The evolution of a slender non-axisymmetric drop in an extensional flow
An asymptotic method for analysing slender non-axisymmetric drops, bubbles and jets in a general straining flow is developed. The method relies on the slenderness of the geometry to reduce the three-dimensional equations to a sequence of weakly coupled, quasi-two-dimensional Stokes flow problems for...
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| Format: | Journal article |
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2004
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| _version_ | 1826300844814893056 |
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| author | Howell, P Siegel, M |
| author_facet | Howell, P Siegel, M |
| author_sort | Howell, P |
| collection | OXFORD |
| description | An asymptotic method for analysing slender non-axisymmetric drops, bubbles and jets in a general straining flow is developed. The method relies on the slenderness of the geometry to reduce the three-dimensional equations to a sequence of weakly coupled, quasi-two-dimensional Stokes flow problems for the cross-sectional evolution. Exact solution techniques for the flow outside a bubble in two-dimensional Stokes flow are generalised to solve for the transverse flow field, allowing large non-axisymmetric deformations to be described. A generalisation to the case where the interior contains a slightly viscous fluid is also presented. Our method is used to compute steady non-axisymmetric solution branches for inviscid bubbles and slightly viscous drops. We also present unsteady numerical solutions showing how the eccentricity of the cross-section adjusts to a non-axisymmetric external flow. Finally, we use our theory to investigate how the pinch-off of a jet of relatively inviscid fluid is affected by a two-dimensional straining cross-flow. |
| first_indexed | 2024-03-07T05:23:19Z |
| format | Journal article |
| id | oxford-uuid:dfadf369-0990-4536-97da-e8dee687575c |
| institution | University of Oxford |
| last_indexed | 2024-03-07T05:23:19Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | oxford-uuid:dfadf369-0990-4536-97da-e8dee687575c2022-03-27T09:41:12ZThe evolution of a slender non-axisymmetric drop in an extensional flowJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:dfadf369-0990-4536-97da-e8dee687575cMathematical Institute - ePrints2004Howell, PSiegel, MAn asymptotic method for analysing slender non-axisymmetric drops, bubbles and jets in a general straining flow is developed. The method relies on the slenderness of the geometry to reduce the three-dimensional equations to a sequence of weakly coupled, quasi-two-dimensional Stokes flow problems for the cross-sectional evolution. Exact solution techniques for the flow outside a bubble in two-dimensional Stokes flow are generalised to solve for the transverse flow field, allowing large non-axisymmetric deformations to be described. A generalisation to the case where the interior contains a slightly viscous fluid is also presented. Our method is used to compute steady non-axisymmetric solution branches for inviscid bubbles and slightly viscous drops. We also present unsteady numerical solutions showing how the eccentricity of the cross-section adjusts to a non-axisymmetric external flow. Finally, we use our theory to investigate how the pinch-off of a jet of relatively inviscid fluid is affected by a two-dimensional straining cross-flow. |
| spellingShingle | Howell, P Siegel, M The evolution of a slender non-axisymmetric drop in an extensional flow |
| title | The evolution of a slender non-axisymmetric drop in an extensional flow |
| title_full | The evolution of a slender non-axisymmetric drop in an extensional flow |
| title_fullStr | The evolution of a slender non-axisymmetric drop in an extensional flow |
| title_full_unstemmed | The evolution of a slender non-axisymmetric drop in an extensional flow |
| title_short | The evolution of a slender non-axisymmetric drop in an extensional flow |
| title_sort | evolution of a slender non axisymmetric drop in an extensional flow |
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