Volume 83, Number 4, August 2008
Article Number 44002
Number of page(s) 4
Section Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics
Published online 19 August 2008
EPL, 83 (2008) 44002
DOI: 10.1209/0295-5075/83/44002

Scaling theory for diffusion-limited cluster aggregation in a porous medium

P. B. Warren

Unilever R&D Port Sunlight - Bebington, Wirral, CH63 3JW, UK, EU

received 1 May 2008; accepted in final form 7 July 2008; published August 2008
published online 19 August 2008

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. The time to reach the final state is also calculated for all three cases.

47.57.eb - Diffusion and aggregation.
61.43.Hv - Fractals; macroscopic aggregates (including diffusion-limited aggregates).
89.75.Da - Systems obeying scaling laws.

© EPLA 2008