Casimir Interaction of Spheres in a Fluid at the Critical Point

Critical fluctuations give rise to long-range Casimir forces between inert uncharged particles immersed in a fluid at the critical point. With simple, exact arguments utilizing conformal invariance, we analyze the Casimir force between two spheres in an unbounded critical fluid, and between a single sphere and the planar boundary of a semi-infinite fluid. The Casimir force has a much longer range than the van der Waals force and should lead to aggregation of colloidal particles.