  Many multiphase fluid systems, such as those involving immiscible polymers or
liquid-liquid systems with surfactants, have shown a breakdown of the no-slip
condition at the material interface. This results in systems where the
tangential velocity of the inner and outer fluid can differ, with the jump in
velocity dependent not only the material properties of the interface but also
the stresses applied by the surrounding fluid. In this work a numerical model
is presented which is capable of investigating general multiphase fluid systems
involving interfacial slip in both two- and three-dimensions. To make the
system computationally feasible, a hybrid Navier-Stokes projection method is
used, whereby the viscosity, density, and pressure are assumed to be continuous
across the interface while the velocity field can experience a jump, which is
handled via the Immersed Interface Method. The numerical model is compared to
experimental results involving polymer-polymer mixtures and computational
results for droplets in extensional flows, showing excellent agreement with
both. It is then used to explore the influence of interfacial slip in a number
of common multiphase fluid systems, including the shearing of a planar
interface, droplet and filament relaxation, and droplets in shear flow, both
unbounded and wall-bound.
