A numerical, finite-difference model has been developed to simulate the dye transfer thermal printing process. This model has been used previously for calculating the amount and depth of the dye diffusion into a receiver. 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 printhead temperature data. This allows different pulse modulation heating schemes to be used in the analysis. The concentration dependence of the diffusivity is taken into account, and this leads to a nonlinear governing equation.As one increases the amount of power delivered by the thermal head, larger quantities of dye will be transferred into the receiver. In a similar fashion, any changes to the dimensionality and/or thermal properties of the materials comprising the donor and receiver will affect the temperature distribution. This, in turn, will cause the amount of dye transfer to change. These changes have been investigated, and the predicted amounts have been calculated for dye transfer. Comparing the amount of calculated dye transfer to that calculated from known operating conditions, one is able to predict the amount of time required for an equivalent transfer to occur. The effects of head power, donor thickness, solubility, and dye concentration have been investigated. Predictions of linetime have been made for each of the parametric changes, as well as an overall “best case” scenario.
Edward J. Ozimek, "Use of a Thermal Dye Diffusion Model to Predict Printing Line-Times" in Proc. IS&T Int'l Conf. on Digital Printing Technologies (NIP19), 2003, pp 371 - 374, https://doi.org/10.2352/ISSN.2169-4451.2003.19.1.art00088_1