Condensation-Driven Aggregation in One Dimension

TL;DR

This paper introduces an exactly solvable one-dimensional model of particle aggregation driven by heterogeneous condensation, revealing a dynamic scaling transition and a new conservation law affecting scaling exponents.

Contribution

It presents a novel exactly solvable model for condensation-driven aggregation in one dimension, deriving new scaling relations and conservation laws.

Findings

Particle size spectra exhibit dynamic scaling with specific exponents.

The scaling exponents satisfy a generalized relation involving a fixed parameter.

Condensation reduces the value of the scaling exponent compared to pure aggregation.

Abstract

We propose a model for aggregation where particles are continuously growing by heterogeneous condensation in one dimension and solve it exactly. We show that the particle size spectra exhibit transition to dynamic scaling $c(x,t)\sim t^{-\beta}\phi(x/t^z)$. The exponents $\beta$ and $z$ satisfy a generalized scaling relation $\beta=(1+q)z$ where the value of $q$ is fixed by a non-trivial conservation law. We have shown that the value of $(1+q)$ is always less than the value 2 of aggregation without condensation.