The subtleties of water in small spaces

The transport of fluids through conduits conjures up notions of pumps, pipes, and valves for students of the engineering sciences. It also represents a basic physical process that can be described by continuum hydrodynamics as long as the diameter of the “pipe” is much larger than any relevant length scale in the fluid, and, for many practical situations, it is. In fact, although the reasons are far from clear, continuum hydrodynamics can make accurate predictions even outside of the range of physical scenarios where it is expected to apply. One notable example is the success of the Stokes-Einstein(-Debye) model that relates the diffusivity of a dilute probe particle to the viscosity of the solvent. Although strictly valid only for Brownian particles that are much larger than the solvent molecules, it also works well for probe particles that are of similar size or even smaller (1). Moreover, experiments have shown that macroscopic hydrodynamics can reliably describe the flow of fluids through channels with cross-sectional dimensions that range from tens to hundreds of micrometers (2). The success of the continuum approach for modeling microfluidics has led some to suggest that the design paradigm for the engineer will soon be to “scale down” rather than “scale up” (3).

However, one cannot simply scale down ad infinitum. For transport through sufficiently narrow channels (tens of nanometers), microscopic fluctuations play an important role, and it no longer makes sense to describe the permeant …