Influence of parametric forcing on Marangoni instability
We study a thin, laterally confined heated liquid layer subjected to mechanical parametric forcing without gravity. In the absence of parametric forcing, the liquid layer exhibits the Marangoni instability, provided the temperature difference across the layer exceeds a threshold. This threshold vari...
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description | We study a thin, laterally confined heated liquid layer subjected to mechanical parametric forcing without gravity. In the absence of parametric forcing, the liquid layer exhibits the Marangoni instability, provided the temperature difference across the layer exceeds a threshold. This threshold varies with the perturbation wavenumber, according to a curve with two minima, which correspond to long- and short-wave instability modes. The most unstable mode depends on the lateral confinement of the liquid layer. In wide containers, the long-wave mode is typically observed, and this can lead to the formation of dry spots. We focus on this mode, as the short-wave mode is found to be unaffected by parametric forcing. We use linear stability analysis and nonlinear computations based on a reduced-order model to investigate how parametric forcing can prevent the formation of dry spots. At low forcing frequencies, the liquid film can be rendered linearly stable within a finite range of forcing amplitudes, which decreases with increasing frequency and ultimately disappears at a cutoff frequency. Outside this range, the flow becomes unstable to either the Marangoni instability (for small amplitudes) or the Faraday instability (for large amplitudes). At high frequencies, beyond the cutoff frequency, linear stabilization through parametric forcing is not possible. However, a nonlinear saturation mechanism, occurring at forcing amplitudes below the Faraday instability threshold, can greatly reduce the film surface deformation and therefore prevent dry spots. Although dry spots can also be avoided at larger forcing amplitudes, this comes at the expense of generating large-amplitude Faraday waves. |
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In the absence of parametric forcing, the liquid layer exhibits the Marangoni instability, provided the temperature difference across the layer exceeds a threshold. This threshold varies with the perturbation wavenumber, according to a curve with two minima, which correspond to long- and short-wave instability modes. The most unstable mode depends on the lateral confinement of the liquid layer. In wide containers, the long-wave mode is typically observed, and this can lead to the formation of dry spots. We focus on this mode, as the short-wave mode is found to be unaffected by parametric forcing. We use linear stability analysis and nonlinear computations based on a reduced-order model to investigate how parametric forcing can prevent the formation of dry spots. At low forcing frequencies, the liquid film can be rendered linearly stable within a finite range of forcing amplitudes, which decreases with increasing frequency and ultimately disappears at a cutoff frequency. Outside this range, the flow becomes unstable to either the Marangoni instability (for small amplitudes) or the Faraday instability (for large amplitudes). At high frequencies, beyond the cutoff frequency, linear stabilization through parametric forcing is not possible. However, a nonlinear saturation mechanism, occurring at forcing amplitudes below the Faraday instability threshold, can greatly reduce the film surface deformation and therefore prevent dry spots. Although dry spots can also be avoided at larger forcing amplitudes, this comes at the expense of generating large-amplitude Faraday waves.</description><identifier>ISSN: 0022-1120</identifier><identifier>EISSN: 1469-7645</identifier><identifier>DOI: 10.1017/jfm.2024.58</identifier><language>eng</language><publisher>Cambridge, UK: Cambridge University Press</publisher><subject>Amplitudes ; Approximation ; Deformation ; Engineering Sciences ; Flow stability ; Fluids mechanics ; Gravity ; Instability ; JFM Papers ; Lateral stability ; Mathematical models ; Mechanics ; Rayleigh number ; Reduced order models ; Saturation ; Stability analysis ; Temperature differences ; Thin films ; Wavelengths</subject><ispartof>Journal of fluid mechanics, 2024-02, Vol.981, Article A8</ispartof><rights>The Author(s), 2024. Published by Cambridge University Press.</rights><rights>The Author(s), 2024. Published by Cambridge University Press. This work is licensed under the Creative Commons Attribution – Non-Commercial License This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial licence (http://creativecommons.org/licenses/by-nc/4.0), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original article is properly cited. The written permission of Cambridge University Press must be obtained prior to any commercial use. (the “License”). 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Fluid Mech</addtitle><description>We study a thin, laterally confined heated liquid layer subjected to mechanical parametric forcing without gravity. In the absence of parametric forcing, the liquid layer exhibits the Marangoni instability, provided the temperature difference across the layer exceeds a threshold. This threshold varies with the perturbation wavenumber, according to a curve with two minima, which correspond to long- and short-wave instability modes. The most unstable mode depends on the lateral confinement of the liquid layer. In wide containers, the long-wave mode is typically observed, and this can lead to the formation of dry spots. We focus on this mode, as the short-wave mode is found to be unaffected by parametric forcing. We use linear stability analysis and nonlinear computations based on a reduced-order model to investigate how parametric forcing can prevent the formation of dry spots. At low forcing frequencies, the liquid film can be rendered linearly stable within a finite range of forcing amplitudes, which decreases with increasing frequency and ultimately disappears at a cutoff frequency. Outside this range, the flow becomes unstable to either the Marangoni instability (for small amplitudes) or the Faraday instability (for large amplitudes). At high frequencies, beyond the cutoff frequency, linear stabilization through parametric forcing is not possible. However, a nonlinear saturation mechanism, occurring at forcing amplitudes below the Faraday instability threshold, can greatly reduce the film surface deformation and therefore prevent dry spots. 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Fluid Mech</addtitle><date>2024-02-16</date><risdate>2024</risdate><volume>981</volume><artnum>A8</artnum><issn>0022-1120</issn><eissn>1469-7645</eissn><abstract>We study a thin, laterally confined heated liquid layer subjected to mechanical parametric forcing without gravity. In the absence of parametric forcing, the liquid layer exhibits the Marangoni instability, provided the temperature difference across the layer exceeds a threshold. This threshold varies with the perturbation wavenumber, according to a curve with two minima, which correspond to long- and short-wave instability modes. The most unstable mode depends on the lateral confinement of the liquid layer. In wide containers, the long-wave mode is typically observed, and this can lead to the formation of dry spots. We focus on this mode, as the short-wave mode is found to be unaffected by parametric forcing. We use linear stability analysis and nonlinear computations based on a reduced-order model to investigate how parametric forcing can prevent the formation of dry spots. At low forcing frequencies, the liquid film can be rendered linearly stable within a finite range of forcing amplitudes, which decreases with increasing frequency and ultimately disappears at a cutoff frequency. Outside this range, the flow becomes unstable to either the Marangoni instability (for small amplitudes) or the Faraday instability (for large amplitudes). At high frequencies, beyond the cutoff frequency, linear stabilization through parametric forcing is not possible. However, a nonlinear saturation mechanism, occurring at forcing amplitudes below the Faraday instability threshold, can greatly reduce the film surface deformation and therefore prevent dry spots. Although dry spots can also be avoided at larger forcing amplitudes, this comes at the expense of generating large-amplitude Faraday waves.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1017/jfm.2024.58</doi><tpages>30</tpages><orcidid>https://orcid.org/0000-0002-4883-1554</orcidid><orcidid>https://orcid.org/0000-0003-2394-5077</orcidid><orcidid>https://orcid.org/0000-0003-1495-5505</orcidid><orcidid>https://orcid.org/0009-0005-7930-7615</orcidid><oa>free_for_read</oa></addata></record> |
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subjects | Amplitudes Approximation Deformation Engineering Sciences Flow stability Fluids mechanics Gravity Instability JFM Papers Lateral stability Mathematical models Mechanics Rayleigh number Reduced order models Saturation Stability analysis Temperature differences Thin films Wavelengths |
title | Influence of parametric forcing on Marangoni instability |
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