Numerical study of the Rosensweig instability in a magnetic fluid subject to diffusion of magnetic particles
The present study is devoted to the classical problem on stability of a magnetic fluid layer under the influence of gravity and a uniform magnetic field. A periodical peak‐shaped stable structure is formed on the fluid surface when the applied magnetic field exceeds a critical value. The mathematica...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2010-04-01
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| Series: | Mathematical Modelling and Analysis |
| Subjects: | |
| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/6004 |
| _version_ | 1818387668283686912 |
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| author | Olga Lavrova Viktor Polevikov Lutz Tobiska |
| author_facet | Olga Lavrova Viktor Polevikov Lutz Tobiska |
| author_sort | Olga Lavrova |
| collection | DOAJ |
| description | The present study is devoted to the classical problem on stability of a magnetic fluid layer under the influence of gravity and a uniform magnetic field. A periodical peak‐shaped stable structure is formed on the fluid surface when the applied magnetic field exceeds a critical value. The mathematical model describes a single peak in the pattern assuming axial symmetry of the peak shape. The field configuration in the whole space, the magnetic particle concentration inside the fluid and the free surface structure are unknown quantities in this model. The unknown free surface is treated explicitly, using a parametric representation with respect to the arc length. The nonlinear problem is discretized by means of a finite element method for the Maxwell's equations and a finite‐difference method for the free surface equations. Numerical modelling allows to get over‐critical equilibrium free surface shapes in a wide range of applied field intensities. Our numerical results show a significant influence of the particle diffusion on the overcritical shapes.
First published online: 09 Jun 2011 |
| first_indexed | 2024-12-14T04:13:36Z |
| format | Article |
| id | doaj.art-911484b0bfbb417b9d0467d53a616f13 |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-12-14T04:13:36Z |
| publishDate | 2010-04-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-911484b0bfbb417b9d0467d53a616f132022-12-21T23:17:36ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102010-04-0115210.3846/1392-6292.2010.15.223-233Numerical study of the Rosensweig instability in a magnetic fluid subject to diffusion of magnetic particlesOlga Lavrova0Viktor Polevikov1Lutz Tobiska2Belarusian State University, Department of Computational Mathematics; Independence Ave. 4, 220030 Minsk, BelarusBelarusian State University, Department of Computational Mathematics; Independence Ave. 4, 220030 Minsk, BelarusOtto von Guericke University Magdeburg, Institute for Analysis and Computational Mathematics; PF4120, D-39106 Magdeburg, GermanyThe present study is devoted to the classical problem on stability of a magnetic fluid layer under the influence of gravity and a uniform magnetic field. A periodical peak‐shaped stable structure is formed on the fluid surface when the applied magnetic field exceeds a critical value. The mathematical model describes a single peak in the pattern assuming axial symmetry of the peak shape. The field configuration in the whole space, the magnetic particle concentration inside the fluid and the free surface structure are unknown quantities in this model. The unknown free surface is treated explicitly, using a parametric representation with respect to the arc length. The nonlinear problem is discretized by means of a finite element method for the Maxwell's equations and a finite‐difference method for the free surface equations. Numerical modelling allows to get over‐critical equilibrium free surface shapes in a wide range of applied field intensities. Our numerical results show a significant influence of the particle diffusion on the overcritical shapes. First published online: 09 Jun 2011https://journals.vgtu.lt/index.php/MMA/article/view/6004magnetic fluidparticle diffusionequilibrium free surfacefinite element methodfinite‐difference scheme |
| spellingShingle | Olga Lavrova Viktor Polevikov Lutz Tobiska Numerical study of the Rosensweig instability in a magnetic fluid subject to diffusion of magnetic particles Mathematical Modelling and Analysis magnetic fluid particle diffusion equilibrium free surface finite element method finite‐difference scheme |
| title | Numerical study of the Rosensweig instability in a magnetic fluid subject to diffusion of magnetic particles |
| title_full | Numerical study of the Rosensweig instability in a magnetic fluid subject to diffusion of magnetic particles |
| title_fullStr | Numerical study of the Rosensweig instability in a magnetic fluid subject to diffusion of magnetic particles |
| title_full_unstemmed | Numerical study of the Rosensweig instability in a magnetic fluid subject to diffusion of magnetic particles |
| title_short | Numerical study of the Rosensweig instability in a magnetic fluid subject to diffusion of magnetic particles |
| title_sort | numerical study of the rosensweig instability in a magnetic fluid subject to diffusion of magnetic particles |
| topic | magnetic fluid particle diffusion equilibrium free surface finite element method finite‐difference scheme |
| url | https://journals.vgtu.lt/index.php/MMA/article/view/6004 |
| work_keys_str_mv | AT olgalavrova numericalstudyoftherosensweiginstabilityinamagneticfluidsubjecttodiffusionofmagneticparticles AT viktorpolevikov numericalstudyoftherosensweiginstabilityinamagneticfluidsubjecttodiffusionofmagneticparticles AT lutztobiska numericalstudyoftherosensweiginstabilityinamagneticfluidsubjecttodiffusionofmagneticparticles |