Physics informed neural networks reveal valid models for reactive diffusion of volatiles through paper

Abstract

Predictive models for the transport of volatile organic compounds in paper need to consider the complex interplay of diffusion, adsorption, desorption, or chemical reactions. The relative importance of each of these processes is determined by the polarity of the volatile. Hence, it is challenging to pick a valid theoretical model that correctly predicts transport regardless of the polarity. Here, physics-informed neural networks (PINNs) assess which of five different models correctly describe transport of DMSO as polar and n-tetradecane as apolar model compound: (i) a pseudo first-order adsorption model for an irreversible sorption process, (ii) a first-order kinetics model allowing reversible sorption, (iii) a second-order model with a reversible process, and an effective diffusion model accounting for a constant (iv) and for a variable effective diffusivity (v). Each tested model is given as set of partial differential equations (PDE). Considering the model under testing and experimentally obtained spatially and temporally resolved concentration profiles through stacks of paper sheets, PINNs predict concentration of the volatiles and associated material constants such as sorption constants and effective diffusion coefficients by solving the inverse problem. Our PINNs revealed two models, pseudo first-order sorption and second-order reversible sorption, that correctly predict concentration profiles and polarity-driven differences in sorption times. While a PINN-based picking of valid transport models has important implications for the development of effective methods for controlling emission of volatiles from paper materials, PINNs represent a versatile mathematical tool to validate or refute the capability of PDE-based theoretical models to describe experimental data.