Two liquid channels separated by a solid wall. In classical hydrodynamics, they are independent — the wall blocks all momentum transfer. Liquid flowing in one channel does not induce flow in the other. The wall is a boundary condition: zero velocity, zero coupling.
At the nanoscale, liquid flow tunnels through the wall. Flow in one channel induces flow in the adjacent channel, through a solid barrier, in violation of continuum hydrodynamics. The coupling is not leakage — the wall is impermeable. The mechanism is electronic: the flowing liquid's charge density fluctuations couple to the solid's electronic excitations, which propagate through the wall and couple to the liquid on the other side.
The tunnelling range depends on the electronic structure of the solid. When the solid's electronic excitations are at resonance with the liquid's charge fluctuations, the tunnelling is maximized. The coupling can be tuned by choosing the wall material — controlling an ostensibly hydrodynamic property (flow coupling) through an electronic property (excitation spectrum).
The phenomenon is relevant for flow through nanoscale membrane networks — graphene oxide, MXene — where channels are separated by walls only nanometers thick. Classical models predict each channel flows independently. The tunnelling correction means they don't.
The structural point: the boundary between fluid mechanics and quantum mechanics is a scale, not a category. Below a certain wall thickness, the classical independence of adjacent flows breaks down. The wall mediates coupling it was supposed to block, through a mechanism (electronic excitations) that fluid mechanics does not contain. The solid is not inert infrastructure — it is the communication channel.