Wetting on cylinders and spheres

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Abstract
A fluid (or Ising-like) system in contact with a uniformly curved substrate, such as a cylinder or sphere, exhibits a surface phase diagram which is different from that when the substrate is flat. Using both an interface model and a Landau theory that includes surface field and surface coupling enhancement parameters, we find that the effects of curvature may be subsumed into an effective bulk (ordering) field. Complete and critical wetting transitions are thus suppressed. At bulk coexistence, the mean-field phase diagram exhibits curvature-induced prewetting and critical prewetting transitions. In d=3, finite-size effects smear the prewetting transitions that would otherwise take place in cylindrical or spherical geometries. The Landau theory employs a nonanalytic, piecewise parabolic approximation to the usual quartic polynomial in the free-energy functional. This approximation produces a global surface phase diagram with the correct topology, even though it is unsuited for the description of multicritical phenomena, such as wetting tricriticality. Other strengths and weaknesses of the approximation are described.

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