Scaling theory for diffusion limited cluster aggregation in a porous medium

TL;DR

This paper develops a scaling theory for diffusion-limited cluster aggregation in porous media, predicting three regimes of particle and cluster sticking behavior based on concentration levels, with smooth transitions between regimes.

Contribution

It introduces a novel scaling framework that describes different aggregation regimes in porous media, connecting microscopic sticking processes to macroscopic network formation.

Findings

Identifies three distinct aggregation regimes based on particle concentration.

Predicts smooth crossovers between regimes.

Provides a theoretical basis for pore-space-filling network formation.

Abstract

A scaling theory is developed for diffusion-limited cluster aggregation in a porous medium, where the primary particles and clusters stick irreversibly to the walls of the pore space as well as to each other. Three scaling regimes are predicted, connected by smooth crossovers. The first regime is at low primary particle concentrations where the primary particles stick individually to the walls. The second regime is at intermediate concentrations where clusters grow to a certain size, smaller than the pore size, then stick individually to the walls. The third regime is at high concentrations where the final state is a pore-space-filling network.