Force balance conditions for droplet formation in cross-flow membrane emulsifications

The membrane emulsification process is becoming of growing interest in many industrial fields. For monitoring the influence of process and membrane parameters on the droplet formation, quantitative information on the droplet detachment, during this process, is important. Until now, droplet formation has theoretically been described using computational fluid dynamics and global force equations. Unlike computational fluid dynamics methods, the global force models are less accurate but easier to handle and instructive. On this basis, in the present paper we present new force balance equations to describe droplet detachment during cross-flow membrane emulsification. In a first approximation, the droplet is supposed to grow leaning on the pore border as long as a force balance exists along the contact line located on the membrane surface. During this phase the base of the droplet, still stuck on the pore border, begins to bend on the membrane surface until its final detachment. Using force balance equations made along the contact lines, we obtain the minimum and maximum sizes that a droplet could have during cross-flow membrane emulsification. This approach is tested with different continuous phase velocities, membrane pore sizes and interfacial tensions. The results are compared to various experimental data, reported in literature. In particular, based on the experimentally found linear correlation between droplet and pore sizes, we show how the proposed balance equations can be used to obtain a satisfactory evaluation of the slopes of this linear correlation and how these force balances could be used to obtain an estimation of the interfacial tensions during the droplet formation.