Theoretical analysis of the transition from field emission to space-charge-limited emission in liquids and gases

Abstract

Discharge formation and breakdown in liquids have critical implications for water purification, medicine, and combustion, thereby motivating characterization of liquid behavior under high voltages. While several experiments with dielectric liquids have demonstrated that current transitions from Fowler–Nordheim (FN) scaling for field emission to Mott–Gurney (MG) scaling for space-charge-limited emission (SCLE) with increasing voltage, there is no common model linking electron emission from the liquid to gas phase. We show that applying a theory unifying FN, MG, and the Child–Langmuir law (CL) for SCLE at vacuum as a function of electron mobility and gap distance [Darr et al., Appl. Phys. Lett. 114, 014103 (2019)] yields excellent agreement with dielectric liquid emission experiments [Dotoku et al., J. Chem. Phys. 69, 1121 (1978)]. Specifically, current follows FN scaling at lower voltages before space charge contributions dominate, although none of the dielectric liquids considered achieve MG scaling in the experimental regime of interest. Considering a higher mobility representative of a vapor in the theory demonstrates the feasibility of achieving CL scaling for the gaps of the size considered experimentally at reasonably achievable applied voltages. Increasing the gap distance by an order of magnitude eliminates the contribution of space charge; decreasing gap distance by an order of magnitude causes a transition to MG. The implications of these results on electron emission in liquids and during a phase change to vapor and gas will be discussed.