Stretching of heated threads with temperature-dependent viscosity: Asymptotic analysis
We consider the stretching of a thin cylindrical thread with viscosity that depends on temperature. The thread is pulled with a prescribed force while receiving continuous heating from an external axially nonuniform heater. We use the canonical equations derived by Huang et al. (2007) and consider t...
| Main Authors: | , , , |
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| Format: | Conference item |
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2007
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| _version_ | 1826259363770138624 |
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| author | Howell, P Wylie, J Huang, H Miura, R |
| author_facet | Howell, P Wylie, J Huang, H Miura, R |
| author_sort | Howell, P |
| collection | OXFORD |
| description | We consider the stretching of a thin cylindrical thread with viscosity that depends on temperature. The thread is pulled with a prescribed force while receiving continuous heating from an external axially nonuniform heater. We use the canonical equations derived by Huang et al. (2007) and consider the limit of large dimensionless heating rate. We show that the asymptotic solution depends only on the local properties of the heating near its maximal heating value. We derive a uniformly valid asymptotic solution for the shape and the temperature profiles during the stretching process. We use a criterion to determine when breaking will occur and derive simple analytical expressions for the shape at breaking that clearly show the influence of heating strength and the degree of localization of the heating. The asymptotic shape profiles give good agreement with numerical simulations. These results are applied to the formation of glass microelectrodes. |
| first_indexed | 2024-03-06T18:48:40Z |
| format | Conference item |
| id | oxford-uuid:0f6ac2d9-f999-4239-a9b4-91275b0676fe |
| institution | University of Oxford |
| last_indexed | 2024-03-06T18:48:40Z |
| publishDate | 2007 |
| record_format | dspace |
| spelling | oxford-uuid:0f6ac2d9-f999-4239-a9b4-91275b0676fe2022-03-26T09:51:08ZStretching of heated threads with temperature-dependent viscosity: Asymptotic analysisConference itemhttp://purl.org/coar/resource_type/c_5794uuid:0f6ac2d9-f999-4239-a9b4-91275b0676feSymplectic Elements at Oxford2007Howell, PWylie, JHuang, HMiura, RWe consider the stretching of a thin cylindrical thread with viscosity that depends on temperature. The thread is pulled with a prescribed force while receiving continuous heating from an external axially nonuniform heater. We use the canonical equations derived by Huang et al. (2007) and consider the limit of large dimensionless heating rate. We show that the asymptotic solution depends only on the local properties of the heating near its maximal heating value. We derive a uniformly valid asymptotic solution for the shape and the temperature profiles during the stretching process. We use a criterion to determine when breaking will occur and derive simple analytical expressions for the shape at breaking that clearly show the influence of heating strength and the degree of localization of the heating. The asymptotic shape profiles give good agreement with numerical simulations. These results are applied to the formation of glass microelectrodes. |
| spellingShingle | Howell, P Wylie, J Huang, H Miura, R Stretching of heated threads with temperature-dependent viscosity: Asymptotic analysis |
| title | Stretching of heated threads with temperature-dependent viscosity: Asymptotic analysis |
| title_full | Stretching of heated threads with temperature-dependent viscosity: Asymptotic analysis |
| title_fullStr | Stretching of heated threads with temperature-dependent viscosity: Asymptotic analysis |
| title_full_unstemmed | Stretching of heated threads with temperature-dependent viscosity: Asymptotic analysis |
| title_short | Stretching of heated threads with temperature-dependent viscosity: Asymptotic analysis |
| title_sort | stretching of heated threads with temperature dependent viscosity asymptotic analysis |
| work_keys_str_mv | AT howellp stretchingofheatedthreadswithtemperaturedependentviscosityasymptoticanalysis AT wyliej stretchingofheatedthreadswithtemperaturedependentviscosityasymptoticanalysis AT huangh stretchingofheatedthreadswithtemperaturedependentviscosityasymptoticanalysis AT miurar stretchingofheatedthreadswithtemperaturedependentviscosityasymptoticanalysis |