The Applicability of Catastrophe Theory to Emulsion Phase Inversion

Abstract

Catastrophe theory, in particular the elementary cusp catastrophe, has been successfully applied to describe the qualitative features of catastrophic phase inversion in emulsions, but quantitative, experimental tests of the cusp catastrophe did not yield satisfactory results. We have shown that the elementary butterfly catastrophe can fit experimental data from the literature with reasonable accuracy. The quality of the fit may be improved, but only at the cost of the introduction of more fit parameters with little or no physical significance. We present an expression derived from physical properties rather than mathematical ones, on the basis of which all observed catastrophic phenomena can be qualitatively described. At values of the interfacial tension typical to coarse emulsions, this model predicts phase separation. However, phase inversion is generally observed under these conditions. We point out that the assumptions that justify a thermodynamical treatment of transitional inversion are not valid for catastrophic inversion. Our conclusions indicate that catastrophic phase inversion, unlike transitional inversion, should be treated on a kinetic basis rather than a thermodynamical one.