On the solidification of a supercooled liquid droplet lying on a surface

We model the solidification and subsequent cooling of a supercooled liquid droplet that is lying on a cold solid substrate after impact. It is assumed that solidification occurs for a given fixed droplet shape. The shapes used by the model are a sphere, truncated spheres, and an experimentally registered droplet shape. The freezing process is conduction-dominant and is modeled as a one-phase Stefan problem. This moving boundary problem is reformulated with the enthalpy method and then solved numerically with an implicit finite-difference technique. The numerical results for the simple case of a spherical droplet touching a surface are similar to those of a freely freezing spherical droplet and are well confirmed by the 1D asymptotic analytical model of Feuillebois et al. (J. Colloid Interface Sci. 169 (1995) 90). A freezing water droplet is considered as an example. The numerical results for full freezing time, subsequent cooling time, and last freezing point coordinate for the various droplets shapes are fitted by analytical functions depending on supercooling, thermal resistance of the target surface (expressed by Biot number), and spreading parameter. These functions are proposed for direct application, thus avoiding the need to solve the full freezing and cooling problem.     

Selection of the wavelength range and spectrophotometric determination of leucovorin and methotrexate in human serum by a net analyte signal based method

Leucovorin (LV) and methotrexate (MTX) were determined in human blood serum samples by using a model based in the net analytical signal concept. The calibration method used is a variation of the original hybrid linear analysis (HLA) method, developed by Goicoechea and Olivieri (HLA/GO). The calibration set was composed by nine serum samples with different amounts of LV and MTX in the range of 0-10 mugml(-1). The selection of the optimum wavelength range involved the calculation of the net analyte signal regression plot for each test sample, in conjunction with the calculation of the minimum error indicator. Relative errors of prediction (REP, %) of 3.0 and 5.3% were calculated for LV and MTX, respectively. Only two factors were necessary to optimize the proposed HLA/GO model. Sensitivity, selectivity, analytical sensitivity and limit of detection of the proposed procedure were calculated. Detection limits of 0.34 and 0.93 mugml(-1) for LV and MTX were determined. The proposed model was tested in the analysis of serum samples, without previous separation steps, obtaining recovery values between 96 and 99%, and between 92 and 103% for LV and MTX, respectively.     

Calculations of the contribution of ring currents to the chemical shielding anisotropy

Ring currents can exert a large effect upon the chemical shielding of NMR resonances. The analytical expression developed by Waugh and Fessenden (Waugh, J. S.; Fessenden, R. W. J. Am. Chem. Soc. 1957, 79, 846) and Johnson and Bovey (Johnson, C. E.; Bovey, F. A. J. Chem. Phys. 1957, 29, 1012) only quantifies the contribution of ring currents to the isotropic component of the shielding tensor. In the work described here an additional analytical expression is developed so that the contribution of ring currents to the full shielding tensor can be calculated, allowing an estimate of the influence of ring currents upon the chemical shielding anisotropy (CSA, Deltasigma). To test that this pair of analytical expressions can provide a reasonable estimate of the contribution of ring currents to the full shielding tensor a series of density functional calculations (DFT) were carried out. A shielding tensor in a model compound was calculated in two distinct ways. For the first series, DFT shielding calculations of the model compound were carried out in the presence of a benzene ring. For the second series a ring current contribution to the shielding tensor was calculated via the new expressions, and this was added to the result of a DFT shielding calculation which used in place of benzene the nonaromatic analogue 1,3 cyclohexadiene. The two series of results proved to be in excellent agreement. The pair of analytical expressions are used to calculate ring current contributions to the CSA (Deltasigma) of 1H(N) backbone amide resonances in a structure of the second type 2 module from the protein fibronectin. Significant CSA variations are predicted in particular for the 1H(N) of G42 which is most likely involved in a N-H...tpi aromatic hydrogen bond.     

