Abstract
We consider an abstract non-inertial model of aggregation under the influence of a Gaussian white noise with prescribed space-covariance, and prove a formula for the mean collision rate R, per unit of time and volume. Specializing the abstract theory to a non-inertial model obtained by an inertial one, with physical constants, in the limit of infinitesimal relaxation time of the particles, and the white noise obtained as an approximation of a Gaussian noise with correlation time τη , up to approximations the formula reads R ∼ τη((Δa,u)2)a · n2 where n is the particle number per unit of volume and ((Δa,u)2) is the square-average of the increment of random velocity field u between points at distance a, the particle radius. If we choose the Kolmogorov time scale τη ∼ (/)1/2 and we assume that a is in the dissipative range where ((Δa,u)2) ∼ (/)a2 , we get Saffman-Turner formula for the collision rate R.