University of North Florida
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Stuart Chalk, Ph.D.
Department of Chemistry
University of North Florida
Phone: 1-904-620-1938
Fax: 1-904-620-3535
Email: schalk@unf.edu
Website: @unf

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Plug flow

Classification: Manifold process -> Plug flow

Citations 13

"Solute Transfer In Online Analytical Flow-through Dialyzers"
Anal. Chim. Acta 1985 Volume 167, Issue 1 Pages 111-122
Bo Bernhardsson, Eduardo Martins and Gillis Johansson

Abstract: Mass transfer in infinite parallel-plate dialysers is investigated for plug-flow, laminar-flow and mixing-cup models with co-flow between the sample and detector streams. Theoretically derived results for the three models are compared with experimental results obtained for the dialysis of Zn(II) across a cellulose acetate membrane. Agreement is fairly good, but errors are caused by differences in hydrostatic pressures on either side of the membrane and by stresses causing membrane bulging.
Zinc(II)

"Description Of An Axially-dispersed Plug Flow Model For The Flow Pattern In Elements Of Fluid Systems"
Anal. Chim. Acta 1986 Volume 185, Issue 1 Pages 315-319
Spas D. Kolev and Ernó Pungor

Abstract: The Laplace transforms of the output signals from a three-sectional system (i.e., fore-section, investigated vessel and after-section), in which the sections have different diameters, are described for δ-function, rectangular and arbitrary input signals by using the axially-dispersed plug flow model. Equations for the means residence time and the variance of the response of the system are reported. The results could be used to evaluate the axial dispersion coefficient flow analysis or process systems, for system modelling and optimization.

"Numerical Solution Of Hydraulic Models Based On The Axially-dispersed Plug Flow Model By Laplace Transforms"
Anal. Chim. Acta 1987 Volume 194, Issue 1 Pages 61-75
Spas D. Kolev and Ernö Pungor

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.

"Mathematical Modeling Of Sequential Determinations By Flow Injection Sandwich Techniques"
Anal. Chim. Acta 1990 Volume 234, Issue 1 Pages 67-74
J. L. Montesinos, J. Bartrolí, M. Poch and M. del Valle, J. L. F. C. Lima and A. N. Araujo

Abstract: A mathematical model was developed for flow injection analysis, in which the sample is injected between two different reagent solution (sandwich technique). The model considers the system to be a tubular reactor with axially dispersed plug flow. The model was applied with the enzymatic determination of glucose as model system. The effects of varying experimental parameters were simulated, and results were compared with experimental data obtained under the same conditions. The model is useful for the description and optimization of the analytical signals obtained in such techniques.
Glucose

"Mathematical Modeling Of A Flow Injection System With A Membrane Separation Module"
Anal. Chim. Acta 1992 Volume 268, Issue 1 Pages 7-27
Spas D. Kolev*, and Willem E. van der Linden

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.

"Mathematical Modeling Of Flow Injection Systems"
Anal. Chim. Acta 1995 Volume 308, Issue 1-3 Pages 36-66
Spas D. Kolev

Abstract: Existing mathematical models of flow injection manifolds were classified on the basis of the main principles on which they were constructed. The models were also compared with respect to their predictive power, the complexity of their mathematical treatment and the requirement for computation time when applied to single-line and conjugated two-line flow injection systems. The axially dispersed plug flow model was found to give an acceptable compromise between mathematical simplicity and precision.

"An Integrated Design Strategy For Flow Injection Analysis Based On The Coupling Of Mathematical Modeling And Optimization Algorithms"
Anal. Chim. Acta 1995 Volume 310, Issue 2 Pages 289-296
A. Araújo, J. L. F. C. Lima, J. Gracia, M. Poch, J. Alonso*, J. Bartrolí and M. Del Valle

Abstract: A methodology to design a flow injection system with optimized performance characteristics was presented based on coupling a descriptive mathematical model to an optimization algorithm. The method was applied to the sequential determination of glucose and glycerol in a flow injection system using the sandwich technique. The axially dispersed plug flow model was coupled with Powell's optimization algorithm to generate a complete set of flow injection configuration, each of them optimized with respect to its objective function (better sensitivity, highest sampling rate, better resolution, etc.). The user selects the configuration which suits the requirements of the particular application.
Glucose Glycerol

"Modeling And Optimization Studies For A Sequential Flow Based Bio-analytical System"
Anal. Chim. Acta 1998 Volume 359, Issue 1-2 Pages 157-171
Sameer Parab, Bernard J. Van Wie*, Ian Byrnes, Edgar J. Robles, Bruce Weyrauch and Thomas O. Tiffany

