Sensitivity analysis of aggregate morphology on mass-mobility relationship and improved parameterizations

Past studies have shown that the diffusion-limited cluster aggregation mechanism yields aggregates with a mass fractal dimension (Df) of around 1.8 and power-law prefactor (kf) ranging between 1.2 and 2.5. For a fixed Df, an increasing kf physically manifests as decreasing shape anisotropy or the degree of "stringiness" of an aggregate. In this work, we investigate the effects of changing kf, monomer size (d), and number of monomers (N) of computer-simulated aggregates on their mass-mobility scaling exponent (Dfm) and prefactor (kfm). Our simulation results for a statistically significant number of Df = 1.78 ± 0.10 aggregates yielded Dfm values of 2.20 ± 0.05. These values are in excellent agreement with previous experimental observations. While variations in Dfm were predominantly influenced by Df, kfm showed sensitivity to fluctuations in kf. The validity and accuracy of the empirical power-law exponent 1.08 used for estimating N in three dimensions from two dimensional projection images was also evaluated. It was found that the exponent was only valid for aggregates with kf close to unity. A correction has been proposed to account for the enhanced apparent screening effects at large kf.