Abstract. For partially wetting, ellipsoidal colloids trapped at a fluid interface, their effective, interfacemediated interactions of capillary and fluctuation-induced type are analyzed. For contact angles different from 90• , static interface deformations arise which lead to anisotropic capillary forces that are substantial already for micrometer-sized particles. The capillary problem is solved using an efficient perturbative treatment which allows a fast determination of the capillary interaction for all distances between and orientations of two particles. Besides static capillary forces, fluctuation-induced forces caused by thermally excited capillary waves arise at fluid interfaces. For the specific choice of a spatially fixed three-phase contact line, the asymptotic behavior of the fluctuation-induced force is determined analytically for both the close-distance and the long-distance regime and compared to numerical solutions.

We calculate the effective fluctuation-induced force between spherical or disklike colloids trapped at a flat, fluid interface mediated by thermally excited capillary waves. This Casimir-type force is determined by the partition function of the system which in turn is calculated in a functional integral approach, where the restrictions on the capillary waves imposed by the colloids are incorporated by auxiliary fields. In the long-range regime the fluctuation-induced force is shown to depend sensitively on the boundary conditions imposed at the three-phase contact line between the colloids and the two fluid phases. Separating the colloid fluctuations from the fluctuations of the capillary wave field leads to competing repulsive and attractive contributions, respectively, which give rise to cancellations of the leading terms. In a second approach based on a multipole expansion of the Casimir interaction, these cancellations can be understood from the vanishing of certain multipole moments enforced by the boundary conditions. We also discuss the connection of the different types of boundary conditions to certain external fields acting on the colloids which appear to be realizable by experimental techniques such as the laser tweezer method.

Abstract. -We calculate the effective force mediated by thermally excited capillary waves between spherical or disklike colloids trapped at a fluid interface. This Casimir type interaction is shown to depend sensitively on the boundary conditions imposed at the three-phase contact line. For large distances between the colloids an unexpected cancellation of attractive and repulsive contributions is observed leading to a fluctuation force which decays algebraically very rapidly. For small separations the resulting force is rather strong and it may play an important role in two-dimensional colloid aggregation if direct van der Waals forces are weak.Introduction and synopsis. -The effective forces between rigid objects immersed in a fluctuating medium have attracted a steadily growing interest because their understanding allows one to design and tune them by choosing suitable media and boundary conditions and by varying the thermodynamic state of the medium. Possible applications range from micromechanical systems to colloidal suspensions and embedded biological macromolecules. Accordingly, these fluctuations may be the zero-temperature, long-ranged quantum fluctuations of the electromagnetic fields giving rise to the original Casimir effect [1] between flat or corrugated immersed metallic bodies [2,3]. Other examples for fluctuation induced longranged effective forces between immersed objects involve media such as bulk fluids near their critical point [4], membranes [5] or interfaces [6].In this work we investigate the latter manifestation of thermal Casimir forces for nanocolloids floating at surface-tension dominated liquid-vapor or liquid-liquid interfaces where they are effectively trapped. In the presence of charges their mutual interactions often exhibit unexpected strong and long-ranged attractions [7] inducing mesoscale pattern formation. However, these unusual patterns, which, e.g., are of interest for optical applications once they are fixated on a solid substrate, appear also for neutral nanocolloids [8]. In spite of some progress [9], the nature of these effective forces between the colloids is not yet fully understood. This pertains in particular to the role of fluctuations for these types of observations. Therefore the present effort aims at determining the fluctuation induced contribution to these forces generated by the inevitable thermally excited capillary waves of the fluid interface. As a first step the colloids are taken to be spherical or disklike and electroneutral. We shall