In this paper we investigate computationally the transient deformation of a droplet flowing along the centerline of a microfluidic cross-junction device. We consider naturally buoyant droplets with size smaller than the cross-section of the square channels comprising the cross-junction, and investigate low-to-strong flow rates and a wide range of fluids viscosity ratio. Our investigation shows that the intersecting flows at the cross-junction act like a constriction, and thus the droplet shows a rich deformation behavior as it passes through the micro-junction. Our work highlights the three-dimensional effects of the asymmetric microfluidic geometry on the droplet deformation, and the different effects of the viscosity ratio on the droplet's overall length scales and the local length scales at the droplet edges. The large edge curvatures and thus the small local length scales developed transiently, especially at the tail of low-viscosity droplets, reveal that the current investigation is a multi-length interfacial dynamics problem. (C) 2015 Elsevier Inc. All rights reserved.