The effect of surfactants on expanding free surfaces
This paper develops a systematic theory for the flow observed in the so-called ``overflowing cylinder'' experiment. The basic phenomenon to be explained is the order of magnitude increase in the surface velocity of a slowly overflowing beaker of water that is caused by the addition of a sm...
| मुख्य लेखकों: | , , , |
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| स्वरूप: | Journal article |
| प्रकाशित: |
2001
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| _version_ | 1826288939042865152 |
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| author | Breward, C Darton, R Howell, P Ockendon, J |
| author_facet | Breward, C Darton, R Howell, P Ockendon, J |
| author_sort | Breward, C |
| collection | OXFORD |
| description | This paper develops a systematic theory for the flow observed in the so-called ``overflowing cylinder'' experiment. The basic phenomenon to be explained is the order of magnitude increase in the surface velocity of a slowly overflowing beaker of water that is caused by the addition of a small amount of soluble surfactant. We perform analyses of (i) an inviscid bulk flow in which diffusion is negligible, (ii) a hydrodynamic boundary layer in which viscous effects become important, (iii) a diffusive boundary layer where diffusion is significant, and by matching these together arrive at a coupled problem for the liquid velocity and surfactant concentration. Our model predicts a relation between surface velocity and surface concentration which is in good agreement with experiment. However a degeneracy in the boundary conditions leaves one free parameter which must be taken from experimental data. We suggest an investigation that may resolve this indeterminacy. |
| first_indexed | 2024-03-07T02:21:18Z |
| format | Journal article |
| id | oxford-uuid:a402d3a5-a211-4f12-8a8d-5dc08fa825e5 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T02:21:18Z |
| publishDate | 2001 |
| record_format | dspace |
| spelling | oxford-uuid:a402d3a5-a211-4f12-8a8d-5dc08fa825e52022-03-27T02:30:59ZThe effect of surfactants on expanding free surfacesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a402d3a5-a211-4f12-8a8d-5dc08fa825e5Mathematical Institute - ePrints2001Breward, CDarton, RHowell, POckendon, JThis paper develops a systematic theory for the flow observed in the so-called ``overflowing cylinder'' experiment. The basic phenomenon to be explained is the order of magnitude increase in the surface velocity of a slowly overflowing beaker of water that is caused by the addition of a small amount of soluble surfactant. We perform analyses of (i) an inviscid bulk flow in which diffusion is negligible, (ii) a hydrodynamic boundary layer in which viscous effects become important, (iii) a diffusive boundary layer where diffusion is significant, and by matching these together arrive at a coupled problem for the liquid velocity and surfactant concentration. Our model predicts a relation between surface velocity and surface concentration which is in good agreement with experiment. However a degeneracy in the boundary conditions leaves one free parameter which must be taken from experimental data. We suggest an investigation that may resolve this indeterminacy. |
| spellingShingle | Breward, C Darton, R Howell, P Ockendon, J The effect of surfactants on expanding free surfaces |
| title | The effect of surfactants on expanding free surfaces |
| title_full | The effect of surfactants on expanding free surfaces |
| title_fullStr | The effect of surfactants on expanding free surfaces |
| title_full_unstemmed | The effect of surfactants on expanding free surfaces |
| title_short | The effect of surfactants on expanding free surfaces |
| title_sort | effect of surfactants on expanding free surfaces |
| work_keys_str_mv | AT brewardc theeffectofsurfactantsonexpandingfreesurfaces AT dartonr theeffectofsurfactantsonexpandingfreesurfaces AT howellp theeffectofsurfactantsonexpandingfreesurfaces AT ockendonj theeffectofsurfactantsonexpandingfreesurfaces AT brewardc effectofsurfactantsonexpandingfreesurfaces AT dartonr effectofsurfactantsonexpandingfreesurfaces AT howellp effectofsurfactantsonexpandingfreesurfaces AT ockendonj effectofsurfactantsonexpandingfreesurfaces |