Modelagem e simulação do processo de difusão de corantes em fibras têxteis e estimativa do coeficiente de difusão mássica via algoritmo genético

Abstract

This work studied the diffusion of dye in textile fibers using a theorical methodology. The diffusion of dye in fiber was modeled by the second Fick’s Law of diffusion in cylindrical coordinates for the unidimensional case in steady state regime. The solution of the mathematical model was obtained by analytical solution. Furthermore, the effective mass diffusivity coefficient of the dyeing process was estimated by means of an optimization of an objective function, using the least squares method. In order to optimize the function, it was used a kind of metaheuristic, the genetic algorithm. At first, it was carried out a brief evaluation of the implementation of the analytical solution and the implementation of the genetic algorithm in order to understand the tools. And then a theoretical - experimental adjust was made to determine the diffusion coefficient. Thus, it can be concluded that the dyeing process can be well described by means of analytical solution, the genetic algorithm has proved to be a robust tool that tends to solve problems in which conventional or deterministic methods can fail and the diffusion coefficients found in this work provided smaller residuals than the coefficients found in the literature.