Energy-based analysis of the capillary rise and meniscus dynamics upon pinning at the exit of a capillary tube

Abstract

The capillary imbibition phenomenon has been widely studied by establishing governing equations, some of which might be too complex to obtain accurate solutions. Moreover, the capillary rise can be influenced by the constraint of capillary edge (i.e., pinning phenomenon), which is difficult to describe by governing equations. Therefore, a new analysis method is proposed in this paper, which can predict the capillary rise with/without contact line movement considering the dynamic contact angle and entrance viscosity dissipation. Firstly, the capillary length is discretized into micro elements. Secondly, every micro fluid level rise is analyzed based on conservation of mechanical energy. Finally, the whole rise process can be predicted by the end-to-end linking of all micro-elements. The accuracy of the proposed method is verified by multiple sets of experimental data. Moreover, we discuss the pinning and depinning phenomena in detail and propose a dimensionless number to judge the occurrence of depinning phenomena.