CM In the literature: open

Boundary slip length of viscous electron flow at sample edges

In plain words

How fast a viscous liquid moves at a wall sets the shape of its flow in a channel. For electron liquids this boundary condition depends on how electrons scatter off sample edges and is poorly known.

Precise statement

For viscous 2D electron flow in a channel of width w with the Navier boundary condition $u = \ell_s\,du/dn$ at the edge, determine the slip length $\ell_s$ as a function of edge roughness, temperature and electron-electron mean free path $\ell_{ee}$ in graphene and GaAs heterostructures. Answer: $\ell_s(T, \mathrm{roughness})$ from theory confirmed by imaging.

What would settle it

Imaging of current profiles across channels with controlled edge roughness compared with kinetic-theory boundary calculations.