Modeling multi-site emission in porous electrosprays resulting from variable electric field and meniscus size

Abstract

A model predicting the number of emission sites and total current from a porous conical electrospray emitter as functions of voltage is derived. A pressure balance between capillary and electric forces is used to determine an onset criterion for individual menisci, and an ionic emission scaling law is invoked to predict the current each meniscus emits. These submodels are integrated over a phenomenological meniscus size distribution and the area of the emitter to yield a model for emitter performance as a function of five free parameters, two for the ionic emission submodel and three for the meniscus size distribution. Bayesian inference is applied to determine these model parameters from an existing dataset [Dressler et al., J. Propul. Power 38, 809 (2022)]. The model predictions after training are compared to the experimental data, and it is found that the majority of the data are within a 90% credible interval. The ability of the model to capture key trends in the experimental data is attributed to the interplay of two effects: the distribution over meniscus size on the emitter and the position-dependent electric field. The calibrated model results also suggest that the emitter surface is wetted by a series of large but sparsely distributed pools of propellant. The performance and extensibility of the model are examined within the context of model-based design for porous electrospray array thrusters.