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Yakubu, Yakubu Salihu (2025) Modelling and simulation of thin film flow in porous media. MPhil thesis, University of Nottingham.

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Abstract

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.

Item Type:	Thesis (University of Nottingham only) (MPhil)
Supervisors:	Icardi, Matteo Anna, Kalogirou
Keywords:	flow dynamics, thin-film equations, fluid mechanics, porous media
Subjects:	Q Science > QA Mathematics > QA801 Analytic mechanics Q Science > QC Physics > QC170 Atomic physics. Constitution and properties of matter
Faculties/Schools:	UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID:	81296
Depositing User:	Yakubu, Salihu
Date Deposited:	31 Jul 2025 04:40
Last Modified:	31 Jul 2025 04:40
URI:	https://eprints.nottingham.ac.uk/id/eprint/81296

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