Mixture diffusion in nanoporous adsorbents: Development of Fickian flux relationship and concentration-swing frequency response method

A frequency response method using concentration variation is developed theoretically and experimentally and applied to investigate mixture diffusion in nanoporous adsorbents. The method is based on periodically time-varying species feed concentrations with a constant total molar inlet flow rate. It can be used without the need of a carrier gas. A mathematical model is formulated considering nanopore diffusion, surface barrier resistance, external film resistance, and axial dispersion. The related analytical solutions for frequency response are derived. For nanopore diffusion, a theory for nonconstant mixture Fickian diffusivity with cross-terms is developed from irreversible thermodynamics and shows that mixture Fickian diffusivities can be expressed as the product of corrected diffusivities and a thermodynamic factor that accounts for concentration dependence. The number of unknown variables for Fickian diffusivities is the same as the number for Onsager coefficients or Maxwell-Stefan diffusivities. Adsorption of CO2, CH4, and their mixtures on carbon molecular sieve (CMS) is investigated systematically for equilibrium and mass transfer rates. The mass transfer mechanisms for pure CO2 and CH4 on CMS measured by a pressure-swing frequency response method are found to be differentthe rate-controlling mechanism for CO2 is only nanopore diffusion, whereas the diffusion rate for CH4 is limited mainly by a surface barrier resistance at the pore mouth of the CMS. All of the mixture experimental data are measured by the new concentration-swing frequency response method and are described well by the nonconstant Fickian diffusivity model with the thermodynamic factor derived for a multicomponent multisite-Langmuir isotherm.