Modeling and structural optimization of steady-state in-plane liquid transport in tree-like fabric patterns

Currently, the mass transfer optimization of tree-like patterns is mainly focused on mass transfer within circular channels in three-dimensional structures. In this work, a tree-like pattern for optimizing liquid water transport inside double-jersey knitted fabric is proposed for, it is believed, the first time, from both macroscopic and microscopic perspectives. Darcy’s law and the Hagen–Poiseuille equation are respectively used to investigate the optimal volume flow rate of two-dimensional tree-like patterns (with the width much larger than the thickness) under constant external pressure; this is further verified by a finite-element model based on experimental data. The results show that the liquid flow rate in the branches reaches its maximum at a fractal dimension of 1, deviating from the prediction of Murray’s law. In addition, a finite-element model with an error range of less than 5% is established based on experimental parameters and results. By comparing the liquid water transport efficiency inside the tree-like pattern under different fractal dimensions, it is found that the calculated results of the finite-element model are in good agreement with the theoretical results, providing a theoretical basis for optimizing the moisture wicking performance of smart functional fabrics and garments.