Coriolis effects on rotating Hele-Shaw flows: A conformal-mapping approach
The zero surface tension fluid-fluid interface dynamics in a radial Hele-Shaw cell driven by both injection and rotation is studied by a conformal-mapping approach. The situation in which one of the fluids is inviscid and has negligible density is analyzed. When Coriolis force effects are ignored, e...
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| Format: | Journal article |
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American Physical Society
2010
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| _version_ | 1797091880555511808 |
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| author | Miranda, J Gadelha, H Dorsey, A |
| author_facet | Miranda, J Gadelha, H Dorsey, A |
| author_sort | Miranda, J |
| collection | OXFORD |
| description | The zero surface tension fluid-fluid interface dynamics in a radial Hele-Shaw cell driven by both injection and rotation is studied by a conformal-mapping approach. The situation in which one of the fluids is inviscid and has negligible density is analyzed. When Coriolis force effects are ignored, exact solutions of the zero surface tension rotating Hele-Shaw problem with injection reveal suppression of cusp singularities for sufficiently high rotation rates. We study how the Coriolis force affects the time-dependent solutions of the problem, and the development of finite time singularities. By employing Richardson's harmonic moments approach we obtain conformal maps which describe the time evolution of the fluid boundary. Our results demonstrate that the inertial Coriolis contribution plays an important role in determining the time for cusp formation. Moreover, it introduces a phase drift that makes the evolving patterns rotate. The Coriolis force acts against centrifugal effects, promoting (inhibiting) cusp breakdown if the more viscous and dense fluid lies outside (inside) the interface. Despite the presence of Coriolis effects, the occurrence of finger bending events has not been detected in the exact solutions. Copyright 2010 The American Physical Society. |
| first_indexed | 2024-03-07T03:38:40Z |
| format | Journal article |
| id | oxford-uuid:bd28237f-7f4f-4859-9063-b6d2a3d70717 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T03:38:40Z |
| publishDate | 2010 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | oxford-uuid:bd28237f-7f4f-4859-9063-b6d2a3d707172022-03-27T05:29:38ZCoriolis effects on rotating Hele-Shaw flows: A conformal-mapping approachJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:bd28237f-7f4f-4859-9063-b6d2a3d70717Symplectic Elements at OxfordAmerican Physical Society2010Miranda, JGadelha, HDorsey, AThe zero surface tension fluid-fluid interface dynamics in a radial Hele-Shaw cell driven by both injection and rotation is studied by a conformal-mapping approach. The situation in which one of the fluids is inviscid and has negligible density is analyzed. When Coriolis force effects are ignored, exact solutions of the zero surface tension rotating Hele-Shaw problem with injection reveal suppression of cusp singularities for sufficiently high rotation rates. We study how the Coriolis force affects the time-dependent solutions of the problem, and the development of finite time singularities. By employing Richardson's harmonic moments approach we obtain conformal maps which describe the time evolution of the fluid boundary. Our results demonstrate that the inertial Coriolis contribution plays an important role in determining the time for cusp formation. Moreover, it introduces a phase drift that makes the evolving patterns rotate. The Coriolis force acts against centrifugal effects, promoting (inhibiting) cusp breakdown if the more viscous and dense fluid lies outside (inside) the interface. Despite the presence of Coriolis effects, the occurrence of finger bending events has not been detected in the exact solutions. Copyright 2010 The American Physical Society. |
| spellingShingle | Miranda, J Gadelha, H Dorsey, A Coriolis effects on rotating Hele-Shaw flows: A conformal-mapping approach |
| title | Coriolis effects on rotating Hele-Shaw flows: A conformal-mapping approach |
| title_full | Coriolis effects on rotating Hele-Shaw flows: A conformal-mapping approach |
| title_fullStr | Coriolis effects on rotating Hele-Shaw flows: A conformal-mapping approach |
| title_full_unstemmed | Coriolis effects on rotating Hele-Shaw flows: A conformal-mapping approach |
| title_short | Coriolis effects on rotating Hele-Shaw flows: A conformal-mapping approach |
| title_sort | coriolis effects on rotating hele shaw flows a conformal mapping approach |
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