Application of Laplace transforms for the solution of transient mass- and heat-transfer problems in flow systems

A fast numerical technique for the solution of partial differential equations describing timedependent two- or three-dimensional transport phenomena is developed. It is based on transforming the original time-domain equations into the Laplace domain where numerical integration is performed and by subsequent numerical inverse transformation the final solution can be obtained. The computation time is thus reduced by more than one order of magnitude in comparison with the conventional finite-difference techniques. The effectiveness of the proposed technique is demonstrated by illustrative examples

Mathematical modelling of a flow-injection system with a membrane separation module

A mathematical 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 analytically in the Laplace domain. The inverse transformation was found to give satisfactory results for reactor Peclet numbers 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 experimentally 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 mathematical 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 technology for characterizing of various membranes and in process engineering for investigating the mass transfer in different dialysers

Equating an adaptive test to a linear test

Two new methods for the equating of an adaptive test to a linear test are presented. The methods are based on the conditional distributions of the observed scores on the two tests, given the examinee’s ability. They are motivated by the fact that conditioning on the examinee’s ability is necessary to allow for differences between observed-score distributions of examinees. The two methods were evaluated empirically against the traditional equipercentile method based on the marginal score distributions on the two tests and a method that uses the test characteristic function (TCF) of the linear test. The criterion in this study was the difference between the distribution of the equated score and the actual observed score on the linear test. The two conditional methods were unbiased and had mean-squared error in the equated scores comparable to the marginal equipercentile method and the TCF methods. The last two methods were strongly biased. It is argued that their bias is a consequence of the fact that they use a single equating transformation for an entire population of examinees and, therefore, have to compromise between the individual score distributions

Determination of water in organic solvents by flow-injection analysis with Karl Fischer reagent and a biamperometric detection system

A flow-injection system with a biamperometric flow-through detector provided with two platinum plate electrodes was tested for the determination of water with a two-component pyridine-free Karl Fischer reagent. The response was shown to be linear in the concentration range 0.03–0.11% water in methanol, ethanol or 2-propanol, with methanol as the carrier solvent. The maximum sampling frequency was about 150 samples per hr. It appeared to be possible to introduce a membrane separation step, thus allowing for the determination of water in fouled process streams. To avoid direct contact between the Karl Fischer solution and the pumping tubes, and thus extend the lifetime of the tubes, an indirect delivery system, based on replacement of the solution by pumped silicone oil, was also applied

Digital simulation of chronopotentiometric and steady-state voltammetric curves at microelectrodes in the presence of a low concentration of supporting electrolyte

A simulation scheme for the calculation of theoretical chronopotentiograms at microelectrodes in solutions containing low amounts of supporting electrolyte is presented. The scheme allows computation of the changes in the concentration profiles of the substrates, products and the supporting electrolyte ions with time. The electrode potentials that are established after reaching the steady-state, together with the appropriate current intensities, can be used for constructing the steady-state voltammograms. The simulation of the mixed diffusional and migrational transport is based on the Crank-Nicolson method with an exponentially expanding time and space grids. The scheme does not impose any limitations on diffusion coefficients and it can be applied both to simple electrode reactions (one reactant-one product) and more complicated reactions under the assumption that the double-layer thickness is small in comparison to the diffusion layer. Five simple types of electrode reactions and an example of a more complicated scheme were considered. The results obtained demonstrate that the dependence of the steady-state limiting current on the support ratio (csupp.el./csubst) depends not only on the charge of the reactant and the product, but also on the diffusion coefficient ratio of the substrate and product. If the difference between diffusion coefficients is large, the predictions based on simpler theories available in literature can become invalid

Algorithmic test design using classical item parameters

Two optimalization models for the construction of tests with a maximal value of coefficient alpha are given. Both models have a linear form and can be solved by using a branch-and-bound algorithm. The first model assumes an item bank calibrated under the Rasch model and can be used, for instance, when classical test theory has to serve as an interface between the item bank system and a user not familiar with modern test theory. Maximization of alpha was obtained by inserting a special constraint in a linear programming model. The second model has wider applicability and can be used with any item bank for which estimates of the classical item parameter are available. The models can be expanded to meet practical constraints with respect to test composition. An empirical study with simulated data using two item banks of 500 items was carried out to evaluate the model assumptions. For Item Bank 1 the underlying response was the Rasch model, and for Item Bank 2 the underlying model was the three-parameter model. An appendix discusses the relation between item response theory and classical parameter values and adds the case of a multidimensional item bank. Three tables present the simulation study data