Influence of space charge on the scale-up of multiplexed electrosprays

The effect of the space charge of the homopolarly charged droplets in a system of multiplexed electrosprays is investigated. The system consists of a microfabricated liquid distributor with multiple electrospray sources held at a high voltage, a nearby extractor electrode plate held at an intermediate voltage, and a grounded electrode further downstream. The system is very compact, with a spatial density as large as 250sources/cm2. Experimentally, we observed that the system performance was limited by the occurrence of path reversal of the satellite droplets, accumulating on the extractor electrode, flooding it and ultimately causing the electrospray to cease operation. To prevent this phenomenon, hereafter referred to as satellite trapping, and “sweep” the satellites downstream, the driving field between the extractor electrode and the ground must be increased. The system behavior was modeled by a simple line-of-charge approximation, which was validated by a more detailed Lagrangian model and by experiments on an individual electrospray. Subsequently, the line-of-charge model was extended to the multiplexed system yielding a satisfactory comparison between the computed minimum driving field that is necessary to prevent satellite path reversal and experimental values. Additional analytical approximations of the multilines-of-charge model yielded a scaling law showing the dependence of the space charge on: (i) the primary droplet residence time, (ii) the current emitted per unit area, and (iii) a dimensionless parameter, αα, that is the ratio of the distance between the extractor electrode and the ground electrode to the distance between neighboring nozzles. As a result, guidelines for the design of multiplexed electrosprays are established on a fundamental basis, without the need for costly and empirical microfabrication prototyping.