ON THE COLLISION RATE OF SMALL PARTICLES IN ISOTROPIC TURBULENCE .1. ZERO-INERTIA CASE

Numerical experiments have been performed to study the geometric colli sion rate of finite-size particles with zero inertia (i.e., fluid elem ents) in isotropic turbulence. The turbulent flow was generated by the pseudospectral method. We argue that the formulation of Saffman and T urner [J. Fluid Mech. 1, 16 (1956)] for the average collision kernel i s correct only under the assumptions that the particles are kept in th e system after collision and allowed to overlap in space. This was con firmed, for the first time, by numerical experiments to within a numer ical uncertainty as small as 1%. Finite corrections to the Saffman and Turner result must be made if one applies the theory to actual coagul ation process where particles are not allowed to overlap before collis ion and particles are removed from a given size group after collision. This is due to the fact that Saffman and Turner assumed a uniform, ti me-independent concentration field in their formulation of the average collision kernel, while in the actual modeling of population evolutio n the particle number concentration changes in time and may be locally nonuniform as a result of a biased removal process due to spatially n onuniform coagulation rates. However, the quantitative level of the de viations from the Saffman and Turner result remain to be explained. Nu merical experiments in simple shear flow were also conducted to elabor ate our findings. (C) 1998 American Institute of Physics.