The hydrodynamic coupling between droplets and viscous stratifications is examined in square micro-channels. A segmented flow of droplets is injected into a viscosity-stratified flow region. The large difference in velocity between parallel streams having dissimilar viscosities produces a variety of droplet dynamics, including breakup into an array of daughter droplets. We characterize stable viscous stratifications generated using hydrodynamic focusing into a square microchannel and we present a general phase-diagram of droplet behavior. The capillary number is shown to influence both the morphology and dynamics of daughter droplets. In particular, the film thickness between droplets and walls is measured along with the droplet velocity. Deformable droplets significantly disrupt viscous stratifications at low Reynolds numbers and a plume is produced in the trail of the last daughter droplet. The formation and evolution of viscous fingers from the edges of high-viscosity stratifications are discussed. This study shows the possibility to displace high-viscosity oil with droplets in microgeometries. (C) 2011 Elsevier Ltd. All rights reserved.