Numerical determination of the solvent diffusion coefficient in a concentrated polymer solution

In chemical engineering applications involving solvent removal from a concentrated polymer solution where diffusion is the governing process (e.g. dry spinning of synthetic silk-like fibres), the determination of the concentration-dependent diffusion coefficient is essential. Diffusion of solvent through such a polymer solution can be described by Fick's law. We propose a numerical procedure to obtain the dependence of the diffusion coefficient on solvent concentration. The procedure employs the finite element method to model a pan weighing experiment, in which a small amount of the polymer solution is placed in a pan and allowed to evaporate into air. In the computational model, the changing depth of the polymer solution is taken into account and the varying diffusion coefficient is determined so as to match the experimentally recorded mass loss.