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.Comment: 15 pages, 5 figures; submitted to J. Chem. Phy

Motion of nanodroplets near edges and wedges

Nanodroplets residing near wedges or edges of solid substrates exhibit a disjoining pressure induced dynamics. Our nanoscale hydrodynamic calculations reveal that non-volatile droplets are attracted or repelled from edges or wedges depending on details of the corresponding laterally varying disjoining pressure generated, e.g., by a possible surface coating.Comment: 12 pages, 7 figure

Kolmogorov turbulence in a random-force-driven Burgers equation

The dynamics of velocity fluctuations, governed by the one-dimensional Burgers equation, driven by a white-in-time random force with the spatial spectrum \overline{|f(k)|^2}\proptok^{-1}, is considered. High-resolution numerical experiments conducted in this work give the energy spectrum $E(k)\propto k^{-\beta}$ with $\beta =5/3\pm 0.02$. The observed two-point correlation function $C(k,\omega)$ reveals $\omega\propto k^z$ with the "dynamical exponent" $z\approx 2/3$. High-order moments of velocity differences show strong intermittency and are dominated by powerful large-scale shocks. The results are compared with predictions of the one-loop renormalized perturbation expansion.Comment: 13 LaTeX pages, psfig.sty macros, Phys. Rev. E 51, R2739 (1995)

Implementation of on-site velocity boundary conditions for D3Q19 lattice Boltzmann

On-site boundary conditions are often desired for lattice Boltzmann simulations of fluid flow in complex geometries such as porous media or microfluidic devices. The possibility to specify the exact position of the boundary, independent of other simulation parameters, simplifies the analysis of the system. For practical applications it should allow to freely specify the direction of the flux, and it should be straight forward to implement in three dimensions. Furthermore, especially for parallelized solvers it is of great advantage if the boundary condition can be applied locally, involving only information available on the current lattice site. We meet this need by describing in detail how to transfer the approach suggested by Zou and He to a D3Q19 lattice. The boundary condition acts locally, is independent of the details of the relaxation process during collision and contains no artificial slip. In particular, the case of an on-site no-slip boundary condition is naturally included. We test the boundary condition in several setups and confirm that it is capable to accurately model the velocity field up to second order and does not contain any numerical slip.Comment: 13 pages, 4 figures, revised versio

Crossover from Hydrodynamics to the Kinetic Regime in Confined Nanoflows

We present an experimental study of a confined nanoflow, which is generated by a sphere oscillating in the proximity of a flat solid wall in a simple fluid. Varying the oscillation frequency, the confining length scale and the fluid mean free path over a broad range provides a detailed map of the flow. We use this experimental map to construct a scaling function, which describes the nanoflow in the entire parameter space, including both the hydrodynamic and the kinetic regimes. Our scaling function unifies previous theories based on the slip boundary condition and the effective viscosity

Finite difference lattice Boltzmann model with flux limiters for liquid-vapor systems

In this paper we apply a finite difference lattice Boltzmann model to study the phase separation in a two-dimensional liquid-vapor system. Spurious numerical effects in macroscopic equations are discussed and an appropriate numerical scheme involving flux limiter techniques is proposed to minimize them and guarantee a better numerical stability at very low viscosity. The phase separation kinetics is investigated and we find evidence of two different growth regimes depending on the value of the fluid viscosity as well as on the liquid-vapor ratio.Comment: 10 pages, 10 figures, to be published in Phys. Rev.

Strong and auxiliary forms of the semi-Lagrangian method for incompressible flows

We present a review of the semi-Lagrangian method for advection-diusion and incompressible Navier-Stokes equations discretized with high-order methods. In particular, we compare the strong form where the departure points are computed directly via backwards integration with the auxiliary form where an auxiliary advection equation is solved instead; the latter is also referred to as Operator Integration Factor Splitting (OIFS) scheme. For intermediate size of time steps the auxiliary form is preferrable but for large time steps only the strong form is stable

Generalization of the JTZ model to open plane wakes

The JTZ model [C. Jung, T. T\'el and E. Ziemniak, Chaos {\bf 3}, (1993) 555], as a theoretical model of a plane wake behind a circular cylinder in a narrow channel at a moderate Reynolds number, has previously been employed to analyze phenomena of chaotic scattering. It is extended here to describe an open plane wake without the confined narrow channel by incorporating a double row of shedding vortices into the intermediate and far wake. The extended JTZ model is found in qualitative agreement with both direct numerical simulations and experimental results in describing streamlines and vorticity contours. To further validate its applications to particle transport processes, the interaction between small spherical particles and vortices in an extended JTZ model flow is studied. It is shown that the particle size has significant influences on the features of particle trajectories, which have two characteristic patterns: one is rotating around the vortex centers and the other accumulating in the exterior of vortices. Numerical results based on the extended JTZ model are found in qualitative agreement with experimental ones in the normal range of particle sizes.Comment: 21 pages, 4 figures, 1 tabl

A hierarchy of models related to nanoflows and surface diffusion

In last years a great interest was brought to molecular transport problems at nanoscales, such as surface diffusion or molecular flows in nano or sub-nano-channels. In a series of papers V. D. Borman, S. Y. Krylov, A. V. Prosyanov and J. J. M. Beenakker proposed to use kinetic theory in order to analyze the mechanisms that determine mobility of molecules in nanoscale channels. This approach proved to be remarkably useful to give new insight on these issues, such as density dependence of the diffusion coefficient. In this paper we revisit these works to derive the kinetic and diffusion models introduced by V. D. Borman, S. Y. Krylov, A. V. Prosyanov and J. J. M. Beenakker by using classical tools of kinetic theory such as scaling and systematic asymptotic analysis. Some results are extended to less restrictive hypothesis

Numerical Methods for the Stochastic Landau-Lifshitz Navier-Stokes Equations

The Landau-Lifshitz Navier-Stokes (LLNS) equations incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. This paper examines explicit Eulerian discretizations of the full LLNS equations. Several CFD approaches are considered (including MacCormack's two-step Lax-Wendroff scheme and the Piecewise Parabolic Method) and are found to give good results (about 10% error) for the variances of momentum and energy fluctuations. However, neither of these schemes accurately reproduces the density fluctuations. We introduce a conservative centered scheme with a third-order Runge-Kutta temporal integrator that does accurately produce density fluctuations. A variety of numerical tests, including the random walk of a standing shock wave, are considered and results from the stochastic LLNS PDE solver are compared with theory, when available, and with molecular simulations using a Direct Simulation Monte Carlo (DSMC) algorithm