One-dimensional coagulation: Scaling and phase-separation dynamics

A simulation of a one-dimensional coagulating system of droplets with mass-dependent diffusion coefficients is presented. The total droplet density is shown to decay as $t^{\mathrm{-}1/3}$ and the density of droplets of mass l decays as exp(-${\mathrm{ct}}^{1/3}$/l) in the long-time limit. Simple kinetic arguments are derived which predict these results. The scaling behavior and the similarity to phase-separation dynamics is investigated. The scattering function is calculated. It develops a well-defined peak which grows in intensity and shifts to lower wave vectors as a function of time. The scattering function and the droplet-size distribution are both shown to assume scaled forms in the late stages.