Parameter estimation and mathematical modeling of the diffusion process of a benzoic acid infused Fricke gel dosimeter

Abstract

This work presents a mathematical model implementation for studying the diffusion process of ferric ions in post-irradiated Fricke gel dosimeters. Fricke gel samples were manufactured in layers for their analysis by optical transmission imaging and benzoic acid was incorporated to improve their radiosensitivity. The developed method consists on designing the dosimeters with a suitable composition for their optical analysis which allows accurate measurements in a wide dose range with noticeable linear responses with an average linear correlation coefficient of r2=0.993. The developed algorithm calculates the diffusion coefficient by means of an inverse problem formulation. Moreover, the proposed method is capable of modeling time-dependent physical properties and evolution over time of the irradiated dosimeters accurately and comparable with experimentally measured data. The obtained results evince the complexity of the diffusion phenomena in this type of materials and the capacity of the proposed method to provide a reliable quantification of the diffusion coefficient as a scalar approximation of the diffusion tensor. The obtained diffusion coefficient varies from 1.21 to 1.61 mm2/h with uncertainties lower than 2%. The model is also transferable to other diffusion driven systems and the numerical solving method can also be adapted to solve diffusion calculation based on other theoretical approaches.