantly differ from those of fluid particles. Even though RTDs are frequently used in numerical or experimental studies, general theoretical results about the effect of the particle characteristics on the RTD are still missing, especially when the suspension is polydisperse. The present work focuses on plane shear and extensional flows, which are of crucial importance in many devices transporting inertial particles. It is known that shear and stretching lead to different signatures in the RTD of fluid particles: algebraic for the former and exponential for the latter. In this paper, these signatures are generalized theoretically to the case of polydisperse suspensions of weakly inertial particles. Our results show how flow gradients and polydispersity contribute to residence time distributions. They are shown to agree with RTDs calculated from statistics obtained from numerical simulations.