A theoretical model for viscophoresis: transport in a liquid viscosity gradient

We recently discovered that imposing a viscosity gradient within a nanofluidic channel made of glass causes ionic current to flow. The current is evidently carried by positively charged counterions in the electric double layers near the channel walls drifting toward the lower viscosity side. We present an explanation based on the Maxwell-Stefan (MS) theory of diffusion. Within the MS theory, transport of a given species is driven by a gradient in its chemical potential, and that driving force is balanced by a friction force with every other molecular species. Relating the MS theory to our nanofluidic experiments, we consider a viscous fluid, a thin fluid, and counterions. The viscous and thin components of the mixture flow in opposite directions inside the channel, and as they do, each one exerts a frictional force on the counterions. There is a net motion of those counterions in the direction of decreasing viscosity because the drag coefficient with the viscous component is larger than the coefficient with the thinner component. There is also no mystery where the energy to drive the current comes from: It comes from the free energy of mixing of the viscous and thin fluids.