Random-Roughness Hydrodynamic Boundary Conditions

Abstract

We report results of lattice Boltzmann simulations of a high-speed drainage of liquid films squeezed between a smooth sphere and a randomly rough plane. A significant decrease in the hydrodynamic resistance force as compared with that predicted for two smooth surfaces is observed. However, this force reduction does not represent slippage. The computed force is exactly the same as that between equivalent smooth surfaces obeying no-slip boundary conditions, but located at an intermediate position between peaks and valleys of asperities. The shift in hydrodynamic thickness is shown to depend on the height and density of roughness elements. Our results do not support some previous experimental conclusions on very large and shear-dependent boundary slip for similar systems.

Hydrodynamic force measurements under precisely controlled conditions: Correlation of slip parameters with the mean free path

“…Thanks to its simplicity, the model (5) finds broad application in the literature 6,10,12,26,[28][29][30][46][47][48] to extract the slip length λ s from experimental data. However, it is mostly employed in the limit k → 0, corresponding to equal slip lengths on both surfaces.…”

“…In numerous modern experiments the influence of tribological parameters, such as roughness, [3][4][5][6] wettability, 7 surface contaminations, 8,9 nanobubbles, 2, 10 and shear velocity, 5,[11][12][13] on the flow of fluids on solid surfaces has been studied. Numerically, molecular dynamics and Monte Carlo simulations [14][15][16][17][18] have improved our understanding of the effects of gas trapping, roughness scales, and momentum exchange at surfaces (accommodation), thereby shedding new light on experimental problems and their origins.…”

Galilean invariant fluid–solid interfacial dynamics in lattice Boltzmann simulations

“…The lattice Boltzmann equation (LBE) [3][4][5][6] eliminated this artifact with the use of a proper equilibrium distribution function in the collision term, and in some investigations a few high-order, even complete Galilean invariant LBE models have been achieved [7][8][9]. Nowadays, LBE is particularly successful in simulations involving interfacial dynamics [10][11][12][13], microflows [14,15], multiphase flows [16][17][18], and complex fluid flows [19][20][21].…”

Quantification of the performance of chaotic micromixers on the basis of finite time Lyapunov exponents

“…Previously, we have shown that a well-resolved velocity field with less than 4% error as compared to the analytical solution can be obtained even for a resolution of 6-8 lattice nodes in the case of a three-dimensional rectangular Poiseuille flow (Narváez et al 2010). We further demonstrated that flow over random rough surfaces can be well resolved even if the smallest obstacles are only described by 2-4 lattice units (Kunert 2007;Kunert et al 2010). In the LB method, the kinematic viscosity is related to the discrete time step through the expression m ¼ c s 2 ð1=x À Dt=2Þ: Since xDt is chosen to be 1 to minimize artifacts due to the mid-grid bounce back boundary conditions and the simulated fluid has the kinematic viscosity of water, When the magnitude of g is 1:2 Â 10 À3 m s À2 along the z direction, the average steady state velocity of the system is u % 6:0 Â 10 À3 m s À1 which corresponds to a subsonic flow.…”