Numerical investigation of the effects of geometry and materials on the onset voltage of electrospray emitters

Guidelines for the design of 2D electrospray emitter arrays that operate at minimal emission onset voltage are established by analyzing the dependence of the emission onset voltage on key emitter dimensions. The electrostatic field, and resulting onset voltage, are determined numerically for different configurations. The relative permittivity of the medium surrounding the emitters is varied between 1 and 10 to consider two types of emitters: capillary emitters standing in vacuum, and capillary emitters embedded in a dielectric material. Results for single electrospray emitters are compared to those of an analytical model. Trends in the data imply minimal onset voltage when using dielectrics with low relative permittivity, small-diameter emitters tall enough to escape shielding from the surrounding features of the device, and a small extractor distance. However, these relationships are complex and are discussed in detail. The data also agrees with previous numerical research into arrays of emitters showing that at an emitter spacing of approximately 2.5 times the emitter height, shielding effects become negligible. These design guidelines and the specific results reported herein are particularly relevant to the rapid development of miniaturized electrospray chips holding hundreds, or even thousands, of emitters that are expected to reach market in the near future.