Electrophoresis of a spherical particle normal to an air-water interface

Electrophoresis of a spherical particle normal to an air-water interface is considered theoretically in this study. The presence of the air-water interface is found to reduce the particle mobility in general, especially when the double layer is very thick. This boundary effect diminishes as the double layer gets very thin. The higher the surface potential, the more significant the reduction of mobility due to the polarization effect from the double layer deformation when the particle is in motion. Local extrema are observed in the mobility profiles with varying double layer thickness as a result. Comparison with a solid planar boundary is made. It is found that the particle mobility near an air-water interface is smaller than that near a solid one when the double layer is thick, and vice versa when the double layer is thin, with a critical threshold value of double layer thickness corresponding roughly to the touch of the interface. The reason behind it is clearly explained as the buildup of electric potential at the air-water interface, which reduces the driving force as a result.