A Closed-Form Solution for Film Flow in Nanoscale Pores with Spatially Varying Viscosity

The viscosity of the film water near hydrophilic surfaces is observed to be significantly higher than that of bulk water, i.e., up to approximately three times that of bulk water. Such an enhancement in viscosity can be attributed to the intensive solid-water interactions, which result in a spatially varying activation energy. An attempt is made herein to investigate the impact of spatially varying viscosity on film flow at the nanoscale. The spatially varying viscosity is described via a proposed viscosity profile equation. A governing equation for film flow incorporating spatially varying viscosity is then established by substituting the proposed viscosity profile equation into the mechanical equilibrium equation. Closed-form solutions for this governing equation are derived by introducing the no-slip boundary condition. The accuracy of the proposed viscosity profile equation and closed-form solutions is evaluated by comparing with experimental and molecular simulation data on viscosity, flow velocity profile, and average flow velocity. The results indicate that overlooking the spatial variation of viscosity can lead to overestimation of flow velocity and hydraulic conductivity for film flow in nanoscale pores by up to 5.5 and 14.0 times, respectively.