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Advective collisions

B. Andersson1, K. Gustavsson1, B. Mehlig1 and M. Wilkinson2

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Small particles advected in a fluid can collide (and therefore aggregate) due to the stretching or shearing of fluid elements. This effect is usually discussed in terms of a theory due to Saffman and Turner (J. Fluid Mech., 1 (1956) 16). We show that in complex or random flows the Saffman-Turner theory for the collision rate describes only an initial transient (which we evaluate exactly). We obtain precise expressions for the steady-state collision rate for flows with small Kubo number, including the influence of fractal clustering on the collision rate for compressible flows. For incompressible turbulent flows, where the Kubo number is of order unity, the Saffman-Turner theory is an upper bound.


PACS

05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion

92.60.Mt Particles and aerosols

45.50.Tn Collisions

Subjects

Mathematical physics

Environmental and Earth science

Statistical physics and nonlinear systems

Dates

Issue 6 (December 2007)

Received 8 October 2007, accepted for publication 23 October 2007

Published 20 November 2007

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  1. Advective collisions

    B. Andersson et al 2007 EPL 80 69001

  2. Ergodic and non-ergodic clustering of inertial particles

    K. Gustavsson and B. Mehlig 2011 EPL 96 60012

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