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

L. Fraštia; U. Thiele; L. M. Pismen

Mathematical Modelling of Natural Phenomena (2010)

- Volume: 6, Issue: 1, page 62-86
- ISSN: 0973-5348

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topFraštia, L., Thiele, U., and Pismen, L. M.. "Determination of the Thickness and Composition Profiles for a Film of Binary Mixture on a Solid Substrate." Mathematical Modelling of Natural Phenomena 6.1 (2010): 62-86. <http://eudml.org/doc/197666>.

@article{Fraštia2010,

abstract = {We determine the steady-state structures that result from liquid-liquid demixing in a
free surface film of binary liquid on a solid substrate. The considered model corresponds
to the static limit of the diffuse interface theory describing the phase separation
process for a binary liquid (model-H), when supplemented by boundary conditions at the
free surface and taking the influence of the solid substrate into account. The resulting
variational problem is numerically solved employing a Finite Element Method on an adaptive
grid. The developed numerical scheme allows us to obtain the coupled steady-state film
thickness profile and the concentration profile inside the film. As an example we
determine steady state profiles for a reflection-symmetric two-dimensional droplet for
various surface tensions of the film and various preferential attraction strength of one
component to the substrate. We discuss the relation of the results of the present diffuse
interface theory to the sharp interface limit and determine the effective interface
tension of the diffuse interface by several means.},

author = {Fraštia, L., Thiele, U., Pismen, L. M.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {Cahn-Hilliard theory; model-H; phase separation; diffuse interface; phase-field model; demixing coupled to dewetting; surface evolution; variational method; FEM},

language = {eng},

month = {6},

number = {1},

pages = {62-86},

publisher = {EDP Sciences},

title = {Determination of the Thickness and Composition Profiles for a Film of Binary Mixture on a Solid Substrate},

url = {http://eudml.org/doc/197666},

volume = {6},

year = {2010},

}

TY - JOUR

AU - Fraštia, L.

AU - Thiele, U.

AU - Pismen, L. M.

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

JO - Mathematical Modelling of Natural Phenomena

DA - 2010/6//

PB - EDP Sciences

VL - 6

IS - 1

SP - 62

EP - 86

AB - We determine the steady-state structures that result from liquid-liquid demixing in a
free surface film of binary liquid on a solid substrate. The considered model corresponds
to the static limit of the diffuse interface theory describing the phase separation
process for a binary liquid (model-H), when supplemented by boundary conditions at the
free surface and taking the influence of the solid substrate into account. The resulting
variational problem is numerically solved employing a Finite Element Method on an adaptive
grid. The developed numerical scheme allows us to obtain the coupled steady-state film
thickness profile and the concentration profile inside the film. As an example we
determine steady state profiles for a reflection-symmetric two-dimensional droplet for
various surface tensions of the film and various preferential attraction strength of one
component to the substrate. We discuss the relation of the results of the present diffuse
interface theory to the sharp interface limit and determine the effective interface
tension of the diffuse interface by several means.

LA - eng

KW - Cahn-Hilliard theory; model-H; phase separation; diffuse interface; phase-field model; demixing coupled to dewetting; surface evolution; variational method; FEM

UR - http://eudml.org/doc/197666

ER -

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