A NOVEL FRACTAL MODEL FOR SPONTANEOUS IMBIBITION IN DAMAGED TREE-LIKE BRANCHING NETWORKS

Abstract

Spontaneous imbibition has attracted considerable attention due to its extensive existence in nature. In this study, we theoretically explored the spontaneous imbibition dynamics in a damaged V-shaped tree-like branching network by comparing with a parallel net with fixed constraints. Additionally, the imbibition capacity is characterized by two dimensionless quantities: imbibition potential and dimensionless imbibition time. The fractal theory is then used to generate the analytical expressions of these two dimensionless quantities. After that, the influence of structural parameters on the imbibition process is systematically investigated. It is found that a larger number of damaged channels will correspond to the lower imbibition potential and dimensionless imbibition time. Notably, the branching number N has an evident enhancement effect on the imbibition potential. A parameter plane is introduced to visualize parameter combinations, enabling the direct evaluation of the imbibition process in a specific network system. The physical mechanisms revealed by the proposed model provide effective guidance for imbibition process analysis in the damaged tree-like networks.