Numerical Bifurcation Analysis of a Film Flowing over a Patterned Surface through Enhanced Lubrication Theory

The bifurcation analysis of a film falling down an hybrid surface is conducted via the numerical solution of the governing lubrication equation. Instability phenomena, that lead to film breakage and growth of fingers, are induced by multiple contamination spots. Contact angles up to <inline-formu...

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Autores principales:	Nicola Suzzi, Giulio Croce
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	lubrication bifurcation analysis heterogeneous surfaces disjoining pressure capillary pressure Thermodynamics QC310.15-319 Descriptive and experimental mechanics QC120-168.85
Acceso en línea:	https://doaj.org/article/076aedca9772418490ce0701f022be19
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spelling	oai:doaj.org-article:076aedca9772418490ce0701f022be192021-11-25T17:31:43ZNumerical Bifurcation Analysis of a Film Flowing over a Patterned Surface through Enhanced Lubrication Theory10.3390/fluids61104052311-5521https://doaj.org/article/076aedca9772418490ce0701f022be192021-11-01T00:00:00Zhttps://www.mdpi.com/2311-5521/6/11/405https://doaj.org/toc/2311-5521The bifurcation analysis of a film falling down an hybrid surface is conducted via the numerical solution of the governing lubrication equation. Instability phenomena, that lead to film breakage and growth of fingers, are induced by multiple contamination spots. Contact angles up to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>75</mn><mo>∘</mo></msup></semantics></math></inline-formula> are investigated due to the full implementation of the free surface curvature, which replaces the small slope approximation, accurate for film slope lower than <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>30</mn><mo>∘</mo></msup></semantics></math></inline-formula>. The dynamic contact angle is first verified with the Hoffman–Voinov–Tanner law in case of a stable film down an inclined plate with uniform surface wettability. Then, contamination spots, characterized by an increased value of the static contact angle, are considered in order to induce film instability and several parametric computations are run, with different film patterns observed. The effects of the flow characteristics and of the hybrid pattern geometry are investigated and the corresponding bifurcation diagram with the number of observed rivulets is built. The long term evolution of induced film instabilities shows a complex behavior: different flow regimes can be observed at the same flow characteristics under slightly different hybrid configurations. This suggest the possibility of controlling the rivulet/film transition via a proper design of the surfaces, thus opening the way for relevant practical application.Nicola SuzziGiulio CroceMDPI AGarticlelubricationbifurcation analysisheterogeneous surfacesdisjoining pressurecapillary pressureThermodynamicsQC310.15-319Descriptive and experimental mechanicsQC120-168.85ENFluids, Vol 6, Iss 405, p 405 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	lubrication bifurcation analysis heterogeneous surfaces disjoining pressure capillary pressure Thermodynamics QC310.15-319 Descriptive and experimental mechanics QC120-168.85
spellingShingle	lubrication bifurcation analysis heterogeneous surfaces disjoining pressure capillary pressure Thermodynamics QC310.15-319 Descriptive and experimental mechanics QC120-168.85 Nicola Suzzi Giulio Croce Numerical Bifurcation Analysis of a Film Flowing over a Patterned Surface through Enhanced Lubrication Theory
description	The bifurcation analysis of a film falling down an hybrid surface is conducted via the numerical solution of the governing lubrication equation. Instability phenomena, that lead to film breakage and growth of fingers, are induced by multiple contamination spots. Contact angles up to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>75</mn><mo>∘</mo></msup></semantics></math></inline-formula> are investigated due to the full implementation of the free surface curvature, which replaces the small slope approximation, accurate for film slope lower than <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>30</mn><mo>∘</mo></msup></semantics></math></inline-formula>. The dynamic contact angle is first verified with the Hoffman–Voinov–Tanner law in case of a stable film down an inclined plate with uniform surface wettability. Then, contamination spots, characterized by an increased value of the static contact angle, are considered in order to induce film instability and several parametric computations are run, with different film patterns observed. The effects of the flow characteristics and of the hybrid pattern geometry are investigated and the corresponding bifurcation diagram with the number of observed rivulets is built. The long term evolution of induced film instabilities shows a complex behavior: different flow regimes can be observed at the same flow characteristics under slightly different hybrid configurations. This suggest the possibility of controlling the rivulet/film transition via a proper design of the surfaces, thus opening the way for relevant practical application.
format	article
author	Nicola Suzzi Giulio Croce
author_facet	Nicola Suzzi Giulio Croce
author_sort	Nicola Suzzi
title	Numerical Bifurcation Analysis of a Film Flowing over a Patterned Surface through Enhanced Lubrication Theory
title_short	Numerical Bifurcation Analysis of a Film Flowing over a Patterned Surface through Enhanced Lubrication Theory
title_full	Numerical Bifurcation Analysis of a Film Flowing over a Patterned Surface through Enhanced Lubrication Theory
title_fullStr	Numerical Bifurcation Analysis of a Film Flowing over a Patterned Surface through Enhanced Lubrication Theory
title_full_unstemmed	Numerical Bifurcation Analysis of a Film Flowing over a Patterned Surface through Enhanced Lubrication Theory
title_sort	numerical bifurcation analysis of a film flowing over a patterned surface through enhanced lubrication theory
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/076aedca9772418490ce0701f022be19
work_keys_str_mv	AT nicolasuzzi numericalbifurcationanalysisofafilmflowingoverapatternedsurfacethroughenhancedlubricationtheory AT giuliocroce numericalbifurcationanalysisofafilmflowingoverapatternedsurfacethroughenhancedlubricationtheory
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Numerical Bifurcation Analysis of a Film Flowing over a Patterned Surface through Enhanced Lubrication Theory

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