A theory is presented for the behavior of an array of multi-lamellar reside
s (the onion phase) upon addition of solvent. A unique feature of this syst
em is the possibility to sustain pressure gradients by tension in the lamel
lae. Tension enables the onions to remain stable beyond the unbinding point
of a flat lamellar stack. The model accounts for various concentration pro
files and interfaces developing in the onion as it swells. In particular, d
ensely packed "onion cores" are shown to appear, as observed in experiments
. The formation of interfaces and onion cores may represent an unusual exam
ple of stabilization of curved interfaces in confined geometry.