טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentRashed Joudat
SubjectCoarsening Dynamics for the Cahn-Hilliard Equation
DepartmentDepartment of Applied Mathematics
Supervisors Professor Amy Novick-Cohen
Professor Michail Zhitomirskii


Abstract

The Cahn-Hilliard (C-H) equation has been proposed as a model to describe the evolution of a conserved concentration field during the spontaneously phase separation of a binary fluid mixture below the critical temperature. After a mixture, in which both components are initially uniformly present in the domain under consideration, undergoes rapid cooling below the critical temperature, the homogenous state becomes unstable. As a result, phase separation occurs and the domain splits into regions which are rich in one component and poor in the other.


So, by decreasing the temperature, the system enters a non-equilibrium state, and rapidly decomposes into micro-structural regions with different phases. Each phase is characterized by a distinct composition of the individual components, in a manner which reduces the bulk chemical energy of the system. This formation of micro-structure occurs on a very fast time scale, and is called spinodal decomposition. Later the dominant length scale of the microstructure grows in a process known as a coarsening.


The purpose of this thesis is to understand coarsening phenomena which occur during phase separation rigorously and to investigate the power laws which govern the evolution of the dominant length scale. Our main goal is to find the most appropriate upper bounds for the coarsening rates and how these upper bounds depend on the parameters of the system, such as the temperature and the mean concentration.