Critical effects and scaling at meniscus osculation transitions

Area of Science:

• Physics
• Soft Matter Physics
• Surface Science

Background:

• Meniscus osculation occurs when a liquid drop's Laplace radius matches the confining geometry's curvature.
• Understanding critical phenomena in confined liquids is crucial for various physical and chemical processes.

Purpose of the Study:

• To propose a scaling theory for critical effects at meniscus osculation transitions in parabolic geometries.
• To identify and characterize distinct regimes of interfacial height scaling based on intermolecular forces.

Main Methods:

• Development of a simple scaling theory.
• Analysis of interfacial height scaling exponent (β_osc) in relation to the confining radius (R_w).
• Confirmation using an interfacial Hamiltonian model and numerical simulations based on density-functional theory.

Main Results:

• Two regimes of interfacial height scaling (β_osc) were identified: fluctuation-dominated and mean-field.
• The upper critical dimension separating these regimes depends on intermolecular force range.
• For short-range forces in 2D, β_osc = 3/7, confirmed by theory and simulation.
• For long-range forces, the mean-field regime yields β_osc = β_s^co, consistent with complete wetting.

Conclusions:

• The study provides a unified scaling theory for meniscus osculation transitions.
• The identified regimes and critical dimension offer new insights into liquid behavior in confined systems.
• The findings are relevant for understanding interfacial phenomena in diverse scientific and technological applications.