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

The dynamics of a fluid flow within an open capillary channel depend on the fluid’s contact angle with the channel substrate, but determining the real value of the contact angle with the solid surface is an ominous problem in capillary microflows. The Lucas-Washburn law assumes a constant contact angle during the fluid motion; however, it is observed that the contact angle of the flowing liquid with the walls differs from its static (Young) value. Correlations for the dynamic contact angle have been proposed, and upon close inspection of Lucas-Washburn behavior in closed channels, a dynamic contact angle should be taken into account depending on the flow velocity. In this work, the dynamic contact angle in open-channel configurations is investigated using experimental data obtained with different liquids. It is shown that a dynamic contact angle must be taken into account in the early stages of the flow, i.e., at the beginning of the viscous regime when flow velocities are sufficiently high. Here, we found that amongst the different correlations for the dynamic contact angle, the Hamraoui correlation— presenting the dynamic contact angle in terms of a friction coefficient—reproduces the experimental results while other correlations overpredict the fluid velocity in open channels.