Electrophoresis of a charge-regulated sphere normal to an air-water interface

The electrophoresis of a charge-regulated sphere normal to an air-water interface is investigated theoretically. The charge-regulated surface considered here is the generalization of conventional constant surface potential and constant surface charge density situations and models excellently well biocolloids or particles coated with a thin film of polyelectrolytes. The thickness of the double layer surrounding the particle can be arbitrary. A pseudospectral method based on Chebyshev polynomials is employed to solve the governing electrokinetic equations. We found, among other things, that the electric potential on the particle surface is the most dominant factor in the determination of the eventual particle electrophoretic mobility. The larger the number of dissociated functional groups on the particle surface (N(s)), the higher the absolute surface potential of the particle and hence the larger the magnitude of the mobility. Moreover, the electric potential on the particle surface depends on both the concentration of dissociated hydrogen ions, [H(+)](0), and the concentration of electrolytes, κa, in the solution. If [H(+)](0) and/or κa are small, the bulk condition is advantageous to the dissociation reaction, yielding a higher surface density (higher surface potential) and hence a higher mobility. The air-water interface retards the particle motion in general, especially when the double layer is thick enough to touch the interface. Up to around 60%, reduction of the mobility is observed for some situation. The boundary effect disappears as the double layer gets very thin. This is mainly due to the buildup of the electric potential at the interface right in front of the particle, which in turn generates a repulsive electrostatic force. Comparison with a solid planar wall is carried out to highlight the fundamental nature of the air-water interface, such as the unique phenomenon of the electric potential buildup mentioned above.