Critical Casimir Forces between Spherical Particles in Fluids

Long-ranged correlations in a fluid close to its critical point $T_c$ cause distinct forces between immersed colloidal particles and the container walls. We calculate such a force and its temperature dependence for the generic case of a spherical particle located at a distance $D$ from a planar wall and find that the force attains a maximum at a temperature $T_{\max }\left(D\right)$ above $T_c$, which facilitates quantitative experimental tests. The corresponding effective pair interaction between the colloidal particles themselves, potentially leading to aggregation, is also discussed.