On the dynamic contact angle of capillary-driven microflows in open channels

The true value of the contact angle between a liquid and a solid is a thorny problem in capillary microfluidics. The Lucas-Washburn-Rideal (LWR) law assumes a constant contact angle during fluid penetration. However, recent experimental studies have shown lower liquid velocities than predicted by the LWR equation, which are attributed to a velocity-dependent dynamic contact angle that is larger than its static value. Inspection of fluid penetration in closed channels has confirmed that a dynamic angle is needed in the LWR equation. In this work, the dynamic contact angle in an open channel configuration is investigated using experimental data obtained with a range of liquids, aqueous and organic, and a PMMA substrate. We demonstrate that a dynamic contact angle must be used to explain the early stages of fluid penetration, i.e., at the start of the viscous regime, when flow velocities are sufficiently high. Moreover, the open channel configuration, with its free surface, enhances the effect of the dynamic contact angle, making its inclusion even more important. We found that for the liquids in our study, the molecular-kinetic theory (MKT) is the most accurate in predicting the effect of the dynamic contact angle on liquid penetration in open channels.