A descriptive force‐balance model for droplet formation at microfluidic Y‐junctions

In a previous article, we studied the basics of emulsification in microfluidic Y‐junctions, however, without considering the effect of viscosity of the disperse phase. As it is known from investigations on many different microstructures that viscosity and viscosity ratio are governing parameters for droplet size, we here investigate whether this is also the case for microfluidic Y‐junctions and do so for a wide range of process conditions. The investigated Y‐junctions have a width of 19.9 or 12.8 μm and a depth of 5.0 μm, and the formed monodisperse droplets (CV < 1%) are between 3 and 20 μm. We varied the disperse‐phase viscosity using different oils (1–105 mPa s), and continuous‐phase viscosity using glycerol–water and ethanol–water mixtures (1.0–6.2 mPa s), which corresponds to disperse‐to‐continuous‐phase viscosity ratios from 0.4 to 105.0. Through the variation of the liquids, also a range in interfacial tensions (12–55 mN m −1 ) is assessed. The disperse‐phase flow rate is varied from 0.039 to 18.0 μL h −1 , the continuous‐phase flow rate from 1.39 μL h −1 to 0.41 mL h −1 , and this corresponds to flow rate ratios from 1.1 × 10 −3 to 0.14, which is once again based on wide range of conditions. For all these conditions, in which droplets are formed in the dripping and jetting regime, the droplet size could be described with a model based on the existing force‐balance model, but now extended to incorporate the cross‐sectional area of the droplet and the resistance with the wall. Surprisingly enough, it was found that the droplet size is not influenced by the disperse‐phase viscosity, or the viscosity ratio, but it is dominated by the resistance with the wall and the continuous‐phase properties. Because of this, emulsification with Y‐junctions is intrinsically simpler than any other shear‐based method as droplet size is only determined by the continuous phase. © 2010 American Institute of Chemical Engineers AIChE J, 2010