Calculus of Variations and Geometric Measure Theory

R. Alicandro - M. Cicalese - L. Sigalotti

Phase transition in presence of surfactants: from discrete to continuum

created by cicalese on 19 Jun 2010
modified by alicandr on 20 Nov 2013


Published Paper

Inserted: 19 jun 2010
Last Updated: 20 nov 2013

Journal: Interfaces and Free Boundaries
Volume: 14
Number: 1
Pages: 65-103
Year: 2012


We study by $\Gamma$-convergence the atomistic-to-continuum limit of the Blume-Emery-Griffiths model describing the phase transition of a binary mixture in presence of a third surfactant phase. In the case of low surfactant concentration we study the dependence of the surface tension on the density of the surfactant and we show the microstructure of the ground states. We then consider more general ($n$-dimensional) energies modeling phase transitions in presence of different species of surfactants and, in the spirit of homogenization theory, we provide an integral representation result for their $\Gamma$-limit. As an application we study the ground states of the system for prescribed volume fractions of the phases.