Advective collisionsB. Andersson1, K. Gustavsson1, B. Mehlig1 and M. Wilkinson2
1 Department of Physics, Göteborg University - 41296 Gothenburg, Sweden
2 Faculty of Mathematics and Computing, The Open University - Walton Hall, Milton Keynes, MK7 6AA, UK
received 8 October 2007; accepted in final form 23 October 2007; published December 2007
published online 20 November 2007
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.
92.60.Mt - Particles and aerosols.
45.50.Tn - Collisions.
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
© EPLA 2007