The Pressure Gate

Classical electrokinetics predicts that streaming conductance — the ratio of ionic current to applied pressure in a charged channel — is a constant. Push harder, get proportionally more current. The proportionality is set by the surface charge and the channel geometry, and it holds from micrometers down to nanometers. It’s a linear transport coefficient, like electrical conductivity or thermal diffusivity.

Lu, Luan, Guo, Duan, Du, and Xie (arXiv:2501.00238) find that in angstrom-scale channels — radii below 2 nanometers — streaming conductance becomes pressure-dependent. Below a threshold pressure, there is no ionic streaming at all. Above it, the conductance increases with pressure before eventually saturating. The linear regime doesn’t exist at this scale.

The mechanism is counterion release. In a channel so narrow that the electrical double layer concept fails, counterions are bound to the charged surface by direct Coulomb interactions, not diffusely distributed in a cloud. Moving these ions requires overcoming an energy barrier — the hydrodynamic force of the flowing fluid must be large enough to rip the counterions off the surface. Below the threshold pressure, the flow can’t detach them. Above it, detachment becomes increasingly efficient.

The counterintuitive detail: the effective surface potential increases as the channel narrows. In classical theory, smaller channels screen more effectively and reduce the apparent surface charge. Here, the opposite occurs — confinement enhances the Coulomb interaction between counterions and surface groups, strengthening the binding. The channel must be pushed harder to liberate its own ions.

The authors model this with Kramers escape theory — the same framework used for chemical reaction rates over energy barriers — and introduce a Damköhler number to characterize the transition from nonlinear to linear streaming regimes. The structural lesson: below 2 nanometers, ionic transport isn’t flow-driven diffusion. It’s a threshold escape process, gated by pressure rather than proportional to it.

Lu, Luan, Guo, Duan, Du, & Xie, “Angstrom-scale ionic streaming when electrical double-layer concept fails,” arXiv:2501.00238 (2025).