Detection of inertial effects in capillary flows in open and closed channels

The Lucas-Washburn-Rideal law is commonly applied to describe capillary flow dynamics in closed or open channels, microporous media, such as paper pads and fiber threads or even granulous soil. It assumes a viscous flow regime where capillary forces are counteracted by friction with the solid structure, a valid assumption given the small flow velocities and device dimensions. However, scenarios exist outside the viscous regime, where inertial effects become significant, meaning capillary and friction forces do not fully balance. One well-documented case is the transient inertial regime at the onset of capillary motion. With the advancement of capillary devices, other configurations also raise the possibility of inertia influencing flow behavior. This study introduces a criterion to identify inertial contributions in capillary-driven flows in spatially varying geometries within open or closed channels and demonstrates how the Bosanquet equation can account for inertial effects in rectangular open-channel configurations.