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Periodic homogenization for inertial particles

Pavliotis, G. A. and Stuart, A. M. (2005) Periodic homogenization for inertial particles. Physica D, 204 (3-4). pp. 161-187. ISSN 0167-2789. doi:10.1016/j.physd.2005.04.011.

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We study the problem of homogenization for inertial particles moving in a periodic velocity field, and subject to molecular diffusion. We show that, under appropriate assumptions on the velocity field, the large scale, long time behavior of the inertial particles is governed by an effective diffusion equation for the position variable alone. To achieve this we use a formal multiple scale expansion in the scale parameter. This expansion relies on the hypo-ellipticity of the underlying diffusion. An expression for the diffusivity tensor is found and various of its properties studied. In particular, an expansion in terms of the non-dimensional particle relaxation time τ (the Stokes number) is shown to co-incide with the known result for passive (non-inertial) tracers in the singular limit τ→0. This requires the solution of a singular perturbation problem, achieved by means of a formal multiple scales expansion in τ Incompressible and potential fields are studied, as well as fields which are neither, and theoretical findings are supported by numerical simulations.

Item Type:Article
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URLURL TypeDescription Paper
Additional Information:© 2005 Elsevier B.V. Received 17 September 2004, Revised 5 April 2005, Accepted 13 April 2005, Available online 17 May 2005.
Subject Keywords:Inertial particles; Periodic homogenization; Effective diffusivity; Hypoellipticity
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Other Numbering System NameOther Numbering System ID
Andrew StuartJ64
Issue or Number:3-4
Record Number:CaltechAUTHORS:20170609-143518545
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Official Citation:G.A. Pavliotis, A.M. Stuart, Periodic homogenization for inertial particles, Physica D: Nonlinear Phenomena, Volume 204, Issue 3, 2005, Pages 161-187, ISSN 0167-2789, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78068
Deposited By: Tony Diaz
Deposited On:09 Jun 2017 22:23
Last Modified:15 Nov 2021 17:36

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