Nonlinear model reconstruction by frequency and amplitude response for a heterogeneous binary reaction in a chemostat

Here we present an analysis of a binary heterogeneous reaction in a chemostat for the particular case of reagents with unequal mass transfer coefficients. For fast irreversible kinetics, there are two potential steady states—the dispersed phase is preferentially populated by one reagent and essentially depleted of the other. The selection of which steady state occurs depends on the operating parameter which is the concentration ratio σ of the slower (B) to the faster (A) transferring reagent in the feed stream. The demarcation between these operating regimes is the critical value of this ratio:

     

Nonlinear frequency response functions of a chromatographic column—A critical evaluation of their potential for estimation of single solute adsorption isotherms

Nonlinear frequency response analysis is applied to study single component adsorption in chromatographic columns. Single component adsorption isotherms can be estimated from local derivatives of the adsorption isotherm at specified steady-state concentrations, which are obtained from the low frequency asymptotic behavior of the higher order frequency response functions (FRFs) of a chromatographic column. The functions relevant for the estimation of adsorption isotherms are the phases and the first derivatives of these FRFs. These functions (up to the third order) are analyzed for different types of adsorption isotherm models, different isotherm parameters, steady-state concentrations and numbers of theoretical plates of the chromatographic column. Based on this analysis, some unified characteristics of these functions are observed, which can be used for critical evaluation of the method and to design efficient experimental procedures for its application. Advantages and limitations of this method are discussed.