Critical Point Wedge Filling

TL;DR

This study uses microscopic density functional theory to investigate wedge filling transitions, revealing that the nature of the transition depends on temperature proximity to the critical point, with implications for universality and experimental observation.

Contribution

It demonstrates the conditions under which wedge filling transitions are first-order or continuous, and confirms macroscopic predictions with microscopic calculations.

Findings

Filling transition is first-order far from critical point.

Transition becomes continuous near the critical temperature.

Critical exponent for meniscus growth is approximately 0.46.

Abstract

We present results of a microscopic density functional theory study of wedge filling transitions, at a right-angle wedge, in the presence of dispersion-like wall-fluid forces. Far from the corner the walls of the wedge show a first-order wetting transition at a temperature $T_w$ which is progressively closer to the bulk critical temperature $T_c$ as the strength of the wall forces is reduced. In addition, the meniscus formed near the corner undergoes a filling transition at a temperature $T_f<T_w$, the value of which is found to be in excellent agreement with macroscopic predictions. We show that the filling transition is {\it first-order} if it occurs far from the critical point but is {\it continuous} if $T_f$ is close to $T_c$ even though the walls still show first-order wetting behaviour. For this continuous transition the distance of the meniscus from the apex grows as $\ell_w\approx (T_f-T)^{-\beta_w}$ with critical exponent $\beta_w\approx 0.46 \pm 0.05$ in good agreement with the phenomenological effective Hamiltonian prediction. Our results suggest that critical filling transitions, with accompanying large scale universal interfacial fluctuation effects, are more generic than thought previously, and are experimentally accessible.