Molecular hydrodynamics of inhomogeneous systems: The origin of slip boundary conditions

Molecular hydrodynamic equations derived by linear response theory for inhomogeneous systems are investigated in two extreme cases: a simple fluid in a gravitational field (an example of a long-range inhomogeneity), and a simple fluid in the presence of a rigid flat wall described by an infinite potential step (an example of a short-range inhomogeneity). In both cases the phenomenological equations result when the molecular equations are smoothed over a length which is large compared to the correlation lenght. For these systems the local equilibrium assumption is shown to be valid. In addition it is shown how the usual slip boundary conditions arise as a consequence of the interaction which causes the short-range inhomogeneity.