Theoretical and numerical study of the Cahn-Hilliard equation

Spinodal decomposition is one of the mechanisms involved in the phase separation dynamics of a mixture of two components, in which a mixed, unstable state decays and therefore enabling the separation between the different components of the mixture.
The mathematical model behind spinodal decomposition is famously known as the Cahn-Hilliard equation, a diffusive differential equation that allows to describe this separation of a binary mixture. This model can be obtained either by classic thermodynamics or by establishing a Langevin equation for a set of semi-microscopic variables. It is crucial to understand this model, as it allows to explain other types of mechanisms related to phase transitions such as dewetting, which is typically characterized by the retraction of a fluid that is covering a non-wettable surface, although it can happen in the interface
between other types of systems (solid-solid, solid-liquid, etc.).
In this thesis, a theoretical and numerical study of the Cahn-Hilliard equation has been performed, showing how the size of the formed domains can be studied through magnitudes like the correlation function and the structure factor in order to verify the existent theories on domain growth. Moreover, some of these techniques are applied to a dewetting experiment in order to look for similarities in the processes in a qualitative way.