Prediction and evolution of the hydraulic tortuosity for unsaturated flow in actual porous media

Hydraulic tortuosity is one of the major parameters when designing and optimizing the porous media structure. Unfortunately, most models and methods (whether experimental, theoretical, or numerical) to determine the tortuosity of porous media related to fluid flow, diffusion or infiltration are indirect, e.g., based on other correlated physical variables or a predefined porous structure model. Herein, we employ a conservative level set method for the transient pore-scale multiphase flow to model the infiltration behaviour of a fluid into a porous media on the basis of the actual porous media topological structure from scanning electron microscopy (SEM) micrographs. We then numerically predict the hydraulic tortuosity for unsaturated porous media using the vector-based tortuosity method (VTM) based on the velocity profile regardless of all the structural parameters of the porous materials, and provide comprehensive and intuitive insight into the spatiotemporal evolution for hydraulic tortuous feature of the porous media. Again, the prediction results of hydraulic tortuosity are compared with several classical and empirical models. Finally, the research findings manifest that the relative error of hydraulic tortuosity for the different liquids across the identical porous media with the mean value is below 1.0%, and the maximum relative errors of the reproducibility and repeatability for the proposed numerical method are less than 2.1% and 1.0%, respectively.