Eur. Phys. J. Special Topics 192, 101-108 (2011)
https://doi.org/10.1140/epjst/e2011-01364-8

Regular Article

Convective instabilities in films of binary mixtures

¹ Universidad Politécnica de Madrid, ETSI Aeronáuticos, Plaza Cardenal Cisneros 3, 28040 Madrid, Spain
² Instituto Pluridisciplinar, Universidad Complutense, Paseo Juan XXIII, 1, 28040 Madrid, Spain
³ Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK

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

Received: 21 January 2011
Revised: 25 January 2011
Published online: 9 March 2011

Abstract

We present a model for the evolution of films of isothermal binary liquid mixtures with a free evolving surface. The model is based on model-H supplemented by appropriate boundary conditions at the free surface and the solid substrate. The equations account for the coupled transport of the concentration of a component (convective Cahn-Hilliard equation) and the momentum (Korteweg-Navier-Stokes equation). The inclusion of convective motion makes surface deflections possible, i.e., the model allows to study couplings between the decomposition of the mixture and the evolving surface corrugations. We present selected steady layered film states for representative polymer mixtures, and show that convective motion favors their destabilization and qualitatively changes the linear instability modes in experimentally accessible ranges of parameters.