A numerical model has been developed to simulate the dye transfer thermal printing process. The simulation incorporates the multiple layers of the head/media interface and uses finite difference techniques to calculate the temperature and mass distributions. Surface boundary conditions have been determined from experimental print head temperature data. This enables us to use different pulse modulation heating schemes. Also, the concentration dependence of diffusivity is taken into account which leads to a non-linear governing equation. The amount of dye transferred and its distribution in the receiving material can be predicted.The model has been extended to incorporate multiple pass printing. Depth profile predictions are made for a variety of input parameters. Various printing line times, pulse modulation schemes, partition coefficients, donor and receiver glass transition temperatures, and receiving layer thickness are used to calculate the dye concentration profile of the receiver. The surface layer concentration and the depth of dye penetration are of particular importance. These predictions are compared to experimental cross-sectional measurements of dye transfer in receiver material.
Edward J. Ozimek, George B. Bodem, John E. LaFleche, "Multiple Pass Thermal Dye Diffusion Modeling Profiles" in Proc. IS&T Int'l Conf. on Digital Printing Technologies (NIP16), 2000, pp 779 - 782, https://doi.org/10.2352/ISSN.2169-4451.2000.16.1.art00090_2