Dispersion of inertial particles in cellular flows in the small-Stokes, large-Péclet regime

Antoine Renaud, Jacques Vanneste

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Abstract

We investigate the transport of inertial particles by cellular flows when advection dominates over inertia and diffusion, that is, for Stokes and Péclet numbers satisfying St≪1 and Pe≫1. Starting from the Maxey--Riley model, we consider the distinguished scaling StPe=O(1) and derive an effective Brownian dynamics approximating the full Langevin dynamics. We then apply homogenisation and matched-asymptotics techniques to obtain an explicit expression for the effective diffusivity D¯¯¯¯ characterising long-time dispersion. This expression quantifies how D¯¯¯¯, proportional to Pe−1/2 when inertia is neglected, increases for particles heavier than the fluid and decreases for lighter particles. In particular, when St≫Pe−1, we find that D¯¯¯¯ is proportional to St1/2/(log(StPe))1/2 for heavy particles and exponentially small in StPe for light particles. We verify our asymptotic predictions against numerical simulations of the particle dynamics.
Original languageEnglish
Number of pages17
JournalJournal of Fluid Mechanics
Volume903
Early online date17 Sep 2020
DOIs
Publication statusPublished - 25 Nov 2020

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