Electrical response of nanofluidic systems subjected to viscosity gradients

Nanofluidic systems subject to viscosity gradients are ubiquitous to technology and nature, including desalination and energy harvesting systems that utilize fresh water and seawater, thermoionics that leverage large temperature gradients of an electrolyte, and even ion channels that are sandwiched in between intercellular and extracellular fluids. However, to date, we lack a fundamental understanding of how a gradient in the viscosity changes the electrical response of these systems. In this work, using the well-known Poisson-Nernst-Planck equations, we derive a simple, self-consistent, analytical expression for the current-voltage, i-V, response of a nanofluidic system subject to a viscosity gradient at isothermal conditions. From this i-V, all the major characteristics are calculated. In particular, we provide a novel expression for the Ohmic conductance, g_{Ohmic}=i/V, as a function of the viscosity field. We also address the open question as to whether or not a viscosity gradient can induce an electrical current and shift it away from the origin of the i-V. We show and explain why the shift does not occur. Our convection-less model predicts current rectification using a different mechanism from the commonly invoked mechanism of electroosmotic flows that are used to rationalize experiments. Our model provides a new, simpler, and more robust mechanism for current rectification. This work provides the first robust and reliable framework for analyzing the experiments and numerical simulations of nanofluidic systems, subject to a viscosity gradient, that are used for energy harvesting purposes.