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

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Original languageEnglish
Number of pages17
JournalJournal of Fluid Mechanics
Volume903
Early online date17 Sep 2020
DOIs
Publication statusPublished - 25 Nov 2020

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.

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