### Contact Info

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

## Modeling

### Citations 85

**"Non-linear Calibration In Single Point Flow Titration Of Protolytes - A Comparison Of Model Options By Using Delta Test"**

*Anal. Chim. Acta
2000 Volume 414, Issue 1-2 Pages 221-237*

Fernando Albertús, Isel Cortés, Manuel Alvarez and Victor Cerda

**Abstract:**The complete description of the non-linear absorbance/concentration relationship obtained for systems used in single point photometric flow injection titrations of acids and bases is presented. The applicability of different models for fitting calibration data, as well as the more frequently used data processing options, are investigated under normal and restraining conditions by using experimental and simulated data sets. Theoretical and empirical models are examined in order to choose the simplest and the more efficient ones to provide good recoveries. The comparison among models is based on a novel statistical criterion (Delta Test) for contrasting the prediction efficiency by detecting systematic errors in estimated concentrations.

**"Integrated Conductimetric Detection: Mass Distribution In A Dynamic Sample Zone Inside A Flow Injection Manifold"**

*Anal. Chim. Acta
1999 Volume 379, Issue 1-2 Pages 99-106*

Francisco J. Andrade, Fernando A. Iñon, Mabel B. Tudino and Osvaldo E. Troccoli

**Abstract:**The insights provided by integrated detection (conductimetric) as a novel approach to follow physical dispersion in continuous-flow manifolds are presented. This approach replaces the conventional instantaneous detection and permits to follow the dispersion phenomena, including details of the radial component as the sample plug travels the manifold. Integrated detection permits to look at the radial dispersion in a detailed manner inaccessible to instantaneous detection. The effect of different experimental parameters affecting mass distribution was studied (e.g., flow rate, tube length and diameter, injected sample volume, and reactor type) and their effects on integrated response curves are discussed. A single channel manifold employing aqueous nitric acid as the conducting carrier, and water injected as sample plug, and playing the role of an insulator, provided the physicochemical model for the reported studies.

**"Continuous, Pulsed And Stopped Flow In A Micro-flow Injection System (numerical Vs Experimental)"**

*Anal. Chim. Acta
1999 Volume 378, Issue 1-3 Pages 111-117*

E. B. van Akker, M. Bos and W. E. van der Linden

**Abstract:**The effects of continuous, pulsed and stopped flow on the dispersion of a sample injected into a µflow injection system were studied. A channel with a volume of 1 µl was used to compare experimental results with numerical results. The injection was 0.067 µl of bromocresolgreen solution into a borax solution, the detection volume was ~0.047 µl. To study the effect of the flow rate, response curves were measured at 0.5, 1.0, 2.0, 3.0, 4.0 and 5.0 µl min-1. Different time intervals ranging from 10 to 400 s were used to investigate the effect of stopped flow. The effect of pulsed flow was studied at different frequencies ranging from 5 to 0.1 Hz. The results for continuous flow obtained with the numerical model are in agreement with the experimental values. For stopped and pulsed flow there is a small difference between the experimental and numerical results that can be explained by the value of the adopted numerical diffusion coefficient. A decrease in the (continuous) flow rate causes a decrease in the dispersion of the sample. The results obtained with a pulsed flow show no significant difference in comparison to the results obtained with continuous flow when the pulse frequency is above a lower limit. The lower pulse limit in the flow system used in this paper is 1 Hz. Stopped flow has virtually no effect on sample dispersion.

**"A Modeling Approach To Establish Experimental Parameters Of A Flow-through Titration"**

*Anal. Chim. Acta
1980 Volume 114, Issue 1 Pages 235-246*

H. F. R. Reijnders and J. F. Van Staden, G. H. B. Eelderink, B. Griepink

**Abstract:**A flow-through titrimeter with optical detection and the flow-through titration of sulphate have been studied by using control engineering methods. Qualitative chemical descriptions and systems analysis yield a model covering different precipitation rates of barium sulphate. The validity of the model is proved by comparing simulated and real experiments. Possible uses of the model are indicated. The signal of the titrimeter is shown to be independent of dilution and turbidity, because of the special detection arrangement.

**"Kinetic Treatment Of Unsegmented Flow Systems. 3. Flow Injection System With Gradient Chamber Evaluated With A Linearly Responding Detector"**

*Anal. Chim. Acta
1986 Volume 179, Issue 1 Pages 169-179*

Harry L. Pardue and Paul Jager

**Abstract:**The flow system was essentially as used in Parts I and II (Anal. Abstr., 1981, 41, 3J7, 3J8). The thin-layer electrochemical detector comprised a platinum working electrode and a vitreous-carbon counter-electrode at a p.d. of 200 mV. The reaction between I3- and S2O32- in phosphate buffer at pH 6.0 was studied as an example. Equations were evaluated for situations in which(I) neither the flow stream nor the gradient chamber,(II) only the flow stream and (iii) both the flow stream and chamber contained S2O32- reactant. Both calibration data and response graphs showed good agreement between theory and experiment except for(II). In(II), the theory accurately predicted the nature of the response but gave slightly longer completion times than were achieved experimentally.

**"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.

**"Unsteady Motion In Single-line Flow Injection Systems"**

*Anal. Chim. Acta
1987 Volume 201, Issue 1 Pages 109-116*

Spas D. Kolev and Ernõ Pungor

**Abstract:**Unsteady motion in single-line flow-injection systems consisting of n tubular elements with valve or hydrodynamic injection is studied theoretically. A formula for the duration of the initial period of unsteady flow is derived. This initial period is much shorter than the mean residence time of the analyte in practical systems. It can therefore be neglected in mathematical modelling of such systems. Experimental data obtained with single-line systems with valve and hydrodynamic injection confirmed the validity of the theoretical equations.

**"Influence Of The Main Parameters Of Single-line Flow Injection Systems Without Chemical Reaction On The Output Signal. 1. Dispersion Characteristics Of The Main Sections Of The Flow System"**

*Anal. Chim. Acta
1988 Volume 208, Issue 1 Pages 117-132*

Spas D. Kolev and Ernö Pungor

**Abstract:**Single-line flow-injection systems with valve, hydrodynamic, syringe or δ-function injection of the analyte are considered. Appropriate equations for calculating the Peclet numbers of their main sections (i.e., the fore-section, the injection section, the reactor, the measurement cell, and the after-section) are described. Two types of reactor with different dispersion characteristics (i.e., straight tube and coiled tube reactors) are considered. The detector is assumed to measure one of three concentrations: (1) the mean concentration in the cross-section of the flow situated in the middle of the measurement cell; (2) the average integral concentration in the whole volume of the measurement cell; or (3) the average integral surface concentration at the inner walls of the measurement cell. Equations for calculating the Laplace transform of the surface and the integral surface concentration, and for the mean and the variance of the corresponding concentration curves are derived. The conclusions made can be used to investigate the influence of the main parameters of single-line flow-injection systems on sample throughput by simulation of the mathematical models.

**"Influence Of The Main Parameters Of Single-line Flow Injection Systems Without Chemical Reaction On The Output Signal. 2. Simulation Of The Mathematical Models"**

*Anal. Chim. Acta
1988 Volume 208, Issue 1 Pages 133-149*

Spas D. Kolev and Ernö Pungor

**Abstract:**Simulations based on the mathematical models outlined in Part 1 are used to study the dependence of peak broadening on design and performance parameters as well as on the diffusion coefficient of the analyte particles (e.g., ions, molecules), the viscosity of the carrier solution and the temperature of the flow. The Peclet numbers of the various sections of the flow system are calculated by the equations discussed in Part 1. The predictions from the simulations agree fairly well with earlier experimental data. On the basis of the results obtained, various possibilities for increasing the sample frequency of single-line flow-injection systems are outlined.

**"Multicomponent Determinations In Flow Systems By Partial Least Squares Modeling"**

*Anal. Chim. Acta
1988 Volume 211, Issue 1-2 Pages 1-10*

Ingrid Lukkari, Walter Lindberg

**Abstract:**Multivariate calibration was used for data analysis in continuous-flow and flow injection systems. Titrations of UV-absorbing organic acids were studied for experimental evaluation of the concepts involved, with single- or multi-wavelength detection and diode-array detection. Experimental arrangements for achieving a concentration. gradient of the sample in the reagent stream are discussed. Multi-component determinations were made, based on the peak shape of the signal.

**"Impulse/response Functions Of Individual Components Of Flow Injection Manifolds"**

*Anal. Chim. Acta
1988 Volume 214, Issue 1-2 Pages 77-86*

I. C. van Nugteren-Osinga, M. Bos and W. E. van der Linden

**Abstract:**Mathematical deconvolution is applied to evaluate the impulse/response functions of the individual parts of a flow injection manifold system. A fast Fourier transform algorithm was used. The results enable prediction of performance of other modular arrangements of such parts.

