On the Slip Mechanism of Microfluidics by Means of a Mean-Field Free-Energy Lattice Boltzmann Method

2005 ◽  
Author(s):  
Junfeng Zhang ◽  
Daniel Y. Kwok
Keyword(s):  
Free Energy ◽  
Lattice Boltzmann ◽  
Slip Length ◽  
Mean Field ◽  
Interaction Strength ◽  
Slip Boundary Condition ◽  
System Size ◽  
Slip Mechanism ◽  
Slip Boundary ◽  
Fluid Solid Interaction

In this paper, we studied liquid-solid slip by employing a mean-field free-energy lattice Boltzmann approach recently proposed [Zhang et al., Phy. Rev. E. 69, 032602, 2004]. With a general bounce-back no-slip boundary condition applied to the interface, liquid slip was observed because of the specific fluid-solid interaction. The slip length is clearly related to the interaction strength: the stronger the interaction, the less hydrophobic the surface and hence results in less slipping. Unlike other lattice Boltzmann models, a contact angle value between 0–180° can be generated here without using a less realistic repulsive fluid-solid interaction. We found that system size does not affect the absolute slip magnitude; however, the ratio of the slip length to system size increases quickly as the system becomes smaller, illustrating that slip becomes important in smaller-scale systems. A small negative slip length can also be produced with a strong fluid-solid attraction. These results are in qualitative agreement with those from experimental and molecular dynamics studies.

Examination of the Slip Boundary Condition by µ-PIV and Lattice Boltzmann Simulations

2002 ◽  
Author(s):  
Derek C. Tretheway ◽  
Luoding Zhu ◽  
Linda Petzold ◽  
Carl D. Meinhart
Keyword(s):  
Boundary Condition ◽  
Shear Rate ◽  
Channel Flow ◽  
Lattice Boltzmann ◽  
Slip Velocity ◽  
Slip Length ◽  
Slip Boundary Condition ◽  
Slip Boundary ◽  
Lattice Boltzmann Simulations ◽  
Bounce Back

This work examines the slip boundary condition by Lattice Boltzmann simulations, addresses the validity of the Navier’s hypothesis that the slip velocity is proportional to the shear rate and compares the Lattice Boltzmann simulations to the experimental results of Tretheway and Meinhart (Phys. of Fluids, 14, L9–L12). The numerical simulation models the boundary condition as the probability, P, of a particle to bounce-back relative to the probability of specular reflection, 1−P. For channel flow, the numerically calculated velocity profiles are consistent with the experimental profiles for both the no-slip and slip cases. No-slip is obtained for a probability of 100% bounce-back, while a probability of 0.03 is required to generate a slip length and slip velocity consistent with the experimental results of Tretheway and Meinhart for a hydrophobic surface. The simulations indicate that for microchannel flow the slip length is nearly constant along the channel walls, while the slip velocity varies with wall position as a results of variations in shear rate. Thus, the resulting velocity profile in a channel flow is more complex than a simple combination of the no-slip solution and slip velocity as is the case for flow between two infinite parallel plates.

scholarly journals Involving the Navier–Stokes equations in the derivation of boundary conditions for the lattice Boltzmann method

2011 ◽  
Vol 369 (1944) ◽  
pp. 2184-2192 ◽  
Author(s):  
Joris C. G. Verschaeve
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Grid Spacing ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Boltzmann Method

By means of the continuity equation of the incompressible Navier–Stokes equations, additional physical arguments for the derivation of a formulation of the no-slip boundary condition for the lattice Boltzmann method for straight walls at rest are obtained. This leads to a boundary condition that is second-order accurate with respect to the grid spacing and conserves mass. In addition, the boundary condition is stable for relaxation frequencies close to two.

scholarly journals Morphological evolution of microscopic dewetting droplets with slip

2017 ◽  
Vol 828 ◽  
pp. 271-288 ◽  
Author(s):  
Tak Shing Chan ◽  
Joshua D. McGraw ◽  
Thomas Salez ◽  
Ralf Seemann ◽  
Martin Brinkmann
Keyword(s):  
Slip Length ◽  
Morphological Evolution ◽  
Early Time ◽  
Slip Boundary Condition ◽  
Similarity Solutions ◽  
Contact Angles ◽  
Equilibrium Contact Angle ◽  
Navier Slip ◽  
Slip Boundary ◽  
Quasistatic Regime

We investigate the dewetting of a droplet on a smooth horizontal solid surface for different slip lengths and equilibrium contact angles. Specifically, we solve for the axisymmetric Stokes flow using the boundary element method with (i) the Navier-slip boundary condition at the solid/liquid boundary and (ii) a time-independent equilibrium contact angle at the contact line. When decreasing the rescaled slip length $\tilde{b}$ with respect to the initial central height of the droplet, the typical non-sphericity of a droplet first increases, reaches a maximum at a characteristic rescaled slip length $\tilde{b}_{m}\approx O(0.1{-}1)$ and then decreases. Regarding different equilibrium contact angles, two universal rescalings are proposed to describe the behaviour of the non-sphericity for rescaled slip lengths larger or smaller than $\tilde{b}_{m}$. Around $\tilde{b}_{m}$, the early time evolution of the profiles at the rim can be described by similarity solutions. The results are explained in terms of the structure of the flow field governed by different dissipation channels: elongational flows for $\tilde{b}\gg \tilde{b}_{m}$, friction at the substrate for $\tilde{b}\approx \tilde{b}_{m}$ and shear flows for $\tilde{b}\ll \tilde{b}_{m}$. Following the changes between these dominant dissipation mechanisms, our study indicates a crossover to the quasistatic regime when $\tilde{b}$ is many orders of magnitude smaller than $\tilde{b}_{m}$.

