A theoretical understanding of ionic current through a nanochannel driven by a viscosity gradient

[Display omitted] •Theory is developed to understand the ionic current resulting from a viscosity gradient across a nanochannel.•Maxwell–Stefan equation is used to derive local diffusion coefficients resulting from mixing two different viscosity solutions.•Model predicts the ionic current for both ideal and non-ideal mixtures and is in good agreement with experiments.•Viscosity gradient along with a small ionic concentration gradient could significantly enhance the resulting ionic current. Different thermodynamic forces owing to the gradient of temperature, electrical potential, or concentration can drive ionic current through charged membranes. It has been recently shown that a viscosity gradient can drive an electrical current through a negatively charged nanochannel (Wiener and Stein, arXiv: 1807.09106). A model description of this phenomenon, based on the Maxwell–Stefan equation will help unravel the dominating physical mechanisms in so-called visco-migration. To understand the physical mechanisms underlying this phenomenon, we employed the Maxwell–Stefan equation to develop a 1D model and obtain a relation between the flux of solvents and the driving forces. Viscosity gradients are known to drive transport, but the development of an electrical current has not been theoretically described prior to this work. Our 1D model shows that the ionic current depends on the ideality of the solvent, though both ideal and non-ideal scenarios demonstrated good agreement with experimental data. We employed the model to understand the impact of solution bulk ionic strength and pH on the drift of ionic species with same reservoirs solution properties. Our modeling results unveiled the significant impact of bulk solution properties on the drift of ions which is in agreement with the experiments. Moreover, we have shown that the diffusion gradient along the nanochannel contributes significantly into driving ionic species if we even apply a small ionic concentration gradient to both reservoirs. Our modeling results may pave the way for finding novel applications for drift of ions in a diffusion gradient, which can be induced by connecting reservoirs of different viscosity fluids.