Inertial Period Corner Rise in the Interstice of Circular Tubes*

We designed a geometry consisting of three tightly held circular capillaries to form a three corner interstice. This configuration induces a rise of the meniscus at the corners of the interstice due to capillary action. Experiments were conducted with five different diameters of circular capillaries. To validate our experimental results, we performed CFD simulations using the Volume of Fluid (VoF) method, incorporating the Kistler dynamic contact angle (DCA) model to accurately capture meniscus behavior in the intrestice capillaries. Observations showed that during the initial inertial phase, the meniscus rises rapidly, with the rate gradually diminishing over time. By balancing forces and applying Onsager’s principle, we derived a relationship between corner height rise and time, choosing characteristic length (H_c) and time (T_c) scales. A plot of dimensionless corner meniscus height (Z_m/H_c) against dimensionless time (t/T_c) demonstrated a time dependence characterized by a power-law behavior. This theory provides valuable insights into the dynamics of meniscus rise in interstices, presenting a novel t^3/4 scaling law for the height of the corner meniscus. This scaling behavior was confirmed both experimentally and through CFD simulations. Our findings contribute to a better understanding of capillary-driven flows in complex geometries and can be useful for various applications, including microfluidic devices and porous media systems.