We study the nature of minimizers for a free energy functional
that models a liquid--vapour transition. the minimization
is carried out under a constraint on the total mass. If this mas is too
small, the minimizer will consist simply of a uniform vapour. As the mas
is increased (and all else held fixed), condenstation occurs. We identify
the critical transition region, and examine the precise geometric nature
of the minimizers in the critical transition region.