Micro-droplets can be formed when a disperse liquid is injected via a needle nozzle into another immiscible co-flowing fluid. The mode of droplet formation depends on many factors such as liquid flow rates of the inner disperse phase and outer continuous phase, liquid viscosity, nozzle dimensions, interface tension force, etc. In this paper, the drop formation in a co-flowing system is simulated numerically using front tracking method to investigate the drop formation mechanism, which is very critical in the design of micro-fluidic devices for generating micro-droplets in a controllable manner. One set of Navier-Stokes equations for both liquid phases are solved numerically on a fixed Eulerian two-dimensional cylindrical coordinate mesh to account for the flow dynamics, and the front tracking method is applied to track the movement of the interface between the two immiscible liquids as well as the surface tension force. In this set of governing equations for modeling, the effects of flow inertial, capillary, viscous, and gravitational forces are all accounted to explore the droplet formation modes and dynamics in co-flowing system. The simulations reasonably predict the process of droplet formation in the co-flowing liquid. In addition, the effects of the continuous phase flow speed, viscosity and the interface tension force on droplet formation are investigated.

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