The Casimir effect in wetting layers

For a long time, the study of thermal effects at three-dimensional (3D) short-ranged wetting transitions considered only the effect of interfacial fluctuations. We show that an entropic Casimir contribution, missed in previous treatments, produces significant effects when it is included; in particular, mean-field predictions are no longer obtained when interfacial fluctuations are ignored. The Casimir term arises from the many different microscopic configurations that correspond to a given interfacial one. By employing a coarse-graining procedure, starting from a microscopic Landau–Ginzburg–Wilson (LGW) Hamiltonian, we identify the interfacial model for 3D wetting and the exact form of the Casimir term. The Casimir contribution does not alter the Nakanishi–Fisher surface phase diagram; it significantly increases the adsorption near a first-order wetting transition and completely changes the predicted critical singularities of tricritical wetting, including the nonuniversality occurring in 3D arising from interfacial fluctuations. We illustrate how the Casimir term leads to a reappraisal of the critical singularities at wetting transitions. Lastly, this paper presents novel results about curvature effects in layers of concentrical spheres and cylinders.