International journal of modern physics. B, Condensed matter physics, statistical physics, applied physics vol:8 issue:3 pages:309-345
A review is presented of recent theoretical advances on a fundamental problem in statistical mechanics that concerns the three-phase contact line L and its tension tau near a wetting phase transition. In addition to answering the intriguing question whether or not L and tau vanish at wetting, recent work has also revealed that tau displays universal singular behavior, reflecting critical phenomena associated with the wetting transition. Three factors are crucial for determining the fate of L and tau at wetting: the order of the wetting transition, the range of the intermolecular forces, and the upper critical dimension d(u), above which mean-field theory holds and below which fluctuations dominate. For most systems studied experimentally, d(u) < 3, so that the mean-field predictions should be correct in d = 3. In the thermal fluctuation regime, for d < d(u), hyperscaling predicts the value 2(d - 2)/(d - 1) for the critical exponent of tau(theta), in the limit that the contact angle theta approaches 0.