Numerical simulation of membrane emulsification: Effect of flow properties in the transition from dripping to jetting

In this work, the roles of the Weber number (We) and Capillary number (Ca) in characterizing different stages, i.e. dripping, jetting and transition states, of droplet formation in a membrane emulsification process have been investigated. A numerical investigation of the emulsification process has been investigated for a range of We (0.009 ≤ We ≤ 1.82) and for Ca (0.004 ≤ Ca ≤ 0.04). The full transient simulation of the process was made using volume of fluid (VOF)/finite volume method and was performed starting from the injection of the dispersed phase to the breakup into droplets, for different operating conditions. Based on the study, a critical Weber number (Wec) has been derived at which the process shows transition from dripping to jetting. Some interesting phenomena such as sudden decrease of droplet diameter and high rate of droplet formation have been observed during the transition from dripping to jetting. The qualitative differences of dispersed phase topology in case of less confined case (membrane emulsification) have been discussed compared to more confined situations (T-junction emulsification) available in the literature. It has been observed that, although the dripping and jetting regions in the present work have shown some topological differences compared to those in T-junction emulsification, the transition phenomenon between the two regions are remarkably similar in both cases. Two ways of dripping to jetting transition have been observed: one at constant Capillary number while varying the Weber number and another at the constant Weber number while varying the Capillary number. Qualitative differences between the dispersed phase flow controlled (We dependence) and surface tension controlled (Ca dependence) transition were observed. In dispersed phase flow controlled case, diameter of the droplet increases initially then decreases rapidly while in surface tension controlled case the diameter decreases continuously. Finally, at large values of the Capillary number a transition from dripping to jetting was observed in the membrane emulsification system, similar to the case of drop formation from a nozzle in an unbounded fluid under gravity.