Transient Flow in Porous Electrosprays

Porous ionic electrospray emitters have received significant interest for space propulsion due to their performance and operational simplicity. We have developed a diffusion equation for describing the transient flow response in a porous electrospray emitter, which allows for the prediction of the settling time for flow in the porous emitter. This equation accounts for both the change in liquid storage at exposed pores on the emitter with pressure, and viscous diffusion through Darcy's law. Transient flow solutions are provided for the most common emitter topologies: pillar, cone, and wedge. Transient flow solutions describe the settling time and magnitude of current overshoot from porous electrosprays. Comparing diffusion of pressure to the onset delay model for electrospray emission shows that diffusion is most relevant at higher voltages and when a porous reservoir is used. Accounting for multiple emission sites on the wedge geometry shows that emission sites settle in proportion to emission site spacing to the power -1.74. Applying the diffusion equation to published results shows good agreement between analytical predictions and experimental data.