  Four results associated with the diffuse-interface model (DIM) for contact
lines are reported in this paper. First, a boundary condition is derived, which
states that the fluid near a solid wall must have a certain density $\rho_{0}$
depending on the solid's properties. Unlike previous derivations, the one
presented here is based on the same physics as the DIM itself and does not
require additional assumptions. Second, asymptotic estimates are used to check
a conjecture lying at the foundation of the DIM, as well as all other models of
contact lines: that liquid-vapor interfaces are nearly isothermal. It turns out
that, for water, they are not -- although, for a more viscous fluid, they can
be. The non-isothermaility occurs locally, near the interface, but can still
affect the contact-line dynamics. Third, the DIM coupled with a realistic
equation of state for water is used to compute the dependence of the surface
tension $\sigma$ on the temperature $T$, which agrees well with the empiric
$\sigma(T)$. Fourth, the same framework is used to compute the static contact
angle of a water-vapor interface. It is shown that, with increasing
temperature, the contact angle becomes either $180^{\circ}$ (perfect
hydrophobicity) or $0^{\circ}$ (perfect hydrophilicity), depending on whether
$\rho_{0}$ matches the density of saturated vapor or liquid, respectively. Such
behavior presumably occurs in all fluids, not just water, and for all
sufficiently strong variations of parameters, not just that of the temperature
-- as corroborated by existing observations of drops under variable electric
field.
