Collision Rate of Particles Advected in Random Flows

Abstract

Collisions of particles suspended in fluids in macroscopic motion is a subject with long history going back to M. v. Smoluchowsky (Zeitschrift f. physik. Chemie, XCII 129-168, (1917)) and P. G. Saffman & J. S. Turner (J. Fluid Mech., 1, 16-30, (1956)). In the case of smooth random flows, the problem can be solved exactly in certain limits, as is demonstrated in this thesis: An exact expression valid at small times for the collision rate between particles suspended in incompressible flows is derived derives and verified by computer simulations. Collision rate for incompressible flows valid at large times in the limit of small Kubo number, as well as collision rates in compressible flows valid in the two limits, small times, and large time in the limit of small Kubo number, are derived in B. Andersson, K. Gustavsson, B. Mehlig and M. Wilkinson (http://www.arxiv.org/pdf/nlin.CD/0702024). Computer simulations are performed to verify the available expressions for the collision rate and good agreement has been found in all cases.