Fig. 1.

The difference between macroscopic and sub-nanometer hydrodynamics. Hagen–Poiseuille’s law envisions a parabolic streaming profile through macroscopic tubes due to a no-slip condition at the channel wall. In contrast, there cannot be a parabolic streaming profile in single-file flow (eight water molecules are drawn in blue – not to scale). Thus, the no-slip condition is not obeyed in narrow biological channels. L denotes the length of the channel, N denotes the number of single-file water molecules and z denotes the distance between adjacent water molecules.