Diffusion-limited droplet coalescence

Paul Meakin

Physica A: Statistical Mechanics and its Applications, 1990, vol. 165, issue 1, 1-18

Abstract: 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.

Date: 1990
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:165:y:1990:i:1:p:1-18

DOI: 10.1016/0378-4371(90)90238-N

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