Approximating three-dimensional fluid flow in a microfluidic device with a two-dimensional, depth-averaged lattice Boltzmann method

lattice boltzmann;pore-scale modeling;reactive transport;fluid flow;depth-averaged;microfluidic

Laleian, Artin ; Werth ; Charles J. ; Valocchi ; Albert J.

关键词: lattice boltzmann;    pore-scale modeling;    reactive transport;    fluid flow;    depth-averaged;    microfluidic;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/49643/Artin_Laleian.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Microfluidic devices (MFDs) are important tools in the study of reactive transport processes in porous media. Laboratory and numerical experiments have studied reactions such as bimolecular complexation, biodegradation and biofilm growth, and mineral precipitation coupled to fluid flow in MFDs that are shallow rectangular channels with regular or irregular interior pore structure. The success of these reactive transport models is dependent on accurate determination of the velocity field, because reaction is coupled to solute transport. The small aspect ratio of these devices has led to their approximation as two-dimensional (2D) objects in numerical models. This approximation may neglect significant three-dimensional (3D) effects on the velocity field and contribute to model error. To avoid the computational cost of a 3D numerical model, some 3D effects may be approximated in a 2D model. In prior work in the literature, viscous drag from the top and bottom boundary surfaces omitted by the 2D simulation has been approximated and applied as an external body force acting on the fluid for the case of constant depth throughout the MFD. This work generalizes the approximation to cases of variable depth to account for the possibility of precipitate or biofilm formation along those surfaces omitted by the 2D simulation. The 2D lattice Boltzmann method (LBM) is reformulated to solve the depth-averaged Stokes equations and the viscous drag body force approximation is applied. The 2D, depth-averaged LBM is benchmarked by comparison to depth-averaged results of the 3D LBM in several test geometries. Excellent agreement is observed between the results of the two methods in contracting-expanding channel geometries. Agreement is not as favorable in more complex flows, such as flow around a cylinder or in a MFD unit cell. In addition, a comparison of run times demonstrates the reduction in computational cost with the 2D, depth-averaged LBM.