Capillary Filling in Nanochannels—Modeling, Fabrication, and Experiments

Abstract

While capillary filling in channels of micrometers scale is experimentally verified to obey Washburn's law well, the speed of capillary filling in nanochannels is noticeably lower than described by Washburn's formula. This article reports the theoretical and experimental results on capillary filling in open-end and closed-end nanochannels. Nanochannels of 45 nm and 80 nm depth, 10 μm width, were etched in silicon and bonded to a glass cover. Experiments on filling of non-electrolytic liquid in silicon nanochannels were carried out. The filling processes were observed and recorded. To estimate the influence of electrokinetics, a mathematical model to calculate the electroviscous effect was established. This model shows that the contribution of the electroviscous effect in the reduction of filling speed is small. This result also agrees well with previous theoretical work on the electroviscous effect. That means that besides the electroviscous effect, there are other phenomena that contribute to the reduction of capillary filling speed in a nanochannel, such as air bubbles formation. Experimental investigation of capillary filling in open-end and closed-end nanochannels with different lengths was performed. The filling processes of ethanol and isopropanol and the behavior of the trapped air were recorded and evaluated. Analytical models based on the continuum assumption were used to evaluate the experimental data. We observed that the filling process consists of two stages. At the initial stage, experimental data agree well with the theoretical model, but with a higher apparent viscosity. In the final stage, condensation of the liquid phase and dissolution of the gas phase lead to total filling of the nanochannel. The observed phenomena are important for understanding the behavior of multiphase systems in nanochannels.