An expression for the drag force of small spherical particles in an ideal-gas media analyzed using configuration-specific kinetic molecular theory

Epstein [P.S. Epstein, Phys. Rev. 23 (1924) 710] provided the benchmark analysis for a series of expressions describing the drag force exerted on small moving particles by an ideal gas media. His expression for elastic collisions shows that the drag force increases according to the function 1 + 4s/9, in which s is the fraction of molecules diffusively reflected. For inelastic collisions in which the particles are thermally conducting and non-conducting, the drag force increases as 1+πs/8 and 1 + 9πs/64, respectively. Analysis using configuration-specific kinetic molecular theory reproduces Epstein’s expression for the drag force where s = 0, but predicts that the drag force decreases according to the function 1-s/6. This work also includes an expression for s derived from Massalimov’s [I.A. Massalimov, Chem. Sust. Dev. 10 (2002) 119] equation for the probability of phonon energy transmission.