Wedge filling, cone filling and the strong-fluctuationregime

Abstract

Interfacial fluctuation effects occurring at wedge- and cone-fillingtransitions are investigated and shown to exhibit very differentcharacteristics. For both geometries we argue that the conditionsfor observing critical (continuous) filling are much lessrestrictive than for critical wetting, which is known to require thefine tuning of the Hamaker constants. Wedge filling is critical ifthe 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 futureexperimental studies.Using mean-field and effective Hamiltonian approaches, which allowfor breather-mode fluctuations which translate the interface up anddown the sides of the confining geometry, we are able to completelyclassify the possible critical behaviours (for purely thermaldisorder). For the three-dimensional wedge, the interfacialfluctuations are very strong and characterized by a universalroughness critical exponent ν⊥W = 1/4 independent ofthe range of the forces. For the physical dimensions d = 2 andd = 3, we show that the effect of the cone geometry on thefluctuations at critical filling is to mimic the analogousinterfacial behaviour occurring at critical wetting in thestrong-fluctuation regime. In particular, for d = 3 and for quitearbitrary choices of the intermolecular potential, the fillingheight and roughness show the same critical properties as thosepredicted for three-dimensional critical wetting with short-rangedforces in the large-wetting-parameter (ω>2) regime.