Numerical study of the effect of the relative mobilities of chemical components on the non-solvent induced phase separation process for membrane elaboration

The filtration membranes are often elaborated through a phase separation process where a polymer rich phase and a polymer poor phase spontaneously form through spinodal decomposition. One process that is still not well understood from a theoretical point of view is the non-solvent induced phase separation, where a thermodynamically stable film of a polymer mixture is put in contact with a bad solvent of the polymer. The invasion of the film by this non-solvent drives the film out of stability and leads to spinodal decomposition. During this phase separation, polymer poor and polymer rich regions form. In this article, we present a numerical study of the effect of kinetic coefficients, namely, the relative mobilities of polymer and solvent/non-solvent, on the observed patterns. Using 2D numerical simulations of the ternary Cahn-Hilliard model, we show that, for a given thermodynamic landscape, this parameter has dramatic effects: depending on its value, phase separation may or may not occur. We also show that it can affect the nature of the resulting pattern. In addition to analyzing 3D simulations, we characterize the final pattern using a quantitative indicator of connectivity and show that, for a wide range of initial compositions of the film, the final pattern is bicontinuous. Finally, we also quantify the transport properties of both polymer rich and polymer poor domains.