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

Abstract

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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.

How to cite

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Fraštia, 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 -

References

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