Dynamics of Euler Characteristic in Drying Porous Media

This study aims to evaluate and compare the dynamics of fluid topology during evaporation from porous media. To do so, a two-dimensional (2-D) micromodel was designed based on actual images of quartz sand to evaluate two scenarios: evaporation with and without drainage. Additionally, a three-dimensional (3-D) drainage-evaporation experiment was conducted by X-ray micro-tomography using glass beads to investigate the relationship between the results obtained in 2-D and 3-D experiments. The fluid topology was represented in the terminologies of Betti numbers and Euler characteristic (EC) which were quantified for both wetting and non-wetting fluids. Although the non-wetting fluid EC revealed similar patterns in the three scenarios, the wetting fluid EC showed different patterns depending on the experiment under investigation. First, in 2-D scenarios, the EC remained constant during drainage because of the corner flow, while the EC decreased during evaporation since there was insufficient liquid to maintain the corner flow. Second, as expected the topological features of liquid bridges (pendular rings) in 2-D and 3-D experiments were different which led to the opposite trends of their EC. The liquid bridge between two solid particles in the 2-D system corresponds to one distinct component without loops but one loop in the 3-D system. Third, the trend of EC was dominated by the number of distinct components in 2-D but by the number of loops in 3-D considering their topological differences in liquid bridges. Our findings suggest that the results obtained in 2-D experiments regarding fluid topology for wetting fluid may not necessarily represent the fluid behavior and trends observed in 3-D experiments.

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Dynamics of Euler Characteristic in Drying Porous Media