Electrospray plume divergence: Background pressure influence

The influence of background pressure on electrospray plume evolution is observed by simulating the emission and propagation of an electrospray particle population into an electric field at a range of relevant background pressures. Differences in plume evolution from atmospheric pressure to one hundredth of atmospheric pressure are evident from plume characteristics such as (1) the overall domain of the resulting plumes and (2) the terminal angle at a downstream terminus of one standard deviation and three standard deviations of particle number density. Plume divergence and terminal angle are shown to correlate strongly with background pressure for pressures above which plume-background collision rates are significant, consistent with experimental observations of increased plume divergence with increased background pressure. The results suggest a simple expression for the pressure below which a system achieves minimum plume divergence: $P_{th}=kT/7.7299{\sigma }_{fl}d$ for a system of temperature $T$, background fluid molecules with cross-section ${\sigma }_{fl}$, and plume species of diameter $d$.