Quantitative analysis of coupling effects in cross-flow membrane emulsification

Membrane emulsification has attracted increasing experimental and theoretical interests over the last decade. On the experimental side, the parameters of this process have been thoroughly investigated and a linear relationship between the droplet size of an emulsion and the pore size of the membrane has been generally observed. Theoretical studies, however, have not provided an adequate description of many effects concerning droplet growth and detachment from membrane pores, such as the influence of the dynamic interfacial tension on the evolution of the droplet size. Most calculations have been based either on an algebraic torque balance equation or on a differential equation for the disperse phase flow rate through the membrane. The present paper offers a procedure for quantitative analysis which includes both the permeation of the disperse phase through the membrane pores and the mechanism of droplet detachment. The behavior of the droplet size of an emulsion versus the pore size of the membrane is determined with different sets of process parameters and it is compared satisfactorily with the experiments of Vladisavljevic and Schubert on Shirasu porous glass membranes. For the same membranes, the procedure is tested to pore sizes below 0.1m and a linear correlation is observed, similarly to micropore sizes.