Mehlig, B.; Wilkinson, M.; Duncan, K.; Weber, T. and Ljunggren, M.
(2005).
*Physical Review E*, 72 051104.

DOI (Digital Object Identifier) Link: | https://doi.org/10.1103/PhysRevE.72.051104 |
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Google Scholar: | Look up in Google Scholar |

## Abstract

We consider the trajectories of particles suspended in a randomly moving fluid. If the Lyapunov exponent of these trajectories is negative, the paths of these particles coalesce, so that particles aggregate. Here we give a detailed account of a method [B. Mehlig and M. Wilkinson, Phys. Rev. Lett. 92, 250602 (2004)] for calculating this exponent: it is expressed as the expectation value of a random variable evolving under a stochastic differential equation. We analyze this equation in detail in the limit where the correlation time of the velocity field of the fluid is very short, such that the stochastic differential equation is a Langevin equation. We derive an asymptotic perturbation expansion of the Lyapunov exponent for particles suspended in three-dimensional flows in terms of a dimensionless measure of the inertia of the particles, epsilon, and a measure of the relative intensities of potential and solenoidal components of the velocity field, Gamma. We determine the phase diagram in the epsilon-Gamma plane.

Item Type: | Journal Item |
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ISSN: | 1539-3755 |

Academic Unit/School: | Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics Faculty of Science, Technology, Engineering and Mathematics (STEM) |

Item ID: | 3486 |

Depositing User: | Michael Wilkinson |

Date Deposited: | 27 Jun 2006 |

Last Modified: | 07 Dec 2018 08:54 |

URI: | http://oro.open.ac.uk/id/eprint/3486 |

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