Borderline Aggregation Kinetics in ``Dry'' and ``Wet'' Environments

TL;DR

This paper analyzes the kinetics of aggregation processes influenced by evaporation and condensation, revealing critical behaviors, scaling laws, and exact solutions for different growth rates and environmental conditions.

Contribution

It provides a comprehensive analysis of aggregation-evaporation and aggregation-condensation kinetics, including exact solutions and asymptotic behaviors for various growth models.

Findings

Critical evaporation rate leads to a $k^{-5/2}$ mass distribution.

Typical cluster mass grows as $t^{2/3}$ at critical evaporation.

Scaling laws depend on the cluster growth rate $L_k$, with different growth behaviors.

Abstract

We investigate the kinetics of constant-kernel aggregation which is augmented by either: (a) evaporation of monomers from finite-mass clusters, or (b) continuous cluster growth -- \ie, condensation. The rate equations for these two processes are analyzed using both exact and asymptotic methods. In aggregation-evaporation, if the evaporation is mass conserving, \ie, the monomers which evaporate remain in the system and continue to be reactive, the competition between evaporation and aggregation leads to several asymptotic outcomes. For weak evaporation, the kinetics is similar to that of aggregation with no evaporation, while equilibrium is quickly reached in the opposite case. At a critical evaporation rate, the cluster mass distribution decays as $k^{-5/2}$, where $k$ is the mass, while the typical cluster mass grows with time as $t^{2/3}$. In aggregation-condensation, we consider the process with a growth rate for clusters of mass $k$, $L_k$, which is: (i) independent of $k$, (ii) proportional to $k$, and (iii) proportional to $k^\mu$, with $0<\mu<1$. In the first case, the mass distribution attains a conventional scaling form, but with the typical cluster mass growing as $t\ln t$. When $L_k\propto k$, the typical mass grows exponentially in time, while the mass distribution again scales. In the intermediate case of $L_k\propto k^\mu$, scaling generally applies, with the typical mass growing as $t^{1/(1-\mu)}$. We also give an exact solution for the linear growth model, $L_k\propto k$, in one dimension.