Droplet detachment in cross-flow membrane emulsification: Comparison among torque- and force-based models

Due to the high product quality achievable, considerable attention of the researchers is being addressed to the cross-flow direct membrane emulsification (CDME). The key advantages of this process over traditional technologies are a better control of the droplet sizes of the emulsion and its efficiency in terms of energy density requirement. In the literature, macroscopic models have been employed to describe the influence of process parameters and membrane properties on droplet formation. These models have been based either on an algebraic torque balance equation (TBE) or on a force balance (FBE) along a contact line, defined on the droplet pore border. The aim of this work is to compare the results obtained using these two approaches against experimental data available in literature in order to assess the reliability in predicting the correct trends with good quantitative agreement. The analysis shows that FBE yields better results than TBE under conditions of wall shear stress equal or larger than 7 Pa and membrane pore diameters below 1.5 m. In the mentioned conditions, using the FBE model, the maximum error in predictions is around 10%. Both methods reproduce the empirical relationship between droplet sizes and cross-flow velocities, although the force balance yields a better behaviour (plateau) for high wall shear stresses. However, the analysed models are unable to reproduce the linear relation between the droplet and pore size observed in the experiments.