  By integrating the Young-Laplace equation, including the effects of gravity,
we have calculated the equilibrium shape of the two-dimensional Plateau borders
along which a vertical soap film contacts two flat, horizontal solid substrates
of given wettability. We show that the Plateau borders, where most of a foam's
liquid resides, can only exist if the values of the Bond number ${\rm Bo}$ and
of the liquid contact angle $\theta_c$ lie within certain domains in
$(\theta_c,{\rm Bo})$ space: under these conditions the substrate is
foam-philic. For values outside these domains, the substrate cannot support a
soap film and is foam-phobic. In other words, on a substrate of a given
wettability, only Plateau borders of a certain range of sizes can form. For
given $(\theta_c,{\rm Bo})$, the top Plateau border can never have greater
width or cross-sectional area than the bottom one. Moreover, the top Plateau
border cannot exist in a steady state for contact angles above 90$^\circ$. Our
conclusions are validated by comparison with both experimental and numerical
(Surface Evolver) data. We conjecture that these results will hold, with slight
modifications, for non-planar soap films and bubbles. Our results are also
relevant to the motion of bubbles and foams in channels, where the friction
force of the substrate on the Plateau borders plays an important role.
