  The conventional boundary conditions at the interface between two flowing
liquids include continuity of the tangential velocity. We have tested this
assumption with molecular dynamics simulations of Couette and Poiseuille flows
of two-layered liquid systems, with various molecular structures and
interactions. When the total liquid density near the interface drops
significantly compared to the bulk values, the tangential velocity varies very
rapidly there, and would appear discontinuous at continuum resolution. The
value of this apparent slip is given by a Navier boundary condition.
