  We study the equilibrium of a liquid film on an attractive spherical
substrate for an intermolecular interaction model exhibiting both fluid-fluid
and fluid-wall long-range forces. We first reexamine the wetting properties of
the model in the zero-curvature limit, i.e., for a planar wall, using an
effective interfacial Hamiltonian approach in the framework of the well known
sharp-kink approximation (SKA). We obtain very good agreement with a mean-field
density functional theory (DFT), fully justifying the use of SKA in this limit.
We then turn our attention to substrates of finite curvature and appropriately
modify the so-called soft-interface approximation (SIA) originally formulated
by Napi\'orkowski and Dietrich [Phys. Rev. B 34, 6469 (1986)] for critical
wetting on a planar wall. A detailed asymptotic analysis of SIA confirms the
SKA functional form for the film growth. However, it turns out that the
agreement between SKA and our DFT is only qualitative. We then show that the
quantitative discrepancy between the two is due to the overestimation of the
liquid-gas surface tension within SKA. On the other hand, by relaxing the
assumption of a sharp interface, with, e.g., a simple smoothing of the density
profile there, markedly improves the predictive capability of the theory,
making it quantitative and showing that the liquid-gas surface tension plays a
crucial role when describing wetting on a curved substrate. In addition, we
show that in contrast to SKA, SIA predicts the expected mean-field critical
exponent of the liquid-gas surface tension.
