CASIMIR FORCES BETWEEN SPHERICAL-PARTICLES IN A CRITICAL FLUID AND CONFORMAL-INVARIANCE

Mesoscopic particles immersed in a critical fluid experience long-range Casimir forces due to critical fluctuations. Using field-theoretical methods, we investigate the Casimir interaction between two spherical particles and between a single particle and a planar boundary of the fluid. We exploit the conformal symmetry at the critical point to map both cases onto a highly symmetric geometry where the fluid is bounded by two concentric spheres with radii R- and R+. In this geometry the singular part of the free energy scrF only depends upon the ratio R-/R+, and the stress tensor, which we use to calculate scrF, has a particularly simple form. Different boundary conditions (surface universality classes) are considered, which either break or preserve the order-parameter symmetry. We also consider profiles of thermodynamic densities in the presence of two spheres. Explicit results are presented for an ordinary critical point to leading order in =4-d and, in the case of preserved symmetry, for the Gaussian model in arbitrary spatial dimension d. Fundamental short-distance properties, such as profile behavior near a surface or the behavior if a sphere has a small radius, are discussed and verified. The relevance for colloidal solutions is pointed out. © 1995 The American Physical Society.