T. Gil et Lv. Mikheev, CURVATURE CONTROLLED WETTING IN 2 DIMENSIONS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 52(1), 1995, pp. 772-780
A complete wetting transition at vanishing curvature of the substrate
in two-dimensional circular geometry is studied by the transfer matrix
method. We find an exact formal mapping of the partition function of
the problem onto that of a (1+1)-dimensional wetting problem in planar
geometry. As the radius of the substrate r(0) --> infinity, the leadi
ng effect of the curvature is adding the Laplace pressure IIL proporti
onal to r(0)(-1) to the pressure balance in the film. At temperatures
and pressures under which the wetting is complete in planar geometry,
Laplace pressure divergence of the mean thickness of the wetting layer
l(w), leading to a power law l(w) proportional to r(0)(1/3). At a cri
tical wetting transition of a planar substrate, curvature adds a relev
ant field; the corresponding multiscaling forms are readily available.
The method allows for the systematic evaluation of corrections to the
leading behavior; the next to the leading term reduces the thickness
by an amount proportional to r(0)(-1/3).