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.

1 aNiavarani, A.1 aPriezjev, N., V uhttps://icer.msu.edu/research/publications/modeling-combined-effect-surface-roughness-shear-rate-slip-flow-simple-fluids01895nas a2200217 4500008004100000245008800041210006900129260001200198490000700210520117900217653001901396653001701415653002801432653001901460653001501479653001401494653001301508100001801521700002001539856011801559 2009 eng d00aThe effective slip length and vortex formation in laminar flow over a rough surface0 aeffective slip length and vortex formation in laminar flow over c05/20090 v213 aThe 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.

10aexternal flows10alaminar flow10aNavier-Stokes equations10arough surfaces10ashear flow10aslip flow10avortices1 aNiavarani, A.1 aPriezjev, N., V uhttps://icer.msu.edu/research/publications/effective-slip-length-vortex-formation-laminar-flow-over-rough-surface01785nas a2200217 4500008004100000245008800041210006900129260001200198490000800210520105900218653001701277653003001294653001801324653001301342653001501355653001401370653002201384100001801406700002001424856012301444 2008 eng d00aRheological study of polymer flow past rough surfaces with slip boundary conditions0 aRheological study of polymer flow past rough surfaces with slip c10/20080 v1293 aThe 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.

10aliquid films10amolecular dynamics method10apolymer melts10arheology10ashear flow10aslip flow10asurface roughness1 aNiavarani, A.1 aPriezjev, N., V uhttps://icer.msu.edu/research/publications/rheological-study-polymer-flow-past-rough-surfaces-slip-boundary-conditions01604nas a2200193 4500008004100000245009100041210006900132260001200201490000700213520093400220653002301154653001501177653001601192653001801208653002801226100001801254700002001272856011801292 2008 eng d00aSlip boundary conditions for shear flow of polymer melts past atomically flat surfaces0 aSlip boundary conditions for shear flow of polymer melts past at c04/20080 v773 aMolecular 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.

10amolecular dynamics10ashear rate10aslip length10aslip velocity10asmooth thermal surfaces1 aNiavarani, A.1 aPriezjev, N., V uhttps://icer.msu.edu/research/publications/slip-boundary-conditions-shear-flow-polymer-melts-past-atomically-flat