Membrane emulsification: modelling interfacial and geometric effects on droplet size
Abstract: Emulsification is an important unit operation used in the pharmaceutical, food, and cosmetic industry. Membrane emulsification is a relatively new membrane technology which allows the production of emulsion droplets under controlled conditions with a narrow droplet size distribution. The continuous phase flows tangentially to the membrane surface and sweeps away dispersed phase droplets forming from pore openings. Both oil-in-water and water-in-oil emulsions are possible depending on the type of membrane used, as is the ability to form double emulsions, however, this work will focus on oil-in-water emulsions. The key feature of the membrane emulsification process which sets it apart from conventional emulsification technologies is that the size distribution of the resulting droplets is primarily governed by the choice of membrane and not by the development of turbulent or extensional droplet break up. This work reviews current developments and deficiencies in modelling membrane emulsification processes and proposes an innovative model developed to the quantify droplet formation mechanism from the point of view of Gibbs free energy. The droplet's shape as it grows is modelled in terms of interfacial energy and thermodynamic work with the help of an interactive finite element program, the Surface Evolver. A program to test the model was written and run which allows the user to identify the point of instability due to free energy, and thus the maximum stable volume attached to the pore, and predicts the radius of the final detached droplet. The inputs of the program are pore geometry, interfacial tension, and contact angle. The model reasonably predicted droplet sizes using pores of a known geometry under quiescent conditions where the force balance approach is not applicable. The model was extended to include the effects of droplet expansion rate and surfactant mass transfer on the interfacial tension. This allowed the increased droplet size to be determined for a given set of operating conditions and prediction of the onset of jetting as a function of dispersed phase flux. By analysing the results from the Surface Evolver, a general relationship between pore shape, contact angle and droplet size was found. This equation can be used independently of the Surface Evolver to predict droplet diameters for cases where either the pore geometry is defined using Ddroplet=8'Area/(cos theta 'Perimeter) or alternatively for cases when the critical pressure in the membrane is known Ddroplet=8'gamma/Pcritical. These equations were tested against literature data for straight-through microchannels, SPG membranes, and ISOPORE polycarbonate membranes. The average relative errors of the predictions were on the order of 8% to 9%. These general equations can significantly aid in the design of membranes through optimising pore size, shape, length and spacing and thereby improving the production capacity of membrane emulsification processes.
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