**"Solution Of Mathematical Models Of Flow Systems Used In Analytical Chemistry And Process Analysis In The Case Of Slug And Time Injection"**

*Anal. Chim. Acta
1990 Volume 229, Issue 1 Pages 183-189*

Spas D. Kolev

**Abstract:**Simple relationships have been derived for reduction of the analytical solutions obtained when using distributed- and lumped-parameter models for slug and time injection to the solutions for step- or δ-function inputs. The relationships allow considerable simplification, and afford substantial economy in computational time if numerical integration is performed. The validity of the approach is demonstrated with hydraulic models frequently used in flow injection analysis and chromatography.

**"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.

**"Mathematical Modeling Of Single-line Flow Injection Analysis Systems With Single-layer Enzyme Electrode Detection. 2. Simulation Of The Mathematical Model"**

*Anal. Chim. Acta
1990 Volume 241, Issue 1 Pages 55-69*

Spas D. Kolev, Géza Nagy and Erno Pungor

**Abstract:**Simulations based on the model (see preceding abstract) were used to study the dependence of the detector sensitivity and the sample throughput on the geometrical parameters and the thickness, enzyme activity, buffer capacity and analyte concentration. at the biocatalytic layer and on the flow rate. From the results electrodes with optimum design could be constructed.

**"Mathematical Modeling Of Single-line Flow Injection Analysis Systems With Single-layer Enzyme Electrode Detection. 1. Development Of The Mathematical Model"**

*Anal. Chim. Acta
1990 Volume 241, Issue 1 Pages 43-53*

Spas D. Kolev, Géza Nagy and Erno Pungor

**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.

**"Mathematical Modeling Of Single-line Flow Injection Analysis Systems With Single-layer Enzyme Electrode Detection. 3. Experimental Verification Of The Model"**

*Anal. Chim. Acta
1991 Volume 254, Issue 1-2 Pages 167-175*

Spas D. KolevGéza Nagy and Ernö Pungor

**Abstract:**Electrodes were prepared by immobilization of glucose oxidase and urease, each by two techniques, and the effects of the initial substrate concentration, the enzyme concentration. in the reaction layer, its thickness and the buffer concentration. on the output signal were determined. The results agreed well with predictions by a mathematical model for such systems.

**"Mathematical Modeling Of Two-analyte Sequential Determinations By Flow Injection Sandwich Techniques"**

*Anal. Chim. Acta
1991 Volume 254, Issue 1-2 Pages 177-187*

J. L. Montesinos, J. Alonso, M. del Valle, J. L. F. C. Lima and M. Poch

**Abstract:**The modeling of the technique, described previously by the authors et al. (Ibid., 1990, 234, 67) was extended to multi-component analysis and was applied to the enzymatic determinations of glucose and glycerol with two different reagent solution The predictions made for the peak height for both individual and two-component determinations showed a good correlation between simulated and experimental values.

**"Influence Of The Main Parameters Of A Parallel-plate Dialyzer Under Laminar Flow Conditions"**

*Anal. Chim. Acta
1992 Volume 257, Issue 2 Pages 317-329*

Spas D. Kolev* and Willem E. van der Linden

**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.

**"Analysis Of Transient Laminar Mass Transfer In A Parallel-plate Dialyzer"**

*Anal. Chim. Acta
1992 Volume 257, Issue 2 Pages 331-342*

Spas D. Kolev* and Willem E. van der Linden

**Abstract:**Mass transfer under laminar flow conditions is discussed on the basis of the Navier-Stokes equations and the axially dispersed plug-flow model. By fitting the data, relationships were derived for predicting the mass-transfer coefficient and the Peclet number in a parallel-plate laminar flow system with one impermeable wall and an opposite wall at which the concentration. is uniform. This single-stream relation can be utilized for calculating the mass-transfer coefficients in both channels of a co-current parallel-plate dialyzer. The Peclet number in the axially dispersed plug-flow model derived for a parallel-plate flow where both sides are impermeable gives better results when applied to the co-current dialyzer than the single-stream relationship. The results obtained allow the math. modeling of process and anal. flow-through manifolds incorporating a dialysis module.

**"Flow Injection Amperometric System For Enzyme Immunoassay"**

*Anal. Chim. Acta
1992 Volume 261, Issue 1-2 Pages 45-52*

D. M. Ivnitskii*, R. A. Sitdikov and V. E. Kurochkin

**Abstract:**A mathematical model has been developed for describing and thus optimizing the operation of a flow injection amperometric detector with a Pt-wire working electrode and a Ag - AgCl (saturated KCl) counter electrode, which was used with a continuously circulating carrier solution of 0.1 M acetate buffer of pH 4.2 containing 0.1 M KCl for the detection of enzymatically produced iodine (from enzyme immunoassay of IgE with a commercial kit) in the injected sample. The agreement between calculated and experimental analytical parameters was satisfactory. Simultaneous evaluation by means of a photometric ELISA reader showed that the electrochemical sensor could be used to determine 1.5 to 100 kiu L-1 of IgE in blood. The technique could be used in conjunction with appropriate immunosorbents for the immunoenzymatic determination of hormones, enzymes, drugs, antibodies and viruses. A flow injection amperometric system was developed for monitoring the results of enzyme immunoassay. The operation of the flow-through amperometric detector is described by a limiting current equation for the working wire electrode. The possibility of the optimization of the geometry and hydrodynamic properties of amperometric detectors in flow systems was demonstrated. The flow system was tested in the determination of peroxidase and IgE in blood serum. Peroxidase (marker enzyme) was determined in the concentration. range 5 x 10^-12 - 4 x 10^-10 M. The detection limit for IgE in blood serum was 3.1 ng mL-1. The sample throughput was 400 hr-1.

**"Simple Model Of Flow Injection Sample Transport For Prediction Of Peak Heights"**

*Anal. Chim. Acta
1992 Volume 261, Issue 1-2 Pages 549-556*

S. R. Bysouth and J. F. Tyson*

**Abstract:**Existing approaches in which a flow injection manifold is considered as a segmented system have been extended so that the number of divisions, both longitudinally and radially, varies with the residence time of the sample plug. This permits peak heights to be reliably predicted when various operating conditions in the flow injection manifolds described are changed. BASIC computer programs were used in the modelling process, which successfully predicted the spectrophotometric peaks produced by using real manifolds and required only minor modification to be extended to other systems of valves and detectors. Detector volume was shown to have little effect on peak shape unless the injected volume was less than the detector volume A model of the flow characteristics of a simple single-line flow injection manifold is described and evaluated for the effects of various operating conditions on peak parameters, in particular peak height. The model is based on the mechanism for dispersion of diffusion across concentration. gradients generated by laminar flow in a closed circular pipe. The flow conduit is considered to be divided into a number of segments both radially and longitudinally. The number of the segments in both dimensions is calculated from an empirically derived relationship from the initial input parameters of length, internal diameter, sample volume, detector volume and flow-rate. An iterative procedure assigns whole number values to the number of segments. Both normal and reverse procedures can be modelled. Diffusion is modelled by averaging the concentration. of any one segment over those with which it has a common boundary and flow by transport of a proportion of the contents of a segment according to a parabolic velocity profile. The performance of the model was evaluated from the predicted peak heights for manifolds in which injector volume, flow-rate and tube length were varied. The predicted effect of changing the volume of the detector was examined The model indicates that detector volume has little effect on peak shape unless the injected volume is less than the detector volume.

**"Dispersion Phenomena In Flow Injection Systems"**

*Anal. Chim. Acta
1992 Volume 267, Issue 1 Pages 1-24*

R. DeLon Hull, Robert E. Malick and John G. Dorsey*

**Abstract:**This review discusses the various models reported to describe sample dispersion in both non-reactive and reactive systems. Predictive models (which describe only the dispersion, e.g., in a flow injection manifold) and descriptive models (which may also describe dispersion in the injection, detection and connecting parts of the assembly) are reviewed. (112 references). A review 112 references. Reproducible dispersion is the basis for anal. by flow injection (FI) methods and is also used in several other sample handling and anal. systems (e.g., liquid chromatography connecting tubing, injectors, detectors, and post-column reactors). However, a uniformly acceptable understanding or description of dispersion is currently not available. Theoretical treatments (mathematical models) of dispersion were developed for both nonreactive (sample does not react with carrier) and kinetic (sample and carrier react) systems. Historically, chemical engineering hydraulic models were used as predictive estimators for FI response curves. These predictive models typically describe only the dispersion in the FI manifold and do not incorporate the influence of the injection, detection, or connecting components of the system. Recently, descriptive models which use deconvolution of the response curve to describe the dispersion produced by the anal. system were reported. This review details the various approaches that were used to describe dispersion in FI systems and includes both predictive and descriptive models.

