Understanding the behaviour of liquids is of great importance for physics, chemistry, biology and technology. However, the liquid state remains, in some sense, the most mysterious form of matter. The challenge to the theorist is to predict from the intermolecular forces the microstructure and macroscopic properties (e.g. heat capacity, viscosity, surface tension) of the system. While there has been enormous progress since the pioneering work of van der Waals, there remain many open questions, particularly regarding interfacial phenomena and nonequilibrium states.

When a fluid is subject to an external potential field, then the density becomes spatially varying. The classical density functional theory (DFT) is an exact framework that enables studies of inhomogeneous fluids. However, for interacting systems exact solutions are not generally available. The theoretical challenge is therefore to explore and develop useful approximations that capture the important physics.

In recent work we have developed a state-of-the-art density functional approximation to treat systems of particles with attractive interactions, going beyond previous mean-field theories of inhomogeneous fluids. This provides not only a useful tool for future studies, but also provides fundamental insight into interfacial phenomena, such as the nature of the liquid-vapour interface.

In 1914 Ornstein and Zernike proposed a theory to describe the phenomenon of critical opalescence in fluids. The Ornstein-Zernike (OZ) equation central to their approach has since become an essential part of many liquid state theories. When the exact OZ equation is supplemented by a closure approximation, then one obtains an integral equation to determine the pair correlation functions in a liquid. As with DFT, the aim of the theorist is to construct a physically correct approximate closure for a given problem.

In recent work we have used the inhomogeneous OZ equation to investigate nonuniform fluids in external fields and strengthened the connections between DFT and liquid state integral equation theory.

The fundamental principles of classical statistical mechanics are very well established and provide a formal route to calculate measurable macroscopic quantities (e.g. pressure) from microscopic information. However, in practice one (almost always) has to resort to some kind of approximation scheme. This usually requires both physical intuition and creativity to guide the mathematics. Current projects in this direction concern transformation between different statistical ensembles and improvements to standard mean-field theories of inhomogeneous liquids.

In statistical mechanics one can calculate physical quantities in a variety of ensembles. The choice which corresponds most closely to Newtonian dynamics is the micro canonical ensemble for which N, V and E are fixed. However, micro-canonical calculations are extremely difficult for any interacting system of interest. The canonical ensemble is somewhat easier and uses the temperature, rather than the energy, as a control parameter. Even more convenient in practice, is the grand canonical ensemble, which employs the chemical potential as a control parameter.

For finite-size systems one observes ensemble differences and these can be very important for systems under confinement (e.g. particles in a cavity). This motivates studies of ensemble transformation.