A practical guide to the staggered herringbone mixer

An analytical model of mixing in the staggered herringbone mixer (SHM) was derived to estimate mixing parameters and provide practical expressions to guide mixer design and operation for a wide range of possible solutes and flow conditions. Mixing in microfluidic systems has historically been characterized by the mixing of a specific solute system or by the redistribution of flow streams; this approach does not give any insight into the ideal operational parameters of the mixer with an arbitrary real system. For Stokes-flow mixers, mixing can be computed from a relationship between solute diffusivity, flow rate, and mixer length. Confocal microscopy and computational fluid dynamics (CFD) modeling were used to directly determine the extent of mixing for several solutes in the staggered herringbone mixer over a range of Reynolds numbers (Re) and Péclet numbers (Pe); the results were used to develop and evaluate an analytical model of its behavior. Mixing was found to be a function of only Pe and downstream position in the mixer. Required mixer length was proportional to log(Pe); this analytical model matched well with the confocal data and CFD model for Pe<5 x 10(4), at which point the experiments reached the limit of resolution. For particular solutes, required length and mixing time depend upon Re and diffusivity. This analytical model is applicable to other solute systems, and possibly to other embodiments of the mixer, to enable optimal design, operation, and estimation of performance.     

Novel three-stage kinetic model for aqueous benzene adsorption on activated carbon

We propose a novel kinetic model for adsorption of aqueous benzene onto both granular activated carbon (GAC) and powdered activated carbon (PAC). The model is based on mass conservation of benzene coupled with three-stage adsorption: (1) the first portion for an instantaneous stage or external surface adsorption, (2) the second portion for a gradual stage with rate-limiting intraparticle diffusion, and (3) the third portion for a constant stage in which the aqueous phase no longer interacts with activated carbon. An analytical solution of the kinetic model was validated with the kinetic data obtained from aqueous benzene adsorption onto GAC and PAC in batch experiments with two different solution concentrations (C(0)=300 mg L(-1), 600 mg L(-1)). Experimental results revealed that benzene adsorption for the two concentrations followed three distinct stages for PAC but two stages for GAC. The analytical solution could successfully describe the kinetic adsorption of aqueous benzene in the batch reaction system, showing a fast instantaneous adsorption followed by a slow rate-limiting adsorption and a final long constant adsorption. Use of the two-stage model gave incorrect values of adsorption coefficients in the analytical solution due to inability to describe the third stage.     

Direct determination of uric acid in serum by a fluorometric-enzymatic method based on uricase

The present paper describes a method for the fluorometric determination of uric acid in blood serum by its reaction with uricase (UOx). The procedure is based on the changes in fluorescence that take place during the enzymatic reaction of UOx with uric acid when the solution is excited at 287 nm and the emission is measured at 330 nm. A mathematical model which relates the analytical signal to the analyte concentration was developed and the model also served to obtain some of the thermodynamic constants of the system (the Michaelis constant and the turnover number). The optimum reaction conditions and its analytical characteristics were studied, linear response range (3x10(-5)-6x10(-4) M) and reproducibility (4%, n=7). The method was applied to the determination of uric acid in three blood serum samples. The results were compared with those obtained by a commercial clinical analyzer and no systematic errors were observed.     

Evaluation of a fluorometric-enzymatic method based on 3alpha-hydroxysteroid dehydrogenase for the mycotoxin zearalenone determination in corn

A new method for the fluorometric determination of zearalenone (ZEN) based on its reaction with βNADH in the presence of the enzyme 3α-hydroxysteroid dehydrogenase (3α-HSD) is described. The procedure is based on the change in fluorescence intensity that takes place during the enzymatic reaction (excitation at 340 nm and emission at 454 nm). The optimum reaction conditions and the analytical characteristics were studied; linear response range (1-10 mg l⁻¹) and reproducibility (8 mg l⁻¹, 2.7%, n=7). Moreover, a mathematical model explaining the analytical signal is proposed. The method has been applied to zearalenone determination in a spiked corn sample.     

Determination of analytical limits in solid sampling ETAAS: a new approach towards the characterization of analytical quality in rapid methods

In the present study the lower analytical limits of solid sampling electrothermal atomization atomic absorption spectrometry (SS-ETAAS) were characterized by means of blank measurements and – for the first time – by means of the calibration curve method, where a calibration near the range of these limits (limit of decision, detection and quantification) was performed. The limit of decision as derived from blank measurements was calculated according to the 3σ-criterion to be 0.003 and 0.019 ng for Cd and Pb, respectively. For Pb and Cd a roughly threefold increase of these limits was observed when the calibration method according to DIN 32 645 was applied. When solid reference material was used, only a slight increase could be observed. The analytical limits were 2 to 20 times lower than reported for sample decomposition methods. The blank measurement and conventional calibration curve method, however, do not account for factors relating to solid sampling such as sample mass and matrix. Therefore, the calibration curve model was applied to data derived from comparisons between direct solid sampling ETAAS and a compound reference method (ETAAS following sample homogenization and digestion). The observed analytical limits were not found to be substantially increased if enough samples with low element contents were available for calibration. Coupling of the calibration curve model with the comparison of methods included real test samples and thus the relevant maximum sample mass and analyte content in the range of the lower analytical limits. As validation procedures frequently include comparisons of methods, the present approach might prove to be of some general interest for the characterization of analytical quality in rapid methods.     

