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 [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.

The Fastest Capillary Flow in Root-like Networks under Gravity

“…Microfluidics devices based on capillary flow have been widely used in biology and chemistry. − Lee et al discussed the influences of cross-sectional area, channel length, and branching numbers on the flow rate in open-channel capillary tree without considering gravity. Wang et al investigated the behavior of capillary flow in damaged root-like networks and discussed the effects of structural parameters such as the number of damaged branches on the flow rate ratio and flow time ratio. Lee studied the effects of structural parameters on dewatering rate in artificial trees driven by capillary force and proposed that the increasing conduit diameter will enhance water flux.…”

A Boundary-Element Analysis of Crack Problems in Multilayered Elastic Media: A Review

“…Among various numerical methods for the analysis of the crack problems to compute crack opening displacement, the boundary element method (BEM) is widely chosen, because it only discretizes boundaries of a domain of interest and consequently enables a more-efficient computation and a more-convenient implementation [34][35][36][37], while most of the other methods, such as the PFM or FEM, require discretization of the whole domain [31]. Furthermore, the BEM exploits existed analytical fundamental solutions, ensuring a potentially more accurate computation [38][39][40][41].…”