Green-Kubo relations for the viscosity

The Green-Kubo relations for the viscosity ar only valid for homogeneous systems. If you have a fluid confined in a slit the system is inhomogeneous. You can still evaluate the Green-Kubo relations but it will not be the viscosity. You can calculate an effective viscosity for the fluid-in-the-slit by displacing one wall relative to the other one, evaluate the shear stress and divide by the velocity gradient.

Sten Sarman