Application of Finite Fourier Transform and Similarity Approach in a Binary System of the Diffusion of Water in a Polymer

Abstract

This paper describes the method of two important mathematical techniques used in chemical engineering applications. Solving a mass transfer problem, weather in finite or semi-infinite domain, may seem difficult without the practice of Finite Fourier Transform (FFT) and Similarity Transformation. Finite systems refer to any closed system that has a specific boundary that can be determined. For example, polymer sheets, membranes, storage tanks, oil reservoirs and a human stomach are determined to be finite systems where FFT is applicable to derive expressions for concentration profiles of the materials in the system. However, Similarity Transformation method is used to identify the concentration profile in semi-infinite systems that have no limits. It has been approved that we may also use the similarity procedure for finite systems since our results are almost the same. Methodologies of both techniques have been discussed thoroughly in order to apply them to a water-polymer diffusion system for the determination of the concentration of water in a polymer sheet of PET. Discussion and comparison between FFT and similarity is included to illustrate the power of each mathematical procedure in predicting and modeling mass concentrations.