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Results from Monte Carlo simulations of wall-attached droplets in thethree-dimensional Ising lattice gas model and in a symmetric binaryLennard-Jones fluid, confined by antisymmetric walls, are analyzed, with theaim to estimate the dependence of the contact angle $(\Theta)$ on the dropletradius $(R)$ of curvature. Sphere-cap shape of the wall-attached droplets isassumed throughout. An approach, based purely on "thermodynamic" observables,e.g., chemical potential, excess density due to the droplet, etc., is used, toavoid ambiguities in the decision which particles belong (or do not belong,respectively) to the droplet. It is found that the results are compatible witha variation $[\Theta(R)-\Theta_{\infty}] \propto 1/R$, $\Theta_{\infty}$ beingthe contact angle in the thermodynamic limit ($R=\infty$). The possibility touse such results to estimate the excess free energy related to the contact lineof the droplet, namely the line tension, at the wall, is discussed. Variousproblems that hamper this approach and were not fully recognized in previousattempts to extract the line tension are identified. It is also found that thedependence of wall tensions on the difference of chemical potential of thedroplet from that at the bulk coexistence provides effectively a change of thecontact angle of similar magnitude. The simulation approach yields preciseestimates for the excess density due to wall-attached droplets and thecorresponding free energy excess, relative to a system without a droplet at thesame chemical potential. It is shown that this information suffices to estimatenucleation barriers, not affected by ambiguities on droplet shape, contactangle and line tension.

Do the contact angle and line tension of surface-attached droplets depend on the radius of curvature?