The effect of polar lipids on tear film dynamics
In this paper we present a mathematical model describing the effect of polar lipids on the evolution of a precorneal tear film, with the aim of explaining the interesting experimentally observed phenomenon that the tear film continues to move upwards even after the upper eyelid has become statio...
| Main Authors: | , , |
|---|---|
| Format: | Journal article |
| Published: |
2009
|
| _version_ | 1797052177002266624 |
|---|---|
| author | Aydemir, E Breward, C Witelski, T |
| author_facet | Aydemir, E Breward, C Witelski, T |
| author_sort | Aydemir, E |
| collection | OXFORD |
| description | In this paper we present a mathematical model describing the effect of polar lipids on the evolution of a precorneal tear film, with the aim of explaining the interesting experimentally observed phenomenon that the tear film continues to move upwards even after the upper eyelid has become stationary. The polar lipid is an insoluble surface species that locally alters the surface tension of the tear film. In the lubrication limit, the model reduces to two coupled nonlinear partial differential equations for the film thickness and the concentration of lipid. We solve the system numerically and observe that the presence of the lipid causes an increase in flow of liquid up the eye. We further exploit the size of the parameters in the problem to explain the initial evolution of the system. |
| first_indexed | 2024-03-06T18:28:50Z |
| format | Journal article |
| id | oxford-uuid:08ec4afb-c817-4445-bcea-b691b661e792 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T18:28:50Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | oxford-uuid:08ec4afb-c817-4445-bcea-b691b661e7922022-03-26T09:15:34ZThe effect of polar lipids on tear film dynamicsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:08ec4afb-c817-4445-bcea-b691b661e792Mathematical Institute - ePrints2009Aydemir, EBreward, CWitelski, T In this paper we present a mathematical model describing the effect of polar lipids on the evolution of a precorneal tear film, with the aim of explaining the interesting experimentally observed phenomenon that the tear film continues to move upwards even after the upper eyelid has become stationary. The polar lipid is an insoluble surface species that locally alters the surface tension of the tear film. In the lubrication limit, the model reduces to two coupled nonlinear partial differential equations for the film thickness and the concentration of lipid. We solve the system numerically and observe that the presence of the lipid causes an increase in flow of liquid up the eye. We further exploit the size of the parameters in the problem to explain the initial evolution of the system. |
| spellingShingle | Aydemir, E Breward, C Witelski, T The effect of polar lipids on tear film dynamics |
| title | The effect of polar lipids on tear film dynamics |
| title_full | The effect of polar lipids on tear film dynamics |
| title_fullStr | The effect of polar lipids on tear film dynamics |
| title_full_unstemmed | The effect of polar lipids on tear film dynamics |
| title_short | The effect of polar lipids on tear film dynamics |
| title_sort | effect of polar lipids on tear film dynamics |
| work_keys_str_mv | AT aydemire theeffectofpolarlipidsontearfilmdynamics AT brewardc theeffectofpolarlipidsontearfilmdynamics AT witelskit theeffectofpolarlipidsontearfilmdynamics AT aydemire effectofpolarlipidsontearfilmdynamics AT brewardc effectofpolarlipidsontearfilmdynamics AT witelskit effectofpolarlipidsontearfilmdynamics |