• Wetting transitions and contact-angle phenomena reveal how interfacial behavior switches between complete and partial wetting under shifts in surface energy and temperature, with transitions discussed as first- or second-order depending on system constraints [1], [13], [9], [15].

• Interfacial free energy and gradient theories provide a unified thermodynamic framework for capillarity, linking nonuniform interfaces to density gradients and molecular correlations through classical and modern formalisms [5], [12], [16], [10].

• Structure and density profiling at interfaces is probed via perturbation theory, Monte Carlo, and MD, revealing layer formation, density oscillations, and width of interfacial regions in Lennard–Jones systems [8], [3], [11], [14], [20].

• Critical phenomena and diffuse interfaces in critical fluids show how interfacial thickness and surface tension evolve near Tc, including delocalization and critical exponents in wetting and binary mixtures [7], [6], [17].

• Interfacial hydrodynamics covers turbulence, Marangoni-driven instabilities, and thin-film drainage, including slip-flow mechanisms that resolve force singularities at moving interfaces [4], [19], [18].