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Computation 2015, 3(4), 600-615; doi:10.3390/computation3040600

An Incompressible, Depth-Averaged Lattice Boltzmann Method for Liquid Flow in Microfluidic Devices with Variable Aperture

1
Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, 205 North Mathews Ave., Urbana, IL 61801, USA
2
Department of Civil, Architectural, and Environmental Engineering, University of Texas at Austin, 301 East Dean Keeton St., Austin, TX 78712, USA
*
Author to whom correspondence should be addressed.
Academic Editors: Qinjun Kang and Li Chen
Received: 2 September 2015 / Revised: 10 November 2015 / Accepted: 16 November 2015 / Published: 24 November 2015
(This article belongs to the Special Issue Advances in Modeling Flow and Transport in Porous Media)
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Abstract

Two-dimensional (2D) pore-scale models have successfully simulated microfluidic experiments of aqueous-phase flow with mixing-controlled reactions in devices with small aperture. A standard 2D model is not generally appropriate when the presence of mineral precipitate or biomass creates complex and irregular three-dimensional (3D) pore geometries. We modify the 2D lattice Boltzmann method (LBM) to incorporate viscous drag from the top and bottom microfluidic device (micromodel) surfaces, typically excluded in a 2D model. Viscous drag from these surfaces can be approximated by uniformly scaling a steady-state 2D velocity field at low Reynolds number. We demonstrate increased accuracy by approximating the viscous drag with an analytically-derived body force which assumes a local parabolic velocity profile across the micromodel depth. Accuracy of the generated 2D velocity field and simulation permeability have not been evaluated in geometries with variable aperture. We obtain permeabilities within approximately 10% error and accurate streamlines from the proposed 2D method relative to results obtained from 3D simulations. In addition, the proposed method requires a CPU run time approximately 40 times less than a standard 3D method, representing a significant computational benefit for permeability calculations. View Full-Text
Keywords: lattice Boltzmann; porous media; microfluidics; permeability lattice Boltzmann; porous media; microfluidics; permeability
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Laleian, A.; Valocchi, A.J.; Werth, C.J. An Incompressible, Depth-Averaged Lattice Boltzmann Method for Liquid Flow in Microfluidic Devices with Variable Aperture. Computation 2015, 3, 600-615.

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