Correlations of droplet formation in T-junction microfluidic devices: from squeezing to dripping

In this work, we have systematically analyzed the scaling law of droplet formation by cross-flow shear method in T-junction microfluidic devices. The droplet formation mechanisms can be distinguished by the capillary number for the continuous phase (Ca-c), which are the squeezing regime (Ca-c < 0.002), dripping regime (0.01 < Ca-c < 0.3), and the transient regime (0.002 < Ca-c < 0.01). Three corresponding correlations have been suggested in the different range of Ca-c. In the dripping regime, we developed a modified capillary number for the continuous phase (Ca-c') by considering the influence of growing droplet size on the continuous phase flow rate. And the modified model could predict droplet diameter more accurately. In the squeezing regime, the final plug length was contributed by the growth and 'squeeze' stages based on the observation of dynamic break-up process. In the transient regime, we firstly suggested a mathematical model by considering the influences of the above two mechanisms. The correlations should be very useful for the application of controlling droplet size in T-junction microfluidic devices.