Molecular dynamics (MD) and continuum simulations are carried out to investigate the influence of shear rate and surface roughness on slip flow of a Newtonian fluid. For weak wall-fluid interaction energy, the nonlinear shear-rate dependence of the intrinsic slip length in the flow over an atomically flat surface is computed by MD simulations. We describe laminar flow away from a curved boundary by means of the effective slip length defined with respect to the mean height of the surface roughness. Both the magnitude of the effective slip length and the slope of its rate dependence are significantly reduced in the presence of periodic surface roughness. We then numerically solve the Navier-Stokes equation for the flow over the rough surface using the rate-dependent intrinsic slip length as a local boundary condition. Continuum simulations reproduce the behavior of the effective slip length obtained from MD simulations at low shear rates. The slight discrepancy between MD and continuum results at high shear rates is explained by examination of the local velocity profiles and the pressure distribution along the wavy surface. We found that in the region where the curved boundary faces the mainstream flow, the local slip is suppressed due to the increase in pressure. The results of the comparative analysis can potentially lead to the development of an efficient algorithm for modeling rate-dependent slip flows over rough surfaces.

}, author = {A. Niavarani and N. V Priezjev} } @article {166, title = {Relationship between induced fluid structure and boundary slip in nanoscale polymer films}, journal = {Physical Review E}, volume = {82}, year = {2010}, author = {N. V Priezjev} } @article {183, title = {The effective slip length and vortex formation in laminar flow over a rough surface}, journal = {Physics of Fluids}, volume = {21}, year = {2009}, month = {05/2009}, abstract = {The flow of viscous incompressible fluid over a periodically corrugated surface is investigated numerically by solving the Navier\–Stokes equation with the local slip and no-slip boundary conditions. We consider the effective slip length which is defined with respect to the level of the mean height of the surface roughness. With increasing corrugation amplitude the effective no-slip boundary plane is shifted toward the bulk of the fluid, which implies a negative effective slip length. The analysis of the wall shear stress indicates that a flow circulation is developed in the grooves of the rough surface provided that the local boundary condition is no-slip. By applying a local slip boundary condition, the center of the vortex is displaced toward the bottom of the grooves and the effective slip length increases. When the intrinsic slip length is larger than the corrugation amplitude, the flow streamlines near the surface are deformed to follow the boundary curvature, the vortex vanishes, and the effective slip length saturates to a constant value. Inertial effects promote vortex flow formation in the grooves and reduce the effective slip length.

}, keywords = {external flows, laminar flow, Navier-Stokes equations, rough surfaces, shear flow, slip flow, vortices}, author = {A. Niavarani and N. V Priezjev} } @article {175, title = {Shear rate threshold for the boundary slip in dense polymer films}, journal = {Phys. Rev. E}, volume = {80}, year = {2009}, month = {09/2009}, pages = {11 Pages}, abstract = {The shear rate dependence of the slip length in thin polymer films confined between atomically flat surfaces is investigated by molecular dynamics simulations. The polymer melt is described by the bead-spring model of linear flexible chains. We found that at low shear rates the velocity profiles acquire a pronounced curvature near the wall and the absolute value of the negative slip length is approximately equal to the thickness of the viscous interfacial layer. At higher shear rates, the velocity profiles become linear and the slip length increases rapidly as a function of shear rate. The gradual transition from no-slip to steady-state slip flow is associated with faster relaxation of the polymer chains near the wall evaluated from decay of the time autocorrelation function of the first normal mode. We also show that at high melt densities the friction coefficient at the interface between the polymer melt and the solid wall follows a power-law decay as a function of the slip velocity. At large slip velocities the friction coefficient is determined by the product of the surface-induced peak in the structure factor, the temperature, and the contact density of the first fluid layer near the solid wall.

}, author = {N. V Priezjev} } @article {209, title = {Rheological study of polymer flow past rough surfaces with slip boundary conditions}, journal = {Journal of Chemical Physics}, volume = {129}, year = {2008}, month = {10/2008}, abstract = {The slip phenomena in thin polymer films confined by either flat or periodically corrugated surfaces are investigated by molecular dynamics and continuum simulations. For atomically flat surfaces and weak wall-fluid interactions, the shear rate dependence of the slip length has a distinct local minimum which is followed by a rapid increase at higher shear rates. For corrugated surfaces with wavelength larger than the radius of gyration of polymer chains, the effective slip length decays monotonically with increasing corrugation amplitude. At small amplitudes, this decay is reproduced accurately by the numerical solution of the Stokes equation with constant and rate-dependent local slip length. When the corrugation wavelength is comparable to the radius of gyration, the continuum predictions overestimate the effective slip length obtained from molecular dynamics simulations. The analysis of the conformational properties indicates that polymer chains tend to stretch in the direction of shear flow above the crests of the wavy surface.

}, keywords = {liquid films, molecular dynamics method, polymer melts, rheology, shear flow, slip flow, surface roughness}, author = {A. Niavarani and N. V Priezjev} } @article {214, title = {Slip boundary conditions for shear flow of polymer melts past atomically flat surfaces}, journal = {Physical Review E}, volume = {77}, year = {2008}, month = {04/2008}, abstract = {Molecular dynamics simulations are carried out to investigate the dynamic behavior of the slip length in thin polymer films confined between atomically smooth thermal surfaces. For weak wall-fluid interactions, the shear rate dependence of the slip length acquires a distinct local minimum followed by a rapid growth at higher shear rates. With increasing fluid density, the position of the local minimum is shifted to lower shear rates. We found that the ratio of the shear viscosity to the slip length, which defines the friction coefficient at the liquid/solid interface, undergoes a transition from a nearly constant value to power law decay as a function of the slip velocity. In a wide range of shear rates and fluid densities, the friction coefficient is determined by the product of the value of the surface-induced peak in the structure factor and the contact density of the first fluid layer near the solid wall.

}, keywords = {molecular dynamics, shear rate, slip length, slip velocity, smooth thermal surfaces}, author = {A. Niavarani and N. V Priezjev} } @article {228, title = {Effect of surface roughness on rate-dependent slip in simple fluids}, journal = {The Journal of Chemical Physics}, volume = {127}, year = {2007}, month = {10/2007}, pages = {144708}, abstract = {Molecular dynamics simulations are used to investigate the influence of molecular-scale surface roughness on the slip behavior in thin liquid films. The slip length increases almost linearly with the shear rate for atomically smooth rigid walls and incommensurate structures of the liquid/solid interface. The thermal fluctuations of the wall atoms lead to an effective surface roughness, which makes the slip length weakly dependent on the shear rate. With increasing the elastic stiffness of the wall, the surface roughness smoothes out and the strong rate dependence is restored again. Both periodically and randomly corrugated rigid surfaces reduce the slip length and its shear rate dependence.

}, keywords = {elastic constants, interface roughness, liquid films, molecular dynamics method, slip, surface roughness, thin films}, author = {N. V Priezjev} } @article {234, title = {Rate-dependent slip boundary conditions for simple fluids}, journal = {Physical Review E}, volume = {75}, year = {2007}, month = {05/2007}, pages = {51605}, abstract = {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.

}, author = {N. V Priezjev} }