Euler characteristic during drying of porous media

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.