Linear stability analysis of a liquid film down on an inclined plane under oscillation with normal and lateral components in the presence and absence of surfactant
In this work, we first study the interface instability of a fluid layer flowing down on an inclined plane under periodic oscillation having both normal and lateral components. After that, we examine the effect of an insoluble surfactant covering the free surface under normal oscillation, lateral osc...
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description | In this work, we first study the interface instability of a fluid layer flowing down on an inclined plane under periodic oscillation having both normal and lateral components. After that, we examine the effect of an insoluble surfactant covering the free surface under normal oscillation, lateral oscillation, and both normal and lateral oscillations. The time periodic linear system, corresponding to the governing equations, is treated using the Chebyshev spectral collocation method for spatial resolution, and for temporal resolution, we use the Floquet theory. We show that the stabilizing effect of normal oscillation amplitude on the gravitational instability, reported by Woods and Lin [J. Fluid Mech. 294, 391 (1995)], is strengthened by introducing lateral oscillation, and this contributes to the complete suppression of this instability. The harmonic and subharmonic zones, initially stable in the work of Woods and Lin [J. Fluid Mech. 294, 391 (1995)], are destabilized by the lateral oscillation, and the first unstable parametric resonance becomes without threshold. Conversely, the unstable domain of the gravitational instability and the second resonance zone reported by Lin, Chen, and Woods [Phys. Fluids 8, 3247 (1996)] can be reduced by introducing normal oscillation. Finally, we show that the surfactant has a stabilizing effect that contributes to accelerate the suppression of the gravitational instability and opposes the destabilizing effect of the lateral oscillation on the first subharmonic resonance to give rise to a competition between the two effects. |
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After that, we examine the effect of an insoluble surfactant covering the free surface under normal oscillation, lateral oscillation, and both normal and lateral oscillations. The time periodic linear system, corresponding to the governing equations, is treated using the Chebyshev spectral collocation method for spatial resolution, and for temporal resolution, we use the Floquet theory. We show that the stabilizing effect of normal oscillation amplitude on the gravitational instability, reported by Woods and Lin [J. Fluid Mech. 294, 391 (1995)], is strengthened by introducing lateral oscillation, and this contributes to the complete suppression of this instability. The harmonic and subharmonic zones, initially stable in the work of Woods and Lin [J. Fluid Mech. 294, 391 (1995)], are destabilized by the lateral oscillation, and the first unstable parametric resonance becomes without threshold. Conversely, the unstable domain of the gravitational instability and the second resonance zone reported by Lin, Chen, and Woods [Phys. Fluids 8, 3247 (1996)] can be reduced by introducing normal oscillation. 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After that, we examine the effect of an insoluble surfactant covering the free surface under normal oscillation, lateral oscillation, and both normal and lateral oscillations. The time periodic linear system, corresponding to the governing equations, is treated using the Chebyshev spectral collocation method for spatial resolution, and for temporal resolution, we use the Floquet theory. We show that the stabilizing effect of normal oscillation amplitude on the gravitational instability, reported by Woods and Lin [J. Fluid Mech. 294, 391 (1995)], is strengthened by introducing lateral oscillation, and this contributes to the complete suppression of this instability. The harmonic and subharmonic zones, initially stable in the work of Woods and Lin [J. Fluid Mech. 294, 391 (1995)], are destabilized by the lateral oscillation, and the first unstable parametric resonance becomes without threshold. Conversely, the unstable domain of the gravitational instability and the second resonance zone reported by Lin, Chen, and Woods [Phys. Fluids 8, 3247 (1996)] can be reduced by introducing normal oscillation. Finally, we show that the surfactant has a stabilizing effect that contributes to accelerate the suppression of the gravitational instability and opposes the destabilizing effect of the lateral oscillation on the first subharmonic resonance to give rise to a competition between the two effects.