Transient phoretic migration of a permselective colloidal particle

摘要

We quantify the phoretic migration of a spherical cation-permselective colloidal particle immersed in a binary electrolyte under a time-dependent electric field. We invoke the thin-Debye-layer approximation, where the size of ionic Debye layer enveloping the particle is much smaller than the particle radius. The imposed electric field generates ion concentration gradients, or concentration polarization, in the bulk (electroneutral) electrolyte outside the Debye layer. The bulk ion concentration polarization-and consequently the particle's phoretic velocity-evolves on the time scale for ion diffusion around the particle, which can be on the order of milliseconds for typical colloidal dimensions. Notably, concentration polarization arises here solely due to the permselectivity of the particle; it does not require non-uniform ionic transport in the Debye layer (i.e., surface conduction). Thus, the phoretic transport of a permselective particle is significantly different to that of a inert, dielectric particle, since surface conduction is necessary to achieve bulk concentration polarization in the (more commonly studied) latter case. Calculations are presented for a permselective particle under oscillatory (ac) and suddenly applied electric fields. In the former case, the particle velocity possesses frequency-dependent components in phase and out of phase with the driving field; in the latter case, the particle approaches its terminal velocity with a long-time (algebraic) tail.