Nikolai V. Priezjev

Slip behavior in liquid films on surfaces of patterned wettability: Comparison between continuum and molecular dynamics simulations

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/sigma greater than or approximately equal O (10) , where sigma is the (fluid) molecular diameter characterizing the Lennard-Jones interaction. In this regime, the effective slip length increases monotonically with a/sigma to a saturation value. For a/sigma less than or approximately O (10) 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/sigma 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.

Influence of periodic wall roughness on the slip behaviour at liquid/solid interfaces: molecular-scale simulations versus continuum predictions

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 molecular-scale 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.

Rate-dependent slip boundary conditions for simple fluids

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.

Effect of surface roughness on rate-dependent slip in simple fluids

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.

Effects of crossflow velocity and transmembrane pressure on microfiltration of oil-in-water emulsions

Abstract This study addresses the issue of oil removal from water using hydrophilic porous membranes. The effective separation of oil-in-water dispersions involves high flux of water through the membrane and, at the same time, high rejection rate of the oil phase. The effects of transmembrane pressure and crossflow velocity on rejection of oil droplets and thin oil films by pores of different cross-section are investigated numerically by solving the Navier–Stokes equation. We found that in the absence of crossflow, the critical transmembrane pressure, which is required for the oil droplet entry into a circular pore of a given surface hydrophilicity, agrees well with analytical predictions based on the Young–Laplace equation. With increasing crossflow velocity, the shape of the oil droplet is strongly deformed near the pore entrance and the critical pressure of permeation increases. We determined numerically the phase diagram for the droplet rejection, permeation, and breakup depending on the transmembrane pressure and shear rate. Finally, an analytical expression for the critical pressure in terms of geometric parameters of the pore cross-section is validated via numerical simulations for a continuous oil film on elliptical and rectangular pores.

Modeling the combined effect of surface roughness and shear rate on slip flow of simple fluids.

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.

Optomechanical properties of stretched polymer dispersed liquid crystal films for scattering polarizer applications

A scattering polarizer is created by subjecting a polymer dispersed liquid crystal film to tensile strain. The optomechanical properties of the film are investigated by simultaneously measuring the stress–strain and polarization dependent optical transmission characteristics. The correlation between transmittances of two orthogonal polarizations and the stress–strain curve reveals that the polymer orientation as well as the droplet shape anisotropy influences the liquid crystal alignment within the droplets. A Monte Carlo simulation based on the P. A. Lebwohl–G. Lasher [Phys. Rev. A 6, 426 (1972)] model is used to explain the subtle influence of polymer orientation on liquid crystal alignment.

Oil droplet behavior at a pore entrance in the presence of crossflow: Implications for microfiltration of oil-water dispersions

Abstract The behavior of an oil droplet pinned at the entrance of a micropore and subject to crossflow-induced shear is investigated numerically by solving the Navier–Stokes equation. We found that in the absence of crossflow, the critical transmembrane pressure required to force the droplet into the pore is in excellent agreement with a theoretical prediction based on the Young–Laplace equation. With increasing shear rate, the critical pressure of permeation increases, and at sufficiently high shear rates the oil droplet breaks up into two segments. The results of numerical simulations indicate that droplet breakup at the pore entrance is facilitated at lower values of the surface tension coefficient, higher oil-to-water viscosity ratio and larger droplet size but is insensitive to the value of the contact angle. Using simple force and torque balance arguments, an estimate for the increase in critical pressure due to crossflow and the breakup capillary number is obtained and validated for different viscosity ratios, surface tension coefficients, contact angles, and drop-to-pore size ratios.

The effective slip length and vortex formation in laminar flow over a rough surface

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 towards 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 towards the bottom 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.

Virtual surfaces, director domains, and the Fréedericksz transition in polymer-stabilized nematic liquid crystals

The critical field of the Freedericksz transition and switching dynamics are investigated for polymer-stabilized nematic liquid crystals as a function of polymer concentration. A simple phenomenological model is proposed to describe the observed critical field and dynamic response time behaviors as a function of concentration. In this model, the polymer fibrils form director domains, which are bounded by “virtual surfaces” with a finite anchoring energy.