Open Access

ARTICLE

Lattice Boltzmann Flow Models for Micro/Nano Fluidics

Kazuhiko Suga^1,2, Takahiko Ito¹

1 Department of Mechanical Engineering, Osaka Prefecture University, Sakai, Osaka 599-8531, Japan
2 Corresponding author: suga@me.osakafu-u.ac.jp

Computer Modeling in Engineering & Sciences 2010, 63(3), 223-242. https://doi.org/10.3970/cmes.2010.063.223

Abstract

Flow passages in micro/nano-electro-mechanical systems (MEMS/ -NEMS) usually have complicated geometries. The present study thus discusses on the latest lattice Boltzmann methods (LBMs) for micro/nano fluidics to evaluate their applicability to micro/nano-flows in complex geometries. Since the flow regime is the continuum to the slip and transitional regime with a moderate Knudsen number (Kn), the LBMs presently focused on feature the wall boundary treatment and the relaxation-time for modeling such flow regimes. The discussed micro flow (µ-flow) LBMs are based on the Bhatnagar-Gross-Krook (BGK) model and the multiple relaxation-time (MRT) model. The presently chosen µ-flow BGK LBM (BGK-1 model) consists of the diffuse-scattering wall condition with the single relaxation-time sensitized to the Knudsen number whereas them-flow MRT LBMs are combined with the diffusive bounce-back wall condition (MRT-1 model) and the bounce-back and specular-reflection condition (MRT-2 model). The simulated flow cases are canonical force-driven Poiseuille flows at 0.01 ≤ Kn ≤ 10 and a flow around an obstacle (a square cylinder) situated in a nanochannel at Kn≈0.1. The second-order truncated system (nine discrete velocity model for two dimensions: D2Q9 model) is applied for the simulations. The results show that the MRT models improve the performance of the BGK-1 model. It is also confirmed that the MRT-1 model is superior to the MRT-2 model for simulating micro/nano-flows with impinging and stagnating regions though further improvement is required, particularly, for predicting flow rates.

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Keywords

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