Surface roughness and interfacial slip boundary condition for quartz crystal microbalances

Slip boundary condition for lattice Boltzmann modeling of liquid flows

Based on the Navier slip model, a slip boundary format for the lattice Boltzmann method is developed for curve walls of which the shape is well considered. The main idea of this method is to convert the slip length into the slip velocity with a simplified algorithm. With the Navier slip model, the slip velocities at the boundary are obtained through the interpolation of the fluid points near the boundary and are then substituted into the velocity boundary conditions to construct the relationship between the slip length and the macroscopic flow field. This format is free from the restriction of the previous combined boundary conditions which can only be applied to flat boundaries. It also overcomes the limitation that the slip boundary can only simulate flows with small slip length. The present slip boundary condition is implemented for the lattice Bhatnagar-Gross-Krook model, which is verified by several cases, including the cylindrical Couette flow and the irregular Poiseuille flow. The numerical results agree well with theoretical analysis. Furthermore, this boundary condition is applied to the hydrofoil to study the drag reduction effect of the boundary slip phenomenon. It is found that the slip boundary can effectively reduce the drag of the hydrofoil at low Reynolds numbers. Moreover, the position of the slip boundary on the hydrofoil also has significant effects on the lift-to-drag ratio.

Molecular dynamics simulations are employed to investigate the Poiseuille flow of NaCl aqueous solution through nanochannels with generic solid walls, with a specific focus on the coupled effects of wall-solution van der Waals interaction (WSI_VdW) energy and surface charge density (δ) on interfacial slip behavior. The results reveal that the contact density (ρc) exhibits a non-monotonic dependence on the δ, characterized by an initial decrease followed by an increase at sufficiently large δ. At low δ, both the fluid velocity and slip length (Ls) are significantly larger under low WSI_VdW energy than under high WSI_VdW energy. This disparity, however, diminishes rapidly with increasing δ. Beyond a critical δ value, the velocity and Ls exhibit minimal variation with further increases in δ and become insensitive to the WSI_VdW energy. The underlying mechanism is elucidated by analyzing the normalized in-plane structure factor S(G1)/S(0). Furthermore, the correlation between slip length and S(G1)/S(0), ρc, and δ is established. It is demonstrated that across a wide range of WSI_VdW energies and δ values, Ls can be accurately described by a single-variable function dependent on S(G1)/S(0), ρc, and δ. This study provides valuable theoretical insights for modeling interfacial slip boundary conditions in electrolyte flows through charged nanochannels.

In this paper, a Lattice Boltzmann method was used to simulate the flow of temperature-sensitive magnetic fluids in a micro porous cavity. According to Navier’s linear slip length model, slip boundary conditions were used on all the walls of the micro porous cavity. The effects of the horizontal slip length and the vertical slip length on the flow and heat transfer characteristics were investigated. The results showed that with the increase of the slip length, the velocities and their gradients became smaller, so the convection was harder to occur, and the temperature was more stable. On the walls, the effects of the slip lengths on the Nusselt numbers at the edges and at the centers were different, so the local heat transfer efficiencies were changed accordingly. It was also found that when the horizontal slip length was set to be zero, the flow developed from one vertex to two vortexes along the vertical direction with the increase of vertical slip length. The corresponding critical vertical slip length first increased and then decreased with the Rayleigh number and the magnetic Rayleigh number.

In order to describe the transition between slip and rigid boundary conditions, a model with a thin interphasial viscoelastic layer is introduced. By changing the relaxation time (ωτ), the transition from a viscous liquid to a solid layer is observed. When the interface layer is in the liquid state with very small shear nodulus the shear stress components on the boundary vanish, resulting in a slip boundary condition. On the other hand, after the layer is solidified, the two semispaces become welded with the transition of shear and longitudinal stresses to one another. It is shown that the ratio of a hydrodynamic boundary layer thickness to the interface layer thickness plays a major role in this transition. A simple approximate equation for the reflection coefficient from the interface is derived and compared to the exact solutions for different transitional stages of the boundary condition. Theoretical predictions are compared to experimental results.

The propagation characteristics of impact waves across a planar interface between a ceramic layer and a ceramic/metal (C/M), composite layer were investigated. Two interfacial boundary conditions were considered: one was a shear coupling boundary condition that simulated a perfectly bonded interface between the ceramic and composite, and the other was a slip boundary condition that only allowed a transmission of the transverse motion and normal stress at the interface. The ceramic was subjected to an incident impact wave. The ceramic and composite was assumed to be elastic during impact. The study was based on a basic method provided by Furlong, westburg and Phillips for predicting the reflection and refraction of spherical waves across a planar interface separating two elastic solids. Emphasis was put on the effect of the metal volume fraction in the composite, ceramic thickness and interfacial boundary condition on the effect of the metal volume fraction in the composite, ceramic thickness and interfacial boundary condition on the reflected waves. New and interesting results are obtained that provide a very useful guidance for design of a ceramic/composite armor and of a C/M functionally graded applique.

The 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.

