Immiscible two-phase flow in the vicinity of the contact line (CL),
where the fluid-fluid interface intersects the solid wall, is a classical
problem that falls beyond the framework of conventional hydrodynamics
In particular, molecular dynamics (MD)
studies have shown relative slipping between the fluids and the wall,
in violation of the no-slip boundary condition.
While there have been numerous ad-hoc models
to address this phenomenon, none has been able to give a quantitative
account of the MD slip velocity profile in the molecular-scale vicinity
of the CL. We give a continuum formulation of the immiscible
flow hydrodynamics, comprising the generalized Navier boundary condition,
the Navier-Stokes equation, and the Cahn-Hilliard interfacial free energy.
Numerical simulation of our hydrodynamic model yields near-complete
slip of the contact line,
with interfacial and velocity profiles matching quantitatively with those
from the molecular dynamics simulations.
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