Fluids at interfaces: Casimir effect, depletion and thermo-osmosis.

The critical Casimir effect is the long-range interaction between two planar walls in a critical fluid due to the confinement, achieved by the wall interfaces, of the critical density fluctuations. In this Thesis we provide a microscopic description of the critical Casimir force, introducing a novel density functional approximation coupled to the hierarchical reference theory of fluids. The depletion interaction is an effective attractive force arising between colloidal particles immersed in a solvent: The first prediction of this effect dates back to the seminal work by Asakura and Oosawa and has been obtained assuming that the colloidal particles were perfectly smooth spheres immersed in an ideal gas. In this Thesis we address the study of the interaction potential mediated by an ideal gas between two rough colloidal particles, as a function of the geometry, the dimension and the spatial configuration of the corrugations. When a thermal gradient is applied to a fluid at contact with a surface a stationary flow develops. This effect, referred to as thermo-osmosis, has been discovered in the late nineteenth century but successful theoretical descriptions have been up to now devised only when the fluid is a rarefied gas. In this thesis we presents a microscopic theory of thermo-osmosis based on a generalisation of linear response theory to inhomogeneous and anisotropic environments and to thermal disturbances.