The size-mobility relationship of ions, aerosols, and other charged particle matter

Electrical Mobility is arguably the property upon which some of the most successful classification criteria are based for aerosol particles and ions in the gas phase. Once the value of mobility is empirically obtained, it can be related to a geometrical descriptor of the charged entity through a size-mobility relationship. Given the multiscale range of sizes in the aerosol field, approaches that can provide accurate transformations from mobility to size are not straightforward, and many times rely on experimentally derived parameters. The most well-known size-mobility analytical expression covering the whole Knudsen range for spherical particles is the semi-empirical Stokes-Millikan correlation. This expression matches Stokes' drag friction coefficient in the continuum regime and the friction factor for a predominantly diffuse reemission of the gas molecule in the free molecular regime, as theorized by Epstein, with empirical slip coefficients chosen to agree with Millikan's oil drop experiments. Despite its success, the Stokes-Millikan correlation has its shortcomings. For example, it needs to be modified to predict the mobility of non-spherical entities and needs correction terms when potential interactions or reduced mass effects are non-negligible. The Stokes-Millikan asymptotic behavior also fails to predict the gradual transition from diffuse to specular reemission behavior that is observed for increasingly smaller ions within the free molecular regime. Here we make an attempt at providing a comprehensive account of the existing mass-mobility relations in the continuum, transition and free molecular regimes for both spherical and non-spherical particles. Epstein's diffuse interaction is critically explored experimentally and numerically for different gases in the free molecular regime with the observation that, as the size of the particle increases, a progression from specular to diffuse reemission occurs for all gases studied. The rate at which this variation happens seems to differ from gas to gas and to be related to the conditions for which diffuse reemission effects stem from a combination of scattering and potential interactions