A thermodynamic model for the O${}_2^{-}$ mobility in Ne gas in broad density and temperature ranges

We report new measurements of the mobility $\mu$ of O${}_2^{-}$ ions in supercritical neon in the range $45\mathrm{K}\le T\le 334\mathrm{K}$ for number density $N\ge 0.5$nm${}^{-3}\mathrm{.}$ We rationalize the experimental data of all isotherms with the Stokes-Cunningham formula by computing the ion hydrodynamic radius as a function of $T$ and $N$ with the thermodynamic free volume model developed for the ion mobility in superfluid He. The model parameters are determined by re-analyzing published data for $T=45$K for $N$ up to $N\approx 1.65N_c$ ($N_c\approx 14.4$nm${}^{-3}$ is the critical number density), which roughly span four orders of magnitude of the Knudsen number $(0.1\le {\mathrm{K}}_n\le 1000)$, covering the transition from the kinetic- to the hydrodynamic transport regime. These parameters provide an excellent description of the dependence of $\mu$ on $N$ for all higher isotherms and yield a strict test of the model validity, thereby bridging the gap between the kinetic- and the hydrodynamic transport regimes.