Wedge filling, cone filling and the strong-fluctuation regime

Abstract

Interfacial fluctuation effects occurring at wedge- and cone-filling transitions are investigated and shown to exhibit very different characteristics. For both geometries we argue that the conditions for observing critical (continuous) filling are much less restrictive than for critical wetting, which is known to require the fine tuning of the Hamaker constants. Wedge filling is critical if the wetting binding potential does not exhibit a local maximum, whilst conic filling is critical if the line tension is negative. This latter scenario is particularly encouraging for future experimental studies. Using mean-field and effective Hamiltonian approaches, which allow for breather-mode fluctuations which translate the interface up and down the sides of the confining geometry, we are able to completely classify the possible critical behaviours (for purely thermal disorder). For the three-dimensional wedge, the interfacial fluctuations are very strong and characterized by a universal roughness critical exponent ν⊥W = 1/4 independent of the range of the forces. For the physical dimensions d = 2 and d = 3, we show that the effect of the cone geometry on the fluctuations at critical filling is to mimic the analogous interfacial behaviour occurring at critical wetting in the strong-fluctuation regime. In particular, for d = 3 and for quite arbitrary choices of the intermolecular potential, the filling height and roughness show the same critical properties as those predicted for three-dimensional critical wetting with short-ranged forces in the large-wetting-parameter (ω>2) regime.

Interfacial structure at a two-dimensional wedge filling transition: Exact results and a renormalization group study

“…For the local properties, we found a very interesting relationship between the wedge 1-point probability distribution function and the corresponding functions in the planar geometry, which can enlighten the origin of the wedge covariance. Regarding the two-point correlation functions, we found a confirmation in the scaling limit of the breather mode picture [3,4], which states that the interface is effectively infinitely stiff in the filled region and is driven by fluctuations of the wedge midpoint interfacial position, i.e., critical effects at 2D wedge filling arise simply from local translations in the height of the flat, filled interfacial region.…”

“…Fluid adsorption in wedge and cone-shaped nonplanar geometries has attracted much attention in the last few years [1][2][3][4][5]. Geometry plays an important role in the surface phase diagram, and new phase transitions as the filling transition arise.…”

Nucleation: theory and applications to protein solutions and colloidal suspensions

“…us that at coexistence a wedge with an angle θ ≤ α is filled with a macroscopic amount of the liquid phase [14]. If such wedges are present then if we start in the vapour phase and increase the chemical potential up to that at coexistence then when we have reached coexistence the wedges will have filled with liquid.…”

The non-classical nucleation of crystals: microscopic mechanisms and applications to molecular crystals, ice and calcium carbonate

“…Thus in a wedge we can have barrier-less nucleation of a fluid phase even when this fluid has a significant contact angle on the solid surface and so is far from wetting it. The disappearance of the nucleation barrier is associated with a surface phase transition called filling 155,156 . This is all for fluids in a wedge.…”