A hydrodynamic analysis of a selective-withdrawal process Suitable for the micro-encapsulation of pancreatic islets is presented. In the micro-encapsulation device, a feeding system located on the upper side of a water-oil interface dispenses individual cells or cell aggregates in a single file by hydrodynamic focusing, while a valveless, diffuser-nozzle micro-pump located on the lower side of the interface removes the encapsulated islets for further processing. The apparatus ensures the separate encapsulation of the individual islets by a Structurally stable, semi-permeable, controlled thickness membrane. In the theoretical model, the feed nozzle is modeled as a point source and the removal nozzle is modeled as a point sink. Small and large deformations of the interface are considered by analytical and boundary element methods, and critical conditions for selective withdrawal are established. (C) 2007 Elsevier Ltd. All rights reserved.