A dyed substrate having at least one dyed surface. At least one dye solution is disposed across at least a portion of the surface in combination with a migration promoting composition and/or a migration limiting composition. The migration promoting composition and/or migration limiting composition adjusts the migration of at least a portion of the dye solution across the substrate in a controlled manner. Dye migration may be arrested by the application of RF (radio frequency) energy as a step in dye fixation. A process for forming the dyed substrate is also provided.