Analysis of mass transport models based on Maxwell–Stefan theory and Fick's law for protein uptake to porous anion exchanger

Parallel mass transport of protein in the pore fluid and on the pore wall of porous adsorbent is modeled based on the Maxwell–Stefan theory that uses chemical potential gradient as the diffusive driving force. The uptake kinetics of proteins (BSA and γ-globulin) to anion exchanger is studied by batch adsorption. The parallel diffusion model based on the MS approach (MS-ParD model) and its simplified form, the surface diffusion model (MS-SD model), are analyzed and compared with those based on the Fick's law (F-ParD and F-SD models). It is found that the models from the MS equation and the Fick's law are quite different from each other. For the MS-ParD model, both the pore and surface diffusion coefficients are constant, while the surface or pore diffusion coefficient for the F-ParD model varies significantly with initial protein concentration. Moreover, the MS-SD model can be used to describe the uptake of a protein that shows nearly a rectangular isotherm, in which the surface diffusion contributes very small to the mass transport. In addition, an equation that describes the relationship between the surface diffusion coefficients for the MS-SD and F-SD models is proposed. It is observed that the ratio of the surface diffusion coefficients for the MS-ParD and F-ParD models for less favorably adsorbed protein can be qualitatively described by a theoretical equation. It is concluded that the MS-ParD model is superior to the F-ParD model for describing the non-ideality of adsorbed protein.