Study on the self-adaptive process of droplet traffic to a perturbation of flow resistance at the arms of a micro-T-junction

The response of the water-oil droplet flow to a perturbation of flow resistance added at the arms of a bypassed micro-T-junction is studied through a numerical method. The capillary number of the continuous flow varies between 0.007 and 0.034. Once an additional flow resistance is introduced at the arms of the T-junction, the flow self-adapts to the perturbation and droplets show complex dynamics at the junction, including splitting, merging, and reshaping. During the self-adaptive process, the instantaneous splitting ratios of the dispersed flow show positive correlations with that of the continuous flow. The correlation coefficient reduces as the increase in the amplitude of the perturbation. The ensemble splitting ratios of them, however, are independent. It shows a rather simple law that the ensemble splitting ratios of oil anchor at around a constant value while the corresponding parameter of water varies from 0 to 1. It illustrates that the droplet flow splitting at a T-junction resembles a resilient system, the stiffness of which depends on the capillary number of the flow. The energy loss of the system induced by a perturbation of the flow resistance is self-reduced by just redistributing of droplets into the two arms.