Diffusion-limited droplet coalescence

Simulations of diffusion limited (Brownian) droplet coalescence have been carried out in which the droplet diffusion coefficients are related to their sizes (masses), s, by D(s)∼sγ. For the case D = d where D is the droplet dimensionality and d is the dimensionality of the substrate, the exponents z and z′ describing the algebraic growth of the mean droplet size, S, and the decrease in the number of droplets, N, are given by z = z′= 1(2d − γ) with no logarithmic corrections for d = 2. If D > d, then for d = 2 the growth of S is given by S ∼[tln(t)]1(1−γ) and the decay of N is given by N ∼ [tln(t)]−1(1−γ). For d > 2, there are no logarithmic corrections and z = z′= D(D−Dγ−d + 2) in all cases. The time dependent cluster size distribution can be described in terms of the scaling form Ns(t)∼s−2f(sS(t)) where Ns(t) is the number of droplets of size s at time t. Simple scaling arguments indicate that these values obtained for the exponents z and z′ describing the asymptotic (t→∞) behavior from computer simulations are exact.