**"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.

**"Simultaneous Enzymic And Tautomeric Reactions Of D-fructose In A Reactor With Immobilized Hexokinase"**

*Anal. Chim. Acta
1993 Volume 271, Issue 1 Pages 39-45*

Mikael Skoog and Gillis Johansson*

**Abstract:**A computer model was developed for the description of the simultaneous enzymatic conversion and tautomerization reactions during phosphorylation of D-fructose by hexokinase in a small immobilized-enzyme reactor. The predicted conversion to fructose-6-phosphate was compared with the value observed in a flow injection system. An iteration procedure was applied to allow the evaluation of competing enzymatic tautomerization rate constants with consideration of four tautomers. The slow ring opening of β-fructopyranose was seen to complicate the determination of fructose by rapid tautomer-selective enzymatic methods.

**"Mathematical Model Of Flow Injection Analysis. First-order Chemical Reaction In A Straight Tube"**

*Anal. Chim. Acta
1993 Volume 278, Issue 2 Pages 307-316*

V. P. Andreev* and M. I. Khidekel

**Abstract:**Analytical expressions for the parameters of sample and chemical reaction product concentration distribution in a straight reaction tube were obtained to analyze the dependence of sample and product peak shapes on their diffusion coefficient, chemical reaction rate constant, tube dimensions and modes of FIA. The model was compared with results available from numerical analysis and experiment.

**"Random Walk Simulation Of Flow Injection Analysis. Evaluation Of Dispersion Profiles"**

*Anal. Chim. Acta
1993 Volume 278, Issue 2 Pages 293-306*

Peter D. Wentzell*, Michael R. Bowdridge, Elizabeth L. Taylor and Craig MacDonald

**Abstract:**The random walk model was used to simulate peak shapes in FIA for the case of dispersion in straight tubes with laminar flow (no reaction). The peak profiles obtained were compared with experimental and other theoretical results. Agreement was favourable, although there were some differences from experimental results. The results show that the model is as effective as others for modeling peak shapes and that modifications to flow parameters can be incorporated easily for testing physical models.

**"Evaluation Of A Predictive Steady-state Flow Injection Method Adapted To An Open Flow Tube With A Tracer"**

*Anal. Chim. Acta
1995 Volume 303, Issue 2-3 Pages 199-210*

Julie A. Roussin, Jianwei Li and Harry L. Pardue*

**Abstract:**Portions of 50-750 µL of 0.39-1.18 mM tri-iodide in a phosphate buffer of pH 6 were analyzed by FIA using flow rates in the range 16.7-31.3 µL/s, and were detected amperometrically at a potential of 200 mV using Pt electrodes. Using the data, a model is described whereby the leading edge of the response peak is processed to predict the steady-state signal that would have been obtained if sufficient undiluted sample had been used to fill the flow cell. The model correlated well with conventional peak height/area/width data processing techniques, the largest deviations from linearity being noted with peak width parameters. The technique however did require a larger minimum sample injection volume.

**"Predictive Model For Coulometric Operation In A Thin-layer Amperometric Flow Cell"**

*Anal. Chim. Acta
1995 Volume 306, Issue 1 Pages 115-122*

Danut-Ionel Vaireanu, Nigel Ruck and Peter R. Fielden*

**Abstract:**A theoretical model is presented that may be usefully employed to establish the limiting geometric and hydrodynamic conditions for a thin-layer cell to attain 100% coulometric efficiency. The thin-layer cell, based on a glassy-carbon electrode 5 cm in length (the flow path) and 2 mm wide was tested for three different channel heights at high and low flow rates (1 and 60 ml/h) using 1 mM potassium hexacyanoferrate(II) as the electrochemical probe in conjunction with a flow injection system.

**"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.

**"Evidence Of Axial Diffusion Accompanied By Axial Dispersion With Zone Circulating Flow Injection And Analysis Data"**

*Anal. Chim. Acta
1995 Volume 309, Issue 1-3 Pages 227-239*

Yoshio Narusawa* and Yuichi Miyamae

**Abstract:**The inter-relationships of axial and radial dispersion with FIA operating parameters are critically examined and discussed. Using a computer-simulation, the relationship between axial dispersion and analyte residence times is clarified, and a model of axial dispersion free from contributing diffusional effects is presented.

**"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.

**"Effect Of Chemical Diffusivity On The Peak Shapes In Flow Injection Analysis With Sample Or Reagent Injection"**

*Anal. Chim. Acta
1995 Volume 310, Issue 2 Pages 329-336*

Jinxin Li*, Guojun Liu, Huichang Ma and Takashi Korenaga

**Abstract:**An FIA signal peak was considered to consist of two overlapping peaks corresponding to the two reagent/sample interfaces. The difference in residence time between the front and rear peaks was investigated in the sample injection (SI) and the reagent injection (RI) modes. A mathematical dispersion model was presented to explain the differences in residence times. The relative reagent and sample concentrations, the injection volumes and the diffusivities of the sample and reagent were shown to effect peak shape and detection sensitivity.

**"Online Fault Detection Of Flow Injection Analysis Systems Based On Recursive Parameter Estimation"**

*Anal. Chim. Acta
1995 Volume 313, Issue 3 Pages 161-176*

Xiaoan Wu and Karl-Heinz Bellgardt*

**Abstract:**A fault detection method for FIA systems was developed based on the estimation, filtering and evaluation of the model parameter. A mathematical process model was used to describe the FIA system with known input and measurable output variables. The model parameters for the system were estimated by the recursive fixed memory method. The estimated model parameters were filtered through a high- and low-pass filter to detect system faults.

**"Assessing The Validity Of Principal-component Regression Models In Different Analytical Conditions"**

*Anal. Chim. Acta
1997 Volume 337, Issue 3 Pages 287-296*

A. Rius*, M. P. Callao, J. Ferré and F. X. Rius

**Abstract:**A methodology was proposed for checking the validity of a principal component regression model when the experimental conditions had changed from those existing during the development of the model. The method was based on re-measuring a subset of the sample set that had been used to construct the model and assessing the trueness and precision of the results by statistical techniques. The approach was evaluated using a simulated data set and also experimental data for the determination of various analytes in water by sequential injection spectrophotometric analysis. This study proposes a methodology for assessing the validity of principal component regression models when the experimental conditions which have been used in the process of modeling may have changed. The methodology proposed is based on the procedure for selecting the validation sample subset which includes the D-optimal criterion and application of Fedorov's exchange algorithm. Two basic performance characteristics define the validity of the models: trueness is assessed by linear regression using the joint confidence test for the slope, and the intercept and precision is estimated by bias corrected MSEP and RRMSEP. The methodology is validated with a simulated data set and three real data sets corresponding to models constructed for spectrophotometric data from determinations of various analytes in waters using sequential injection analysis (SIA). Using a reduced number of samples can be very useful in several applications, such as in process analysis control, and is especially useful as an initial step to check the need for standardization.

**"Evaluation Of Natural Computation Techniques In The Modeling And Optimization Of A Sequential Injection Flow System For Colorimetric Iron(III) Determination"**

*Anal. Chim. Acta
1997 Volume 348, Issue 1-3 Pages 143-150*

J. de Graciaa, M. L. M. F. S. Saraviab, A. N. Araújob, J. L. F. C. Limab, M. del Vallec and M. Pochd,*

**Abstract:**The present study shows and gives evidence of the applicability of natural computation techniques in the modeling and optimization of a sequential injection flow system of anal. for colorimetric iron(III) determination in water samples. The reaction with thiocyanate is used as reagent color. A neural network consisting of two hidden layers, each one formed by eight neurons, was used to model the system. Optimization of the system in terms of sensitivity, linearity and sampling rate was carried out by using jointly the neural network and genetic algorithms. The latter were used with a set of 50 crossed and mutated chromosomes over 100 generations. In the system thus developed, 140 µL of sample and 70 µL of reagent were sequentially introduced into the holding coil and propelled toward the detector at a flow of 5 mL/min. The system gave a sampling rate of 110 samples per h. A comparison of the results obtained in the anal. of six samples with those obtained using the reference method (atomic absorption spectrophotometry) showed the high quality of results provided.

