Eur. Phys. J. B 65, 279-288 (2008)
https://doi.org/10.1140/epjb/e2008-00354-y

Perturbation theory for large Stokes number particles in random velocity fields

¹ ISAC-CNR and INFN, Sez. Cagliari, 09042 Monserrato, Italy
² Dipartimento di Fisica and INFN, Università di Cagliari, 09042 Monserrato, Italy

Corresponding author: ^a olla@dsf.unica.it

Received: 21 January 2008
Revised: 15 June 2008
Published online: 23 September 2008

Abstract

We derive a perturbative approach to study, in the large inertia limit, the dynamics of solid particles in a smooth, incompressible and finite-time correlated random velocity field. We carry on an expansion in powers of the inverse square root of the Stokes number, defined as the ratio of the relaxation time for the particle velocities and the correlation time of the velocity field. We describe in this limit the residual concentration fluctuations of the particle suspension, and determine the contribution to the collision velocity statistics produced by clustering. For both concentration fluctuations and collision velocities, we analyze the differences with the compressible one-dimensional case. and 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion