Critical effects and scaling at meniscus osculation transitions

We propose a simple scaling theory describing critical effects at rounded meniscus osculation transitions which occur when the Laplace radius of a condensed macroscopic drop of liquid coincides with the local radius of curvature R w in a confining parabolic geometry. We argue that the exponent ss osc characterizing the scale of the interfacial height l (0 proportional to). R ss osc w at osculation, for large R w, falls into two regimes representing fluctuation-dominated and mean-field-like behavior, respectively. These two regimes are separated by an upper critical dimension, which is determined here explicitly and depends on the range of the intermolecular forces. In the fluctuation-dominated regime, representing the universality class of systems with short-range forces, the exponent is related to the value of the interfacial wandering exponent. by ss(osc) = 3./(4 -.). In contrast, in the mean-field regime, which was not previously identified and which occurs for systems with longer-range forces (and higher dimensions), the exponent ss osc takes the same value as the exponent ss(cos) for complete wetting, which is determined directly by the intermolecular forces. The prediction ss osc = 3/7 in d = 2 for systems with short-range forces (corresponding to. = 1/2) is confirmed using an interfacial Hamiltonian model which determines the exact scaling form for the decay of the interfacial height probability distribution function. A numerical study in d = 3, based on a microscopic model density-functional theory, determines that ss(osc) approximate to ss(cos) approximate to 0.326 close to the predicted value of 1/3 appropriate to the mean-field regime for dispersion forces.

Automated summary

We propose a simple scaling theory to describe the critical effects at rounded meniscus osculation transitions. The theory identifies two regimes, fluctuation-dominated and mean-field-like behavior, separated by an upper critical dimension. The exponent characterizing the scale of the interfacial height is determined by the intermolecular forces in each regime. Numerical studies confirm the theoretical predictions for systems with short-range and longer-range forces.