caa a22 4500 463170539 CHVBK 20180406164812.0 cr unu---uuuuu 170326e20071201xx s 000 0 eng 10.1007/s10450-007-9035-3 doi (NATIONALLICENCE)springer-10.1007/s10450-007-9035-3 Theoretical investigation of the adsorption of a binary mixture inachromatographic column using the nonlinear frequency response technique [Elektronische Daten] [Milica Ilić, Menka Petkovska, Andreas Seidel-Morgenstern] The nonlinear frequency response of a chromatographic column for the adsorption of two dissolved components is analyzed using the concept of higher order frequency response functions (FRFs) which is based on the Volterra series and generalized Fourier transform. By applying this concept a nonlinear model of a system is replaced by an infinite series of the FRFs of the first, second, etc. order. The FRFs up to the third order are derived theoretically starting from the equilibrium-dispersive model, which is used for description of a chromatographic column, and applying the harmonic probing method. The functions that relate outlet concentration changes of each component to the corresponding inlet concentration changes are derived. At the inlet of a chromatographic column, it is considered: (a)the concentration change of one of the components keeping the concentration of the other component constant and (b)the concentration change of both components keeping their ratio constant. The FRFs are calculated numerically for different steady-state concentrations and relative mixture compositions. It has been found that, despite certain differences in initial conditions, the FRFs exhibit similar behavior. For higher frequencies, the amplitudes of the FRFs tend to zero and phases to −∞. In the low frequency range, which is of interest for investigation of equilibrium parameters, these functions have similar behavior, but tend to different asymptotic values. Correlations between coefficients of competitive adsorption isotherms, i.e. partial isotherm derivatives, and the derived FRFs are established. This theoretical result offers the potential to use the analysis of the nonlinear frequency response of a chromatographic column for estimation of competitive adsorption isotherms. Springer Science+Business Media, LLC, 2007 Binary mixture nationallicence Competitive adsorption isotherm nationallicence Nonlinear frequency response nationallicence Higher order frequency response functions nationallicence $\tilde{a}_{ij}$ : Coefficient of the dimensionless competitive adsorption isotherm nationallicence $\tilde{b}_{ij}$ : Coefficient of the dimensionless competitive adsorption isotherm nationallicence b L , b S : Parameters of the adsorption isotherm, l/g nationallicence c : Dimensionless concentration in the liquid phase nationallicence $\tilde{c}_{ij}$ : Coefficient of the dimensionless competitive adsorption isotherm nationallicence C : Concentration in the liquid phase, g/l nationallicence C s : Steady-state concentration in the liquid phase, g/l nationallicence D app : Apparent dispersion coefficient, cm2/s nationallicence f : Dimensionless factor nationallicence F n ( x , ω 1, ω 2, , ω n ) : n-th order frequency response function that relates the concentration change of the component 2 at distance x from the column inlet with the inlet concentration change nationallicence F n * ( ω 1, ω 2, , ω n ) : n-th order frequency response function that relates the concentration change of the component 2 at the column outlet with the inlet concentration change nationallicence G n ( x , ω 1, ω 2, , ω n ) : n-th order frequency response function that relates the concentration change of the component 1 at distance x from the column inlet with the inlet concentration change nationallicence G n * ( ω 1, ω 2, , ω n ) : n-th order frequency response function that relates the concentration change of the component 1 at the column outlet with the inlet concentration change nationallicence L : Column length, cm nationallicence N tp : Number of theoretical plates nationallicence q : Dimensionless concentration in the solid phase nationallicence Q : Concentration in the solid phase, g/l nationallicence Q s : Steady-state concentration in the solid phase, g/l nationallicence Q 0 : Saturation capacity (parameter of the adsorption isotherm), g/l nationallicence t : Dimensionless time nationallicence u ( τ ) : Input function nationallicence υ : Interstitial fluid velocity, cm/s nationallicence x : Dimensionless space coordinate nationallicence y ( τ ) : Output function nationallicence z : Space coordinate, cm nationallicence ε : Total column porosity nationallicence τ : Time, s nationallicence ω : Dimensionless frequency nationallicence ω * : Frequency, rad/s nationallicence Ilić Milica Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany aut Petkovska Menka Department of Chemical Engineering, Faculty of Technology and Metallurgy, Belgrade, Serbia aut Seidel-Morgenstern Andreas Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany aut Adsorption Springer US; http://www.springer-ny.com 13/5-6(2007-12-01), 541-567 0929-5607 13:5-6<541 2007 13 10450 https://doi.org/10.1007/s10450-007-9035-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10450-007-9035-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ilić Milica Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany aut NATIONALLICENCE 700 1- Petkovska Menka Department of Chemical Engineering, Faculty of Technology and Metallurgy, Belgrade, Serbia aut NATIONALLICENCE 700 1- Seidel-Morgenstern Andreas Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany aut NATIONALLICENCE 773 0- Adsorption Springer US; http://www.springer-ny.com 13/5-6(2007-12-01), 541-567 0929-5607 13:5-6<541 2007 13 10450 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer