Kinetics of fragmentation-annihilation processes

Abstract

We investigate the kinetics of systems in which particles of one species undergo binary fragmentation and pair annihilation. In the latter, nonlinear process, fragments react at collision to produce an inert species, causing loss of mass. We analyze these systems in the reaction-limited regime by solving a continuous model within the mean-field approximation. The rate of fragmentation for a particle of mass x to break into fragments of masses y and x-y has the form ${\mathit{x}}^{\ensuremath{\lambda}\mathrm{\ensuremath{-}}1}$ (\ensuremath{\lambda}>0), and the annihilation rate is constant and independent of the masses of the reactants. We find that the asymptotic regime is characterized by the annihilation of small-mass clusters, with the cluster density decaying as in pure annihilation and the average cluster mass as in pure fragmentation. The results are compared with those for a model with linear mass loss (i.e., with a sink rather than a reaction). We also study more complex models, in which the processes of fragmentation and annihilation are controlled by mutually reacting catalysts. Both pair and linear annihilation are considered. Depending on the specific model and initial densities of the catalysts, the time decay of the cluster density can now be very unconventional and even nonuniversal. The interplay between the fragmentation and annihilation processes and the existence of a scaling regime are determined by the asymptotic behavior of the average mass and of the mass density, which may either decay indefinitely or tend to a constant value. We discuss further developments of this class of models and their potential applications. \textcopyright{} 1996 The American Physical Society.