A novel geometry-informed drag term formulation for pseudo-3D Stokes simulations with varying apertures

Alterations in the pore morphology of porous materials cause changes to the characteristic hydraulic properties, which are mostly non-linear and inherently difficult to predetermine. Assuming the alterations are known with sufficient accuracy, the relation between the altered pore structure, measured in terms of porosity, and intrinsic permeability may be determined by simulations with enormous computational effort. We focus on microfluidic experiments during the course of which the pore space becomes increasingly occupied with solid precipitate over elapsed process time. To analyze these domains, we present a novel geometry-informed drag formulation which allows for solving pseudo-3D Stokes equations for image-based input data of clogging porous media with accuracy and efficiency. In a pre-processing step, local pore space properties are analyzed and employed to spatially vary the magnitude of the drag term, which reflects the influence of neglected 3D effects. Calibration and validation is achieved through fully 3D Finite Difference Stokes simulations of different benchmark cases. With the proposed formulation we achieve the high accuracy of the pseudo-3D methods as far as permeability is concerned ($<$30% deviation), but also with respect to local velocities, for a microfluidic domain throughout the clogging process. Noteworthy, the computational cost is being reduced to less than 1%. Combining the efficiency of a Stokes 2D simulation and accuracy of a 3D model the presented approach is rendered an interesting option to investigate remaining open questions, for example on anisotropy of effective hydraulic parameters during the clogging process.