Molecular streaming (nanofluidics)

Molecular streaming, in nanofluidics, is the pressure-driven flow of an ionic solution through a channel only a few molecules high, studied for the electric current that the flow carries. The phrase is the title of a 2019 paper in Nature by Mouterde, Keerthi and colleagues from the University of Manchester and the École normale supérieure in Paris. They pushed potassium chloride solutions through slits 6.8 Å high, and found that applying a bias of a fraction of a volt raised the pressure-driven transport, measured as a streaming mobility, by up to 20 times.^[1] The authors called the result a "transistor-like electrohydrodynamic effect".

Most surfaces in water carry charge, and the solution next to them holds an excess of counter-ions in a thin layer, the electric double layer, whose thickness is the Debye length. For a salt with ions of single charge at 25 °C the Debye length is 0.304 nm divided by the square root of the concentration in moles per liter.^[2] It is 9.6 nm at 1 mM and 0.30 nm at 1 M. When pressure drives the liquid along a channel, it carries the charge of that layer with it, and the movement of charge is a current. The current is called the streaming current, or, if the channel is closed to current, the streaming potential that builds up in its place.^[3]

Georg Quincke reported the effect in 1859, and Hermann von Helmholtz gave a theory of the layer in 1879.^[4][5] For a channel whose walls are far apart compared with the Debye length, the streaming current is

where ε is the permittivity of the liquid, ζ the zeta potential of the wall, η the viscosity, A and L the cross-section and length of the channel, and ΔP the pressure difference. The quantity −εζ/η is the streaming mobility μ, with the units of an electrophoretic mobility. A wall with a zeta potential of −25 mV in water gives a streaming mobility of 1.8 × 10⁻⁸ m²/(V s).^[a]

File:Angstrom slit streaming.svg Channels with walls a few atoms apart became possible when sheets of two-dimensional crystals could be stacked with atomic precision. In 2016 a Manchester group built capillaries from atomically flat sheets separated by spacers of graphene layers, giving voids whose height was a chosen number of atomic planes, and reported water flowing through them at up to 1 m/s.^[6] A year later the same technique, with a single atomic plane removed from a crystal, showed that ions with hydrated diameters larger than the slit can still pass, with reduced mobility. The slits there were 6.6 and 6.7 Å high, and the hydrated diameter of potassium and of chloride is about 6.6 Å.^[7]

In the graphite devices of 2019, 200 parallel channels, each 130 nm wide and a few micrometers long, lay between two graphite crystals held apart by strips of bilayer graphene, which sets the height at 6.8 Å. Matching devices had walls of hexagonal boron nitride. The reservoirs held potassium chloride at 1 to 300 mM, and the pressure was raised in steps of 25 mbar to 125 mbar. The streaming current rose linearly with pressure, and the mobility came out near 10⁻⁷ m²/(V s). That is about twice the electrophoretic mobility of potassium ions in bulk water, 7.6 × 10⁻⁸ m²/(V s), and an order of magnitude above the value for silica channels.^[1]

The authors translated the mobility into a zeta potential with the bulk properties of water, as the equation above allows, and obtained an apparent value of about −0.4 V, against the 25 mV typical of the literature. Taking the permittivity of confined water as about 2 instead of 80 gave −16 V. They concluded that such a value "does not reflect anomalously high surface potential of the graphite" and "merely highlights the high streaming mobility arising from the fast transport of ions by water at molecular distances from surfaces". At the concentrations used, the Debye length ran from 9.6 nm at 1 mM to 0.55 nm at 300 mM, so the double layers filled a 0.68 nm slit at every concentration except, at most, the highest.

The voltage effect was the new result. With pressure and bias applied together, the current stayed proportional to the pressure gradient, but the slope changed with the bias: in a graphite device at 100 mM, 50 mV raised the streaming current by more than 100%. Graphite and boron nitride behaved differently, and the authors traced the difference to the friction between water, ions and each kind of wall in an extended continuum model.^[1]

Molecular Reality Corporation uses the same two words for a different thing: molecules passing through a sensor, and data sent over a network. The founder's message of March 28, 2026, "Marching orders", introduces the company's term with the sentence "Nobody outside the corps calls it molecular streaming yet" and names a single earlier use of "streaming" in the literature, "ionic streaming" in a paper from the group of Andre Geim.^[8] Geim is a co-author of the 2019 paper that has the phrase in its title.^[1][9] The company's usage is described in the article on molecular streaming, and the broader field in the article on nanofluidics.

• Nanofluidics
• Electroosmotic flow
• Electric double layer
• Debye length
• Molecular streaming