This, to a certain extent previous, area of research is in the field of wetting transitions and interfacial fluctuation effects. The idea is to attempt to gain a better understanding of the interplay between internal properties of an interface (surface tension, surface stiffness, roughness) and external effects, such as binding forces or geometry. Ultimately, the hope is that the knowledge gained can be utilised in novel device manufacture or chemical processes on micro- or even nano-scales. This latter area is often referred to as microfluidics; the device as a "lab-on-a-chip". The development of dynamics (time-dependence) for such theories is also highly desirable.
My PhD thesis [T] and the papers I completed during my time at imperial college concerned the effect of surface geometry, in particular the linear wedge, on the wetting transition. We were able to show in 2D how the wedge exhibits a filling transition prior to the wetting transition and is dependent on the wedge angle [1]. The solution can also be extended to solving for correlation functions, which show a disorder point [4], and where the medium is random in character [3]. These calculations led to the formulation of the two-dimensional case in terms of simple invariance laws [8]. This work has been extended greatly since by Prof. Parry and co-workers.
In three dimensions there are two possibilities, a linear wedge or a cone [5]. The former case is the most interesting as the fluctuations are highly anisotropic and lead to a dimensional reduction. This enables novel critical exponents to be computed [2,6] that have since been verified by extensive Monte Carlo simulations.
The effects may also be examined within the Ising model. For this model exact answers are available for surface energies and this enables detailed predictions to be made for Monte Carlo results [7, 9]. We were recently able to extend these results to the case for a triangular lattice where the corresponding surface energies were formly unknown [10, 11].
We have also investigated a novel form of structural transition, where we force an interface to lie at an angle across an Ising strip. A phase transition is induced by introducing a line of defect bonds running parallel to the walls of such a strip. Competition now emerges as the interface may now pin to the defect line rather than take the shortest path across the strip. We according named this the GZZ (Geodesic-to-ZigZag) transition [13]. This transition can also be investigated using a Solid-on-Solid calculation [12], which may then be extended to include dynamics [14]. Finally the unusual mechanism for the transition (a move from pole-dominated to saddle-dominated behaviour in the partition function integral) [15] can be exploited to compute exact finite size effects [16].