Droplet deformation and breakup in general planar flows

The deformation and breakup of droplets in immiscible liquid–liquid systems are central to predicting blend morphology in industrial mixing flows. In this work, we extend the Maffettone–Minale (MM) model to general planar mixed flows, deriving analytical expressions for droplet deformation and orientation from the steady-state solution of the shape tensor dynamics. Using these results, we formulate generalized breakup curves spanning from purely shear to purely extensional flows. The proposed breakup criterion preserves the functional structure of the MM model while introducing flow-type-dependent parameters calibrated through a combination of experimental data and new direct numerical simulations. The generalized breakup conditions are tested within an existing morphology-evolution framework for a two-dimensional twin-screw extruder configuration, in order to assess the sensitivity of the predicted droplet-size distribution to the adopted breakup criterion. The framework developed here provides a robust, computationally efficient tool for modeling droplet deformation and breakup in complex industrial flows.