Collisions of particles advected in random flows
Abstract
We consider collisions of particles advected in a fluid. As already pointed out by Smoluchowski (1917 Z. Phys. Chem. 92 129-68), macroscopic motion of the fluid can significantly enhance the frequency of collisions between the suspended particles. This effect was invoked by Saffman and Turner (1956 J. Fluid Mech. 1 16-30) to estimate collision rates of small water droplets in turbulent rain clouds, the macroscopic motion being caused by turbulence. Here, we show that the Saffman-Turner theory is unsatisfactory because it describes an initial transient only. The reason for this failure is that the local flow in the vicinity of a particle is treated as if it were a steady hyperbolic flow, whereas, in reality, it must fluctuate. We derive exact expressions for the steady-state collision rate for particles suspended in rapidly fluctuating random flows and compute how this steady state is approached. For incompressible flows, the Saffman-Turner expression is an upper bound.
- Publication:
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New Journal of Physics
- Pub Date:
- July 2008
- DOI:
- 10.1088/1367-2630/10/7/075014
- arXiv:
- arXiv:0801.2927
- Bibcode:
- 2008NJPh...10g5014G
- Keywords:
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- Nonlinear Sciences - Chaotic Dynamics
- E-Print:
- 24 pages, 3 figures