Dynamics and growth of particles undergoing ballistic coalescence

Abstract

The irreversible evolution of a model for ballistic coalescence of spherical particles, whereby colliding particles merge into a single, larger sphere with conservation of mass and momentum, is analyzed on the basis of scaling assumptions, mean-field theory, and kinetic theory for arbitrary dimensionality and size-mass relation. The asymptotic growth regime is characterized by scaling laws associated with the instantaneous mean mass and kinetic energy of the particles. A hyperscaling relation between the mass and energy exponents is derived. The predictions of the theoretical analysis are tested by extensive simulations of the two-dimensional version of the model. Due to multiple coalescence events, the exponents are found to be nonuniversal (i.e., density dependent) and to differ significantly from the mean-field predictions. The distribution of masses turns out to be universal and exponential. Particle energies follow a Boltzmann distribution, with a time-dependent temperature, or relax toward such a distribution, even when the initial distribution is highly non-Maxwellian. In the case where the particles are “swollen” [i.e., the size-mass relation involves the Flory exponentv=3/(d+2)], an asymptotic scaling regime is observed only for sufficiently low initial packing fractions. At higher densities, the irreversible evolution terminates in a “catastrophic” coalescence event involving all remaining particles.