Casimir forces in binary liquid mixtures

If two or more bodies are immersed in a critical fluid, critical fluctuations of the order parameter generate long-ranged forces between these bodies. Due to the underlying mechanism these forces are close analogs of the well-known Casimir forces in electromagnetism. For the special case of a binary liquid mixture near its critical demixing transition, confined to a simple parallel plate geometry, it is shown that the corresponding critical Casimir forces can be of the same order of magnitude as the dispersion (van der Waals) forces between the plates. In wetting experiments or by direct measurements with an atomic force microscope, the resulting modification of the usual dispersion forces in the critical regime should therefore be easily detectable. Analytical estimates for the Casimir amplitudes $\Delta$ in $d=4\mathrm{}-\varepsilon$ are compared with corresponding Monte Carlo results in $d=3\mathrm{}$, and their quantitative effect on the thickness of critical wetting layers and on force measurements is discussed.