Modelling and simulation of thin film flow in porous media
This thesis explores the behaviour of thin film flow in both porous and non-porous media, considering both single and two-fluid systems. It establishes a comprehensive mathematical framework to describe the flow dynamics under different physical conditions, aiming to clarify the transition between t...
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| Format: | Thesis (University of Nottingham only) |
| Language: | English |
| Published: |
2025
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| Online Access: | https://eprints.nottingham.ac.uk/81296/ |
| _version_ | 1848801310961303552 |
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| author | Yakubu, Yakubu Salihu |
| author_facet | Yakubu, Yakubu Salihu |
| author_sort | Yakubu, Yakubu Salihu |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | This thesis explores the behaviour of thin film flow in both porous and non-porous media, considering both single and two-fluid systems. It establishes a comprehensive mathematical framework to describe the flow dynamics under different physical conditions, aiming to clarify the transition between these two regimes. In the case of porous media, the flow is described by the Brinkman equation, which incorporates the effects of permeability and viscous shear.
On the other hand, the Navier-Stokes equation is used to model flow in non-porous media. The model for porous media seamlessly transitions to the non-porous scenario as the permeability parameter, $\alpha $ approaches zero, ensuring a consistent approach across both domains. Likewise, the two-fluid system simplifies to a single-fluid model when the parameter $n$, which indicates the viscosity ratio of the fluid, is set to zero.
The thin-film equations are solved numerically with the Chebfun framework, known for its efficient and accurate spectral methods suitable for complex equations. The numerical results examine key parameters such as stability and flow rates and emphasize the relationship between permeability, fluid interactions, and boundary conditions. |
| first_indexed | 2025-11-14T21:05:26Z |
| format | Thesis (University of Nottingham only) |
| id | nottingham-81296 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T21:05:26Z |
| publishDate | 2025 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-812962025-07-31T04:40:29Z https://eprints.nottingham.ac.uk/81296/ Modelling and simulation of thin film flow in porous media Yakubu, Yakubu Salihu This thesis explores the behaviour of thin film flow in both porous and non-porous media, considering both single and two-fluid systems. It establishes a comprehensive mathematical framework to describe the flow dynamics under different physical conditions, aiming to clarify the transition between these two regimes. In the case of porous media, the flow is described by the Brinkman equation, which incorporates the effects of permeability and viscous shear. On the other hand, the Navier-Stokes equation is used to model flow in non-porous media. The model for porous media seamlessly transitions to the non-porous scenario as the permeability parameter, $\alpha $ approaches zero, ensuring a consistent approach across both domains. Likewise, the two-fluid system simplifies to a single-fluid model when the parameter $n$, which indicates the viscosity ratio of the fluid, is set to zero. The thin-film equations are solved numerically with the Chebfun framework, known for its efficient and accurate spectral methods suitable for complex equations. The numerical results examine key parameters such as stability and flow rates and emphasize the relationship between permeability, fluid interactions, and boundary conditions. 2025-07-31 Thesis (University of Nottingham only) NonPeerReviewed application/pdf en cc_by https://eprints.nottingham.ac.uk/81296/1/Final%20version%20of%20myThesis.pdf Yakubu, Yakubu Salihu (2025) Modelling and simulation of thin film flow in porous media. MPhil thesis, University of Nottingham. flow dynamics thin-film equations fluid mechanics porous media |
| spellingShingle | flow dynamics thin-film equations fluid mechanics porous media Yakubu, Yakubu Salihu Modelling and simulation of thin film flow in porous media |
| title | Modelling and simulation of thin film flow in porous media |
| title_full | Modelling and simulation of thin film flow in porous media |
| title_fullStr | Modelling and simulation of thin film flow in porous media |
| title_full_unstemmed | Modelling and simulation of thin film flow in porous media |
| title_short | Modelling and simulation of thin film flow in porous media |
| title_sort | modelling and simulation of thin film flow in porous media |
| topic | flow dynamics thin-film equations fluid mechanics porous media |
| url | https://eprints.nottingham.ac.uk/81296/ |