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

Abstract

We herein report a theoretical study of the geometrical structure of porous dust aggregates formed via ballistic cluster-cluster aggregation (BCCA). We calculated the gyration radius $R_{\mathrm{gyr}}$ and the graph-based geodesic radius $R_{\mathrm{geo}}$ as a function of the number of constituent particles $N$. We found that $R_{\mathrm{gyr}}/r_0\sim N^{0.531\pm 0.011}$ and $R_{\mathrm{geo}}/r_0\sim N^{0.710\pm 0.013}$, where $r_0$ is the radius of constituent particles. Furthermore, we defined two constants that characterize the geometrical structure of fractal aggregates: $D_{\mathrm{f}}$ and $\alpha$. The definition of $D_{\mathrm{f}}$ and $\alpha$ are $N\sim {(R_{\mathrm{gyr}}/r_0)}^{D_{\mathrm{f}}}$ and $R_{\mathrm{geo}}/r_0\sim {\left(R_{\mathrm{gyr}}/r_0\right)}^{\alpha }$, respectively. Our study revealed that $D_{\mathrm{f}}\simeq 1.88$ and $\alpha \simeq 1.34$ for the clusters of the BCCA. In addition, we also studied the filling factor dependence of thermal conductivity of statically compressed fractal aggregates. From this study, we reveal that the thermal conductivity of statically compressed aggregates $k$ is given by $k\sim 2k_{\mathrm{mat}}(r_{\mathrm{c}}/r_0){\varphi }^{(1+\alpha )/(3-D_{\mathrm{f}})}$, where $k_{\mathrm{mat}}$ is the material thermal conductivity, $r_{\mathrm{c}}$ is the contact radius of constituent particles, and $\varphi$ is the filling factor of dust aggregates.

14 pages, 8 figures. Accepted for publication in PTEP

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• Investigating the Bouncing Barrier with Collision Simulations of Compressed Dust Aggregates
• On the elastoplastic behavior in collisional compression of spherical dust aggregates
• Interpebble contact radius in a comet nucleus
• Interparticle normal force in highly porous granular matter during compression
• Root mean squares of distance and geodesic between two constituent particles within fractal aggregates prepared by BCCA, DLA, and GSAW procedures
• Numerical Investigation on the Compressive Behavior of Hierarchical Granular Piles