Abstract: The clinical applications of the sequential flow technique are emphasized in this study by considering glucose determinations in a standard blood chemical analysis. The sequential flow configuration is modeled to predict experimental behavior. A rigorous theoretical formulation of the model is presented incorporating temperature relationships for the hydrodynamic and kinetic parameters. A comparisons of model predictions with experiments show agreement satisfactory for determining optimal design strategies. To perform this analysis, factorial design results of model predictions are used to locate regions where a full set of model predictions should be made. Also, experimental results and theoretical predictions are used to determine the best temperature for glucose determinations
Glucose Blood

"Sandwich Standardization In Flow Injection Analysis"
Talanta 1989 Volume 36, Issue 5 Pages 612-614
Angel Rios, M. D. Luque de Castro and Miguel Valcarcel

Abstract: The basic flow injection analysis configuration for sandwich standardization is illustrated. Sample and calibration solution fill the loops of two valves in an injection unit (illustrated), and, by continuous injection of the contents of both loops, sample and standards are introduced in a standard - sample - standard sequence. The resulting sandwich of plugs then merges with the reagent, thus creating three reaction zones each providing a signal on passage through the detector. The application of the method is demonstrated with the determination of formaldehyde in water by using the SO32- - pararosaniline system with spectrophotometric monitoring at 578 nm. Advantages of derivative over normal recordings are discussed. The basic flow injection analysis configuration for sandwich standardization is illustrated. Sample and calibration solution fill the loops of two valves in an injection unit (illustrated), and, by continuous injection of the contents of both loops, sample and standards are introduced in a standard - sample - standard sequence. The resulting sandwich of plugs then merges with the reagent, thus creating three reaction zones each providing a signal on passage through the detector. The application of the method is demonstrated with the determination of formaldehyde in water by using the SO32- - pararosaniline system with spectrophotometric monitoring at 578 nm. Advantages of derivative over normal recordings are discussed.
Formaldehyde Water

"Determination Of Rate Constants By A Double-line Flow Injection Method Incorporating A Well-stirred Tank Reactor"
Talanta 1994 Volume 41, Issue 10 Pages 1775-1784
Roger T. Echols and Julian F. Tyson*,

Abstract: Equations for the concentration-time profiles of reactants and products in a first order reaction obtained when a reactant plug passes through a single well-stirred tank and for physical dispersion of such a reactor under plug flow conditions were used to derive an expression for the reaction rate constant. The method was tested for reactions between Ce and oxalic acid and between dichromate and ascorbic acid. Good agreement with other experimentally determined values was obtained. The scope and limitations of the method are discussed with model equations.

"Optimal Design Of An Enzymatic Reactor For Flow Injection Analysis"
Biotechnol. Prog. 1993 Volume 9, Issue 5 Pages 473-480
M. Poch, J. L. Montesinos, M. del Valle, J. Alonso, A. Araujo, and J. L. F. C. Lima

Abstract: A simulation procedure for the optimization of enzymatic reactors used in sandwich flow injection systems is evaluated. The system is modeled as a plug-flow reactor with axial dispersion. To calibrate it, dispersion coefficients can be evaluated using residence time distribution techniques; meanwhile, enzymatic kinetics must be determined for the system considered, according to the values of the substrate conversion attained. The model has been linked to an optimization routine based on the Powell algorithm. The proposed approach has been evaluated in a system performing simultaneous determinations of glucose and glycerol, considered the common carbon sources in a fermentation process.
Glucose Glycerol Fermentation broth

"Development Of The Rotation Mixing Technology For Approaching To Plug-flow In A FIA Reaction Tube"
Bunseki Kagaku 1998 Volume 47, Issue 7 Pages 411-415
Kiyoshi Hirakawa, Masashi Nishida, Isao Yoshida and Daido Ishii

Abstract: The new technol. for approaching plug flow in a flow injection analysis was developed. A flexible fused SiO2 capillary of 0.35 mm outer diameter as the axis of rotation was inserted into a Teflon-made reaction tube of 1.0 mm inner diameter, 100 cm length. A plug containing the sample and reagents was mixed only in the radius direction, and did not mix in the stream direction, and the resulted stream was changed into a plug flow. The obtained FIA signal was improved to be a sym., such as a Gauss curve.

"Fluid Dispersion-generalization And Comparison Of Mathematical Models. 2. Comparison Of Models"
Chem. Eng. Sci. 1962 Volume 17, Issue 4 Pages 257-264
K. B. Bischoff and Octave Levenspiel

Abstract: The models for axial-dispersed plug flow and dispersed plug flow are interrelated and are also related to more general models which do not assume plug flow and constant values for the dispersion coefficients. These relations are considered with restrictions.