Viscous flow through a finite-width slit: Boundary conditions and dissipation

We study the hydrodynamic viscous electronic transport in a two-dimensional sample separated into two semi-infinite planes by one-dimensional infinite barrier. The are electrically connected via finite-size slit calculate current through assuming finite voltage drop between and neglecting disorder-induced Ohmic resistance, so dissipation resistance purely viscosity induced. find that only solution to Stokes equation this geometry, which yields at (and, hence, is not self-contradictory), one fulfills both no-stress no-slip boundary conditions simultaneously. As remarkable consequence, obtained velocity profile satisfies so-called partial-slip (Maxwell) condition for any value of slip length, drops out from all final results. also temperature small large heat conductivity asymmetric (with respect barrier) patterns former case.