Hydrophobic droplets in amphiphilic bilayers: a coarse-grained   mean-field theory study
  Hydrophobic molecules such as oils and certain drugs can be encapsulated between the two leaflets of an amphiphilic bilayer in both lipid and polymer systems. We investigate the case where the hydrophobic molecules are incompatible with the amphiphile tails and so form droplets. Using a coarse-grained mean-field model (self-consistent field theory, or SCFT), we find that droplets of a wide range of sizes have the same characteristic lens shape, and explain this result in terms of simple capillarity arguments, consistent with the measured variations of surface concentrations of amphiphile in the bilayer and in the monolayers that cover the droplet. We study the effect of the strength chi_BO of the repulsion between the hydrophobic liquid and the amphiphile tails on the droplet shape, and find a gradual flattening of the droplet as chi_BO is reduced. The droplet remains at least metastable even at very low values of chi_BO. This is in contrast to the behavior as the length of the hydrophobic molecules is varied. Specifically, if these molecules are at least as long as the amphiphile tails, increasing their length further is found to have little effect on the droplet shape, while reducing their length below this value quickly causes the droplet to become unstable. 
M. J. Greenall and C. M. Marques
cond-mat.soft