  We map molecular dynamics simulations of fluid-fluid interfaces onto
mesoscale continuum theories for partially miscible fluids. Unlike most
previous work, we examine not only the interface order parameter and density
profiles, but also the stress. This allows a complete mapping from the length
scales of molecular dynamics simulations onto a mesoscale model suitable for a
lattice Boltzmann or other mesoscale simulation method. Typical assumptions of
mesoscale models, such as incompressibility, are found to fail at the
interface, and this has a significant impact on the surface tension. Spurious
velocities, found in a number of discrete models of curved interfaces, are
found to be minimized when the parameters of the mesoscopic model are made
consistent with molecular dynamics results. An improved mesoscale model is
given and demonstrated to produce results consistent with molecular dynamics
simulations for interfaces with widths down to near molecular size.
