Hadi Mehrabian & James J. Feng
J. Fluid Mech. 752, 670-692 (2014).
Abstract - Wicking flow inside capillary tubes can attain considerable momentum so as to produce a liquid jet at the end of the tube. Auto-ejection refers to the formation of droplets at the tip of such a jet. Experimental observations suggest that a tapering nozzle at the end of the capillary tube is necessary for auto-ejection; it has never been reported for a straight tube. Besides, most experimental realizations require microgravity, although it is possible under normal gravity if the nozzle has a sufficiently sharp contraction. This computational study focuses on two related issues: the critical condition for auto-ejection, and the hydrodynamics of the liquid meniscus as affected by geometric parameters. We adopt a diffuse-interface Cahn-Hilliard model for the moving contact line, and allow the dynamic contact angle to deviate from the static one through wall energy relaxation. From analyzing the dynamics of the meniscus in the straight tube and the nozzle, we develop a criterion for the onset of auto-ejection based on a Weber number defined at the exit of the nozzle and an effective length that encompasses the geometric features of the tube-nozzle combination. In particular, this criterion shows that capillary ejection is not possible in straight tubes. With steeper contraction in the nozzle, we predict two additional regimes of interfacial rupture: rapid ejection of multiple droplets and air bubble entrapment. The numerical results are in general agreement with available experiments.