  If two ore 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 analogues 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-epsilon are compared with
corresponding Monte-Carlo results in d=3 and their quantitative effect on the
thickness of critical wetting layers and on force measurements is discussed.
