Research

 

Mean field theory of inhomogeneous fluid mixtures

 

J. G. Segovia-López*, A. Zamora**, J. Antonio Santiago***

 

* División Académica de Ciencias Básicas, Universidad Juárez Autónoma de Tabasco, Km 1 Carretera Cunduacán-Jalpa, A.P. 24, 86690, Cunduacán, Tabasco, México.

** Departamento de Matemáticas Aplicadas y Sistemas, Universidad Autónoma Metropolitana - Cuajimalpa, México D.F. 01120, México.

*** Departamento de Matemáticas Aplicadas y Sistemas, Universidad Autónoma Metropolitana - Cuajimalpa, México D.F. 01120, México.

 

Received 2 February 2012;
Accepted 29 January 2013

 

Abstract

By using density functional theory, we analyze an inhomogeneous fluid mixture composed of an arbitrary number of species within mean field approximation. Under the assumption that the interfacial region behaves as an elastic continuous medium, we calculate the stress tensor and the equilibrium grand potential of the system for different surfaces. It is found that, unlike the single component system, there exist multiple coexistence regions induced by the diversity of interaction potentials between the different species. Surface properties are calculated for a step-like density profile and consistency with the monocomponent system is verified for both the same formalism and other approaches at the level of surface tension.

Keywords: Stress tensor; density functional theory; surface tension; density profile.

 

PACS: 05.20.Jj; 64.75.Cd; 68.35.Md

 

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Acknowledgments

The authors wish to thank V. Romero-Rochín for helpful comments and stimulating discussion. This work was supported partially by PFICA-UJAT under grant UJAT-2009-C05-61 and by PROMEP-MEXICO (Contract No. 364 UJAT-CA-15).

 

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