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.