| Summary: | 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.
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