Dynamics of liquid rise in the interstices of circular capillaries under a non-inertial regime

Capillary rise of liquids in confined geometries plays a vital role in natural and engineered systems such as microfluidic devices, porous media, and heat pipes. In this study, we investigate the transient dynamics of capillary rise, at later times, within the corners of the interstice between three closely packed circular micro-capillaries, with diameters in the range 300 μm to 10 mm, a commonly occurring geometry in many applications. Utilizing a combination of experiments and 3D VoF simulations with a dynamic contact angle model, we study the corner capillary rise by liquids over wide ranges of Capillary, Froude and Ohnesorge numbers. In the non-inertial regime, where the gravitational effects are more dominant, we use Onsager's principle of energy minimization and propose that the dimensionless corner meniscus height in later times must scale as the cubic root of the dimensionless time with a novel prefactor for the circular profiles. This result differs from earlier findings for general quadratic profile corners. The corresponding dimensionless velocity at the tip of the corner meniscus is proposed to scale with the negative two-thirds power of the dimensionless time. These scaling laws are shown to exactly predict the observed variations of the corner meniscus heights and velocities in our experiments and simulations. Our study clarifies the non-local nature of the capillary rise in the corners of interstices and the negligible contribution of the bulk meniscus to the corner meniscus rise, the latter exemplified by the independence of corner meniscus height on the circular capillary radius.