Journal
PHYSICS OF FLUIDS
Volume 24, Issue 6, Pages -Publisher
AMER INST PHYSICS
DOI: 10.1063/1.4727888
Keywords
bifurcation; convection; decomposition; diffusion; film flow; flow instability; free energy; liquid films; liquid mixtures; Navier-Stokes equations
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Funding
- European Union [PITN-GA-2008-214919]
- Libyan Ministry of Higher Education
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We study two-dimensional steady concentration and film thickness profiles for isothermal free surface films of a binary liquid mixture on a solid substrate employing model-H that couples the diffusive transport of the components of the mixture (convective Cahn-Hilliard equation) and the transport of momentum (Navier-Stokes-Korteweg equations). The analysis is based on minimising the underlying free energy equivalent to solving the static limit of model-H. Additionally, the linear stability (in time) of relevant layered films is analyzed. This allows for a comparison of the position of certain branching points in the bifurcation diagrams of steady solutions with the value predicted as onset of a linear instability. Results are presented for the cases of (i) a flat film without energetic bias at the free surface, (ii) a flat film with energetic bias, (iii) a height-modulated film without energetic bias, and (iv) a height-modulated film with energetic bias. In all cases we discuss symmetries of the various steady solutions allowing us to order them and to infer properties of solution branches and relations between them. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4727888]
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