Mixtures of alkanes, water, and nonionic surfactant have been prepared in a state where the surfactant monolayers have a negative mean curvature and quenched to lower temperatures where the spontaneous curvature is positive. Small angle neutron scattering has been used to measure the sizes of oil and water domains that are formed before, during, and after the temperature quench. During the quench, the mixtures form a bicontinuous microemulsion, which is then fragmented into droplets with sizes corresponding to the distances of domains in the bicontinuous microemulsion. After the quench, this emulsion decomposes into smaller droplets, at the equilibrium curvature, and larger ones, which take up the excess oil. The transfer of oil from smaller domains to larger ones occurs through permeation of oil molecules across surfactant films during collisions of droplets. Addition of ionic surfactants inhibits this permeation and may help in retaining emulsions with nanometric droplets.