Eur. Phys. J. Special Topics 219, 3-12 (2013)
https://doi.org/10.1140/epjst/e2013-01775-5

Regular Article

Two-dimensional steady states in off-critical mixtures with high interface tension

¹ Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire LE11 3TU, UK
² Department of Mathematics, Zawia University, Zawia, Libya
³ ETSI Aeronáuticos, Universidad Politécnica de Madrid, Plaza Cardenal Cisneros 3, 28040 Madrid, Spain

^a e-mail: santiago.madruga@upm.es

Received: 1 July 2012
Revised: 18 January 2013
Published online: 19 March 2013

Abstract

We present 2D steady concentration profiles of confined layers of off-critical polymer blends. The layer rests on a solid substrate and has a flat free surface due to very high surface tension. The profiles correspond to non-linear steady solutions of the Cahn-Hilliard equation in a rectangular domain. The free polymer-gas interface is considered to be sharp, while the internal interfaces are diffuse. We explore the rich solution structure (including laterally structured layers, stratified layers, checkerboard structures, oblique states and droplets) as a function of mean concentration.