The aggregation rate of ice crystals depends on their shape and intercrystal relative velocity. Unlike spherical particles, the nonspherical ones can have various orientations relative to the gravitational force in the vertical direction and can approach each other at many different angles. Furthermore, the fall velocity of such particles could deviate from the vertical direction velocity. These properties add to the computational complexity of nonspherical particle collisions. In this study, we derive general mathematical expressions for gravity-induced swept volumes of spheroidal particles. The swept volumes are shown to depend on the particles' joint orientation distribution and relative velocities. Assuming that the particles are Stokesian prolate and oblate spheroids of different sizes and aspect ratios, the swept volumes were calculated and compared to those of equivalent volume spheres.Most calculated swept volumes were larger than the swept volumes of equivalent spherical particles, sometimes by several orders of magnitude. This was due to both the complex geometry and the side drift, experienced by spheroids falling with their major axes not parallel to gravity.We expect that the collision rate between nonspherical particles is substantially higher than that of equivalent volume spheres because the collision process is nonlinear. These results suggest that the simplistic approach of equivalent spheres might lead to serious errors in the computation of the collision rate.
Bibliographical noteFunding Information:
Acknowledgments. The study was supported by the Israel Science Foundation (Grant 2027/17) and the U.S. Department of Energy (Grants DE-FOA-0001638, DE-AC05-76RL01830 81). We thank Kaushal Gianchandani for his help and valuable suggestions.
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- Cloud microphysics
- Cumulus clouds
- Ice crystals
- Ice loss/growth