Recently, we reported how viscoelasticity affects drop dynamics in a microchannel flow using the finite element-front tracking method (FE-FTM). In this work, we investigate drop dynamics for a wider range of parameters: viscosity ratio between droplet and medium (chi), capillary number (Ca), droplet size, and fluid elasticity. The Oldroyd-B model is adopted as the constitutive equation for the viscoelastic fluid. We observe that the drop deformation in a microfluidic channel is dependent on Ca, which is more pronounced for smaller chi values. The present work shows that viscoelasticity plays an important role in drop dynamics with increasing chi values for Newtonian droplet in viscoelastic medium, which can be attributed to high normal stress developed in narrow film thickness between droplet and channel for higher chi values. We also study circulation problem inside droplets, which is important in practice, such as in droplet reactor application. The present work shows that circulation intensity is enhanced with decreasing chi values. We find that the relevance of viscoelastic effects on internal circulation is dependent on chi values, and the circulation intensity is distinctively decreased with increasing elasticity for high chi values for Newtonian droplet in viscoelastic medium. We expect that the present work be helpful not only in controlling droplets but also to improve our physical insight on drop dynamics in microchannel flows. (C) 2009 Elsevier Ltd. All rights reserved.