The electric conductance characterizes the response of a nanochannel or nanopore to an electrical potential drop. It has long been known that at low concentrations the electric conductance is independent of the bulk electrolyte concentration but depends on the surface-charge density. In recent years, several works have demonstrated that the low-concentration conductance is concentration dependent. This dependence is implicit through the mechanism known as surface-charge regulation which causes the surface-charge density to depend on the concentration, ${\tilde{c}}_0$. As a result, the conductance, $\tilde{G}$, has power-law dependency such that $\tilde{G}\sim {\tilde{c}}_0^{\alpha }$ with a slope of $\alpha$. It is typically assumed the slope takes on the particular values $\alpha =0,\frac{1}{3},\frac{1}{2}$. Here, we will analytically show that slope varies continuously from 0 to $\frac{1}{2}$ as the system parameters vary. Thereafter, we will account for convection and the effects of a slip length at the channel surface. We will show that convection without slip increases the conductance but does not vary the slope $\alpha$. The inclusion of slip not only increases the conductance but also increases the slope to $2\alpha$. Direct numerical simulations confirm our theoretical predictions. The consequences of these findings are important in the design of any electrokinetically driven nanofluidic system insofar as they provide the experimentalist an accurate prediction of the system response as a function of the material properties.

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• Electrical conductivity
• Electrokinetic flows
• Nanofluidics