| Authors: |
M. Rauscher
and G. Gruen
and K.R. Mecke
|
| Editors: |
Luciano Pietronero
and Vittorio Loreto
and Stefano Zapperi
|
| URL: |
http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=194 |
| Tags: |
dewetting
film
flow
fluctuations
statphys23
thermal
thin
topic-6
wetting
|
| Abstract: |
We develop a stochastic version of the thin film equation for Newtonian incompressible fluids, see [1].
In the thin
film approximation, the stochastic incompressible hydrodynamic equations
reduce to the deterministic thin film
equation for the film thickness $h(r;t)$ plus a conserved multiplicative noise term $\eta({r};t)$.
Intermolecular forces, determining the wetting properties of the substrate are taken into account in terms of the disjoining pressure $\Pi(z)$. The Gaussian noise term
has zero mean and the correlator
$\langle \eta_i({r};t)\eta_j({r}';t')\rangle
=2\,\delta_{ij}\,\delta({r}-{r}') \,\delta(t-t')$\/.
With the functional Fokker-Planck equation we show that the noise term is
consistent with the thermodynamical equilibrium height distribution of the film
thickness.
We also develop a numerical scheme for the one dimensional version of
the stochastic thin film equation. Numerical solutions indicate that
thermal fluctuations significantly influence the time scales of
spinodal dewetting, in particular, they accelerate the process of hole formation
by a factor of five for experimental parameter values. This is roughly the
difference in rupture time between the experiments and the deterministic
simulation.
We also find clear indications for thermal
fluctuations in the early linear regime of spinodal dewetting
[2]. Thermal fluctuations change the capillary wave spectrum from
exponentially damped to a power law behavior for large wave numbers/short
wavelengths. Recently, evidence for this has been found in atomic force
microscopy data from dewetting thin polymer films. Instead of
measuring the power spectrum of the surface roughness, we analyze the mean
deviation of the surface slope $\langle \left({\nabla}h\right)^2\rangle$,
which turns out to be a more robust parameter. Also, the averaging procedure can
be restricted to certain parts of the film more easily.
1) G. Gruen, K.R. Mecke, M. Rauscher: Thin-film flow
influenced by thermal noise. J. Stat. Phys. 122, 1261--1291 (2006)\\
2) K.R. Mecke, M. Rauscher: On thermal fluctuations in thin film
flow. J. Phys.: Condens. Matter 17, S3515--S3522 (2005) |
@incollection{statphys23_0194,
title = {Thin film dynamics influenced by thermal fluctuations},
address = {Genova, Italy},
author = {M. Rauscher and G. Gruen and K.R. Mecke},
booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics},
editor = {Luciano Pietronero and Vittorio Loreto and Stefano Zapperi},
month = {9-13 July},
url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=194},
year = {2007},
abstract = {We develop a stochastic version of the thin film equation for Newtonian incompressible fluids, see [1].
In the thin
film approximation, the stochastic incompressible hydrodynamic equations
reduce to the deterministic thin film
equation for the film thickness $h(r;t)$ plus a conserved multiplicative noise term $\eta({r};t)$.
Intermolecular forces, determining the wetting properties of the substrate are taken into account in terms of the disjoining pressure $\Pi(z)$. The Gaussian noise term
has zero mean and the correlator
$\langle \eta_i({r};t)\eta_j({r}';t')\rangle
=2\,\delta_{ij}\,\delta({r}-{r}') \,\delta(t-t')$\/.
With the functional Fokker-Planck equation we show that the noise term is
consistent with the thermodynamical equilibrium height distribution of the film
thickness.
We also develop a numerical scheme for the one dimensional version of
the stochastic thin film equation. Numerical solutions indicate that
thermal fluctuations significantly influence the time scales of
spinodal dewetting, in particular, they accelerate the process of hole formation
by a factor of five for experimental parameter values. This is roughly the
difference in rupture time between the experiments and the deterministic
simulation.
We also find clear indications for thermal
fluctuations in the early linear regime of spinodal dewetting
[2]. Thermal fluctuations change the capillary wave spectrum from
exponentially damped to a power law behavior for large wave numbers/short
wavelengths. Recently, evidence for this has been found in atomic force
microscopy data from dewetting thin polymer films. Instead of
measuring the power spectrum of the surface roughness, we analyze the mean
deviation of the surface slope $\langle \left({\nabla}h\right)^2\rangle$,
which turns out to be a more robust parameter. Also, the averaging procedure can
be restricted to certain parts of the film more easily.
1) G. Gruen, K.R. Mecke, M. Rauscher: Thin-film flow
influenced by thermal noise. J. Stat. Phys. 122, 1261--1291 (2006)\\
2) K.R. Mecke, M. Rauscher: On thermal fluctuations in thin film
flow. J. Phys.: Condens. Matter 17, S3515--S3522 (2005)},
keywords = {dewetting film flow fluctuations statphys23 thermal thin topic-6 wetting }
}
::