In the present study, hydrophobic roughness is used to induce near-wall slip in a single rotating-disk micropump operating with Newtonian water. The amount of induced slip is altered by employing different sizes of surface roughness on the rotating disk. The magnitudes of slip length and slip velocities increase as the average size of the surface roughness becomes larger. In the present study, increased slip magnitudes from roughness are then associated with reduced pressure rise through the pump and lower radial-line-averaged shear stress magnitudes (determined within slip planes). Such shear stress and pressure rise variations are similar to those which would be present if the slip is induced by the intermolecular interactions which are associated with near-wall microscale effects. The present slip-roughness effects are quantified experimentally over rotational speeds from 50 to 1200 rpm, pressure increases from 0 to 312 kPa, net flow rates of 0–100 μl/min, and fluid chamber heights from 6.85 to 29.2 μm. Verification is provided by comparisons with analytic results determined from the rotating Couette flow forms of the Navier–Stokes equations, with different disk rotational speeds, disk roughness levels, and fluid chamber heights. These data show that slip length magnitudes show significant dependence on radial-line-averaged shear stress for average disk roughness heights of 404 and 770 nm. These slip length data additionally show a high degree of organization when normalized using by either the average roughness height or the fluid chamber height. For the latter case, such behavior provides evidence that the flow over a significant portion of the passage height is affected by the roughness, and near-wall slip velocities, especially when the average roughness height amounts to 11% of the h=6.86 μm passage height of the channel. Such scaling of the disk slip length bdisk with fluid chamber height h is consistent with d-type roughness scaling in macroscale flows.

Rarefied gas flows in rough microchannels are investigated by non-equilibrium molecular dynamics simulations. The surface roughness is modelled by an array of triangular modules. The Maxwell slip model is found to break down due to the surface roughness for gas flows in microchannels with large surface roughness. Non-Maxwell slippage shows that the slip length is smaller than that predicted by the Maxwell model and is nonlinearly related to the mean free path. For larger surface roughness and smaller Knudsen number, the non-Maxwell effect becomes more pronounced. The boundary conditions, generally including velocity slip, no-slip and negative slip, depend not only on the Knudsen number but also on the surface roughness. Simulation results show that A/λ ≈ 1 is a good criterion to validate the no-slip boundary condition and A/λ > 0.3 can be a criterion to judge the occurrence of non-Maxwell slippage, where A is the surface roughness size and λ is the mean free path of gas molecules. The permeability enhanced by the surface roughness may be responsible for the roughness-induced non-Maxwell slippage.

The slip boundary condition in the dynamics of solid particles immersed in Stokesian flows

In this paper, we analyze Nitsche’s method for the stationary Navier–Stokes equations on Lipschitz domains under minimal regularity assumptions. Our analysis provides a robust formulation for implementing slip (i.e., Navier) boundary conditions in arbitrarily complex boundaries. The well-posedness of the discrete problem is established using the Banach Nečas–Babuška and Banach fixed point theorems under standard small data assumptions. We also provide optimal convergence rates for the approximation error. Furthermore, we propose a quasi-static VMS-LES formulation with Nitsche for the Navier–Stokes equations with slip boundary conditions to address the simulation of incompressible fluids at high Reynolds numbers. We validate our theory through several numerical tests in well-established benchmark problems.

Analysis of the decay of the fluorescence anisotropy of 2,4,6,8-decatetraene in a viscous hydrocarbon solution: the off-axis orientation of the transition dipole moment

Flow singularity and slip velocity in plane extrudate swell computations

This theoretical study deals with the Navier–Stokes equations posed in a 3D thin domain with thickness , assuming power‐law slip boundary conditions, with an anisotropic tensor, on the bottom. This condition, introduced in (Djoko et al. Comput. Math. Appl. 128 (2022) 198–213), represents a generalization of the Navier slip boundary condition. The goal is to study the influence of the power‐law slip boundary conditions with an anisotropic tensor of order , with and flow index , on the behavior of the fluid with thickness by using asymptotic analysis when , depending on the values of . As a result, we deduce the existence of a critical value of given by and so, three different limit boundary conditions are derived. The critical case corresponds to a limit condition of type power‐law slip. The supercritical case corresponds to a limit boundary condition of type perfect slip. The subcritical case corresponds to a limit boundary condition of type no‐slip.

As robotic technologies advance and robots move out of factories and labs into the real world, grip on a variety of surfaces (e.g. smooth or rough) in a variety of conditions (e.g. dry or wet) becomes increasingly important. Bioinspired "microspines" have been previously explored, but primarily for vertical climbing applications or for small-scale robots applying low forces (less than 1 N). Further, these works primarily focused on rough surfaces. To advance this area of research, we present a composite material comprising high- friction rubber and compliant nitinol microspines which can passively retract below the surface of the rubber. We show that the composite can support large loads (greater than 75 N) with a high coefficient of friction on both smooth and rough surfaces (p > 1.1), outperforming microspines alone on smooth surfaces and rubber alone on rough surfaces, especially when wet and oily. Further, due to the retraction of the microspines, the composite does not damage relatively soft, smooth surfaces, like wood flooring. We also test durability, and show that it is improved by microspine compliance, and test the effects of varying microspine diameter, angle, and tip shape. Finally, we demonstrate that a small RC car can climb steeper slopes and stop more quickly in wet conditions with microspines.