Fates of a Nonwetting Slug in Tapered Microcapillaries under Gravity and Zero Gravity Conditions: Dynamics, Asymptotic Equilibrium Analysis, and Computational Fluid Dynamics Verifications

It has been determined experimentally and numerically that a nonwetting slug in a tapered capillary tube, under the sole action of capillary force, self-propels itself toward the wider end of the tube until an equilibrium state is reached. The aim of this work is to highlight the state of the slug at equilibrium in terms of configuration and location. Furthermore, it turns out that gravity adds richness to this phenomenon, and more fates become possible. A modified Bond number is developed that determines the relative importance of gravity and capillarity for this system. According to the magnitude of the Bond number, three more fates are possible. Therefore, in a tapered capillary tube held vertically upward with its wider end at the top, in the absence of gravity or under microgravity conditions, the nonwetting slug moves upward toward the wider end of the tube until it reaches equilibrium with the two menisci part of a single sphere. The location of the slug at equilibrium in this case represents the farthest fate among the other fates. When gravity exists yet capillarity dominates, the slug still moves upward toward the wider end. However, in this case, the two menisci become parts of two different spheres of different curvatures. For this scenario, the slug climbs upward but reaches a lower level compared to the previous scenario. On the other hand, when gravity dominates, the slug experiences a net downward pull toward the narrower end of the tube and starts to move in the direction of gravity until capillary force establishes a balance, then it stops. When gravity sufficiently dominates, it pulls the slug downward until it completely drains off the tube. A computational fluid dynamics (CFD) analysis is conducted in order to build a framework for verification exercises. Excellent agreements between the results of the developed model and the CFD analysis are obtained. A fate map and a scheme are developed to identify these four fates based on two Bond numbers; namely, the initial Bond number and that associated with the slug when it is at the exit.