  A generalized physics-based expression for the drag coefficient of spherical
particles moving in a fluid is derived. The proposed correlation incorporates
essential rarefied physics, low-speed hydrodynamics, and shock-wave physics to
accurately model the particle-drag force for a wide range of Mach and Knudsen
numbers (and therefore Reynolds number) a particle may experience. Owing to the
basis of the derivation in physics-based scaling laws, the proposed correlation
embeds gas-specific properties and has explicit dependence on the ratio of
specific heat capacities at constant pressure and constant volume. The
correlation is applicable for arbitrary particle relative velocity, particle
diameter, gas pressure, gas temperature, and surface temperature. Compared to
existing drag models, the correlation is shown to more accurately reproduce a
wide range of experimental data. Finally, the new correlation is applied to
simulate dust particles' trajectories in high-speed flow, relevant to a
spacecraft entering the Martian atmosphere. The enhanced surface heat flux due
to particle impact is found to be sensitive to the particle drag model.
