Critical adsorption and Casimir torque in wedges and at ridges

TL;DR

This paper investigates how geometrical structures like wedges and ridges affect fluid adsorption near critical points, calculating universal amplitudes and analyzing the critical Casimir torque within mean-field theory.

Contribution

It provides the first mean-field calculation of the temperature-dependent order parameter profile and universal adsorption amplitudes for wedges and ridges, including the Casimir torque.

Findings

Universal amplitudes Gamma_±(gamma) diverge as 1/gamma for small angles.

Gamma_±(gamma) vary linearly near gamma=pi for gamma<pi.

Gamma_±(gamma) increase exponentially as gamma approaches 2pi.

Abstract

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 mean-field theory, the temperature dependence of the order parameter profile in a wedge with opening angle gamma<pi and close to a ridge (gamma>pi) for T>T_c and T<T_c and in the presence of surface fields. For a suitably defined reduced excess adsorption Gamma_\pm(gamma,t -> +/-0)~Gamma_\pm(gamma)|t|^{beta-2nu} we compute the universal amplitudes Gamma_\pm(gamma), which diverge as Gamma_\pm(gamma ->0)~1/gamma for small opening angles, vary linearly close to gamma=pi for gamma<pi, and increase exponentially for gamma -> 2pi. There is evidence that, within 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.