Self-similar collapse of a circular cavity of a power-law liquid
Using the lubrication approximation we investigate the self-similar axisymmetric flow of a power-law liquid towards a central circular cavity. It is shown that this problem has a self-similar solution of the second kind. The self-similarity exponent is found by solving a non-linear eigenvalue proble...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_03770257_v165_n3-4_p158_Gratton |
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todo:paper_03770257_v165_n3-4_p158_Gratton2023-10-03T15:31:19Z Self-similar collapse of a circular cavity of a power-law liquid Gratton, J. Perazzo, C.A. Gravity currents Power-law liquid Self-similarity Axisymmetric flow Circular cavity Eigenvalues Governing equations Gravity currents Integral curves Lubrication approximations Nonlinear eigenvalue problem Numerical integrations Phase plane Physical variables Power-law liquids Rheological indices Self-similar Self-similar solution Self-similarities Singular points Eigenvalues and eigenfunctions Gravitation Gravity waves Numerical methods Rheology Liquids Using the lubrication approximation we investigate the self-similar axisymmetric flow of a power-law liquid towards a central circular cavity. It is shown that this problem has a self-similar solution of the second kind. The self-similarity exponent is found by solving a non-linear eigenvalue problem arising from the requirement that the integral curve that represents the solution must join the appropriate singular points in the phase plane of the governing equation. The eigenvalues for different values of the rheological index are computed. Numerical integration of the equations allows us to determine the shape of the solution in terms of the physical variables. We make a detailed analysis of the influence of the rheology on the properties of the solutions. © 2009 Elsevier B.V. All rights reserved. Fil:Gratton, J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Perazzo, C.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03770257_v165_n3-4_p158_Gratton |
| institution |
Universidad de Buenos Aires |
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I-28 |
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R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Gravity currents Power-law liquid Self-similarity Axisymmetric flow Circular cavity Eigenvalues Governing equations Gravity currents Integral curves Lubrication approximations Nonlinear eigenvalue problem Numerical integrations Phase plane Physical variables Power-law liquids Rheological indices Self-similar Self-similar solution Self-similarities Singular points Eigenvalues and eigenfunctions Gravitation Gravity waves Numerical methods Rheology Liquids |
| spellingShingle |
Gravity currents Power-law liquid Self-similarity Axisymmetric flow Circular cavity Eigenvalues Governing equations Gravity currents Integral curves Lubrication approximations Nonlinear eigenvalue problem Numerical integrations Phase plane Physical variables Power-law liquids Rheological indices Self-similar Self-similar solution Self-similarities Singular points Eigenvalues and eigenfunctions Gravitation Gravity waves Numerical methods Rheology Liquids Gratton, J. Perazzo, C.A. Self-similar collapse of a circular cavity of a power-law liquid |
| topic_facet |
Gravity currents Power-law liquid Self-similarity Axisymmetric flow Circular cavity Eigenvalues Governing equations Gravity currents Integral curves Lubrication approximations Nonlinear eigenvalue problem Numerical integrations Phase plane Physical variables Power-law liquids Rheological indices Self-similar Self-similar solution Self-similarities Singular points Eigenvalues and eigenfunctions Gravitation Gravity waves Numerical methods Rheology Liquids |
| description |
Using the lubrication approximation we investigate the self-similar axisymmetric flow of a power-law liquid towards a central circular cavity. It is shown that this problem has a self-similar solution of the second kind. The self-similarity exponent is found by solving a non-linear eigenvalue problem arising from the requirement that the integral curve that represents the solution must join the appropriate singular points in the phase plane of the governing equation. The eigenvalues for different values of the rheological index are computed. Numerical integration of the equations allows us to determine the shape of the solution in terms of the physical variables. We make a detailed analysis of the influence of the rheology on the properties of the solutions. © 2009 Elsevier B.V. All rights reserved. |
| format |
JOUR |
| author |
Gratton, J. Perazzo, C.A. |
| author_facet |
Gratton, J. Perazzo, C.A. |
| author_sort |
Gratton, J. |
| title |
Self-similar collapse of a circular cavity of a power-law liquid |
| title_short |
Self-similar collapse of a circular cavity of a power-law liquid |
| title_full |
Self-similar collapse of a circular cavity of a power-law liquid |
| title_fullStr |
Self-similar collapse of a circular cavity of a power-law liquid |
| title_full_unstemmed |
Self-similar collapse of a circular cavity of a power-law liquid |
| title_sort |
self-similar collapse of a circular cavity of a power-law liquid |
| url |
http://hdl.handle.net/20.500.12110/paper_03770257_v165_n3-4_p158_Gratton |
| work_keys_str_mv |
AT grattonj selfsimilarcollapseofacircularcavityofapowerlawliquid AT perazzoca selfsimilarcollapseofacircularcavityofapowerlawliquid |
| _version_ |
1807324012189057024 |