AN INVESTIGATION ON SPONTANEOUS IMBIBITION IN TREE-LIKE BRANCHING NETWORK WITH FRACTAL ROUGHENED SURFACES

Abstract

The tree-like branching network widely exists in nature and human society. The heat and mass transfer of tree-like branching network has been studied for a long time. The research indicates that a tree-like branching network has excellent heat and mass transfer performance. In this paper, a model of spontaneous imbibition in the tree-like branching network with fractal roughened surfaces is proposed. Based on the series-parallel equivalent model, the analytical expression of the time-varying imbibition height and the expression of the equilibrium height are derived. It is found that the structural parameters of the branching network have an important influence on the imbibition process, including the diameter in the 0th branching level, the length ratio, the diameter ratio, the branching number, the total number of branching levels, the relative roughness and the branching angle. For instance, the equilibrium height increases with the increase in the total number of branching levels, but the time required to reach the equilibrium height also increases with the increase in the total number of branching levels. It is also seen that the equilibrium height increases with the increase in fractal dimension of roughened elements and length ratio, and decreases with the increase in diameter ratio. In addition, an interesting phenomenon is that the time required to reach the equilibrium height increases with the increase in branching angle, but the equilibrium height remains the same. Every parameter of the presented model has a clear physical meaning, revealing the imbibition mechanism of the tree-like branching network.