We considered effective diffusion, characterized by magnitudes of effective diffusion coefficients, in order to quantify mass transport due to the onset and development of elastic instabilities. Effective diffusion coefficient magnitudes were determined using different analytic approaches, as they were applied to tracked visualizations of fluorescein dye front variations, as circumferential advection was imposed upon a flow environment produced using a rotating Couette flow arrangement. Effective diffusion coefficient results were provided for a range of flow shear rates, which were produced using different Couette flow rotation speeds and two different flow environment fluid depths. To visualize the flow behavior within the rotating Couette flow environment, minute amounts of fluorescein dye were injected into the center of the flow container using a syringe pump. This dye was then redistributed within the flow by radial diffusion only when no disk rotation was used, and by radial diffusion and by circumferential advection when disk rotation was present. Associated effective diffusion coefficient values, for the latter arrangement, were compared to coefficients values with no disk rotation, which were due to molecular diffusion alone, in order to quantify enhancements due to elastic instabilities. Experiments were conducted using viscoelastic fluids, which were based on a 65% sucrose solution, with different polymer concentrations ranging from 0 ppm to 300 ppm. Associated Reynolds numbers based on the fluid depth and radially averaged maximum flow velocity ranged from 0.00 to 0.5. The resulting effective diffusion coefficient values for different flow shear rates and polymer concentrations quantified the onset of elastic instabilities, as well as significant and dramatic changes to local mass transport magnitudes, which are associated with the further development of elastic instabilities.