</description><subject>Chebyshev approximation</subject><subject>Collocation methods</subject><subject>Fluid dynamics</subject><subject>Fluids</subject><subject>Free surfaces</subject><subject>Gravitation</subject><subject>Gravitational instability</subject><subject>Interface stability</subject><subject>Lateral oscillation</subject><subject>Lateral stability</subject><subject>Physics</subject><subject>Resonance</subject><subject>Spatial resolution</subject><subject>Stability analysis</subject><subject>Surfactants</subject><subject>Temporal resolution</subject><issn>1070-6631</issn><issn>1089-7666</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp90ctKxDAUBuAgCo6jC98g4EqhYy5t2i5l8AYDbnRd0lyYDGnSSVKGeR5f1Mxl7So_4csJ_AeAe4wWGDH6jBcVpk3bkAsww6hpi5oxdnnINSoYo_ga3MS4QQjRlrAZ-F0Zp3iAMfHeWJP2kDtu99FE6DXk0JrtZCTUxg5Q-p2D3mUBjRM2P5RwtNwpODmpAvRRGGt5MtnsTFpD58PAbfYS5msVchZ-GL1TLsU8A6a1gmNQUTmhjoz3p5z_jlPQXCTu0i240txGdXc-5-Dn7fV7-VGsvt4_ly-rQpCWpKJCkhKGRNNojEqBqWRUqpKLSpaoKstSctxTogmq-5qKqpe871UrtJZSSIboHDyc5o7BbycVU7fxU8h1xI7QGtW0ZS3L6vGkRPAxBqW7MZiBh32HUXfYQYe78w6yfTrZ3Ew6FvMP_gMGAYoU</recordid><startdate>20200301</startdate><enddate>20200301</enddate><creator>El Jaouahiry, Abdelouahab</creator><creator>Aniss, Saïd</creator><general>American Institute of Physics</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope><orcidid>https://orcid.org/0000-0002-8700-974X</orcidid></search><sort><creationdate>20200301</creationdate><title>Linear stability analysis of a liquid film down on an inclined plane under oscillation with normal and lateral components in the presence and absence of surfactant</title><author>El Jaouahiry, Abdelouahab ; Aniss, Saïd</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c292t-50d3260c88f104c13d63de4ac5d405444da1b32f207b73c5bdabbe9cffddcd603</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Chebyshev approximation</topic><topic>Collocation methods</topic><topic>Fluid dynamics</topic><topic>Fluids</topic><topic>Free surfaces</topic><topic>Gravitation</topic><topic>Gravitational instability</topic><topic>Interface stability</topic><topic>Lateral oscillation</topic><topic>Lateral stability</topic><topic>Physics</topic><topic>Resonance</topic><topic>Spatial resolution</topic><topic>Stability analysis</topic><topic>Surfactants</topic><topic>Temporal resolution</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>El Jaouahiry, Abdelouahab</creatorcontrib><creatorcontrib>Aniss, Saïd</creatorcontrib><collection>CrossRef</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Physics of fluids (1994)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>El Jaouahiry, Abdelouahab</au><au>Aniss, Saïd</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Linear stability analysis of a liquid film down on an inclined plane under oscillation with normal and lateral components in the presence and absence of surfactant</atitle><jtitle>Physics of fluids (1994)</jtitle><date>2020-03-01</date><risdate>2020</risdate><volume>32</volume><issue>3</issue><issn>1070-6631</issn><eissn>1089-7666</eissn><coden>PHFLE6</coden><abstract>In this work, we first study the interface instability of a fluid layer flowing down on an inclined plane under periodic oscillation having both normal and lateral components. After that, we examine the effect of an insoluble surfactant covering the free surface under normal oscillation, lateral oscillation, and both normal and lateral oscillations. The time periodic linear system, corresponding to the governing equations, is treated using the Chebyshev spectral collocation method for spatial resolution, and for temporal resolution, we use the Floquet theory. We show that the stabilizing effect of normal oscillation amplitude on the gravitational instability, reported by Woods and Lin [J. Fluid Mech. 294, 391 (1995)], is strengthened by introducing lateral oscillation, and this contributes to the complete suppression of this instability. The harmonic and subharmonic zones, initially stable in the work of Woods and Lin [J. Fluid Mech. 294, 391 (1995)], are destabilized by the lateral oscillation, and the first unstable parametric resonance becomes without threshold. Conversely, the unstable domain of the gravitational instability and the second resonance zone reported by Lin, Chen, and Woods [Phys. Fluids 8, 3247 (1996)] can be reduced by introducing normal oscillation. Finally, we show that the surfactant has a stabilizing effect that contributes to accelerate the suppression of the gravitational instability and opposes the destabilizing effect of the lateral oscillation on the first subharmonic resonance to give rise to a competition between the two effects.</abstract><cop>Melville</cop><pub>American Institute of Physics</pub><doi>10.1063/1.5138982</doi><tpages>15</tpages><orcidid>https://orcid.org/0000-0002-8700-974X</orcidid></addata></record> |
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subjects | Chebyshev approximation Collocation methods Fluid dynamics Fluids Free surfaces Gravitation Gravitational instability Interface stability Lateral oscillation Lateral stability Physics Resonance Spatial resolution Stability analysis Surfactants Temporal resolution |
title | Linear stability analysis of a liquid film down on an inclined plane under oscillation with normal and lateral components in the presence and absence of surfactant |
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