Wetting on spherical and cylindrical substrates: Global phase diagrams

A Landau theory for wetting on spherical and cylindrical substrates is studied. The substrate parameters are the radius $r_1$, the surface field $h_1$, and the surface-coupling enhancement g. The adsorbate is characterized by correlation length ξ and critical temperature $T_c$. The global phase diagrams reveal important features which were omitted in previous works. For T$T_c$, the phase diagrams are obtained numerically and with use of analytic approximations. For T≥$T_c$, they are obtained exactly. For T$T_c$, there are two distinct regimes of adsorption phase transitions: The regime ξ≲$r_1$≤∞ where the curvature of the substrate is small and the adsorbate is away from criticality, and the regime 0$r_1$≲ξ where the curvature is high and the adsorbate is near-critical. In the former regime, the phase transitions are referred to as ‘‘surface’’ transitions, and in the latter regime as ‘‘point’’ transitions (for spheres) and ‘‘line’’ transitions (for cylinders). The two regimes merge at a critical double point in the phase diagram. Beyond this point adsorption phase transitions can occur for arbitrary curvature and for all temperatures, including $T_c$. The wetting layer thicknesses behave as ξ ln($r_1$/ξ) for $r_1$≫ξ and as ξ for $r_1$≪ξ. The finite-size rounding of the phase transitions is discussed, and the experimental relevance of our findings is outlined.