Computing the aerodynamic drag of fractal aggregates in free-molecular and transition regimes

For fine particles moving in the gas different regimes of aerodynamic drag are distinguished depending on their sizes and dust to gas relative velocities. In the Epstein or free-molecular regime, the drag force depends on the projected area or cross-section of the body, and in the Stokes or transition regime, on its linear size. Finding the linear size and the projected area for nonspherical particles is a non-trivial task. To describe the mobility of some type of nonspherical particles - fluffy aggregates, considered as a set of spheres - monomers, the value Df called fractal dimension is often used. For such aggregates with fixed fractal dimension D0, several authors suggested the approximations of the linear size (called Smoluchowski radius Rs) and projected area PA as a function of N - the number of monomers in the aggregate. These authors validated their approximations on experimental data. On the other hand, new direct numerical simulation (DNS) data on mobility of fractal aggregates have been obtained recently. In the paper we constructed new functions PA(Df,N) and Rs(Df, N) interpolating available from the literature approximations of PA(Df = D0,N) and Rs(Df = D0,N) and minimizing the deviation from recent DNS data. These functions are designed for global simulations of protoplanetary discs dynamics and planet formation, but can be used in different applications.