Multicomponent mass transfer kinetics in nanocomposite (NC) bifunctional matrixes: NC selectivity and diffusion concentration waves

Abstract

In this review, the author’s results are observed in the field of the computerized modeling of the multicomponent mass transport kinetic processes in the bifunctional matrixes of the various shapes: spherical r-bead, cylindrical ro-fiber, planar L-membrane for the updated sorbent materials – nanocomposites (NC). The new contemporary NC model is developed for investigations of the multicomponent mass transfer kinetics in the bifunctional matrix of NC materials. The key concept of the author’s model is based on the two routes approach (I and II) for the multicomponent mass transfer inside the bifunctional NC matrix. These two routes function simultaneously and together: route I – for the mass transformation in reactions of dissociation (Ia) and association (Ib) onto the active nanocenters-nanosites (R0) expressed in the “sinks” and “sources” terms, and simultaneously there is carried out along the second II route the multicomponent diffusion of the i components (Di) in the pores of the bifunctional (I+II) NC matrix with the forming of the diffusion i concentration waves. Transformations of the masses of the diffusing i components that occur on I-route are described by the equilibria relations of mass action laws and may be determined as “selectivity” of the nanosites – R0 in the NC matrix. All factors of the author’s NC model are included into the description of the NC kinetics by multicomponent mass transfer partial differential equations. The propagating concentration waves represent the results of the computerized solution of the mass transfer equations. The equations for the all i components participating in the NC mass transport processes are completed by the additional Jk fluxes that are described by the “sinks” and “sources” mechanism for the mass transformation on the I route. One of the main result of the computer modeling with the formulated NC model positions: it has been shown that the basic properties of the multicomponent mass transfer in the rather simple NC system are analogous to the characteristics of the dynamic process of chromatography. This similarity concludes in the fact that the multicomponent selectivity (I) and diffusion (II, Di) influence on the propagating concentration i waves are in analogy to the sorption isotherms and HETP parameters of the theory of multicomponent chromatography. The corresponding estimations in the NC kinetics are presented by using the integral parameters: Center of Mass (CMR), and Dispersion (DispR) for the kR0 concentration waves of the formed R0 nanosite distribution. There is a demonstrated analogy between the propagation of the kinetic kR0 concentration wave and dynamic wave behavior in the chromatographic column. The essential feature concludes in the propagation of the formed kR0 wave inside the NC matrix, though its diffusivity is zero (DR=0, as the R0 nanosites are fixed). The new displacement effect is displayed in the result of the computer simulation for the two i concentration diffusion waves invading and interfering into the ion exchange (IEX) matrix (including the 3d concentration wave coming out from the IEX matrix) for the ternary nonselective IEX kinetics where selectivity factor (I) is absent.