in Wiley InterScience (www.interscience.wiley.com).There is much experimental and mathematical work that describes chemical transport from multilayered films of planar geometries. There is less so, however, for chemical transport from multilayered spheres, a common structure for controlled-release materials. Based on the Sturm-Liouville approach of Ramkrishna and Amundson (1974), explicit analytical solutions for the concentration profiles and release kinetics from spherical capsules are presented. Fluorescent dye-release studies using singleshelled microspheres called nanoparticle-assembled capsules were performed to validate the model for uniformly and nonuniformly sized capsules. The combined experiment-modeling approach allows optical microscopy images and release measurements to be readily analyzed for estimating diffusion coefficients in capsule core and shell walls. V
IntroductionThe availability of new types of materials with engineered composition, porosity, internal gradation, and morphology is providing exciting opportunities in encapsulation and delivery applications, like in the biotechnology arena. Unilamellar and multilamellar vesicles, for example, have long been studied as drug and chemical delivery agents, 1,2 in which the NACs were synthesized by first mixing 14 ml of 5 mg/ml of PAH solution with 35 ml of 14.2 mM citrate solution in a 250 ml beaker under gentle magnetic stirring (speed ''4'' of 0 through 10) for 10 s. The resulting suspension turned turbid instantly indicating the formation of polymer-salt aggregates. After aging these aggregates for 20 min, 35 ml of a 1 mg/ml fluorescein sodium salt (''Na-Flu'') dye solution was added under gentle magnetic stirring for 10 s. This mixture was aged for another 10 min and 35 ml of 1.2 wt % To compare our model predictions of the fractional release rate with experiments, the following parameters were required to be estimated from experiments: (i) x 1 , the ratio between the inner and outer radii, (ii) P 12 , partition coefficient between the polymer-salt aggregate and the interior of the shell, (iii) P 2b , the partition coefficient between the outer shell surface
