DNS is performed to study passive scalar mixing in vortex rings in the presence, and absence of crossflow. For vortex rings without crossflow, the 'formation number' (Gharib et. al 1998) is found to be 3.6. Simulations are performed for a range of stroke ratios encompassing the formation number. In the absence of crossflow, the optimal stroke ratio for mixing and entrainment is shown to be at the formation number; the trailing column is not seen to be as beneficial as the ring itself. However, in the presence of crossflow, the trailing column is shown to contribute significantly to the overall mixing and entrainment. The trailing column enhances the entrainment significantly because of the high pressure gradient created by deformation of the column upon interacting with crossflow. It is shown that the crossflow reduces the stroke ratio beyond which the trailing column forms. This reduction in stroke ratio is due to entrainment of crossflow fluid during formation of the ring, and depends on the velocity ratio.