**"Simultaneous Dermination Of Iron (II) And Iron(III) By Flow Injection Analysis. A Mathematical Simulation Of The Detector Response"**

*Anal. Chim. Acta
1997 Volume 348, Issue 1-3 Pages 101-112*

Milko Novi, Marjana Novi*, Jure Zupan, Nadja Zafran and Boris Pihlar

**Abstract:**A mathematical model for the description of the detector signal obtained in flow injection asynchronous merging zone technique (FIA-AMZ) is proposed. FIA-AMZ is based on the separate injection of a sample and an appropriate reagent in such a way that both injected solutions are covered only partly. The resulted detector signal consists of two consecutive peaks whose heights are proportional to the concentration of the detectable component present in the sample and another component which becomes detectable after the reagent has been added. The detector signals (the concentration profiles of the analytes) are described by a modified Gauss curve, which proved to be better than a combination of Gauss-Lorentz curves. The conversion of undetectable to detectable form of the analyte is described by a sigmoidal function the slope of which corresponds to the frontal dispersion of the added reagent and to the reaction kinetics. The model is tested on the system for the simultaneous spectrophotometric determination Fe2+ and Fe3+. It is shown that fitting of the experimental curves with a model function enables the optimization of the experimental conditions at applied FIA manifold, and consequently the simultaneous determination of concentrations of Fe2+ and Fe3+ ions in a single measurement.

**"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

###### 'Convection And Diffusion In A Micro-flow Injection System', Anal. Chim. Acta, 1998 373(2-3) 227-239

**"Convection And Diffusion In A Micro-flow Injection System"**

*Anal. Chim. Acta
1998 Volume 373, Issue 2-3 Pages 227-239*

E. B. van Akker*, M. Bos and W. E. van der Linden

**Abstract:**Five micro-structures were used to study the effect of the convection and diffusion behavior (dispersion) of a dye in a micro-flow system. Besides a straight manifold, manifolds with curved bends and manifolds with rectangular bends were constructed. The dispersion resulting from hydrodynamic injection of a dye sample in a micro-flow system was measured for two structures. The detection was done spectrophotometrically. The sample dispersion through the five structures was also studied with a computational fluid dynamics (CFD) software tool. Both the numerical and a structure with 40 rectangular bends exhibits a slightly larger dispersion compared to a straight channel or a channel with curved or a few rectangular bends. However, the difference in dispersion is minimal. The use of sharp bends to establish a flow system with a certain traveling distance within a small area has minimal effects on the dispersion of a sample under the conditions described. The general numerical model allows the calculation of the flow profile, pressure distribution and the concentration. distribution of the sample, three dimensionally, throughout an arbitrary channel.

**"Specific Rotation Measurements From Peak Height Data, With A Gaussian Peak Model"**

*Talanta
1989 Volume 36, Issue 4 Pages 473-478*

Patrick D. Rice, Yvonne Y. Shao, Steven R. Erskine, Timothy G. Teague and Donald R. Bobbitt*

**Abstract:**A method is described whereby a sensitive laser-based polarimeter can be used to make very accurate and precise specific rotation measurements on microgram quantities of optically active materials. Flow injection or liquid chromatography systems provide reproducible introduction of the sample into the polarimetric system. If a Gaussian distribution of the analyte concentration is assumed, the peak height can be used in the determination of specific rotation. This method provides a direct calibration with an absolute standard which yields more accurate and precise results than those obtainable by using peak area.

**"Decisive Problems Of Zone-circulating Flow Injection Analysis And Its Solution"**

*Talanta
1998 Volume 45, Issue 3 Pages 519-529*

Yoshio Narusawa* and Yuichi Miyamae

**Abstract:**Although experiment and computer anal. of zone-circulating flow injection analysis (ZCFIA) data were studied, there are still some essential problems inherent to ZCFIA. Computer program of high dimensional modified simplex method was used for resolving peaks of ZCFIA damped response curves. Peaks are resolved from the criterion that each area of the peak surrounded by the curve and the abscissa is equal, because each sample zone circulates repeatedly in the manifold in equal volume As a result, the peaks of the damped response curve were resolved into each component and the curve obtained by summing these components is equal to the original response curve. By following up the data anal. of ZCFIA, there were many conflicts in the manual anal. of data by Li. At least, the dispersion in a flow system should not be studied by ZCFIA, and it might be studied by the single-line manifold of FIA.

**"Models For Dispersion In Flow Injection Analysis. 1. Basic Requirements And Study Of Factors Affecting Dispersion"**

*Analyst
1987 Volume 112, Issue 4 Pages 515-521*

David C. Stone and Julian F. Tyson

**Abstract:**The various approaches adopted for accounting for dispersion behavior in flow injection analysis are examined and the advantages of a modelling approach are discussed. The variation of the dispersion coefficient as a function of (a) flow-rate, (b) tube length, (c) tube inner diameter and (d) method of injection obtained under typical flow injection conditions are studied and discussed. Explanations for some of the effects observed are presented in terms of molecular diffusion and convective flow patterns. The advantages of time injection over the more usual slug injection are clearly demonstrated and the use of the single well stirred tank model to describe the relationship between volume injected and dispersion coefficient under conditions of time injection are examined. The applications of this model to describing the entire curve shape for slug injection and of the potentially more versatile two-tank model are briefly introduced.

**"Use Of A Model Gut System To Study The Effects Of Dietary Fibre And Multivitamins On The Speciation Of Copper, Zinc And Iron"**

*Analyst
1995 Volume 120, Issue 8 Pages 2085-2088*

Mustafa S. Dundar and Stephen J. Haswell

**Abstract:**A model gut system, representing the stomach and intestinal tract and incorporating an enzymolysis procedure, was designed to examine the speciation of Cu, Zn and Fe and their complexation with fiber and multivitamins. Samples were treated in two ways: (i) incubation with pepsin at pH 3.5 for 4 h at 37°C; (ii) as for (i) followed by incubation with pancreatin and amylase at pH 7.4 for 4 h at 37°C. In both cases, the reaction mixture was centrifuged after enzymolysis was complete. The solid residue was digested with HNO3/HCl and then analyzed together with the supernatant solution for Cu, Zn and Fe by flow injection ICP-MS (details given). The solubility of Cu, Zn and Fe increased in the gut but decreased in the intestinal tract. Fiber had the greatest influence on the solubility of Cu, Zn and Fe in the intestinal tract, while multivitamins had a less pronounced effect. The reduction in solubility was greatest for Zn but significantly less for Fe and Cu. The results are discussed.

**"Automatic Determination Of Optimum Dilution Levels For Laser-enhanced Ionization Detection Of Matrix-interfered Sample By Flow Injection"**

*Analyst
1995 Volume 120, Issue 10 Pages 2593-2599*

Shau-Chun Wang and King-Chuen Lin

**Abstract:**A flow injection (FI) system was interfaced to a laser-enhanced ionization (LEI) apparatus in order to reduce electrical interference in the latter. The technique involved the injection of a water plug into a carrier stream of the sample solution. The concentration gradient generated significantly reduced the electrical interference induced by the sample matrix and enabled a LEI signal to be obtained for the analyte. The use of FI also allowed the automatic determination of the optimum dilution levels for maximum LEI signal enhancement. The theoretical basis of the FI-LEI technique was also studied. Equations were derived that enabled the relative intensity of the FI-LEI signal, as a function of the sample matrix concentration, to be predicted. The method was illustreated with the detection of 4 ppm In in a solution containing an Na-matrix concentration greater than the threshold level (4-10 ppm under optimum conditions) at which no conventional LEI signal is detectable.

**"Validation Of An Automatic Urea Analyser Used In The Continuous Monitoring Of Haemodialysis Parameters"**

*Analyst
1996 Volume 121, Issue 7 Pages 959-964*

M. Jurkiewicz, S. Solé, J. Almirall, M. García, S. Alegret and E. Martínez-Fàbregas

**Abstract:**The performance of an automated urea analyzer., based on a flow injection system incorporating an immobilized urease reactor with potentiometric detection, was evaluated for the monitoring of haemodialysis parameters. The analyzer. was used to measure the urea concentration in haemodialysis effluents online. A mathematical model was employed to process the data and to calculate the dialysis parameters, viz., dialysis delivery (KT/V) and protein catabolism (PCRn). The results obtained were compared with those obtained by the method traditionally employed in hospital laboratories. No significant differences were found between the two sets of results.

**"Multivariate Statistical Process Control Applied To Sulfate Determination By Sequential Injection Analysis"**

*Analyst
1997 Volume 122, Issue 8 Pages 737-741*

A. Rius, M. P. Callao and F. X. Rius

**Abstract:**A carrier solution of 0.1 M HClO4 was aspirated (2 ml/min) into a holding coil (200 cm x 0.8 mm i.d.) for 55 s followed by the sample (2 ml/min) for 2 s and a reagent solution (2 ml/min) of 0.02 M iron(III) nitrate in 0.34 M HClO4 for 5 s. The mixture was then propelled (2 ml/min) through a reaction coil (70 cm x 0.8 mm i.d.) for 20 s and the absorbance spectrum was recorded from 300-400 nm 20 s after the flow had stopped. A partial least squares multivariate calibration model was developed and used to predict the sulfate concentration in the sample (range covered: 0-500 mg/l sulfate). The throughput was 20 samples/h. Multivariate statistical process control techniques were used to check the stability of the system before developing the model and the validity of the model when it was used to predict the concentrations of unknown samples. The method was applied to natural waters.

