Patterns and Their Large-Scale Distortions in Marangoni Convection with Insoluble Surfactant
Nonlinear dynamics of patterns near the threshold of long-wave monotonic Marangoni instability of conductive state in a heated thin layer of liquid covered by insoluble surfactant is considered. Pattern selection between roll and square planforms is analyzed. The dependence of pattern stability on t...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-08-01
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| Series: | Fluids |
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| Online Access: | https://www.mdpi.com/2311-5521/6/8/282 |
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| author | Alexander B. Mikishev Alexander A. Nepomnyashchy |
| author_facet | Alexander B. Mikishev Alexander A. Nepomnyashchy |
| author_sort | Alexander B. Mikishev |
| collection | DOAJ |
| description | Nonlinear dynamics of patterns near the threshold of long-wave monotonic Marangoni instability of conductive state in a heated thin layer of liquid covered by insoluble surfactant is considered. Pattern selection between roll and square planforms is analyzed. The dependence of pattern stability on the heat transfer from the free surface of the liquid characterized by Biot number and the gravity described by Galileo number at different surfactant concentrations is studied. Using weakly nonlinear analysis, we derive a set of amplitude equations governing the large-scale roll distortions in the presence of the surface deformation and the surfactant redistribution. These equations are used for the linear analysis of modulational instability of stationary rolls. |
| first_indexed | 2024-03-10T08:50:01Z |
| format | Article |
| id | doaj.art-b453d00d02f04e73b243b73e23f37c62 |
| institution | Directory Open Access Journal |
| issn | 2311-5521 |
| language | English |
| last_indexed | 2024-03-10T08:50:01Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fluids |
| spelling | doaj.art-b453d00d02f04e73b243b73e23f37c622023-11-22T07:36:56ZengMDPI AGFluids2311-55212021-08-016828210.3390/fluids6080282Patterns and Their Large-Scale Distortions in Marangoni Convection with Insoluble SurfactantAlexander B. Mikishev0Alexander A. Nepomnyashchy1Department of Engineering Technology, Sam Houston State University, Huntsville, TX 77341, USADepartment of Mathematics, Technion-Israel Institutute of Technology, Technion, Haifa 32000, IsraelNonlinear dynamics of patterns near the threshold of long-wave monotonic Marangoni instability of conductive state in a heated thin layer of liquid covered by insoluble surfactant is considered. Pattern selection between roll and square planforms is analyzed. The dependence of pattern stability on the heat transfer from the free surface of the liquid characterized by Biot number and the gravity described by Galileo number at different surfactant concentrations is studied. Using weakly nonlinear analysis, we derive a set of amplitude equations governing the large-scale roll distortions in the presence of the surface deformation and the surfactant redistribution. These equations are used for the linear analysis of modulational instability of stationary rolls.https://www.mdpi.com/2311-5521/6/8/282Marangoni convectionsurfactantinstability |
| spellingShingle | Alexander B. Mikishev Alexander A. Nepomnyashchy Patterns and Their Large-Scale Distortions in Marangoni Convection with Insoluble Surfactant Fluids Marangoni convection surfactant instability |
| title | Patterns and Their Large-Scale Distortions in Marangoni Convection with Insoluble Surfactant |
| title_full | Patterns and Their Large-Scale Distortions in Marangoni Convection with Insoluble Surfactant |
| title_fullStr | Patterns and Their Large-Scale Distortions in Marangoni Convection with Insoluble Surfactant |
| title_full_unstemmed | Patterns and Their Large-Scale Distortions in Marangoni Convection with Insoluble Surfactant |
| title_short | Patterns and Their Large-Scale Distortions in Marangoni Convection with Insoluble Surfactant |
| title_sort | patterns and their large scale distortions in marangoni convection with insoluble surfactant |
| topic | Marangoni convection surfactant instability |
| url | https://www.mdpi.com/2311-5521/6/8/282 |
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