Pervaporation of emulsion droplets for the templated assembly of spherical particles: A population balance model

Abstract

The emulsion droplet solvent evaporation method is used in the preparation of spherical particles, which form due to processes such as the clustering of nanocrystals or precipitation of polymers as the volume of solvent in the droplets decreases. A population balance model is presented to describe this transport of solvent from nanocrystal‐ or polymer‐laden droplets in an emulsion that flows through a pervaporation unit. The solvent transport and lateral migration of droplets was simulated using a high‐resolution finite‐volume algorithm, which provided a smooth solution with second‐order accuracy. Concentration gradients in the continuous phase become prominent when the resistance to solvent transport in the continuous phase dominates that in the membrane. In contrast, with the membrane resistance controlling the overall transport rate, a lumped capacitance assumption can be made and a simpler plug flow model would be sufficient. The simulations also indicate that the particle‐size distributions are generally bimodal, and are broader for low dispersed‐phase volume fractions and very low‐solvent solubilities. Furthermore, the distributions show that radial diffusion of the particles occurs to a significant degree. Such simulations offer insight into how the solvent is removed from emulsion droplets as they flow down a pervaporation fiber and should be useful in the design of pervaporation systems for that purpose. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3975–3985, 2013