Statistical Analysis of Droplet Charge Acquired during Contact with Electrodes in Strong Electric Fields

High-Voltage Electrodes in Moist Air Accumulate Charge That is Retained after Removing the Electric Field

Applying a high voltage to a metal electrode that is disconnected from a circuit rapidly induces a capacitive charge, which quickly relaxes after removal of the applied voltage. Here, we report that if the electrode is placed in air at a sufficiently high relative humidity and provided the connection between the high-voltage supply and the electrode is composed of two different metals, the expected capacitive charge is followed by a gradual increase in charge. Surprisingly, this extra charge persists after the removal of the applied voltage and even after physically removing the electrode from the Faraday cup used to measure the charge. We report the median charge, average charge rate, and residual charge for different applied voltages, different metal-metal connections, and varied humidity. We interpret the results in terms of a proposed water ionization mechanism and discuss the implications of the findings for high-voltage fluidic systems.

Effect of Deformation on Droplet Contact Charge Electrophoresis

The effect of deformation on the droplet contact charge electrophoresis (CCEP) was investigated for consistent droplet movement control. Through systematic experiments and numerical simulations, it has been found that overcharging by deformation is up to about 130% of the sphere and is mainly driven by the concentration of the electric field near the tip of the droplet rather than an increase in the surface area. Dimensional analysis revealed a consistent droplet CCEP motion with the electric capillary number range of 0.01-0.09. We also found that the dimensionless droplet charge follows a universal curve proportional to the electric capillary number, regardless of the droplet size, and the weak dependence on the droplet size shown in the experimental results is due to hydrodynamic effects, not electrostatic ones. Changes in droplet velocity distribution with droplet size and the electric capillary number were also investigated. Using the perfect conductor theory and Stokes law, we derived an analytical relationship between the droplet center velocity and the electric capillary number and analyzed the experimental results based on this relationship. This study implies that if proper hydrodynamic correction is applied, the droplet CCEP and its deformation effect can be explained by a perfect conductor theory.

Wall Effects on Hydrodynamic Drag and the Corresponding Accuracy of Charge Measurement in Droplet Contact Charge Electrophoresis

Droplet size dependent wall effects on hydrodynamic drag and the corresponding droplet contact charge estimations were experimentally and theoretically investigated. The consistent reduction in the dimensionless droplet contact charges proportional to droplet size was reported and explained by the parallel and approaching wall effects on the drag coefficient. Extrapolation of the size dependent droplet charge data showed that the droplet charge follows the perfect conductor theory when the droplet radius approaches zero. The proposed model was applied to the drag calculation to estimate and compare dimensionless charges before and after consideration of the wall effects. The droplet free fall test concluded that the droplets in the current experimental setup follow Stokes' law. The theoretical velocity profile of the droplet approaching the wall perpendicularly is proposed considering the approaching wall effect on hydrodynamic drag and verified by comparison with the experiment. The droplet size dependent velocity profile shape change was also explained by this approaching wall effect. The shape of the asymmetric velocity profile along the direction of droplet movement was explained by the effect of the image charge through direct numerical calculation of the electric force. The direct calculation of the electric force also showed that the electric correction at the center of the cuvette is negligible; thus, it is sufficient to consider only hydrodynamic correction for accurate charge measurement in this experimental system. The present study will contribute to the accurate measurement of the droplet charges under contact charge electrophoresis. It also provides the basis for precise control of droplet movement in lab-on-a-chip devices.