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

Abstract

The structure and dynamics of an aggregation have been studied when the aggregate grows from a lattice gas with a nonzero gas density $n_g$. At low $n_g$ 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∼${\xi }^{\mathrm{-}1}$∼$n_g^{1/\left(d\mathrm{-}{D}_f\right)}$, with $D_f$ being the fractal dimension of DLA. Extensive Monte Carlo simulations in two dimensions confirm the above theoretical hypothesis of the velocity selection mechanism with $D_f$=1.71. The interfacial width w is also found to be compatible with the expectation w∝$n_g^{\mathrm{-}1/2\left(d\mathrm{-}{D}_f\right)}$. .AE