Collision rates in chaotic flows: Dilute suspensions

We have computed collision rates between passive marker particles subject to the blinking vortex flow, a chaotic flow. The case of low number densities is considered, which is relevant for the later stages of the aggregation processes. The theory pertaining to this case is first reviewed. The computational results indicate that the time-averaged collision frequency achieves an asymptotic value (〈f〉_∞) for all number densities that is nearly independent of the initial positions of the particles. The dependence of 〈f〉_∞ on the system parameters was found to be similar to the predictions of the gradient theory of Levich $[---Physico-Chemical Hydrodynamics (Prentice-Hall, Englewood Cliffs, NJ, 1962), Sec. 40]; the magnitude of the collision rate was significantly smaller. The deviation, attributed to the structure in the flow, decreases rapidly with increasing number density. The results imply validity of the gradient theory for low number densities for chaotic flows.