  This paper studies multiphase flow within grooved textures exposed to
external unsteadiness. We derive analytical expressions for multiphase unsteady
Stokes flow driven by oscillating streamwise/spanwise velocity in the presence
of periodic grooves. Good agreement is obtained between the analytical solution
and direct numerical simulations performed using the volume of fluid method.
The effects of oscillation frequency, Reynolds number, and the multiphase
interface location on the transfer function between the input signal external
to the groove and output near the interface, are examined. The effective slip
length and the shear stress over the grooved plane are described.
