Electrical Response of Nanofluidic Systems Subjected to Viscosity Gradients

It is expected that the introduction of a viscosity gradient across a nanofluidic system will drastically vary its current-voltage response, $i-V$. However, to date, there is no self-consistent theoretical model that can be used to fully characterize such a system. This work provides an internally self-consistent model that details all the key characteristics of ion transport through a nanofluidic system for an arbitrary viscosity field. In particular, this work addresses three separate issues. First, we provide a new expression for the Ohmic conductance, $g_{Ohmic} = i/V$. Second, several previous theoretical studies have suggested that the introduction of a viscosity gradient can result in the shift of the $i-V$ such that it does not cross the origin. This work unequivocally shows that the $i-V$ is expected to always cross the origin. Third, we demonstrate that even without electroosmotic flows, the introduction of a viscosity gradient results in current rectification. Importantly, all theoretical results are verified by non-approximated numerical simulations. This work provides the appropriate framework to analyze and interpret experimental and numerical simulations of nanofluidic systems subject to a viscosity gradient.