An inverse problem in determining the acid and salt diffusivities simultaneously for polymer solution in a wet spinning process

The wet spinning process depends strongly on the acid and salt diffusivity coefficients in the fiber; however, these two coefficients are normally function of concentration of salt and are difficult to be measured directly. For this reason the technology for the inverse mass transfer problems need be applied to resolve these two concentration-dependent diffusivities simultaneously. An Iterative Regularization Method (IRM) using Conjugate Gradient Method (CGM) is applied in this study to determine simultaneously the unknown diffusivities of acid and salt for polymer solution in a wet spinning process by using measurements of concentration components. The accuracy of this inverse mass transfer problem is examined by using the simulated exact and inexact concentration measurements in the numerical experiments. Results show that the diffusivity of acid can be estimated more accurately than the diffusivity of salt and the estimation of the diffusivities can be obtained in a very short CPU time on a HP d2000 2.66 GHz personal computer.