scholarly journals Immersed boundary (IB) - Lattice Boltzmann Method (LBM) coupled with Adaptive MESH Refinement (AMR) techniques for simulation of Incompressible Viscous Flow

2021 ◽  
Author(s):  
Xixiong Guo
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Adaptive Mesh Refinement ◽  
Moving Objects ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Slip Boundary Condition ◽  
Immersed Boundary ◽  
Slip Boundary ◽  
Boltzmann Method

This study is aimed at developing a novel computational framework that seamlessly incorporates the feedback forcing model and adaptive mesh refinement mesh refinement (AMR) techniques in the immersed-boundary (IB) lattice Boltzmann method (LBM) approach, so that challenging problems, including the interactions between flowing fluids and moving objects, can be numerically investigated. Owing to the feedback forcing based IB model, the advantages, such as simple mechanics principle, explicit interpolations, and inherent satisfaction of no-slip boundary condition for solid surfaces are fully exhibited. Additionally, the "bubble' function is employed in the local mesh refinement process, so that the solution of second order accuracy at newly generated nodes can be obtained only by the spatial interpolation but no temporal interpolation. Focusing on both steady and unsteady flow around a single cylinder and bi-cylinders, a number of test cases performed in this study have demonstrated the usefulness and effectiveness of the present AMR IB-LBM approach.

Liquid Slippage in Confined Flows: Effect of Periodic Micropatterns of Arbitrary Pitch and Amplitude

2016 ◽  
Author(s):  
Avinash Kumar ◽  
Subhra Datta ◽  
Dinesh Kalyanasundaram
Keyword(s):  
Slip Length ◽  
Fluid Dynamic ◽  
Low Cost ◽  
Slip Boundary Condition ◽  
Friction Reduction ◽  
Fourier Decomposition ◽  
Slip Boundary ◽  
Local Degree ◽  
Effective Slip Length ◽  
Effective Slip

The recently confirmed violation of the no-slip boundary condition in the flow of small-molecule liquids through microchannels and nanochannels has technological implications such as friction reduction. However, for significant friction reduction at low cost, the microchannel wall needs to be chemically inhomogeneous. The direct fluid dynamic consequence of this requirement is a spatial variation in the local degree of liquid slippage. In this work, the pressure-driven flow in a channel with periodically patterned slippage on the channel walls is studied using a spectrally accurate semi-analytical approach based on Fourier decomposition. The method puts no restrictions on the pitch (or wavelength) and amplitude of the pattern. The predicted effective slip length in the limits of small pattern amplitude and thick channels is found to be consistent with previously published results. The effective degree of slippage decreases with the patterning amplitude. Finer microchannels and longer pattern wavelengths promote slippage.

A New Partial Slip Boundary Condition for the Lattice-Boltzmann Method

2013 ◽  
Author(s):  
Marc-Florian Uth ◽  
Alf Crüger ◽  
Heinz Herwig
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Slip Model ◽  
Navier Stokes Equations ◽  
Navier Slip ◽  
Slip Boundary ◽  
Boltzmann Method

In micro or nano flows a slip boundary condition is often needed to account for the special flow situation that occurs at this level of refinement. A common model used in the Finite Volume Method (FVM) is the Navier-Slip model which is based on the velocity gradient at the wall. It can be implemented very easily for a Navier-Stokes (NS) Solver. Instead of directly solving the Navier-Stokes equations, the Lattice-Boltzmann method (LBM) models the fluid on a particle basis. It models the streaming and interaction of particles statistically. The pressure and the velocity can be calculated at every time step from the current particle distribution functions. The resulting fields are solutions of the Navier-Stokes equations. Boundary conditions in LBM always not only have to define values for the macroscopic variables but also for the particle distribution function. Therefore a slip model cannot be implemented in the same way as in a FVM-NS solver. An additional problem is the structure of the grid. Curved boundaries or boundaries that are non-parallel to the grid have to be approximated by a stair-like step profile. While this is no problem for no-slip boundaries, any other velocity boundary condition such as a slip condition is difficult to implement. In this paper we will present two different implementations of slip boundary conditions for the Lattice-Boltzmann approach. One will be an implementation that takes advantage of the microscopic nature of the method as it works on a particle basis. The other one is based on the Navier-Slip model. We will compare their applicability for different amounts of slip and different shapes of walls relative to the numerical grid. We will also show what limits the slip rate and give an outlook of how this can be avoided.

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