The diffusive penetrability of particles into energy barriers

Particles can normally only move against a force or adverse potential gradient by diffusion. This motion is described for a conservative field to show that, if Einsteinʹs relation between the mobility and diffusivity of a particle is used, particle concentrations fall off exponentially as the potential energy difference divided by kT. When there is a particle current against the field gradient driven by deposition on a surface, the exponential fall-off is slightly modified, but it still mainly determines the magnitude of the current. Applications to aerosol science are considered for electric and gravitational fields. By considering its derivation in detail, the approximate Boltzmann distribution for the steady-state charge distribution on an aerosol in a bipolar environment is shown to arise from diffusive ion penetrabilities onto charged aerosol particles. The origin of the Boltzmann factor is the total ion penetrability needed to make the charge, and reflects on the approximate ion equilibrium in the field gradients. Aerosol penetration to and deposition on a ceiling or roof is considered for simple and turbulent diffusion against the gravitational field, and the importance of aerosol penetration into the stratosphere is stressed in relation to extra-terrestrial aerosols.