Geometrical structure and thermal conductivity of dust aggregates formed via ballistic cluster–cluster aggregation

We report on a theoretical study of the geometrical structure of porous dust aggregates formed via ballistic cluster–cluster aggregation (BCCA). We calculated the gyration radius Rgyr and the graph-based geodesic radius Rgeo as a function of the number of constituent particles N. We found that Rgyr / r₀ ~ N0.531 ± 0.011 and Rgeo / r₀ ~ N0.710 ± 0.013, where r₀ is the radius of the constituent particles. Furthermore, we defined two constants that characterize the geometrical structure of fractal aggregates: Df and α. The definitions of Df and α are N ~ ( Rgyr / r₀ )^Df and Rgeo / r₀ ~ ( Rgyr / r₀ )α, respectively. Our study revealed that Df 1.88 and α 1.34 for the clusters of the BCCA. In addition, we also studied the filling factor dependence of the thermal conductivity of statically compressed fractal aggregates. From this study we reveal that the thermal conductivity of statically compressed aggregates k is given by k ~ 2 kₘₐₜ ( rc / r₀ ) φ^(1 + α) / (3 - Df), where kₘₐₜ is the material thermal conductivity, rc is the contact radius of the constituent particles, and φ is the filling factor of the dust aggregates.