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Computations of Drop Formation from a Micro Capillary in Co-Flowing Ambient Immiscible Liquid

Shunji Homma, Muneyuki Yokotsuka, and Jiro Koga. Division of Materials Science, Graduate School of Science and Engineering, Saitama University, 255 Shimo-Okubo, Sakura-ku, Saitama, 338-8570, Japan

When a liquid is injected from a micro capillary into another immiscible fluid, the liquid is dispersed into many micro droplets. There are two modes in the production of the droplets: dripping and jetting. The droplets are formed near the micro capillary in dripping mode, whereas, in jetting mode, a jet is formed and the droplets are broken off at the tip of the jet. The jetting mode occurs in high Weber number conditions, where the momentum of the liquid injected dominates over the interfacial tension. Recently, Utada et al. [Phys. Rev. Lett., 99, 094502 (2007)] have shown that the jetting mode occurs even low Weber numbers when the flow is applied to the ambient fluid along the same direction as the jet grows.

In this study, the formation of droplets from a micro capillary is simulated by a Front-Tracking / Finite Difference method under the circumstance where the ambient fluid co-flows with the dispersed liquid. The shape of the interfaces as well as the size of the resulting droplets, are well compared with experiments by Utada et al. and with computations by Hua et al. [AIChE. J., 53, 2534 (2007)]. Extensive numerical experiments are carried out in order to find the transition from dripping to jetting. The transition points obtained by our computations are also in good agreement with experiments. In jetting mode, it is confirmed by numerical simulations that the uniform velocity distribution is developed inside and outside the jet due to the dragging by the co-flowing ambient fluid. This situation corresponds to the assumption of linear stability theory, and thus supports the fact that the size of the resulting droplets in jetting mode is in good agreement with the one predicted by linear stability theory.