Fractal modeling for capillary flow through fiber bundle

Moisture transport in fiber assembly is one of the critical factors affecting physiological comfort. It is useful to model bundle structure for understanding capillary flow in complex geometries representative of the void spaces formed between fibers. This paper investigates the capillary rise in vertical fiber bundles. Regarding fiber bundles as a porous media, a mathematical model was developed by using a fractal analysis approach based on the fractal nature of pores in fiber assembly. The wicking height of the liquid in fiber bundles was derived as an exponent function of the wicking time, where the coefficients depend on microstructure parameters of capillary channels in fiber bundles, the surface tension of liquid, and contact angle between the liquid surface and the fiber. The predicted wicking heights are compared with the experimental data. Good agreement is found between the present model predictions and the experimental data. As the time approaches infinite, the predicted maximum wicking height is also found to be similar to that of classic mechanics model.