Aggregation growth in a gas of finite density: Velocity selection via fractal dimension of diffusion-limited aggregation

The structure and dynamics of an aggregation have been studied when the aggregate grows from a lattice gas with a nonzero gas density ng. At low ng and for a short length scale up to {ξ}, the structure of the aggregation is fractal and similar to the diffusion-limited aggregation (DLA). For a large length scale it is compact and has a nonzero asymptotic density. The steady growth rate V in d-dimensional space is inversely proportional to the characteristic length {ξ}, and depends on the density as V{~}ξ^-1{~}ng^1/(d-Df), with Df being the fractal dimension of DLA. Extensive Monte Carlo simulations in two dimensions confirm the above theoretical hypothesis of the velocity selection mechanism with Df=1.71. The interfacial width w is also found to be compatible with the expectation w{∝}ng^-1/2(d-Df). .AE