Electrical conductance of charged nanopores

A nanopores's response to an electrical potential drop is characterized by its electrical conductance, \tilde{G}. It has long been thought that at low concentrations, the conductance is independent of the electrolyte concentration, \tilde{c}_0, such that \tilde{G} ~ \tilde{c}_0^0. It has been recently demonstrated that surface charge regulation changes the dependency to be \tilde{G} ~ \tilde{c}_0^{\alpha} where the slope typically takes the values \alpha = 1/3 or 1/2. Yet, experiments have observed slopes of 2/3 and 1 suggesting that additional mechanisms, such as convection and slip-lengths, appear. We show that the inclusion of convection doesn't vary the slope, while the inclusion of a slip length doubles the slope value. Here, we elucidate the interplay between surface charge regulation, convection, and slip-lengths. We show that when all effects are accounted for \alpha can take any value between 0 and 1. This result is of utmost importance in designing any electro-kinetically driven nanofluidic system characterized by its conductance.