(54c) Forced Wetting in a Square Capillary

Under certain conditions, capillary flows in corners are enhanced
resulting in the rise of thin films in the corner known as
rivulets. These rivulets can influence the overall fluid movement in
microfluidic devices and porous media. In this study, we investigate the
forced wetting dynamics in a square capillary using a combination of theory,
numerical simulations and experiments.

The forced wetting is accomplished in two ways. In the first case
(immersion), the square capillary is forced into a liquid pool at a constant
speed. In the second case, denoted as pumping, the fluid is fed into the capillary from below at a
constant volumetric flow rate. In both scenarios, we characterize the
dynamics by measuring the liquid heights in the center (main meniscus) and in
the corner (rivulet) of the square capillary.

Under immersion, after an initial transient regime, the main meniscus relaxes
to a steady regime where it descends at a constant speed which is
always smaller than the immersion speed. The main meniscus under pumping always
ascends at the same speed as the external speed without any delay. By
accounting for the dominant forces acting on the liquid column, we have
developed a one-dimensional model which shows excellent agreement with the
experiments in predicting the main meniscus height and its speed.

Similar to the main meniscus, the rivulets initially exhibit the same trend:
descending under immersion and rising under pumping, both at a constant
speed. In both cases, the rivulet speeds during this stage are always smaller
than the external forcing speed. The descending rivulet under immersion
eventually merges with the main meniscus at steady state. Similarly, the
rising rivulet merges with the main meniscus under pumping.