Abstract: The problem of solving hydraulic models based on the axially-dispersed plug flow model which are applicable for the mathematical modelling of different flow-through systems both in chemical analysis (e.g., chromatography, flow injection analysis) and chemical industry (e.g., different tubular reactors) is discussed. Methods for numerical inversion of the model solution in the Laplace domain by expanding it into series of orthogonal functions are compared. Best results with respect to precision and consumption of computation time are given by the methods employing Chebyshov polynomials of the first kind and Fourier sine series. These methods were found to be better in these respects than some other frequently used numerical inversion methods.

Abstract: The model included unification of the mathematical descriptions of the kinetics of the enzyme-catalyzed reaction and the mass transport within the membrane and the flow system. Analytical solutions were obtained in the Laplace and time domains for pseudo-first-order kinetics, and calculations based on the model showed that better rectilinearity of the calibration graphs under flow injection conditions could be expected than with steady state measurements.

Abstract: A math. model describing the mass transfer in a parallel-plate dialyzer with cocurrent laminar flow in both channels based on the Navier-Stokes equations and Fick's 2nd law was developed. Numerical solutions are presented for pulse- and stepwise concentration. changes of the solute in one of the channels using the Laplace transform technique. By simulation the effect of the main design and operational parameters of the dialyzer and the most important phys. constants for the mass-transfer process were investigated. Conclusions with regard to optimum design and operation were drawn and some possibilities for simplifying the model were established.

Abstract: The mathematical model developed takes into account the geometrical dimensions and dispersion properties of the main section of the manifold, the mass transfer in the chambers of the separation module and the thickness and diffusion coefficient of the membrane. The model was solved analytically by the Laplace transform technique, in which the equations reduce to ordinary linear differential equations of the second order (details given). Details are given of the experimental flow scheme, which incorporates a dialysis module, and the stimulus - response technique (Levenspiel and Bischoff, Adv. Chem. Eng., 1963, 4, 95) was used to identify the unknown parameters in the model under flow injection conditions. Three experimental series were run: one with a PTFE dialysis membrane impermeable to the KCl tracer; a second series with a Cuprophan membrane which was permeable to KCl; and the third series with water as carrier solution in the acceptor line and 1.6 mM KCl in the donor line. The response curves at the inlet and outlet of each channel were monitored at different flow rates. Applications include the optimization of sensitivity and sample throughput, and characterization and improvement of the membranes. A math. model for a flow injection system with a membrane separation module based on the axially dispersed plug flow model was developed. It takes into account the geometrical dimensions and dispersion properties of the main sections of the manifold, the mass transfer in the channels of the separation module, and the characteristics of the membrane (thickness and diffusion coefficient within it). The model was solved anal. in the Laplace domain. The inverse transformation was found to give satisfactory results for reactor Peclet nos. less than 120. Otherwise a numerical solution based on the implicit alternating-direction finite difference method was preferred. The adequacy of the model was confirmed experimental on a flow injection manifold with a parallel-plate dialysis module. The unknown flow and membrane parameters were determined by curve fitting. The membrane parameters were determined also by steady-state measurements. Fairly good agreement between the dynamic and steady-state results and with results given in the literature was observed, which, together with other experimental results, supported the validity of the model and showed that it can be used successfully for the math. description and optimization of flow injection systems with membrane separation modules. In this connection, the influence of the reactor parameters and the sample volume on the performance of such a system were investigated and conclusions for improving its sensitivity and sample throughput were drawn. Other possible applications of the model are in membrane technol. for characterizing of various membranes and in process engineering for investigating the mass transfer in different dialyzers.

Abstract: A computational technique is presented for obtaining the dynamic response to a gas diffusion module as part of a flow injection analysis (FIA) system. Based on orthogonal collocation, Laplace transformation, and Fourier series, the method provides a relatively quick way to account for dispersive effects occurring via longitudinal convection and lateral diffusion. Simulation examples, including a comparison with a dynamic signal obtained with an actual FIA system, are provided.