Travelling wave dipolophoresis of ideally polarizable nano-particles with overlapping electric double layers in cylindrical pores

We provide a general integral formulation for the dipolophoretic transport of a polarizable colloid in a likewise polarizable nanochannel which takes into account electric double layer (EDL) overlap between the channel walls and resultant background flow as well as the overlap between the wall EDL and that of the particle. The analysis is based on extension of the Lorentz reciprocal theorem for Stokes flows and necessitates the solving of two auxiliary problems; the background induced-charge electroosmotic flow in the channel and the Stokesian motion of a nanoparticle under confinement. To demonstrate our general methodology, we provide a closed form analytical solution for the specific case of a polarizable spherical colloid, located at the axis of a cylindrical nanopore whose walls are subject to a travelling-wave alternating-current electric signal. We quantify the level of EDL overlap via the introduction of a new parameter, ξ which represents the undefined ionic density at the centerline under Boltzmann distribution and depends on the EDL thickness, λ₀. Both the background electroosmotic flow and the phoretic velocity of the particle are found to be a function of the frequency of the applied field, while displaying distinct dispersion characteristics. In the thin EDL limit, maximum velocity and mass transport are obtained in the kilo-Hertz range.