Euler characteristic during drying of porous media

Abstract

This study aims to elucidate the dynamics of fluid topology during drainage and evaporation of wetting and non-wetting fluids via evaluation of their Euler characteristic (EC) and Betti numbers from designed experiments. The results showed that the EC of the non-wetting fluid remained constant at a high wetting fluid saturation and then decreased nonlinearly. However, the EC of the wetting fluid exhibited more complex trends. In the 2-D micromodel, the number of loops decreased monotonously, reached zero, and remained constant for lower saturations, while the number of distinct components fluctuated because of the appearance and disappearance of disconnected clusters. In the 2-D model, the number of distinct components played a significant role; in the 3-D X-ray CT experiment, the number of loops of pendular rings dominated the EC. The findings suggest that the trends observed in the 2-D micromodel may not apply under 3-D conditions.

Keywords:

• Betti numbers
• porous media flow
• evaporation
• micromodel
• X-ray CT

Acknowledgements

The authors are responsible for their opinions and comments.

Disclosure of interest statement

The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the paper.

Data availability statement

The data presented in this study can be obtained from the corresponding author (Shao-Yiu Hsu) upon request ([email protected]).

Additional information

Funding

This research was funded by the Taiwanese Ministry of Science and Technology (MOST) under Grant MOST-109-2621-M-002-015, MOST 106-2628-M-002-009-MY3, and MOST 107-2221-E-008-029 and the Polish National Centre for Research and Development (contract no.: PL-TW/IV/5/2017). This article was subsidized for English editing by National Taiwan University under the Excellence Improvement Program for Doctoral Students (grant number 108-2926-I-002-002-MY4), sponsored by Ministry of Science and Technology, Taiwan.