The mathematics of foam
The aim of this thesis is to derive and solve mathematical models for the flow of liquid in a foam. A primary concern is to investigate how so-called `Marangoni stresses' (i.e. surface tension gradients), generated for example by the presence of a surfactant, act to stabilise a foam. We aim to...
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| Format: | Thesis |
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University of Oxford;Mathematical Institute
1999
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| _version_ | 1797112511573524480 |
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| author | Breward, C |
| author_facet | Breward, C |
| author_sort | Breward, C |
| collection | OXFORD |
| description | The aim of this thesis is to derive and solve mathematical models for the flow of liquid in a foam. A primary concern is to investigate how so-called `Marangoni stresses' (i.e. surface tension gradients), generated for example by the presence of a surfactant, act to stabilise a foam. We aim to provide the key microscopic components for future foam modelling. We begin by describing in detail the influence of surface tension gradients on a general liquid flow, and various physical mechanisms which can give rise to such gradients. We apply the models thus devised to an experimental configuration designed to investigate Marangoni effects. Next we turn our attention to the flow in the thin liquid films (`lamellae') which make up a foam. Our methodology is to simplify the field equations (e.g. the Navier-Stokes equations for the liquid) and free surface conditions using systematic asymptotic methods. The models so derived explain the `stiffening' effect of surfactants at free surfaces, which extends considerably the lifetime of a foam. Finally, we look at the macroscopic behaviour of foam using an ad-hoc averaging of the thin film models. |
| first_indexed | 2024-03-07T08:25:09Z |
| format | Thesis |
| id | oxford-uuid:b790abc8-a47e-4069-a2ac-f04de653f032 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T08:25:09Z |
| publishDate | 1999 |
| publisher | University of Oxford;Mathematical Institute |
| record_format | dspace |
| spelling | oxford-uuid:b790abc8-a47e-4069-a2ac-f04de653f0322024-02-12T11:42:30ZThe mathematics of foamThesishttp://purl.org/coar/resource_type/c_db06uuid:b790abc8-a47e-4069-a2ac-f04de653f032Mathematical Institute - ePrintsUniversity of Oxford;Mathematical Institute1999Breward, CThe aim of this thesis is to derive and solve mathematical models for the flow of liquid in a foam. A primary concern is to investigate how so-called `Marangoni stresses' (i.e. surface tension gradients), generated for example by the presence of a surfactant, act to stabilise a foam. We aim to provide the key microscopic components for future foam modelling. We begin by describing in detail the influence of surface tension gradients on a general liquid flow, and various physical mechanisms which can give rise to such gradients. We apply the models thus devised to an experimental configuration designed to investigate Marangoni effects. Next we turn our attention to the flow in the thin liquid films (`lamellae') which make up a foam. Our methodology is to simplify the field equations (e.g. the Navier-Stokes equations for the liquid) and free surface conditions using systematic asymptotic methods. The models so derived explain the `stiffening' effect of surfactants at free surfaces, which extends considerably the lifetime of a foam. Finally, we look at the macroscopic behaviour of foam using an ad-hoc averaging of the thin film models. |
| spellingShingle | Breward, C The mathematics of foam |
| title | The mathematics of foam |
| title_full | The mathematics of foam |
| title_fullStr | The mathematics of foam |
| title_full_unstemmed | The mathematics of foam |
| title_short | The mathematics of foam |
| title_sort | mathematics of foam |
| work_keys_str_mv | AT brewardc themathematicsoffoam AT brewardc mathematicsoffoam |