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Instability, Rupture and Fluctuations in Thin Liquid Films: Theory and Computations

Thin liquid films are ubiquitous in natural phenomena and technological applications. They have been extensively studied via deterministic hydrodynamic equations, but thermal fluctuations often play a crucial role that needs to be understood. An example of this is dewetting, which involves the ruptu...

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Autores principales: Durán-Olivencia, Miguel A., Gvalani, Rishabh S., Kalliadasis, Serafim, Pavliotis, Grigorios A.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2019
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6394745/
https://www.ncbi.nlm.nih.gov/pubmed/30880838
http://dx.doi.org/10.1007/s10955-018-2200-0
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author Durán-Olivencia, Miguel A.
Gvalani, Rishabh S.
Kalliadasis, Serafim
Pavliotis, Grigorios A.
author_facet Durán-Olivencia, Miguel A.
Gvalani, Rishabh S.
Kalliadasis, Serafim
Pavliotis, Grigorios A.
author_sort Durán-Olivencia, Miguel A.
collection PubMed
description Thin liquid films are ubiquitous in natural phenomena and technological applications. They have been extensively studied via deterministic hydrodynamic equations, but thermal fluctuations often play a crucial role that needs to be understood. An example of this is dewetting, which involves the rupture of a thin liquid film and the formation of droplets. Such a process is thermally activated and requires fluctuations to be taken into account self-consistently. In this work we present an analytical and numerical study of a stochastic thin-film equation derived from first principles. Following a brief review of the derivation, we scrutinise the behaviour of the equation in the limit of perfectly correlated noise along the wall-normal direction, as opposed to the perfectly uncorrelated limit studied by Grün et al. (J Stat Phys 122(6):1261–1291, 2006). We also present a numerical scheme based on a spectral collocation method, which is then utilised to simulate the stochastic thin-film equation. This scheme seems to be very convenient for numerical studies of the stochastic thin-film equation, since it makes it easier to select the frequency modes of the noise (following the spirit of the long-wave approximation). With our numerical scheme we explore the fluctuating dynamics of the thin film and the behaviour of its free energy in the vicinity of rupture. Finally, we study the effect of the noise intensity on the rupture time, using a large number of sample paths as compared to previous studies.
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spelling pubmed-63947452019-03-15 Instability, Rupture and Fluctuations in Thin Liquid Films: Theory and Computations Durán-Olivencia, Miguel A. Gvalani, Rishabh S. Kalliadasis, Serafim Pavliotis, Grigorios A. J Stat Phys Article Thin liquid films are ubiquitous in natural phenomena and technological applications. They have been extensively studied via deterministic hydrodynamic equations, but thermal fluctuations often play a crucial role that needs to be understood. An example of this is dewetting, which involves the rupture of a thin liquid film and the formation of droplets. Such a process is thermally activated and requires fluctuations to be taken into account self-consistently. In this work we present an analytical and numerical study of a stochastic thin-film equation derived from first principles. Following a brief review of the derivation, we scrutinise the behaviour of the equation in the limit of perfectly correlated noise along the wall-normal direction, as opposed to the perfectly uncorrelated limit studied by Grün et al. (J Stat Phys 122(6):1261–1291, 2006). We also present a numerical scheme based on a spectral collocation method, which is then utilised to simulate the stochastic thin-film equation. This scheme seems to be very convenient for numerical studies of the stochastic thin-film equation, since it makes it easier to select the frequency modes of the noise (following the spirit of the long-wave approximation). With our numerical scheme we explore the fluctuating dynamics of the thin film and the behaviour of its free energy in the vicinity of rupture. Finally, we study the effect of the noise intensity on the rupture time, using a large number of sample paths as compared to previous studies. Springer US 2019-01-21 2019 /pmc/articles/PMC6394745/ /pubmed/30880838 http://dx.doi.org/10.1007/s10955-018-2200-0 Text en © The Author(s) 2019 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Article
Durán-Olivencia, Miguel A.
Gvalani, Rishabh S.
Kalliadasis, Serafim
Pavliotis, Grigorios A.
Instability, Rupture and Fluctuations in Thin Liquid Films: Theory and Computations
title Instability, Rupture and Fluctuations in Thin Liquid Films: Theory and Computations
title_full Instability, Rupture and Fluctuations in Thin Liquid Films: Theory and Computations
title_fullStr Instability, Rupture and Fluctuations in Thin Liquid Films: Theory and Computations
title_full_unstemmed Instability, Rupture and Fluctuations in Thin Liquid Films: Theory and Computations
title_short Instability, Rupture and Fluctuations in Thin Liquid Films: Theory and Computations
title_sort instability, rupture and fluctuations in thin liquid films: theory and computations
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6394745/
https://www.ncbi.nlm.nih.gov/pubmed/30880838
http://dx.doi.org/10.1007/s10955-018-2200-0
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