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We consider electric conductance through a narrow nanochannel in the thick-double-layer limit, where the space-charge Debye layers adjacent to the channel walls overlap. At moderate surface-charge densities the electrolyte solution filling the channel comprises mainly of counterions. This allows to derive an analytic closed-form approximation for the channel conductance, independent of the salt concentration in the channel reservoirs. The derived expression consists of two terms. The first, representing electromigratory transport, is independent of the channel depth. The second, representing convective transport, depends upon it weakly.

We provide a macroscale description of electrokinetic particle-electrode interactions at high frequencies, where chemical reactions at the electrodes are negligible. Using a thin-double-layer approximation, our starting point is the set of macroscale equations governing the "bounded" configuration comprising of a particle suspended between two electrodes, wherein the electrodes are governed by a capacitive charging condition and the imposed voltage is expressed as an integral constraint. In the large-cell limit the bounded model is transformed into an effectively equivalent "unbounded" model describing the interaction between the particle and a single electrode, where the imposed-voltage condition is manifested in a uniform field at infinity together with a Robin-type condition applying at the electrode. This condition, together with the standard no-flux condition applying at the particle surface, leads to a linear problem governing the electric potential in the fluid domain in which the dimensionless frequency ω of the applied voltage appears as a governing parameter. In the high-frequency limit ω>>1 the flow is dominated by electro-osmotic slip at the particle surface, the contribution of electrode electro-osmosis being O(ω(-2)) small. That simplification allows for a convenient analytical investigation of the prevailing case where the clearance between the particle and the adjacent electrode is small. Use of tangent-sphere coordinates allows to calculate the electric and flows fields as integral Hankel transforms. At large distances from the particle, along the electrode, both fields decay with the fourth power of distance.

We consider the one-dimensional transport of ions into a perm-selective solid. Direct attempts to evaluate the current-voltage characteristics for currents exceeding the diffusion limit are frustrated by the appearance of nonconverging integrals. We describe how to overcome this obstacle using a regularization scheme.