What Is the Lower Limit of Epstein’s (& Stokes-Cunningham's) Equation for Aerosol Diffusivity in the Free Molecule Regime?
SOTIRIS PRATSINIS, ETH Zurich, Switzerland
Abstract Number: 21
Working Group: Aerosol Physics
Abstract
Epstein’s equation1 for aerosol diffusivity in the free molecule regime has been the standard in nearly all textbooks as it described well micron-sized droplet diffusion at low pressures2. However, such experiments might be missing the corresponding atomic level interactions between aerosol particles and surrounding gas molecules that are crucial for tiny aerosol (cluster) transport as well as for diffusion of gas molecules best described by the Chapman-Enskog and Fuller et al. equations3. Such interactions lead to multi-body, grazing and orbiting4 collisions (besides the well-known specular ones) between gas molecules alone that nearly halve5 the gas mean free path, 66 nm, quoted in all aerosol textbooks. Here diffusion coefficients of tiny (0.4 - 7 nm in diameter) fullerene6, zinc, titania and silica6 nanoparticles in air are obtained by molecular dynamics (MD) wherein both particles and gas molecules are considered in their full atomistic representation (force field and shape). Below 3 nm these MD-derived diffusivities are in excellent agreement with the experimentally-based equation for gas diffusivities by Fuller et al3 but show systematic deviations from the Epstein1 and the widely-used Stokes-Cunningham equations. These deviations become most pronounced as the nanoparticle size approaches that of gas molecules. Above 5 nm, the MD-derived diffusivities nicely converge to these equations indicating the lower limit of Epstein’s equation1 and the need for research below. These diffusivities are compared also to other literature equations for particle diffusivity in this size regime at ambient conditions.
[1] P.S. Epstein, Phys. Rev., 23, 710–733 (1924).
[2] R.A. Millikan, Phys. Rev. 22, 1–23 (1923).
[3] E.L. Cussler, Diffusion Mass Transfer in Fluid Systems, 3rd ed.; Cambridge, 2009.
[4] D. Tsalikis et al., Phys. Fluids, 35, 097131 (2023).
[5] D. Tsalikis at al., Aerosol Sci. Technol., 58, 930-941 (2024).
[6] K. Karadima et al., J. Phys. Chem. A. in press (2025).