No 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 [Formula: see text] 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.

A novel gas diffusivity model for dry porous media with a damaged tree-like branching network is proposed by using the fractal theory in this study. We systematically investigated the effects of the number of damaged channels and the other structural parameters on the dimensionless gas diffusivity (DGD) and concentration drop. As the number of damaged channels increases, the DGD presents a decreasing trend, while the ratio of concentration drop shows a rising tendency. Meanwhile, the DGD is negatively correlated to the length exponent, the total number of branching levels, and the branching angle, respectively. On the other hand, the DGD is positively correlated with the diameter exponent. Besides, the ratio of concentration drop is negatively correlated with the length exponent and the total number of branching levels. However, it is positively associated with the diameter exponent and branching levels. In addition, during the calculation of the value of concentration drop, the total concentration drop can be disassembled into two equal-ratio sequences. And the scale factors in sequences are constants that are independent of the number of damaged channels. The reliability of the model predictions was verified by a comparison with the experimental data available in the literature. The physical mechanism of gas diffusion in the damaged network may be well explained by the proposed model.