Critical adsorption and Casimir torque in wedges and at ridges

Geometrical structures of confining surfaces profoundly influence the adsorption of fluids upon approaching a critical point T(c) in their bulk phase diagram, i.e., for t= (T- T(c) ) / T(c) -->+/-0 . Guided by general scaling considerations, we calculate, within the mean-field theory, the temperature dependence of the order parameter profile in a wedge with opening angle gammapi) for T>< T(c) and in the presence of surface fields. For a suitably defined reduced excess adsorption Gamma (+/-) (gamma,t-->+/-0) approximately Gamma (+/-) (gamma) mid R:tmid R:(beta-2nu) we compute the universal amplitudes Gamma (+/-) (gamma) , which diverge as Gamma (+/-) (gamma-->0) approximately 1/gamma for small opening angles, vary linearly close to gamma=pi for gamma2pi . There is evidence that, within the mean-field theory, the ratio Gamma (+) (gamma) / Gamma (-) (gamma) is independent of gamma . We also discuss the critical Casimir torque acting on the sides of the wedge as a function of the opening angle and temperature.