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 ͑MD͒ 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 / տ O͑10͒, where is the ͑fluid͒ molecular diameter characterizing the Lennard-Jones interaction. In this regime, the effective slip length increases monotonically with a / to a saturation value. For a / Շ O͑10͒ and transverse flow configurations, the nonuniform 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 / increases the value of the effective slip length far above the hydrodynamic predictions. The strong 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 noninertial flows.

The behavior of the slip length in thin polymer films subject to planar shear is investigated using molecular dynamics simulations. At low shear rates, the slip length extracted from the velocity profiles correlates well with that computed from a Green-Kubo analysis. Beyond chain lengths of about N 10, the molecular weight dependence of the slip length is dominated strongly by the bulk viscosity. The dynamical response of the slip length with increasing shear rate is well captured by a power law up to a critical value where the momentum transfer between wall and fluid reaches its maximum. is the bulk fluid viscosity, and wall is the reduced viscosity of the first fluid layer near the wall. Since then, a number of molecular dynamics (MD) studies have focused on the functional dependence of the slip length at low shear rates on molecular parameters affecting momentum transfer at a wall-fluid interface [9][10][11][12][13][14][15][16]. Stratification of the fluid layers near the wall plays an especially significant role [10] in determining the degree of slip. Recent equilibrium studies of simple fluids [17,18] have elucidated the dependence of the slip length on the fluid-wall contact density, the interaction energy, the inplane diffusion coefficient, and the structure factor of the first fluid layer.Even less is known about the dynamic behavior of the slip length with increasing shear rate. MD simulations In this Letter we use MD simulations to examine the dependence of the slip length on molecular parameters and shear rate in thin polymer films subject to planar shear. The emphasis on polymeric fluids is timely since most experiments devoted to slip phenomena rely on polymers in order to diminish evaporative effects and to enhance the degree of slip for measurement purposes [19][20][21][22]. Results of our simulations support the view that the low [17] and high shear [4] behavior of the slip length reported earlier for simple fluid systems is more generally applicable to polymeric systems. It is also shown that beyond chain lengths of about N 10, the net molecular weight dependence of the slip length at low shear rates is dominated by the bulk fluid viscosity.The simulation cell consisted of a simple or polymeric fluid (3456 monomers) subject to planar shear in thex x direction. The fluid monomers interacted through the LJ potential V LJ r 4 r 12 ÿ r 6 with a cutoff distance r c 2:5, where and represent the energy and length scales of the fluid phase. The wall-fluid parameters were chosen to be wf 0:6, wf 0:75, and r c 2:5; the fluid phase density and temperature T were held fixed at 0:81 ÿ3 and 1:1=k B , respectively. The polymer fluid was modeled as a collection of bead-spring units (N 2-16 beads) interacting through a finitely extensible nonlinear elastic (FENE) potential [23] V FENE r ÿ The upper and lower walls of the shear cell each consisted of 1152 atoms distributed between two (111) planes of an fcc lattice of density w 4. The direction of shear was oriented along 11 2 2. The fluid was confined to a gap w...

The dynamic behavior of the slip length in a fluid flow confined between atomically smooth surfaces is investigated using molecular dynamics simulations. At weak wall-fluid interactions, the slip length increases nonlinearly with the shear rate provided that the liquid/solid interface forms incommensurable structures. A gradual transition to the linear rate dependence is observed upon increasing the wall-fluid interaction. We found that the slip length can be well described by a function of a single variable that in turn depends on the in-plane structure factor, contact density, and temperature of the first fluid layer near the solid wall. Extensive simulations show that this formula is valid in a wide range of shear rates and wall-fluid interactions.

The influence of surface roughness on the slip behaviour of a Newtonian liquid in steady planar shear is investigated using three different approaches, namely Stokes flow calculations, molecular dynamics (MD) simulations and a statistical mechanical model for the friction coefficient between a corrugated wall and the first liquid layer. These approaches are used to probe the behaviour of the slip length as a function of the slope parameter ka = 2πa/λ, where a and λ represent the amplitude and wavelength characterizing the periodic corrugation of the bounding surface. The molecular and continuum approaches both confirm a monotonic decay in the slip length with increasing ka but the rate of decay as well as the magnitude of the slip length obtained from the Stokes flow solutions exceed the MD predictions as the wall feature sizes approach the liquid molecular dimensions. In the limit of molecularscale wall corrugation, a Green-Kubo analysis based on the fluctuation-dissipation theorem accurately reproduces the MD results for the behaviour of the slip length as a function of a. In combination, these three approaches provide a detailed picture of the influence of periodic roughness on the slip length which spans multiple length scales ranging from molecular to macroscopic dimensions.