Slip-flow boundary condition for straight walls in the lattice Boltzmann model

Abstract

A slip-flow boundary condition has been developed in the lattice Boltzmann model combining an interpolation method and a simple slip boundary condition for straight walls placed at arbitrary distance from the last fluid node. An analytical expression has been derived to connect the model parameters with the slip velocity for Couette and Poiseuille flows in the nearly continuum limit. The proposed interpolation method ensures that the slip velocity is independent of the wall position in first order of the Knudsen number. Computer simulations have been carried out to validate the model. The Couette and Poiseuille flows agree with the analytical results to machine order. Numerical simulation of a moving square demonstrates the accuracy of the model for walls moving in both the tangential and normal directions.

Simulation of thermal micro-flow using lattice Boltzmann method with Langmuir slip model

“…Recently, the mesoscopic lattice Boltzmann (LB) method developed from kinetic theory has been applied to study microfluidic flows (Nie et al, 2002;Lim et al, 2002;Succi, 2002;Zhang et al, 2005;Lee and Lin, 2005;Ansumali et al, 2006;Ansumali and Karlin, 2005;Shan et al, 2006;Kunert and Harting, 2007;Niu et al, 2007;Shi et al, 2007;Szalmas, 2006;Verhaeghe et al, 2009;Tang et al, 2008;Kim and Pitsch, 2008;Guo et al, 2008), to cite only a few. Different from MD and DSMC schemes, the LB method is more efficient intuitively in computation because its computational cost is comparable to that of the NS solvers .…”

Momentum transfer correction for macroscopic-gradient boundary conditions in lattice Boltzmann methods

“…The development of Neumann boundary treatments in LB largely focuses on the definition of slip boundaries, or stressrelated conditions, as they are linked to the development of wall boundary-conditions for microflows [31][32][33]. Although the use of kinetic boundary conditions to impose a pre-defined stresses has been attempted for planar walls, no satisfactory result has been obtained in curved geometries, for which their application becomes complex or impossible [32,34].…”

“…Although the use of kinetic boundary conditions to impose a pre-defined stresses has been attempted for planar walls, no satisfactory result has been obtained in curved geometries, for which their application becomes complex or impossible [32,34].…”

The Effect of Boundary Slip on the Transient Pulsatile Flow of a Modified Second-Grade Fluid

“…In all of the above mentioned models, the so-called noslip boundary condition is used; namely, the velocity of flow relative to the solid is zero on the fluid-solid interface [12]. Although the no-slip condition is supported by many experimental results, the existence of slip of a fluid on the solid surface was also observed by many other researches [13][14][15][16][17][18][19][20]. The Navier slip condition has been used by various researchers to describe boundary slip and is a more general boundary condition, in which the fluid velocity component tangential to the solid surface, relative to the solid surface, is proportional to the shear stress on the fluid-solid interface and the slip length.…”