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 Casimir interaction between two parallel wires and between a wire and a metall plate. The dielectric properties of the objects are described by the plasma, Drude and perfect metal models. We find that at asymptotically large separation interactions involving plasma wires and/or plates are independent of the material properties, but depend on the dc conductivity σ for Drude wires. Counterintuitively, at intermediate separations the interaction involving Drude wires can become independent of σ. At smaller separations, we compute the interaction numerically and observe an approach to the proximity approximation.Effective interactions between nanowires and nanotubes have attracted lots of attention due to their growing applications in micro-and nanomechanical systems [1][2][3]. The knowledge of the interactions between single walled carbon nanotubes (SWCNT) with different chirality and hence electromagnetic response is important to separate a polydisperse solution of SWCNT in fractions of equal chirality [4]. Under many circumstances, van der Waals or Casimir forces are the dominant interaction and hence a precise understanding of them is needed. Furthermore, cylindrical shapes are important for precision Casimir force measurements, in comparison to spheres, because of the larger effective area of interaction [5,6]. Approximations of the Casimir force between cylinders and plates [6] have shown that the temperature dependence varies based on the description of the material properties. Thus there is a need for exact calculations of the Casimir force for cylindrical shapes taking into account realistic material response.It has been demonstrated that Casimir interactions strongly depend on the combined effects of shape and material properties, see, e.g., [7,8]. The interplay is particularly strong for quasi one-dimensional conducting materials due to strongly anisotropic collective charge fluctuations. Indeed, for two parallel perfectly conducting wires of distance d the retarded interaction energy per length is E/L ∼ c/d 2 , apart from a logarithmic factor [9]. It decays only slowly compared to the retarded interaction E/L ∼ cR 4 /d 6 between insulating cylinders that do not support collective fluctuations. Most studies of interactions between one-dimensional systems over a wide range of separations concentrate on these two situations. However, low dimensionality in combination with finite conductivity and plasmon excitations should give rise to interesting new effects that might be probed experimentally using, e.g., the coupling to mechanical oscillation modes. The often employed technique for these effects, the proximity force approximation (PFA) cannot capture the correlations of shape and material response since it is based on the interaction between planar surfaces. There have been attempts to compute the van der Waals in-teraction between cylinders (and plates) for particular frequency dependent permittivities [9][10][11][12][13][14][15]. However, the interplay between shape and material effects ...

We study the effective interaction between two ellipsoidal particles at the interface of two fluid phases which are mediated by thermal fluctuations of the interface. In this system the restriction of the long-ranged interface fluctuations by particles gives rise to fluctuation-induced forces which are equivalent to interactions of Casimir type and which are anisotropic in the interface plane. Since the position and the orientation of the colloids with respect to the interface normal may also fluctuate, this system is an example of the Casimir effect with fluctuating boundary conditions. In the approach taken here, the Casimir interaction is rewritten as the interaction between fluctuating multipole moments of an auxiliary charge-density-like field defined on the area enclosed by the contact lines. These fluctuations are coupled to fluctuations of multipole moments of the contact line position (due to the possible position and orientational fluctuations of the colloids). We obtain explicit expressions for the behavior of the Casimir interaction at large distances for arbitrary ellipsoid aspect ratios. If colloid fluctuations are suppressed, the Casimir interaction at large distances is isotropic, attractive, and long ranged (double logarithmic in the distance). If, however, colloid fluctuations are included, the Casimir interaction at large distances changes to a power law in the inverse distance and becomes anisotropic. The leading power is 4 if only vertical fluctuations of the colloid center are allowed, and it becomes 8 if also orientational fluctuations are included.

A recently introduced numerical scheme for calculating self-diffusion coefficients of solid objects embedded in lipid bilayer membranes is extended to enable calculation of hydrodynamic interactions between multiple objects. The method is used to validate recent analytical predictions by Oppenheimer and Diamant [Biophys. J. 96, 3041 2009] related to the coupled diffusion of membrane embedded proteins and is shown to converge to known near-field lubrication results as objects closely approach one another; however, the present methodology also applies outside of the limiting regimes where analytical results are available. Multiple different examples involving pairs of disk-like objects with various constraints imposed on their relative motions demonstrate the importance of hydrodynamic interactions in the dynamics of proteins and lipid domains on membrane surfaces. It is demonstrated that the relative change in self-diffusion of a membrane embedded object upon perturbation by a similar proximal solid object displays a maximum for object sizes comparable to the Saffman-Delbrück length of the membrane.

We investigate the Casimir interaction between two parallel metallic cylinders and between a metallic cylinder and plate. The material properties of the metallic objects are implemented by the plasma, Drude and perfect metal model dielectric functions. We calculate the Casimir interaction numerically at all separation distances and analytically at large separations. The large-distance asymptotic interaction between one plasma cylinder parallel to another plasma cylinder or plate does not depend on the material properties, but for a Drude cylinder it depends on the dc conductivity σ. At intermediate separations, for plasma cylinders the asymptotic interaction depends on the plasma wave length λp while for Drude cylinders the Casimir interaction can become independent of the material properties. We confirm the analytical results by the numerics and show that at short separations, the numerical results approach the proximity force approximation.

We develop the scattering formalism to calculate the interaction between colloidal particles trapped at a fluid interface. Since, in addition to the interface, the colloids may also fluctuate in this system, we implement the fluctuation of the boundaries into the scattering formalism and investigate how the interaction between colloids is modified by their fluctuations. This general method can be applied to any number of colloids with various geometries at an interface. We apply the formalism derived in this work to a system of spherical colloids at the interface between two fluid phases. For two spherical colloids, this method very effectively reproduces the previous known results. For three particles we find analytical expressions for the large separation asymptotic energies and numerically calculate the Casimir interaction at all separations. Our results show an interesting three body effect for fixed and fluctuating colloids. While the three body effect strengthens the attractive interaction between fluctuating colloids, it diminishes the attractive force between colloids fixed at an interface.

We study the Casimir interaction between a metallic cylindrical wire and a metallic spherical particle by employing the scattering formalism. At large separations, we derive the asymptotic form of the interaction. In addition, we find the interaction between a metallic wire and an isotropic atom, both in the non-retarded and retarded limits. We identify the conditions under which the asymptotic Casimir interaction does not depend on the material properties of the metallic wire and the particle. Moreover, we compute the exact Casimir interaction between the particle and the wire numerically. We show that there is a complete agreement between the numerics and the asymptotic energies at large separations. For short separations, our numerical results show good agreement with the proximity force approximation.

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