Interfacial elastic fingering in Hele-Shaw cells: a weakly nonlinear study
We study a variant of the classic viscous fingering instability in Hele-Shaw cells where the interface separating the fluids is elastic, and presents a curvature-dependent bending rigidity. By employing a second-order mode-coupling approach we investigate how the elastic nature of the interface infl...
| Main Authors: | , , |
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| Format: | Journal article |
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American Physical Society
2013
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| _version_ | 1797101864728133632 |
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| author | Carvalho, G Miranda, J Gadelha, H |
| author_facet | Carvalho, G Miranda, J Gadelha, H |
| author_sort | Carvalho, G |
| collection | OXFORD |
| description | We study a variant of the classic viscous fingering instability in Hele-Shaw cells where the interface separating the fluids is elastic, and presents a curvature-dependent bending rigidity. By employing a second-order mode-coupling approach we investigate how the elastic nature of the interface influences the morphology of emerging interfacial patterns. This is done by focusing our attention on a conventionally stable situation in which the fluids involved have the same viscosity. In this framework, we show that the inclusion of nonlinear effects plays a crucial role in inducing sizable interfacial instabilities, as well as in determining the ultimate shape of the pattern-forming structures. Particularly, we have found that the emergence of either narrow or wide fingers can be regulated by tuning a rigidity fraction parameter. Our weakly nonlinear findings reinforce the importance of the so-called curvature weakening effect, which favors the development of fingers in regions of lower rigidity. |
| first_indexed | 2024-03-07T05:57:58Z |
| format | Journal article |
| id | oxford-uuid:eb2d6dab-97ab-4f1b-9fda-4ea4d939d50e |
| institution | University of Oxford |
| last_indexed | 2024-03-07T05:57:58Z |
| publishDate | 2013 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | oxford-uuid:eb2d6dab-97ab-4f1b-9fda-4ea4d939d50e2022-03-27T11:07:43ZInterfacial elastic fingering in Hele-Shaw cells: a weakly nonlinear studyJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:eb2d6dab-97ab-4f1b-9fda-4ea4d939d50eMathematical Institute - ePrintsAmerican Physical Society2013Carvalho, GMiranda, JGadelha, HWe study a variant of the classic viscous fingering instability in Hele-Shaw cells where the interface separating the fluids is elastic, and presents a curvature-dependent bending rigidity. By employing a second-order mode-coupling approach we investigate how the elastic nature of the interface influences the morphology of emerging interfacial patterns. This is done by focusing our attention on a conventionally stable situation in which the fluids involved have the same viscosity. In this framework, we show that the inclusion of nonlinear effects plays a crucial role in inducing sizable interfacial instabilities, as well as in determining the ultimate shape of the pattern-forming structures. Particularly, we have found that the emergence of either narrow or wide fingers can be regulated by tuning a rigidity fraction parameter. Our weakly nonlinear findings reinforce the importance of the so-called curvature weakening effect, which favors the development of fingers in regions of lower rigidity. |
| spellingShingle | Carvalho, G Miranda, J Gadelha, H Interfacial elastic fingering in Hele-Shaw cells: a weakly nonlinear study |
| title | Interfacial elastic fingering in Hele-Shaw cells: a weakly nonlinear study |
| title_full | Interfacial elastic fingering in Hele-Shaw cells: a weakly nonlinear study |
| title_fullStr | Interfacial elastic fingering in Hele-Shaw cells: a weakly nonlinear study |
| title_full_unstemmed | Interfacial elastic fingering in Hele-Shaw cells: a weakly nonlinear study |
| title_short | Interfacial elastic fingering in Hele-Shaw cells: a weakly nonlinear study |
| title_sort | interfacial elastic fingering in hele shaw cells a weakly nonlinear study |
| work_keys_str_mv | AT carvalhog interfacialelasticfingeringinheleshawcellsaweaklynonlinearstudy AT mirandaj interfacialelasticfingeringinheleshawcellsaweaklynonlinearstudy AT gadelhah interfacialelasticfingeringinheleshawcellsaweaklynonlinearstudy |