How are drops formed in microfluidic devices?
There are two hydrodynamic regimes that are well understood in the formation of drops. These two regimes are identified by fluid flow or where drops pinch-off relative to the nozzle. In our case, with microfluidic devices,drops are formed by either pinching-off at the end of the orifice of a capillary or at the end of a fluid stream. The former case is called dripping and the latter case is called jetting. For now, we consider the case of drop generation in the dripping regime, where droplets pinch-off at the orifice of the capillary.
The shearing force of the outer, immiscible fluid is what ultimately causes droplet pinch-off in microfluidics. Interfacial forces are pulling forces, so they pull on the droplet in the opposite direction to the shearing forces and the flow. For drop pinch-off at the nozzle of a capillary the shearing force, or viscous drag eventually become larger than the interfacial forces causing the drop to snap-off.
In microfluidics, to help control the size of the droplet, a second capillary is installed with its tapered orifice in juxtaposition with the orifice of the injection capillary. This second capillary, which is called the collection or exit capillary, increases the flow velocity of the continuous phase surrounding the drop; its flow rate controls the timing of drop pinch-off; it does this with shearing forces. As the drop emerges from the orifice of the capillary it increases in size radially while being pulled away from the orifice by the second fluid until it pinches off.
What about the inertial force? The inertial force is not important here. For laminar flow, which describes the dripping regime, the viscous forces dominate.
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Capillary number
One of the most important parameters for drop formation is the capillary number; the capillary number is the ratio of the viscous forces/surface tension forces.
Reynolds Number
One of the most important parameters in fluid dynamics, if not the most important parameter, is the Reynolds number; the Reynolds number is the ratio of inertial forces to viscous forces. Typically this number is Re<<1 for emulsions moving in microfluidic devices meaning that the flow of the emulsion is dominated by viscous effects. Inertia effects, such as the combined density and speed of the fluid, are not important and are considered negligible for Re<<1. A sample calculation can be found here.