Mathematical modelling of a viscida network
We develop a general model to describe a network of interconnected thin viscous sheets, or viscidas, which evolve under the action of surface tension. A junction between two viscidas is analysed by considering a single viscida containing a smoothed corner, where the centreline angle changes rapidly...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Cambridge University Press
2019
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| _version_ | 1826283451846754304 |
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| author | Mavroyiakoumou, C Griffiths, I Howell, P |
| author_facet | Mavroyiakoumou, C Griffiths, I Howell, P |
| author_sort | Mavroyiakoumou, C |
| collection | OXFORD |
| description |
We develop a general model to describe a network of interconnected thin viscous sheets, or viscidas, which evolve under the action of surface tension. A junction between two viscidas is analysed by considering a single viscida containing a smoothed corner, where the centreline angle changes rapidly, and then considering the limit as the smoothing tends to zero. The analysis is generalized to derive a simple model for the behaviour at a junction between an arbitrary number of viscidas, which is then coupled to the governing equation for each viscida. We thus obtain a general theory, consisting of partial differential equations and algebraic conservation laws, for a system of viscidas connected at junctions. This approach provides a framework to understand the fabrication of microstructured optical fibres containing closely spaced holes separated by interconnected thin viscous struts. We show sample solutions for simple networks with and or 3. We also demonstrate that there is no uniquely defined junction model to describe interconnections between viscidas of different thicknesses. |
| first_indexed | 2024-03-07T00:59:06Z |
| format | Journal article |
| id | oxford-uuid:891ab04e-5f0b-4058-8a34-eb4077532428 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:59:06Z |
| publishDate | 2019 |
| publisher | Cambridge University Press |
| record_format | dspace |
| spelling | oxford-uuid:891ab04e-5f0b-4058-8a34-eb40775324282022-03-26T22:22:10ZMathematical modelling of a viscida networkJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:891ab04e-5f0b-4058-8a34-eb4077532428EnglishSymplectic Elements at OxfordCambridge University Press2019Mavroyiakoumou, CGriffiths, IHowell, P We develop a general model to describe a network of interconnected thin viscous sheets, or viscidas, which evolve under the action of surface tension. A junction between two viscidas is analysed by considering a single viscida containing a smoothed corner, where the centreline angle changes rapidly, and then considering the limit as the smoothing tends to zero. The analysis is generalized to derive a simple model for the behaviour at a junction between an arbitrary number of viscidas, which is then coupled to the governing equation for each viscida. We thus obtain a general theory, consisting of partial differential equations and algebraic conservation laws, for a system of viscidas connected at junctions. This approach provides a framework to understand the fabrication of microstructured optical fibres containing closely spaced holes separated by interconnected thin viscous struts. We show sample solutions for simple networks with and or 3. We also demonstrate that there is no uniquely defined junction model to describe interconnections between viscidas of different thicknesses. |
| spellingShingle | Mavroyiakoumou, C Griffiths, I Howell, P Mathematical modelling of a viscida network |
| title | Mathematical modelling of a viscida network |
| title_full | Mathematical modelling of a viscida network |
| title_fullStr | Mathematical modelling of a viscida network |
| title_full_unstemmed | Mathematical modelling of a viscida network |
| title_short | Mathematical modelling of a viscida network |
| title_sort | mathematical modelling of a viscida network |
| work_keys_str_mv | AT mavroyiakoumouc mathematicalmodellingofaviscidanetwork AT griffithsi mathematicalmodellingofaviscidanetwork AT howellp mathematicalmodellingofaviscidanetwork |