Dipolophoresis of interacting conducting nano-particles of finite electric double layer thickness

A general integral method is presented for calculating the dipolophoretic velocities of two interacting, ideally polarizable colloids of arbitrary electric double layer thickness under weak AC electric forcing. The 12 non-linear mobilities are comprised of induced-charge-electrophoresis (ICEP), dielectrophoresis (DEP), and Faxén-Stokes contributions. The explicit integral scheme, based on the Teubner [J. Chem. Phys. 76, 5564 (1982)] formulation, is demonstrated for the case of two-sphere interaction. Further simplifications using the remote-sphere approximation are employed and the asymptotic results thus obtained are compared against those recently obtained by Saintillan [Phys. Fluids 20, 067104 (2008)] and extend the latter for finite Debye scales and forcing frequencies. It is also shown that the same methodology can be used to determine the mobility of a polarized particle in the proximity of an insulating or conducting plane boundary. The case of a spherical colloid near an uncharged insulating planar wall is of special interest and by using the Lorentz image solution, we readily recover the large-spacing approximation of Yariv [Proc. R. Soc. A. London Ser. A 465, 709 (2009)] as a limiting case.