Effects of electronic friction from the walls on water flow in carbon nanotubes and on water desalination

A mechanism for removal of salt from salt water is discussed, which results from friction due to Ohm's law heating, resulting from motion of an electron charge induced in the tube walls by the water molecules’ dipoles and the ions’ charges. The desalination occurs because this friction is larger for salt ions than for water molecules. Friction due to Ohm's law heating might also provide an explanation for the observation by Secchi et al. [Nature 537, 210 (2016)] that the flow velocity of water in carbon nanotubes for a given pressure gradient increases rapidly as the tube radius decreases from 50 to 15 nm, which does not occur for boron nitride nanotubes, which are insulators. This friction can have the right magnitude to produce the slip lengths reported by Secchi et al. One possibility is that the nanotubes in this experiment were metallic, and their conductivity becomes large as their radius decreases, due to ballistic conduction. Another possibility is that when the tube circumference drops below the electron mean-free path, the wall switches from behaving as a two-dimensional conductor to behaving as a one-dimensional conductor for which the electrons are more strongly localized. When the conductivity is sufficiently small, small displacements of the localized electron states can provide the dominant contribution to the motion of the induced charge, rather than current flow, thus reducing the friction due to Ohm's law heating.

Figure 1

The moving charge distribution induced in a conducting sheet is illustrated for (a) a moving positive point charge and (b) a moving dipole moving above the conducting sheet.

Figure 2

Illustration of desalination by having salt water flow between two electrically conducting walls.