  With the aim to characterize the formation and propagation of bulges in
cylindrical rubber balloons, we carry out an expansion of the non-linear
axisymmetric membrane model assuming slow axial variations. We obtain a diffuse
interface model similar to that introduced by van der Waals in the context of
liquid-vapor phase transitions. This provides a quantitative basis to the
well-known analogy between propagating bulges and phase transitions. The
diffuse interface model is amenable to numerical as well as analytical
solutions, including linear and non-linear bifurcation analyses. Comparisons to
the original membrane model reveal that the diffuse interface model captures
the bulging phenomenon very accurately, even for well-localized phase
boundaries.
