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.
Highlights
Understanding reactive flow and transport processes at the pore scale has benefited from model validation against experimental results using microfluidic devices
Recall that the viscous drag term was originally derived for Hele-Shaw flow
A 2D depth-averaged lattice Boltzmann method (LBM) is presented to approximate the depth-averaged results of a 3D LBM in micromodels with variable aperture, created by impermeable precipitate or biomass
Summary
Understanding reactive flow and transport processes at the pore scale has benefited from model validation against experimental results using microfluidic devices. Referred to as micromodels, these devices serve as model porous media in laboratory experiments studying pore-scale reactive transport processes [1,2] (see Figure 1). For special cases where the micromodel aperture is constant, 2D numerical models appear to accurately capture flow, transport, and reaction [3,7]. Such models are computationally efficient and avert costly 3D numerical methods. When micromodel aperture is variable due to reactions that promote biomass or mineral precipitate growth on its top and bottom surfaces, 2D flow models are not expected to accurately capture the complex 3D flow paths that develop
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