Molecular dynamics and continuum simulations of fluid flows with slip boundary conditions

Microfluidics is a rapidly developing field with applications ranging from molecular biology, environmental monitoring, and clinical diagnostics. Microfluidic systems are characterized by large surface-to-volume ratios, and, therefore, fluid flows are significantly influenced by boundary conditions. The fundamental assumption in fluid mechanics is the no-slip boundary condition, which states that the tangential fluid velocity is equal to the adjacent wall speed. Although this assumption is successful in describing fluid flows on macroscopic length scales, recent experimental and numerical studies have shown that it breaks down at microscopic scales due to the possibility of slip of the fluid relative to the wall. The effect of slip is more pronounced for highly viscous liquids like polymer melts or in the region near the moving contact line due to the large gradient in shear stress at the liquid/solid interface. The measure of slip is the so-called slip length, which is defined as a distance between the real interface and imaginary plane where the extrapolated velocity profile vanishes. The slip length value is sensitive to several key parameters, such as surface energy, surface roughness, fluid structure, and shear rate.;In this dissertation, the slip phenomena in thin liquid films confined by either flat or structured surfaces are investigated by molecular dynamics (MD) and continuum simulations. It is found that for flows of both monatomic and polymeric fluids over smooth surfaces, the slip length depends nonlinearly on shear rate at sufficiently high rates. The laminar flow away from a curved boundary is usually described by means of the effective slip length, which is defined with respect to the mean roughness height. MD simulations show that for corrugated surfaces with wavelength larger than the size of polymer chains, the effective slip length decreases monotonically with increasing corrugation amplitude. A detailed comparison between the solution of the Navier-Stokes equation with the local rate-dependent slip condition and results of MD simulations indicates that there is excellent agreement between the velocity profiles and the effective slip lengths at low shear rate and small-scale surface roughness. It was found that the main cause of the slight discrepancy between MD and continuum results at high shear rates is the reduction of the local slip length in the higher pressure regions where the boundary slope becomes relatively large with respect to the mainstream flow. It was further shown that for the Stokes flow with the local no-slip boundary condition, the effective slip length decreases with increasing corrugation amplitude and a flow circulation is developed in sufficiently deep grooves. Analysis of a numerical solution of the Navier-Stokes equation with the local slip condition shows that the inertial effects promote the asymmetric vortex flow formation and reduce the effective slip length...