Abstract:
The main content of this work is concerned with the numerical modelling of the effects of shear on microemulsions within a Ginzburg-Landau frame-work. Particular emphasis was placed on investigating shear induced transitions from an isotropic microemulsion structure to a lamellar arrangement. The project can thus be broadly split into four parts:-
1. Finding an appropriate Ginzburg-Landau model to describe a microemulsion phase.
2. Gaining knowledge about suitable numerical techniques to investigate such a model.
3. Developing code to produce equilibrium microemulsion structures in the absence of shear.
4. Further developing code to take account of the effects of shear on these equilibrium structures.
At the time of writing progress has been made on all four of these. In particular numerical methods have been developed and are described which should allow the effects of a simple planar shear on a microemulsion to be investigated. Furthermore the code developed allows the use of fast implicit methods (see chapter 4), so the investigation should be numerically efficient. As an example, our numerical methods have been applied to the well studied problem of binary liquid demixing (phase separation of for example oil and water) (see chapter 5 and the end of chapter 6).
Due to time constraints little progress has actually been made on implementing these numerical techniques in order to actually perform the investigation on the microemulsions alas. The author is hopeful that he will be able to continue working on the problem after thesis submission.