**"Flow Injection Atomic Absorption Spectrometry: The Kinetics Of Instrument Response"**

*J. Anal. At. Spectrom.
1986 Volume 1, Issue 1 Pages 63-74*

John M. H. Appleton and Julian F. Tyson

**Abstract:**The non-ideality of AAS for detection in flow injection analysis, i.e., the effect of the AAS detector itself on the observed signal, has been modelled, with general success.

**"Impulse Nebulization Atomic Absorption Spectrometry. 1. Model For The Response Of A Flame Atomizer"**

*J. Anal. At. Spectrom.
1988 Volume 3, Issue 1 Pages 217-225*

László Bezúr

**Abstract:**A model for predicting the instrumental response with impulse-nebulization or flow injection sample introduction is developed, based on the mass balance of the atomizer, axial dispersion and the time constant of the spectrometer, and involving all the important parameters, e.g., sample concentration, volume and flow rate, nebulization efficiency and gas flow rate. It gives good agreement with experiment for impulse nebulization, and shows that the dispersion increases from the front to the rear of a flow injection AAS peak.

**"Critical Evaluation Of The Efficiency And Synergistic Effects Of Flow Injection Techniques For Sensitivity Enhancement In Flame Atomic Absorption Spectrometry"**

*J. Anal. At. Spectrom.
1992 Volume 7, Issue 2 Pages 293-300*

Zhaolun Fang, Liping Dong and Shukun Xu

**Abstract:**A mathematical model for evaluating sensitivity enhancement effects of batch offline and flow injection online pre-concentration. in flame AAS is proposed. Preconcentration by column ion exchange, C18 column sorbent extraction and co-precipitation with Fe(II) hexamethylenedithiocarbamate (with and without slotted-tube atom trap) was investigated. The validity of the model was tested in the determination of Pb by flame AAS with flow injection precipitation with a slotted-tube atom trap. A 135-fold sensitivity enhancement was achieved at a sampling frequency of 72 h-1. Math. models for evaluating sensitivity enhancement effects of batch off-line and flow injection (FI) online pre-concentration. systems for flame atomic absorption spectrometry (FAS) are proposed. The performance of four different FI pre-concentration. systems, including pre-concentration. by ion exchange, sorbent extraction and coprecipitation, with additional enhancement effects from organic solvents and slotted-tube atom traps, are critically evaluated in terms of apparent enrichment factors, enhancement factors, concentration. efficiency and consumptive index. The experimental results show good agreement with calculated results based on equations of the math. model. The synergistic effects of different enhancement approaches are illustrated by the determination of lead by FAAS using an FI coprecipitation pre-concentration. system equipped with a slotted-tube atom trap. A 135-fold sensitivity enhancement was achieved at a sampling frequency of 72 h-1 and with the consumption of 2.7 mL of sample solution

**"Dispersion In Segmented Flow-through Glass Tubing In Continuous-flow Analysis: The Ideal Model"**

*Anal. Chem.
1976 Volume 48, Issue 7 Pages 1017-1022*

L. R. Snyder and H. J. Adler

**Abstract:**Sample dispersion or carryover in the flow of air-segmented liquid streams through open tubing is of broad analytical importance, and especially so in the technique of continuous-flow (AutoAnalyzer) analysis. A detailed model for the prediction of such dispersion under certain limiting conditions of practical interest is rederived, expanded, and experimentally verified. This so called "ideal" model assumes perfect mixing within each moving liquid segment.

**"Dispersion In Segmented Flow-through Glass Tubing In Continuous-flow Analysis: The Non-ideal Model"**

*Anal. Chem.
1976 Volume 48, Issue 7 Pages 1022-1027*

L. R. Snyder and H. J. Adler

**Abstract:**The "ideal" model of sample dispersion in the flow of air-segmented liquid streams through open tubing is expanded here to include the effects of slow mixing within moving liquid segments. The resulting "non-ideal" model allows prediction of sample dispersion in segmented flow over a broad range of experimental conditions. Comparison of experimental dispersion data with values calculated from the non-ideal model shows excellent agreement. The design of continuous-flow (AutoAnalyzer) systems for minimum dispersion and sample interaction, and/or maximum analysis rates can now be done theoretically, rather than empirically as in the past.

**"Hydrodynamic And Interfacial Origin Of Phase Segmentation In Solvent Extraction/flow Injection Analysis"**

*Anal. Chem.
1985 Volume 57, Issue 1 Pages 329-331*

Frederick F. Cantwell and Jamal A. Sweileh

**Abstract:**A semi-quantitative physico-chemical model has been developed to establish the theoretical basis for understanding the segment-forming process of the cited technique. The segmentor design used for the experimental data was based on a simple T-joint made of Kel-F, which has been used successfully in several applications of this technique.

**"Modeling Chemical Response Surfaces With The Kalman Filter"**

*Anal. Chem.
1988 Volume 60, Issue 9 Pages 905-911*

Peter D. Wentzell, A. P. Wade, and S. R. Crouch

**Abstract:**A method for the ieast-squares modeling of response swlaces based on the Kahnan filter is described. The method is shown to produce resuits that are identical with more traditional methods, such as dngular value decomposition, but uses a recurslve procedure. The new method is applied to three dlfferent chemical systems, including two flow injection analysts systems and a poiamgraphk system, to demonstrate L features. Advantages of the Kahnan fitter approach arWng from its recurslve nature and its shnplklty are dkwrsed, and its relationship to simplex optimization is addressed.

**"Mathematical Modeling Of Single-line Flow Injection Analysis Systems Without Chemical Reaction"**

*Anal. Chem.
1988 Volume 60, Issue 17 Pages 1700-1709*

Spas D. Kolev and Erno Pungor

**Abstract:**Mathematical models are described that take into consideration differences in dispersion properties and geometrical dimensions between each section of the systems considered. The models are designed for use with various methods of sample injection and detection. The application of the models was demonstrated by using single-line flow injection manifolds with syringe, hydrodynamic and valve injection of the sample. Results agreed fairly well with theoretical predictions, demonstrating the use of the models for optimization of flow injection systems without chemical reaction.

**"Amperometric Responses Of Poly(chlorotrifluoroethylene) - Graphite Composite Electrodes With Varying Compositions And Particle Sizes Under Flow Injection And Liquid Chromatographic Conditions"**

*Anal. Chem.
1991 Volume 63, Issue 15 Pages 1651-1658*

Tse Yuan Ou and James L. Anderson

**Abstract:**A mathematical model is presented describing the amperometric response of the cited electrode type under steady-state and LC flow conditions in a thin-layer flow-through cell. The experimental and theoretical results were in agreement. The current response of composite electrodes can be calculated by ratio to that predicted (or measured) for a solid electrode under LC or flow injection conditions.

**"Mathematical Series For Signal Modeling Using Exponentially Modified Functions"**

*Anal. Chem.
1991 Volume 63, Issue 17 Pages 1879-1884*

Alain Berthod

**Abstract:**A method is described for the generation of an acceptable approximation of exponentially modified functions representing parameter changes vs. time. Exponentially modified Gaussian functions give an ideal peak shape model, but not for tailing peaks. Flow injection analysis peaks are more accurately described by exponentially modified square functions.

**"Chemically Facilitated Donnan Dialysis And Its Application In A Fibre-optic Heavy-metal Sensor"**

*Anal. Chem.
1994 Volume 66, Issue 15 Pages 2544-2551*

Zhihao Lin and Lloyd W. Burgess

**Abstract:**A simplified model to describe the mass transport of the cited dialysis process (CFDD) was established, which related the diffusion behavior of metal ions through a Nafion cation-exchange membrane with the stability constant of complexation, the ionic strength of the receiving and sample solutions, the flow rate of the receiving solution and the area-to-volume ratio of the membrane dialysis cell. A heavy metal sensor is also described, in which the CFDD cell was directly interfaced with a fiber-optic colorimetric detection system. A Nafion tubular membrane with one end plugged was placed in sample solution and a fused-silica capillary was inserted into the open end of the membrane to deliver the receiving solution (sodium thiosulfate in acetate buffer of pH 5.1). After dialysis, the receiving solution was mixed with 4-(2-pyridylazo)resorcinol in borate buffer of pH 10.8. The absorbance of the resulting orange-red complexes was measured at 560 nm for Pb(II), 500 nm for Cd(II) and at a reference of 660 nm. The theoretical model was used to identify factors affecting the selectivity and dynamic range of the sensor. Under optimum conditions, using a stopped-flow operation mode, detection limits for both analytes were 3 nM with 20 min accumulation.

