Geodesic
Phase transitions in presence of surfactants: From discrete to continuum
Roberto Alicandro1 ; Marco Cicalese2 orcid ; Laura Sigalotti3
1Università degli Studi di Cassino, Italy
2Università degli Studi di Napoli Federico II, Italy
3Università di Roma "La Sapienza", Italy
Interfaces and free boundaries, Tome 14 (2012) no. 1, pp. 65-103

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DOI

We study by Γ-convergence the discrete-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 describe 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 Γ-limit. As an application we study the ground states of these systems for prescribed volume fractions of the phases.
DOI : 10.4171/ifb/274
Classification : 49-XX, 82-XX, 00-XX
Mots-clés : Atomistic-to-continuum limit; spin systems; surface tension models; surfactants; Γ-convergence; calculus of variations

Roberto Alicandro  1   ; Marco Cicalese  2   ; Laura Sigalotti  3

1 Università degli Studi di Cassino, Italy
2 Università degli Studi di Napoli Federico II, Italy
3 Università di Roma "La Sapienza", Italy 
Roberto Alicandro; Marco Cicalese; Laura Sigalotti. Phase transitions in presence of surfactants: From discrete to continuum. Interfaces and free boundaries, Tome 14 (2012) no. 1, pp. 65-103. doi: 10.4171/ifb/274
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     pages = {65--103},
     year = {2012},
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     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/274/}
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