Determination of the Thickness and Composition Profiles for a Film of Binary Mixture on a Solid Substrate

Fraštia, Ľubor; Thiele, Uwe; Pismen, L. M.

doi:10.1051/mmnp/20116104

Cited by 5 publications

(5 citation statements)

References 43 publications

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“…The analogy was first noted by Mitlin [8] resulting in the notion of 'spinodal dewetting'. Note that there exist other choices for f (φ) and M c in the Cahn-Hilliard equation [36,37].…”

Section: Introductionmentioning

confidence: 99%

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Thin film evolution equations from (evaporating) dewetting liquid layers to epitaxial growth

Thiele

2010

J. Phys.: Condens. Matter

141

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In the present contribution we review basic mathematical results for three physical systems involving self-organizing solid or liquid films at solid surfaces. The films may undergo a structuring process by dewetting, evaporation/condensation or epitaxial growth, respectively. We highlight similarities and differences of the three systems based on the observation that in certain limits all of them may be described using models of similar form, i.e. time evolution equations for the film thickness profile. Those equations represent gradient dynamics characterized by mobility functions and an underlying energy functional. Two basic steps of mathematical analysis are used to compare the different systems. First, we discuss the linear stability of homogeneous steady states, i.e. flat films, and second the systematics of non-trivial steady states, i.e. drop/hole states for dewetting films and quantum-dot states in epitaxial growth, respectively. Our aim is to illustrate that the underlying solution structure might be very complex as in the case of epitaxial growth but can be better understood when comparing the much simpler results for the dewetting liquid film. We furthermore show that the numerical continuation techniques employed can shed some light on this structure in a more convenient way than time-stepping methods. Finally we discuss that the usage of the employed general formulation does not only relate seemingly unrelated physical systems mathematically, but does allow as well for discussing model extensions in a more unified way.

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“…The analogy was first noted by Mitlin [8] resulting in the notion of 'spinodal dewetting'. Note that there exist other choices for f (φ) and M c in the Cahn-Hilliard equation [36,37].…”

Section: Introductionmentioning

confidence: 99%

“…The analogy was first noted by Mitlin [8] resulting in the notion of 'spinodal dewetting'. Note that there exist other choices for f (φ) and M c in the Cahn-Hilliard equation [36,37]. Equations of similar form may as well model the epitaxial evolution of surfaces of crystalline solids [38][39][40]2].…”

Section: Introductionmentioning

confidence: 99%

Thin film evolution equations from (evaporating) dewetting liquid layers to epitaxial growth

Thiele

2010

J. Phys.: Condens. Matter

141

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“…17, whereas the numerical method to obtain fully two-dimensional steady state solutions is introduced in Ref. 34.…”

Section: Model and Numerical Proceduresmentioning

confidence: 99%

“…Compare Ref. 34 for an example with an energetic bias at the substrate but a neutral free surface. Furthermore, we have chosen to study a symmetrical blend (critical case) where the mean concentration of the two components are equal.…”

Section: Films Of Medium Thickness (H = 50)mentioning

confidence: 99%

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Decomposition driven interface evolution for layers of binary mixtures. III. Two-dimensional steady films with flat and modulated surfaces

2012

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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.

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Dewetting and decomposing films of simple and complex liquids

Thiele

2012

Multiphase Microfluidics: The Diffuse Interface Model

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Determination of the Thickness and Composition Profiles for a Film of Binary Mixture on a Solid Substrate

Cited by 5 publications

References 43 publications

Thin film evolution equations from (evaporating) dewetting liquid layers to epitaxial growth

Thin film evolution equations from (evaporating) dewetting liquid layers to epitaxial growth

Decomposition driven interface evolution for layers of binary mixtures. III. Two-dimensional steady films with flat and modulated surfaces

Dewetting and decomposing films of simple and complex liquids

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