Diffusion-controlled growth in a crowded environment

A growth rate expression was derived for the diffusion-controlled growth of particles in a crowded open system where new solute materials are continuously introduced. The interparticle effect was represented by a "crowding factor", η, which depends on particle size, diffusion layer thickness, and interparticle distance. For diffusion-controlled growth in a noncrowded system, η is equal to one. However, when the interparticle distance is smaller than or comparable to the finite diffusion layer thickness, η is greater than one. This results in a significant increase in the growth rate for a given supersaturation. The theoretical concepts were used to explain the effect of interparticle distance on the growth rates of AgBr crystals reported in the literature.