**"Amperometric Response Of Mediating Layers On Electrode Surfaces To Gaussian Concentration Profiles In Flowing Streams"**

*Electroanalysis
1992 Volume 4, Issue 8 Pages 751-756*

John F. Cassidy, William Breen, Anthony McGee, Johannes G. Vos, Michael E. G. Lyons

**Abstract:**A model is presented for a semi-porous layer containing catalytic sites, coated on an electrode and used for the mediation of analytes. The coated electrodes are applicable as detectors in flow injection analysis or HPLC. Thin layers with high catalyst loading and high rates of electron exchange led to rectilinear graphs of peak current vs. concentration. for chemically modified electrodes in flowing streams. A model for a layer, containing catalytic centers, coated on an electrode and used for the mediation of analyte in a flowing stream is proposed and solved. The model applies to a situation of a Gaussian concentration. profile of analyte impinging on the outer edge of the mediating layer. The important parameters that limit the current magnitude are the diffusion coefficient of the analyte through the layer, the effective electron diffusion coefficient through the layer, and the rate of reaction between the mediator and the analyte. Literature data showed that layers, high catalyst loading, and high rates of electron exchange lead to linear peak current height vs. concentration. plots.

**"Electroinjection Analysis. Concept, Mathematical Model And Applications"**

*J. Chromatogr. A
1997 Volume 772, Issue 1-2 Pages 115-127*

Victor P. Andreev*, Natalia B. Ilyina, Elena V. Lebedeva, Alexandr G. Kamenev and Nicolai S. Popov

**Abstract:**Mathematical models for the mutually complementary techniques of electroinjection analysis (EIA; a combination of FIA and CZE; Talanta, 1996, 43, 909) and electrophoretically mediated microanalysis (EMMA; Patterson et al., J. Chromatogr., A, 1996, 732, 119) are presented. EIA and EMMA are demonstrated by the determination of Cr(VI) and Co2+, respectively, in water (detection limits 1.4 and 1 ng/ml, respectively).

**"Stacked Modules For Micro-flow Systems In Chemical Analysis: Concept And Studies Using An Enlarged Model"**

*Sens. Actuat. B
1993 Volume 17, Issue 1 Pages 19-25*

J. C. Fettinger, A. Manz*, H. Lüdi and H. M. Widmer

**Abstract:**A valveless FIA system is described comprising a stacked series of 2 mm thick x 50 mm diameter polished Plexiglass elements. The elements have a 35 mm diameter ring of 11 or 12 evenly spaced 1 mm diameter holes with either a 1 cm, 10 cm or 20 cm central hole, a channel, a channel and central hole or no central hole, and are stacked to provide mixing T-pieces, mixing chambers etc. (diagrams given). The use of this modular system was demonstrated with the use of 2.5 mM C. I. Reactive Blue 2 (details given) for sample introduction and injection and was coupled to an optical detector. Samples retained 96-97% of their concentration and calibration graphs were linear with standard deviations of 1%.

**"Evaluation Of A Mathematical Model To Simulate Dynamic Response Of Tubular Potentiometric Sensors In Flow Injection Systems"**

*Sens. Actuat. A
1993 Volume 37, Issue 1 Pages 607-611*

J. de Gracia, J. L. Montesinos and M. Poch, J. Alonso and J. Bartrolí, I. M. P. L. V. O. Ferreira and J. L. F. C. Lima

**Abstract:**Potentiometric detectors based on ion-selective electrodes are specially suited to flow measurements because of their low cost and high selectivity. Simultaneously in flow analysis the use of tubular-electrode configuration seems ideal as the flow characteristics can be kept constant throughout the system. The design of very simple manifolds, which increases the robustness and the system reliability, is constrained by the knowledge of the influence of hydrodynamic parameters in the detector response. With the aim to optimize the design of this kind of systems a mathematical model, that simulates the response of tubular potentiometric detectors in flow-injection systems, has been developed and tested. Results provided by simulation are compared with experimental ones, and the model capabilities are discussed.

**"Dispersion Of Discrete Sample Signals Within Aerosol Spray Chambers: Preliminary Investigations"**

*Spectrochim. Acta B
1996 Volume 51, Issue 14 Pages 1733-1745*

John A. Koropchak*, Salma Sadain and Bogdan Szostek

**Abstract:**A cylindrical glass spray chamber (14.8 cm x 3.1 cm i.d.) ed a three-plate (separation 1.2 cm) polypropylene baffle gave aerosol particle sizes that were generally too large for diffusion to influence band broadening to an extent that would be significant in mass-senve systems, e.g., flow injection ICP-AES, but such diffusion as did occur would probably be important in particle-number-sensitive detectors. A barrel-type spray chamber with a baffle system and various other structures were used for characterization of band-broadening phenomena occurring within aerosol spray chambers, with an ICP-AES detector used in this case. Absolute values of aerosol particle size distributions from nebulizer/spray chamber systems were measured and found to be affected by the relative positions of impact surfaces with respect to the nebulizer. Smaller particles, but less total mass was observed as the baffle was moved closer to the nebulizer tip. However, based on measurements herein, it does not appear that particle sizes in any case will be small enough within the spray chamber for diffusion to influence band broadening for the bulk of the aerosol mass, as particularly important for mass sensitive detectors such as ICP-AES, although diffusion is likely to be important to particle number sensitive detectors. 26 References

**"Simulation And Modeling In Chemical Analysis"**

*Anal. Proc.
1984 Volume 21, Issue 4 Pages 139-140*

D. Betteridge

**Abstract:**A short review, with 4 references, is presented of computer simulation and modeling in the optimization of an auto-analyzer., in the application of queuing theory to the analysis of sample throughput and in simulation of flow injection analysis.

**"A Comparison Of Copper Speciation Results Obtained Using Electrothermal Atomization Atomic Absorption Spectrometry And Computer Modelled Data"**

*Anal. Proc.
1995 Volume 32, Issue 4 Pages 133-135*

Mustafa S. Dundar and Stephen J. Haswell

**Abstract:**A comparative study is described between the direct determination of copper species obtained by electrothermal atomization atomic absorption spectrometry (ETAAS) and the predicted data using the NSPEC computer speciation program. Inorganic copper nitrate and copper citrate species were determined at different pH levels using ETAAS following a range of solid-phase extraction procedures. The results indicated that the NSPEC speciation program and experimental data identified the anionic species to be dominant. For a relatively simple system the NSPEC program can therefore be used to compare theoretical data with experimental data.

**"Applications Of Controlled-dispersion Flow Injection Techniques"**

*Analusis
1988 Volume 16, Issue 9-10 Pages 155-159*

Tyson, J.F.;Bysouth, S.R.;Stone, D.C.;Marsden, A.B.

**Abstract:**Factors affecting dispersion in flow injection analysis are discussed with particular reference to the design of manifolds for analyzes involving online chemical reactions. Mathematical models for flow injection analysis are presented, based on the passage of finite volume of liquid through well stirred tanks, and applications and limitations of the models are discussed.

**"Evaluation Of Artificial Neural Networks For Modelling Enzymatic Glucose Determination By Flow Injection Analysis"**

*Analusis
1992 Volume 20, Issue 3 Pages 127-133*

Campmajo C.; Poch M.; Robuste J.; Valero F.; Lafuente J.

**Abstract:**Artificial neural networks, which are mathematical algorithms from artificial intelligence techniques that try to model the human brain, are described in detail. The application of these networks to the analysis of complex FIA systems is evaluated with use of an enzymatic glucose analyzer. manifold as a case study. The abilities of the networks to predict the effects of flow rates, injection volume and coil lengths on the response of the FIA system are presented. The networks do not require any prior knowledge of the structure of the relationships that exist between important variables; it is sufficient to supply the networks with pertinent information so that they can learn to relate input and output. Results show that the networks are able to simulate FIA peaks but at present the computer time required for the learning process is very long. Although deterministic models have produced some promising results in the description of FIA single channel manifolds, modeling of more complex systems presents further difficulties to be solved. It is therefore interesting to study the application of new modeling techniques to this problem. The object of this paper is to study the use of neural networks in FIA systems modeling. As a case study, an enzymatic glucose analyzer manifold has been chosen. The abilities of neural networks to predict the effects of flow rates, injection volume and coil lengths on the response of the FIA system are presented. The distinctive advantage of neural networks over some other modeling methods is that they do not require any prior knowledge of the structure of the relationships that exist between important variables. All that is needed is to feed the neural network with sufficient pertinent information so that it can learn to relate input and output. The results obtained show that this methodology is able to simulate FIA peaks, but in the present state of knowledge it has drawbacks related to computer time required for the neural network learning process.

**"Combining Mathematical Modelling And The Powell Algorithm For The Optimization Of Flow Injection Sandwich Systems"**

*Analusis
1992 Volume 20, Issue 6 Pages 319-324*

Poch, M.;Montesinos, J.L.;Del Valle, M.;Alonso, J.;Araujo, A.N.;Lima, J.L.F.C.

