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

Abstract

considers the influences of channel geometry (height-towidth 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. List of symbolsChannel height L eqv Equivalent droplet length of the uniform cross section L fill Droplet length that penetrates into the main channel at the end of the filling stage L gutter Length of the gutter at the end of the necking stage L pinch Distance between the two points of the V-shape at the end of the necking stage L pinch Variation of the V-shape in the droplet length direction during the necking stage N drop Number of the captured droplets in one video N frame Total number of frames in one video P 1 Pressure of the forming droplet at the end of the filling stage P 2 Pressure of the continuous phase at the cross at the end of the filling stage P 3Pressure of the continuous phase surrounding Abstract 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 the tip of forming droplet at the end of the filling stage P 3D Pressure drop from the 3D numerical simulations P asy Pressure drop from the asymptotic model P neck Pressure of the continuous phase at the cross at the end of necking stage P tip Pressure of the continuous phase surrounding the tip of forming droplet at the end of the necking stage Q Flow ratē Q gutter Average flow rate through the gutter during the necking stage R neck Radius of the V-shape neck at the end of the necking stage s Spacing between two droplets T Droplet generation period t filling Filling period t necking Necking period u Fluid velocitȳ u g Average fluid velocity in the gutter V BF Volume of droplet at the beginning of the filling stage V BN Volume of the continuous phase in the V-shape at the beginning of the necking sta...

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