Study on the capillary flow in non-uniform capillary tube based on Poiseuille law

Liquid transport in non-uniform capillary fibrous materials was previously investigated based on the 2D plane Poiseuille flow. Although the 2D model is relatively simple in expression, insufficient structural description of the 3D non-uniform capillary limits the accuracy of the 2D model. In this study, a 3D N-section non-uniform capillary model based on the Poiseuille flow equation and capillary pressure equation was established to further to investigate the liquid transport behavior in yarn. The 3D non-uniform capillary model is to simulate the non-uniform wicking path in the twisted yarn. The capillary flow time equation and the normalized capillary flow time equation were established based on the structural parameters of the non-uniform capillary, the physical parameters of liquid, and the contact angle between the liquid and fiber. And the effects of structural parameters of the non-uniform capillary such as the number of converging and diverging sections, the height ratio and the radius ratio on the liquid transport efficiency were deeply analyzed. The results showed that the liquid transport efficiency of the non-uniform capillary tubes with frequent alternating converging and diverging sections is lower, while the non-uniform capillary tubes with larger equivalent radius are more efficient to rapid liquid transport. Experiments on 300 D/64 F and 600 D/58 F polypropylene filaments with different twist coefficients verified the validity of the model. The experimental results are in agreement with the theoretical prediction. This study deepens the understanding of liquid transport in twisted yarn, and provides new ideas and methods for related scientific research and microfluidic device design.