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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.
Burkhardt et al. (Mon,) studied this question.