  The dihedral contact angles between interfaces in three-fluid-phase
equilibria must be continuous functions of the bulk thermodynamic fields. This
general argument, which we propose, predicts a nonwetting gap in the phase
diagram, challenging the common belief in "critical-point wetting", even for
short-range forces. A demonstration is provided by exact solution of a
mean-field two-density functional theory for three-phase equilibria near a
tricritical point (TCP). Complete wetting is found in a tiny vicinity of the
TCP. Away from it, nonwetting prevails and no wetting transition takes place,
not even when a critical endpoint is approached. Far from the TCP, reentrant
wetting may occur, with a different wetting phase. These findings shed light on
hitherto unexplained experiments on ternary water-oil-nonionic amphiphile
mixtures in which nonwetting continues to exist as one approaches either one of
the two critical endpoints.
