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.