**Abstract:**In the sandwich procedure, the sample plug is situated between two reagent solution; diffusion at the two interfaces can be used to determine two species, provided that the configuration is optimized. The Powell algorithm is an iterative method in which an initial unidirectional search is made, e.g., up or down a range of values of a given parameter of the system. The initial search then defines a new direction of search and the process is repeated until convergence occurs. This algorithm was applied to the optimization of the injection volume, flow rate and mixing-coil length. A mathematical model was then applied, based on the separate contributions of the leading and trailing edges of the sample plug, which computes the detector response. Peak heights, retention times and degree of overlap can then be optimized.

**"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.

**"Mathematical Model Analysis Of Mouse Epidermal-cell Kinetics Measured By Bivariate DNA Antibromodeoxyuridine Flow Cytometry And Continuous (H-3) Thymidine Labeling"**

*Cell Tiss. Kin.
1990 Volume 23, Issue 5 Pages 409-424*

E. Aarnæs1*, B. Kirkhus and O. P. F. Clausen

**Abstract:**In a previous study the epidermal cell kinetics of hairless mice were investigated with bivariate DNA/anti-bromodeoxyuridine (BrdU) flow cytometry of isolated basal cells after BrdU pulse labelling. The results confirmed our previous observations of two kinetically distinct sub-populations in the G2 phase. However, the results also showed that almost all BrdU-positive cells had left S phase 6-12 h after pulse labelling, contradicting our previous assumption of a distinct, slowly cycling, major sub-population in S phase. The latter study was based on an experiment combining continuous tritiated thymidine [( 3H]TdR) labelling and cell sorting. The purpose of the present study was to use a mathematical model to analyze epidermal cell kinetics by simulating bivariate DNA/BrdU data in order to get more details about the kinetic organization and cell cycle parameter values. We also wanted to re-evaluate our assumption of slowly cycling cells in S phase. The mathematical model shows a good fit to the experimental BrdU data initiated either at 08.00 hours or 20.00 hours. Simultaneously, it was also possible to obtain a good fit to our previous continuous labelling data without including a sub-population of slowly cycling cells in S phase. This was achieved by improving the way in which the continuous [3H]TdR labelling was simulated. The presence of two distinct subpopulations in G2 phase was confirmed and a similar kinetic organization with rapidly and slowly cycling cells in G1 phase is suggested. The sizes of the slowly cycling fractions in G1 and G2 showed the same distinct circadian dependency. The model analysis indicates that a small fraction of BrdU labelled cells (3-5%) was arrested in G2 phase due to BrdU toxicity. This is insignificant compared with the total number of labelled cells and has a negligible effect on the average cell cycle data. However, it comprises 1/3 to 1/2 of the BrdU positive G2 cells after the pulse labelled cells have been distributed among the cell cycle compartments.

**"Studies On The Chemical-kinetics In Flow Injection Analysis System"**

*Gaodeng Xuexiao Huaxue Xuebao
1997 Volume 18, Issue 1 Pages 33-36*

Liu, Z.;Zou, G.W.;Zhang, Y.K.

**Abstract:**Convection-diffusion model was used to study the chemical kinetics in flow injection analysis(FIA) system, Based on the expression of concentration distribution of physical dispersion of sample without chemical reaction, the expressions of concentration distribution of product in single-line FIA system with first-order and second-order chemical reaction under certain conditions were derived by mathematical inductive method, The analytical solutions are very simple so that they can be applied to simulate the produced curves with computer easily, The experimental fact that double-humped peak occurred when sample volume is very large in second-order reaction system was interpreted by the results computer-simulated. In addition, other information concerning chemical kinetics was discussed. 12 References

**"Flow Models In Flow-through Enthalpimetry With A Small Tube Cross Section"**

*Chem. Tech.
1988 Volume 40, Issue 7 Pages 305-306*

Berge, H.;Lammert, R.

**Abstract:**The practical use of single-line construction, hydrodynamic injection, and displacing dosage are demonstrated and advantages and disadvantages of different constructions are discussed. The combination of flow-through enthalpimeter with flow-injection anal. technique enabled attaining high throughput rates for samples and low accumulation of heat. (SFS)

**"Investigation Of The Error Structure Of The Calibration Curve For Periodate Determination By Flow Injection Analysis And Chemiluminescence Detection"**

*Chemom. Intell. Lab. Syst.
1991 Volume 12, Issue 1 Pages 39-47*

N. P. Evmiridis* and E. M. Papamichael

**Abstract:**Experimental data on periodate determination by flow injection analysis and chemiluminescence detection is fitted to a model equation using the pattern search method. A large number of parameter estimates are obtained from simulated data generated by means of a computer program implemented by a random number generator and their parameter estimate means and variances are compared with the set of parameters obtained from the experimental data. The %-bias, %-excess variance, skewness and excess kurtosis, of the parameter estimates from the simulation study are also calculated to determine the effect of errors on the parameter values. The procedure was followed for different criteria of convergence of the fitting routine and type of errors in the response value and outliers selected at random. The statistical parameters of the model equation parameter estimates are compared in relation to the various convergence criteria for best performance.

**"Statistical Evaluation Of Phosphorus Breakthrough Profiles Using A Segmented Exponential Model"**

*Commun. Soil Sci. Plant Anal.
1997 Volume 28, Issue 3-5 Pages 395-406*

McGeehan, S.L.;Shafii, B.;Naylor, D.V.;Price, W.J.

**Abstract:**Few studies have utilized a statistical approach for the evaluation and comparison of breakthrough profiles obtained from soil column investigations. Our objective was to investigate the use of nonlinear estimation techniques to identify the phosphorus (P) breakthrough point and other parameters endemic to breakthrough data. Four soils exhibiting a range in physical and chemical properties were leached under saturated-flow conditions with a 10 mg P/Z solution for 34 days. Leachate P concentrations were analyzed by flow injection colorimetric analysis. A four-parameter segmented exponential model provided a good fit for the breakthrough data in each soil tested. In addition to identifying the breakthrough point, the model parameters provided estimates of other identifiable aspects of a breakthrough profile including background P concentration, equilibrium P concentration, and the rate of concentration change once breakthrough is attained. Estimation of these parameters also facilitated statistical comparison of breakthrough profiles from different soils. Single and joint hypothesis tests showed that significant differences existed among the breakthrough profiles, the breakthrough points, and the rates of concentration change. Additionally, simulation was used to examine the correlation structure between the estimated breakthrough point and 17 soil properties. The simulation showed that six soil properties-ammonium oxalate extractable aluminum (Al) and iron (Fe), citrate dithionite extractable Al, CaCl2, and acetate extractable P, and P sorption capacity-were strongly correlated with P breakthrough. 23 references.

**"Effect Of Refractive Index On The Peak Shapes In Flow Injection Analysis"**

*Fenxi Kexue Xuebao
1995 Volume 11, Issue 1 Pages 23-28*

J. Li; G. Liu; H. Ma

**Abstract:**Using water as carrier stream, the study was performed with ethanol as the analyte by using the refraction principle, Fresnel equation and fluid dynamics. Results indicated that (i) higher absorption was obtained when water was injected into ethanol than when the sequence was reversed; and (ii) when using a spectrophotometric method for the detection of RI of the reagent, sensitivity of the counter-flow injection was 2.5 times better than the forward-flow injection. Subsequently a curve-correction equation of interface of the two fluids was proposed.

**"Computer-controlled Apparatus For Automated Development Of Continuous-flow Methods"**

*J. Autom. Methods Manag. Chem.
1989 Volume 11, Issue 5 Pages 227-234*

PETER D. WENTZELL, MICHAEL J. HATTON, PAUL M. SHIUNDU, RONALD M. REE, ADRIAN P. WADE, D. BETTERIDGE, and TIMOTHY J. SLY

**Abstract:**The automated apparatus described is capable of controlling and/or monitoring three types of pump, two types of valve and four types of detector by means of an IBM PC-AT compatible computer. The components of the system and the interface circuitry are described; circuit diagrams are included. The apparatus has been applied in optimization of various automated analyzes (e.g., the flow injection determination of Fe) and in response surface modeling.

