The diffusion of fractal aggregates constructed with the method by Thouy and Jullien (1994) comprised of Np spherical primary particles was studied as a function of the aggregate mass and fractal dimension using molecular dynamics simulations. It was shown that finite-size effects had a strong impact on the apparent value of the diffusion coefficient (D), but these could be corrected by carrying out simulations using different simulation box sizes. Specifically, the diffusion coefficient was inversely proportional to the length of a cubic simulation box, and the constant of proportionality appeared to be independent of the aggregate mass and fractal dimension. Using this result, it was possible to compute infinite dilution diffusion coefficients (Do) for aggregates of arbitrary size and fractal dimension, and it was found that Do Np -1/df, as was often assumed by investigators simulating Brownian aggregation of fractal aggregates. The ratio of hydrodynamic radius to radius of gyration was computed and shown to be independent of mass for aggregates of fixed fractal dimension, thus enabling an estimate of the diffusion coefficient for a fractal aggregate based on its radius of gyration.

Molecular Dynamics Simulation of Fractal Aggregate Diffusion. Pranami, G., Lamm, M.H., Vigil, R.D.: Physical Review E, 2010, 82[5], 051402