Droplet formation in microfluidic T-junction generators operating in the transitional regime. II. Modeling.

This is the second part of a two-part study on the generation of droplets at a microfluidic T-junction operating in the transition regime. In the preceding paper [Phys. Rev. E 85, 016322 (2012)], we presented our experimental observations of droplet formation and decomposed the process into three sequential stages defined as the lag, filling, and necking stages. Here we develop a model that describes the performance of microfluidic T-junction generators working in the squeezing to transition regimes where confinement of the droplet dominates the formation process. The model incorporates a detailed geometric description of the drop shape during the formation process combined with a force balance and necking criteria to define the droplet size, production rate, and spacing. The model inherently captures the influence of the intersection geometry, including the channel width ratio and height-to-width ratio, capillary number, and flow ratio, on the performance of the generator. The model is validated by comparing it to speed videos of the formation process for several T-junction geometries across a range of capillary numbers and viscosity ratios.