A new equation for the mean free path of air

Abstract

A recent rigorous methodology for determining the mean free path, λ, of air at ambient conditions [Tsalikis, D. G., Mavrantzas, V. G., & Pratsinis, S. E. (2023). Physics of Fluids, 35, 097131] is extended to pressures, P, from 0.5 to 5 atm and temperatures, T, from 100 to 3000 K that are of environmental and industrial relevance, allowing to derive a new simple equation for λ as a function of T and P. This entails molecular dynamics (MD) simulations of air accounting for the actual shape and force field of nitrogen and oxygen and analysis of the computed microcanonical ensemble of free paths to derive λ at any P and T. Simulations are rigorously validated by comparing MD-predicted air densities, diffusivities and viscosities at various temperatures and pressures against experimental measurements, theoretical expressions and ab initio simulations. At all T and P, the MD-computed λ are systematically smaller (at least 40%) than those from classic kinetic theory and its variants. The new equation for λ is: (Formula presented.) and can be also expressed in terms of the standard Jennings’ expression, (Formula presented.) [Jennings, S. G. (1998). Journal of Aerosol Science, 19(2), 159–166], relating λ to air viscosity, μ, and density, ρ, using just a new value for its numerical factor u, u = 0.81475 ± 0.00288, which is 63% larger than the current u = 0.4987445.