A boundary condition with adjustable slip length for Lattice Boltzmann simulations

TL;DR

This paper extends a boundary condition for Lattice Boltzmann simulations to accurately model slip flows, demonstrating independence from shear rate and density, and confirming its effectiveness through various flow tests and surface pattern analyses.

Contribution

The work introduces an extended boundary condition for Lattice Boltzmann simulations that accurately models slip flows without artificial slip, independent of shear rate and density.

Findings

Slip length is proportional to BGK relaxation time.

Patterned walls induce anisotropic slip lengths.

Simulation results match theoretical angle dependence.

Abstract

A velocity boundary condition for the Lattice Boltzmann simulation technique has been proposed recently by Hecht and Harting[arxiv:0811.4593]. This boundary condition is independent of the relaxation process during collision and contains no artificial slip. In this work, this boundary condition is extended to simulate slip-flows. The extended boundary condition has been tested and it is found that the slip length is independent of the shear rate and the density, and proportional to the BGK relaxation time. The method is used to study slip in Poiseuille flow and in linear shear flow. Patterned walls with stripes of different slip parameters are also studied, and an anisotropy of the slip length in accordance with the surface pattern is found. The angle dependence of the simulation results perfectly agrees with theoretical expectations. The results confirm that the proposed boundary conditions can be used for simulating slip-flows in micro fluidics using single relaxation time lattice Boltzmann, without any numerical slip, giving an accuracy of the second order.