Entrance loss of capillary flow in narrow slit nanochannels

The entrance loss of capillary flow at the nanoscale is crucial but often overlooked. This study investigates the entrance loss of capillary flow in narrow slit nanochannels using molecular dynamics simulations. The results show that the early stage of capillary flow is determined by entrance loss. During this period, capillary length increases linearly, while the capillary velocity remains constant. The effect of length-dependent friction loss becomes more apparent in the subsequent stages, causing the capillary length to deviate from linear and the capillary velocity to decrease. Roscoe's equation, which describes the flow through an infinitely thin slit, is used to model the entrance loss. Finite element simulations of flow through slits of varying height and length demonstrate the validity of Roscoe's equation in the continuum theory framework. Based on this, a capillary flow model is proposed that can accurately depict the hydrodynamic behavior of a capillary flow. Additionally, an approximate model ignoring the friction loss is proposed that predicts the linear increase in capillary length at the early stage. Theoretical analysis shows that the effect of entrance loss on capillary velocity is limited to the early stage, while the effect on capillary length can be extended to a large scale. Overall, the results of this study and the proposed models provide important theoretical support for applications related to capillary flows in nanoslits. The study emphasizes the importance of considering entrance loss in the early stages of a capillary flow and demonstrates the applicability of Roscoe's equation in modeling capillary flows in nanochannels.