A direct and theoretically consistent method for the calculation of the settling speed of prolate spheroidal particles in the atmosphere

Abstract

We propose a new method for calculating the settling speed of aerosol particles with prolate shape in the atmosphere. This method takes into account the known theoretical results on the speed–force relationships for prolate spheroids moving in a fluid, and the results in Mallios et al. (2021) regarding the orientation of prolate particles settling in the atmosphere. Unlike other studies, we focus not on the resistance problem (calculating the aerodynamic force as a function of speed) but on the mobility problem (calculate terminal velocity as a function of the external force). The result of this approach is a set of equations that permit to directly calculate the settling speed of a prolate particle in the atmosphere as a function of its shape and characteristics, which is a very important quantity in atmospheric science since the settling speed of a falling particle is a key factor to determine its lifetime in the atmosphere. With this approach, we show that the settling speed is reduced by up to 20% for particles with aspect ratio 4 compared to same-volume spheres. We compare the results of the present study to CFD results of Sanjeevi et al. (2022) and to laboratory measurements of Bhowmick et al. (2024), the latter comparison showing that the estimates for settling speed from our method is within $\pm 5\text{\%}$ compared to the measured value. Finally, since calculating the terminal speed of settling particles is an important issue in atmospheric modeling, we provide a Fortran module implementing the method described in the present study.