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.