**"Single Turnover Mechanism Of A Trypsin-reactor With High Enzyme Concentration"**

*J. Biotechnol.
1998 Volume 60, Issue 1-2 Pages 81-95*

Paola Fermi, Riccardo Biffi, Virna Conti, Roberto Ramoni, Stefano Grolli, Paolo Accornero and Enrico Bignetti*

**Abstract:**A small column containing 2 mM CH-Sepharose 4B-immobilized trypsin was connected to a flow injection device equipped for potentiometric measurements (0.01-2 mM protons) and for post-column analysis by spectrophotometry and capillary electrophoresis (CE). The device was engaged with N-α-benzoyl-l-arginine pNO2-anilide (BAPNA), β-lactoglobulin (β-Lac) and peptides of V8-protease predigested β-Lac. At a given flow rate, the reaction with BAPNA or β-Lac (below 2 mM) produced about 1 proton per substrate mol. in each sample (linear relation to substrate amount) with peptides (below 22 mM), the reaction did not exceed 0.17 acid equivalent per substrate molecule. (hyperbolic dependence). Final experiments demonstrated that the reactor gave a correct estimate of available lysine in peptides of β-Lac modified with 5-nitrosalicylaldehyde. The data could be predicted by a kinetic model describing the reactor performance in 'single turnover' conditions. The interplay between resident time and the non-catalytic amount of trypsin prevented each enzyme molecule from recycling as well as each substrate molecule (containing one or more cleavage sites) from encountering the enzyme more than once. In conclusion, both from the experimental and the theoretical point of view, this work permitted the analysis of trypsin behavior in some extreme working conditions and indicates how to modulate the performance of an endoprotease-based reactor. A brief discussion on potential applications in protein mapping and tagging and in the quanitative analysis of protein bioavailability by means of a biosensorial strategy is also described.

**"Window Factor Analysis: Theoretical Derivation And Application To Flow Injection Analysis Data"**

*J. Chemom.
1992 Volume 6, Issue 1 Pages 29-40*

Edmund R. Malinowski

**Abstract:**A detailed derivation of the window factor analysis methodology is presented, showing how quantification of a single species can be achieved. The method takes advantage of the fact that each component lies in a specific region along the evolutionary axis, called the 'window'. For comparative and illustrative purposes the method was applied to the flow injection analysis data of Gemperline and Hamilton (Ibid., 1989, 3, 455). Window factor anal. (WFA) is a self-modeling method for extracting the concentration profiles of individual components from evolutionary processes such as flow injection, chromatography, titrations and reaction kinetics. The method takes advantage of the fact that each component lies in a specific region along the evolutionary axis, called the 'window'. Theoretical equations are derived. The method is used to extract the concentration profiles and spectra of seven bismuth species from data obtained by Gemperline and Hamilton, who injected bismuth perchlorate into a flowing stream of hydrochloric acid.

**"Multivariate Resolution Of Rank-deficient Spectrophotometric Data From First-order Kinetic Decomposition Reactions"**

*J. Chemom.
1998 Volume 12, Issue 3 Pages 183-203*

J. Saurina, S. Hernández-Cassou, R. Tauler*, A. Izquierdo-Ridorsa

**Abstract:**The effect of a rank deficiency upon curve resolution in simple kinetic reaction-based systems is studied. Firstly, simulated rank-deficient spectrophotometric data of a mixture of two reagents, each one yielding its own reaction product by a first-order kinetic reaction, are analyzed. Four different situations are considered according to the differences in the spectral responses of the reaction constituents and to the differences in the rate constants between the two kinetic processes. A variation of the rate constant between runs for a certain kinetic process is also taken into account. Secondly, the resolution of a real rank-deficient data system, corresponding to the study of the pH-dependent decomposition of 1,2-naphthoquinone-4-sulfonate, is investigated. All these studies were carried out using a multivariate curve resolution method based on the alternating least squares optimization of the kinetic and spectral profiles of the species present in the system.

**"Simulation Of Flow Injection Analysis Peak Without Molecular Diffusion In Laminar Capillary Flow Injection"**

*J. Flow Injection Anal.
1986 Volume 3, Issue 2 Pages 91-102*

Takashi KORENAGA, Hirofumi YOSHIDA, Yo YOKOTA, Satoru KASENO and Teruo TAKAHASHI

**Abstract:**The transport phenomena of the injected samples in flowing carrier stream are analyzed elementally. The FIA peak in laminar capillary flow is simulated without considering molecular diffusion by computer. The results obtained by simulation are compared with those obtained by microscopic and photometric detection methods in order to attain higher sampling rate and peak height in FIA. It was found that FIA peak should closely be simulated with the finite element method (FEM) in consideration with molecular diffusion coefficients of the samples.

###### 'Joint Use Of FIA In Multicomponent Determinations', Lihua Jianyan, Huaxue Fence, 1997 33(4) 181-184

**"Joint Use Of FIA In Multicomponent Determinations"**

*Lihua Jianyan, Huaxue Fence
1997 Volume 33, Issue 4 Pages 181-184*

Zhu, Y.J.;Wei, T.J.;Feng, G.Y.

**Abstract:**A review is presented of the use of hyphenated FIA techniques, such FIA with FTIR spectrometry, FT ICP-AES, FT ICP-MS and other spectrophotometric methods. Differential kinetic measurement, corresponding dissolution, chemometrics and online separation/pre-concentration are also discussed. 49 references

**"The Dimeric DNA Binding Domain Of The Human Papillomavirus E2 Protein Folds Through A Monomeric Intermediate Which Cannot Be Native-like"**

*Nat. Struct. Biol.
1996 Volume 3, Issue 8 Pages 711-717*

Yu-Keung Mok, Mark Bycroft and Gonzalo de Prat-Gay

**Abstract:**The dimeric DNA binding domain of the human papillomavirus E2 protein displays a two-state concerted unfolding and dissociation, with no detectable monomeric intermediate species accumulated at equilibrium. We investigated the kinetic folding mechanism of the dimeric domain using stopped-flow spectroscopic techniques and observed a fast forming monomeric intermediate, followed by a slower bimolecular reaction. Both phases involve secondary structure rearrangements of similar magnitude. Our results support a folding pathway in which the formation of an early monomeric intermediate, with characteristics of hydrophobic collapse, is followed by a bimolecular step encompassing association and folding. The interwoven folding topology of this particular type of dimeric β-barrel found in the E2 DNA binding domain strongly suggests that any monomeric species formed could not be native-like.

**"Acid Base Flow Titration Based On The Use Of An Automatic Burette"**

*Quim. Anal.
1994 Volume 13, Issue 1 Pages 31-35*

Bartroli, J.;Alerm, L.;Garcia Raurich, J.;Masip, J.

**Abstract:**Continuous-flow titrations were conducted using a combination of FIA and an automatic burette. The optimization process for the flow system allowed the evaluation of the influence of flow rate and reaction coil length in the observed equivalence volume. The results obtained using two detection systems, a flat-membrane glass electrode and a pH-sensitive ISFET sensor, are compared. Acetic acid was used as a carrier solution and NaOH as the titrant. The injection of small volumes of the titrant in the carrier channel gave a titration graph. From this curve, an equivalence volume could be derived. A calibration surface could be produced by plotting the equivalence volume for each concentration of the acid carrier and the basic titrant. By using the surface polynomial equation acid-base titrations could be performed over a wide working range. Use of the ISFET sensor improved analytical speed and resolution.

**"Flow Injection Analysis. 3. Some Theoretical Problems In Flow Injection Analysis"**

*Yankuang Ceshi
1992 Volume 11, Issue 3 Pages 276-280*

Ma, H.C.

**Abstract:**A review is presented, with 16 references, including sample dispersion models, stimulus response models and dispersion coefficient.

**"Computational Fluid Dynamics Model For Optimal Flow Injection Analysis Biosensor Design"**

*IEEE Proc.
2005 Volume SENS, Issue 1 Pages 365-368*

Vermeir, S.; Verboven, P.; Atalay, Y.T.; Nicolai, B.M.; Lammertyn, J.; Irudayaraj, J.;

**Abstract:**This paper presents the optimization of a flow injection analysis (FIA) biosensor with respect to its design and operational parameters such as flow cell geometry, microfluidic channel dimensions, and flow rate. Since it is time consuming and costly to investigate the effect of each factor on the biosensor performance by building it, computational fluid dynamics (CFD) theory is presented as a great tool for finding optimal parameter values. This modeling approach has a high potential in the design of high accuracy FIA-biosensors, regardless of the chosen enzyme substrate system. As an example the optimal design for a glucose/glucose oxidase FIA biosensor is calculated with the CFD theory.

**"A Simulation Model For Determination Of The Economic Production Rate Of The Auto Analyzer System"**

*Clin. Biochem.
1975 Volume 8, Issue 1-6 Pages 87-95*

Arthur S. Slutsky and Andrew A. Cunningham

**Abstract:**1. The problem is considered of determining the appropriate rate of operation of an Auto Analyzer System. A computer model is presented which simulates the operation of the system, so as to describe the frequency of such events as repeated samples. 2. Estimates may be obtained of average total running costs, incorporating those of consumables and technician time and the rate which minimises the average cost, subject to stated test quality constraints, may then be calculated.