Macroscopic and CFD modelling of droplet formation during cross–flow membrane emulsification
Multi-scale and/or multi-disciplinary approach to process-product innovation
CFD & Chemical Engineering- I (T3-4a)
Keywords: Membrane Emulsification, Modelling, CFD, Droplet Formation
Emulsions play an important role in the formulation of foods, cosmetics, pharmaceuticals, lubricants, dyes and take part in many industrial processes. Generally, the quality and proprieties of emulsions depend upon the mean value and distribution of the droplet diameters. Therefore, accurate predictions of the droplet dimension as a function of the experimental conditions and apparatuses are crucial to efficient and optimised production of desired emulsions. Traditional production methods are generally based on the establishment of turbulent flow in the fluid mixtures using, for example, rotor-stator systems and high pressure homogenisers. The Cross-flow Direct Membrane Emulsification (CDME) shows considerable advantages in terms of better control of droplet size distribution and lower energy density requirement. The effects of process and membrane parameters on droplet size during the CDME process have been extensively investigated in several experimental works. These are mostly focussed on either understanding the key mechanisms underneath this efficient process or represent attempts to broaden the range of applicability by increasing the emulsion productivity. However, theoretical studies have not yet provided adequate descriptions of the observed behaviour.
In the present work, we illustrate two modelling approaches used to represent the formation process of a droplet as it grows on a membrane pore until the detachment caused by the cross flowing continuous phase. A macroscopic approach based on overall balance of forces acting on the droplet (force balance equations, FBE) is shown to allow expressing the final droplet diameter as function of the unit geometry and process conditions (membrane module, pore size and shape, cross-flow velocity, emulsifier interfacial tension). The model equations, considering the droplet stuck on the pore as a result of contact angles developing at its base (advancing and receding contact angles), are solved for various operative conditions. The FBE results are compared against values from a torque balance approach and experimental data. The agreement with experimental data, available in literature, is good for small pore sizes and high cross-flow velocities. Also microscopic modelling of droplet formation has been attempted through a detailed solution of the two-phase flow field by means of a finite element CFD commercial code. The traditional Navier-Stokes equations have coupled with the Level Set function method and the system integrated to trace the evolution of the moving interface as the droplet grows on the membrane pore under various cross-flow conditions. A preliminary comparison of the results obtained using the two modelling scale is provided in order to assess the reliability of the macroscopic approach, especially in terms of the simplifying assumptions leading to its derivation.
Presented Tuesday 18, 11:20 to 11:40, in session CFD & Chemical Engineering- I (T3-4a).
