We investigate the behavior of the slip length in Newtonian liquids subject
to planar shear bounded by substrates with mixed boundary conditions. The upper
wall, consisting of a homogenous surface of finite or vanishing slip, moves at
a constant speed parallel to a lower stationary wall, whose surface is
patterned with an array of stripes representing alternating regions of no-shear
and finite or no-slip. Velocity fields and effective slip lengths are computed
both from molecular dynamics (MD) simulations and solution of the Stokes
equation for flow configurations either parallel or perpendicular to the
stripes. Excellent agreement between the hydrodynamic and MD results is
obtained when the normalized width of the slip regions, a/σ≳O(10), where σ is the (fluid) molecular diameter characterizing the
Lennard-Jones interaction. In this regime, the effective slip length increases
monotonically with a/σ to a saturation value. For a/σ≲O(10) and transverse flow configurations, the non-uniform interaction
potential at the lower wall constitutes a rough surface whose molecular scale
corrugations strongly reduce the effective slip length below the hydrodynamic
results. The translational symmetry for longitudinal flow eliminates the
influence of molecular scale roughness; however, the reduced molecular ordering
above the wetting regions of finite slip for small values of a/σ
increases the value of the effective slip length far above the hydrodynamic
predictions. The strong inverse correlation between the effective slip length
and the liquid structure factor representative of the first fluid layer near
the patterned wall illustrates the influence of molecular ordering effects on
slip in non-inertial flows.Comment: 12 pages, 10 figures Web reference added for animations:
http://www.egr.msu.edu/~priezjev/bubble/bubble.htm