Biomixing is the study of fluid mixing caused by swimming organisms.  The swimming of large organisms can lead to mixing by the turbulent flows in their wakes, but the wakes created by small swimming organisms are less turbulent.  Instead, the main mechanism of mixing by smaller organisms is the net particle displacement (drift) induced by the swimmer.  Several experiments have been performed to examine this drift for small jellyfish; these produce vortex rings that trap and transport a fair amount of fluid.  However, since inviscid theory implies infinite particle displacements, the effects of viscosity must be included to understand the damping of real vortex motion.  We use a model viscous vortex to compute particle displacements and other relevant quantities, such as the mean kinetic energy fluctuations.  This is joint work with Thomas Morrell and Saverio Spagnolie.