Computer simulation of diffusion-limited cluster-cluster aggregation with an Epstein drag force.

The motion of particles, dispersed in a medium, between collisions with each other can, in limiting situations, be either ballistic (straight line) or diffusive (random walker). The diffusive regime can be divided into two distinct subregimes. The "continuum regime" exhibits Stokes-Einstein-type diffusion (no-slip surface boundary condition) with a frictional coefficient proportional to the particle size (linear dimension). The "Epstein regime," as we shall refer to it, is characterized by a frictional coefficient proportional to the particle cross-sectional area, hence an Epstein-type diffusion (slip surface). The purpose of the current study is to illuminate the dynamics of dilute-limit aggregation in the Epstein regime. We present results from low volume fraction Monte Carlo simulations of cluster-cluster aggregation in the Epstein regime with the particle motion based on each particle's cross-sectional area. Our findings indicate that aggregates grown under Epstein conditions have a fractal dimension of approximately 1.8, similar to that of diffusion-limited cluster-cluster aggregates (DLCA) in the continuum regime. The kinetic exponent z in the Epstein regime is found to be z approximately 0.8, lower than its value for both the continuum regime DLCA (z = 1) and for the ballistic cluster aggregation regime (z approximately 2). Cluster size distribution data for Epstein systems are found to scale at large cluster sizes with exponents consistent with the kinetic data. A scaling argument for predicting the kinetic exponent and kernel homogeneity based on the mass or size dependence of the particle velocity and collision cross section is presented and is seen to give accurate results for dilute and intermediate values of particle volume fractions not only for the current study, but also for work done by other researchers with various choices for the aggregation kernel.