A kinetic theory of inhomogeneous fluids: the mean field approximation

A kinetic equation is derved, at the mean field level, for a single-component system composed of liquid and vapor phases separated by a planar interface. Three kinetic sum rules are derived and used to verify previously obtained configurational sum rules. The density gradient, which plays a key role in the interfacial dynamics, is discussed and used to construct a surface projection operator. The kinetic equation is then analyzed using this projection operator in conjunction with expansions in terms of momentum and spatial moments. The surface-related terms of the kinetic equation lead to propagating surface modes which exhibit a dispersion identical to that of capillary waves.