A model for capillary rise in nano-channels with inherent surface roughness

This paper presents the results of an analytical model for the capillary rise in nano-channels considering the effect of inherent surface roughness. The model was derived using the classical Lucas-Washburn model and the momentum conservation equation, while considering the inherent surface roughness of an equivalent porous medium layer (PML). The calculated frictional resistance due to the PML reflects the friction of fluid flowing through nano-channels. The capillary imbibition in the nano-channels is in the range of low-Reynolds-number flow, and because of its low flow-rate, the inertia force can be ignored in this study. This analytical model was validated by comparing it with nano-capillary rise experiments and other simulated values such as the classical Lucas-Washburn (LW) model and the classical LW model with a 40% fluid viscosity increment. The analytical model produces the closest results to those obtained in the experiments, and it can explain the lower-than-expected (using the LW equation) height of capillary rise obtained in the experiments.