Model of droplet generation in flow focusing generators operating in the squeezing regime

Flow focusing generators have been widely used to generate droplets for many applications which call for accurate physical models that describe the droplet formation process in such configurations for design and operation purposes. Most existing models are empirical correlations obtained based on extensive experimental results and thus very sensitive to their own data sets. A comprehensive model that involves less parameter fitting by incorporating more theoretical arguments and thus has an improved applicability is urgently needed to guide the design and operation of flow focusing generators. This work presents a 3D physical model describing the droplet formation process in microfluidic flow focusing generators that operate in the squeezing regime where droplet size is usually larger than the channel width. This model incorporates an accurate geometric description of the 3D droplet shape during the formation process, an estimation of the time period for the formation cycle based on the conservation of mass and a semi-analytical model predicting the pressure drop over the 3D corner gutter between the droplet curvature and channel walls, which allow an accurate determination of the droplet size, spacing and formation frequency. The model considers the influences of channel geometry (height-to-width ratio), viscosity contrast, flow rate ratio and capillary number with a wide variety. This model is validated by comparing predictions from the model with experimental results obtained through high-speed imaging.