  Molecular dynamic (MD) simulation is used to study slip at the fluid-solid
boundary in an unsteady flow based on the Stokes second problem. An increase in
slip is observed in comparison to the steady flow for shear rates below the
critical shear rate of the corresponding steady flow. This increased slip is
attributed to fluid inertial forces not represented in a steady flow. An
unsteady mathematical model for slip is established, which estimates the
increment in slip at the boundary. The model shows that slip is also dependent
on acceleration in addition to the shear rate of fluid at the wall. By writing
acceleration in terms of shear rate, it is shown that slip at the wall in
unsteady flows is governed by the gradient of shear rate and shear rate of the
fluid. Non-dimensionalizing the model gives a universal curve which can be used
to find the slip boundary condition at the fluid-solid interface based on the
information of shear rate and gradient of shear rate of the fluid. A governing
non-dimensional number, defined as the ratio of phase speed to speed of sound,
is identified to help in explaining the mechanism responsible for the
transition of slip boundary condition from finite to a perfect slip and
determining when this would occur. Phase lag in fluid velocity relative to wall
is observed. The lag increases with decreasing time period of wall oscillation
and increasing wall hydrophobicity. The phenomenon of hysteresis is seen when
looking into the variation of slip velocity as a function of wall velocity and
slip velocity as a function of fluid shear rate. The cause for hysteresis is
attributed to the unsteady inertial forces of the fluid.
