Precise droplet formation in a T-junction micro-droplet generator

In a T-junction microdroplet generator, a mathematical model which can describe the linear relation between the droplet length and the flow-rate ratio for different geometries of the T-junctions is established. For different viscosity of the fluids, the droplet length as a function of the flow-rate ratio is measured experimentally. We observe that the droplet length is a linear function of the flow-rate ratio for different Capillary numbers, while the droplet length varies nonlinearly with the flow-rate ratio at a high Capillary number. Particularly, two geometries of the T-junction microchannels are designed for droplet formation, and good agreements are found between the predicted and the measured droplet length for low Capillary numbers. More importantly, the linear model of droplet formation is only determined by the geometry of a T-junction and independent of the viscosity of the fluids for high Capillary numbers. As a result, our linear model can be experimentally validated, and the size of the droplets can be precisely predicted for different geometries of the T-junctions.