Abstract
A high-fidelity physics-based model of mixed-gas transport coupled with kinetic and equilibrium adsorption is derived, and experiments were performed in order to calibrate and exercise the model. In the literature, a continuum-scale model that couples Fickian diffusion with Henry’s law absorption, and kinetic Langmuir adsorption was previously developed to describe the diffusion and sorption of moisture in porous materials. Here, we expand the model to gases, rather than moisture, derive, and implement a competitive adsorption mechanism into the model to enable mixed-gas sorption. This model facilitates a mechanistic-based understanding of the sorption and diffusion processes of mixed gases in polymeric materials. Diffusion and sorption experiments were conducted for a range of partial pressures; model validation and calibration were carried out by comparing modeled mass uptake and experimental data considering the uncertainties of conceptualized (or assumed) physical processes and system parameters. Uncertainty quantification and sensitivity analysis methods are described and exercised here to demonstrate the capability of this predictive model.
Highlights
Gas transport in polymeric materials is of importance to a variety of industries and applications (Dhingra and Marand 1998; Yeom et al 2000; Harley et al 2012, 2014; Sun et al 2015)
Transport of mixed gases coupled with kinetic adsorption and equilibrium absorption is a challenging problem with a variety of applications
Previous understanding in competitive sorption is limited to equilibrium isotherms and fails to address the complex dynamic behavior of mass uptake
Summary
Gas transport in polymeric materials is of importance to a variety of industries and applications (Dhingra and Marand 1998; Yeom et al 2000; Harley et al 2012, 2014; Sun et al 2015). The most popular procedure for calibrating mass uptake physics is to use the Crank analytical solution (Crank 1975, Eq (4.23), P50) to a one-dimensional diffusion coupled with a linear absorption (Cox et al 2001; Harley et al 2012) This solution requires constant initial and boundary conditions, homogeneous domain, and linear sorption that simplifies the derivation of the standard diffusion equation using an effective diffusivity. The gravimetric sorption and desorption method has been used to study steady-state (equilibrium) mass uptake behavior for a constant boundary concentration and temperature (e.g., Cavenati et al 2004), the dynamic and transient diffusion and kinetic adsorption have not been well described mathematically. This work explores and quantifies uncertainties of gas concentrations in terms of uncertain physical processes and system parameters
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