Diffusion coefficient for sublimation diffusion of disperse dye using error function

Abstract

This study on the sublimation diffusion of disperse dye from paste into PET film was performed by using a film roll method. The Laplace transform was applied to finding the solution of the diffusion equation for the diffusion in a semi-infinite medium. The process to calculate the diffusion coefficient using the iterated complementary error function was proposed. For the sublimation diffusion of disperse dye to PET by treating at 190°Cfor 3 hours, the mean dye concentration for each layer was determined colorimetrically and the diffusion coefficient was calculated by obtaining the variable value of the iterated complementary error function derived from the ratio of the mean dye concentrations between adjacent layers. The mean diffusion coefficient for all the layers was unsuitable because ofits large standard deviation, while that for below the 5th layer was estimated to be appropriate.The surface concentration calculated by the equation of the iterated complementary error function for the third layer was suitable.