Finite element approximation of a two-layered liquid film in the presence of insoluble surfactants
John W. Barrett; Linda El Alaoui
ESAIM: Mathematical Modelling and Numerical Analysis (2008)
- Volume: 42, Issue: 5, page 749-775
- ISSN: 0764-583X
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topBarrett, John W., and El Alaoui, Linda. "Finite element approximation of a two-layered liquid film in the presence of insoluble surfactants." ESAIM: Mathematical Modelling and Numerical Analysis 42.5 (2008): 749-775. <http://eudml.org/doc/250368>.
@article{Barrett2008,
abstract = {
We consider a system
of degenerate parabolic equations modelling a
thin film, consisting of two layers of immiscible Newtonian liquids, on
a solid horizontal substrate.
In addition, the model includes the presence of insoluble surfactants on
both the free liquid-liquid and liquid-air interfaces,
and the presence of both attractive and repulsive van der Waals forces
in terms of the heights of the two layers.
We show that this system formally satisfies a Lyapunov structure,
and a second energy inequality controlling the Laplacian
of the liquid heights.
We introduce a fully practical finite element approximation
of this nonlinear degenerate parabolic system, that satisfies discrete analogues
of these energy inequalities. Finally, we prove convergence of this approximation,
and hence existence of a solution
to this nonlinear degenerate parabolic system.
},
author = {Barrett, John W., El Alaoui, Linda},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Thin film; surfactant; bilayer; fourth order degenerate parabolic system; finite
elements; convergence analysis.; fourth-order degenerate parabolic system; convergence; energy inequality; existence},
language = {eng},
month = {7},
number = {5},
pages = {749-775},
publisher = {EDP Sciences},
title = {Finite element approximation of a two-layered liquid film in the presence of insoluble surfactants},
url = {http://eudml.org/doc/250368},
volume = {42},
year = {2008},
}
TY - JOUR
AU - Barrett, John W.
AU - El Alaoui, Linda
TI - Finite element approximation of a two-layered liquid film in the presence of insoluble surfactants
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2008/7//
PB - EDP Sciences
VL - 42
IS - 5
SP - 749
EP - 775
AB -
We consider a system
of degenerate parabolic equations modelling a
thin film, consisting of two layers of immiscible Newtonian liquids, on
a solid horizontal substrate.
In addition, the model includes the presence of insoluble surfactants on
both the free liquid-liquid and liquid-air interfaces,
and the presence of both attractive and repulsive van der Waals forces
in terms of the heights of the two layers.
We show that this system formally satisfies a Lyapunov structure,
and a second energy inequality controlling the Laplacian
of the liquid heights.
We introduce a fully practical finite element approximation
of this nonlinear degenerate parabolic system, that satisfies discrete analogues
of these energy inequalities. Finally, we prove convergence of this approximation,
and hence existence of a solution
to this nonlinear degenerate parabolic system.
LA - eng
KW - Thin film; surfactant; bilayer; fourth order degenerate parabolic system; finite
elements; convergence analysis.; fourth-order degenerate parabolic system; convergence; energy inequality; existence
UR - http://eudml.org/doc/250368
ER -
References
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