Numerical and analytical studies of the electrical conductivity of a concentrated colloidal suspension

In the past few years, different models and analytical approximations have been developed facing the problem of the electrical conductivity of a concentrated colloidal suspension, according to the cell-model concept. Most of them make use of the Kuwabara cell model to account for hydrodynamic particle-particle interactions, but they differ in the choice of electrostatic boundary conditions at the outer surface of the cell. Most analytical and numerical studies have been developed using two different sets of boundary conditions of the Neumann or Dirichlet type for the electrical potential, ionic concentrations or electrochemical potentials at that outer surface. In this contribution, we study and compare numerical conductivity predictions with results obtained using different analytical formulas valid for arbitrary zeta potentials and thin double layers for each of the two common sets of boundary conditions referred to above. The conductivity will be analyzed as a function of particle volume fraction, phi, zeta potential, zeta, and electrokinetic radius, kappaa (kappa(-1) is the double layer thickness, and a is the radius of the particle). A comparison with some experimental conductivity results in the literature is also given. We demonstrate in this work that the two analytical conductivity formulas, which are mainly based on Neumann- and Dirichlet-type boundary conditions for the electrochemical potential, predict values of the conductivity very close to their corresponding numerical results for the same boundary conditions, whatever the suspension or solution parameters, under the assumption of thin double layers where these approximations are valid. Furthermore, both analytical conductivity equations fulfill the Maxwell limit for uncharged nonconductive spheres, which coincides with the limit kappaa --> infinity. However, some experimental data will show that the Neumann, either numerical or analytical, approach is unable to make predictions in agreement with experiments, unlike the Dirichlet approach which correctly predicts the experimental conductivity results. In consequence, a deeper study has been performed with numerical and analytical predictions based on Dirichlet-type boundary conditions.     

Modeling the analytical response of optical fiber sensors for aromatic compounds determination

In recent years, there has been an increasing interest in the application of optical fiber sensors for in situ monitoring of chemical pollutants, including volatile organic compounds, regarding air quality assurance. In order to enhance the usefulness and applicability of this methodology to environmental analysis, a proper study of the analytical signal and an adequate calibration model are required. This contribution is focused on the model for optical fiber sensors calibration, discussing some problems associated with the estimates of the figures of merit of these analytical systems. We also suggest and discuss a calibration model based on a cumulative symmetric double sigmoidal (SDS) function, as a suitable and general alternative to the more limited and classical linear calibration model.     

Estimation of residual stresses in SiC/Ti 15-3 composites and their relaxation during a fatigue test. Part I: Presentation of the models

Different models for the calculation of residual stresses induced by cooling down from elaboration process in SiC/Ti-15-3 composite were presented. First of all, an analytical model (derived from those of Eshelby and of Mikata and Taya) already used for ceramic matrix composites is explained. It is a suitable method for elementary composites but we present an extension of this model to real (1D) composites. Then, we also briefly present the finite model using MARC anc MENTAT softwares. Finaly, an analytical model to predict the evolution of TRS during a fatigue test is detailed. The part II of the paper will present the results obtained using all these differents models.     

Analytical calculation of the collimated detector response for the characterization of nuclear waste drums by segmented gamma scanning

Improved methods for the reconstruction of the isotope specific activity content in nuclear waste drums with data obtained by a gamma scanning system developed at Shanghai Jiao Tong University require an analytical function of the detector response. In this work we derive an analytical detector response function for a collimated HPGe detector with a square collimation window. The model is based on a purely geometric model respecting the configuration of the collimated detector system, the positions of radioactive point sources and the absorption of γ-rays in the matrix as well as in the HPGe crystal. We show that the derived analytical detector response function is in good agreement with data simulated by MCNP5.     

Determination of analytical limits in solid sampling ETAAS: a new approach towards the characterization of analytical quality in rapid methods

In the present study the lower analytical limits of solid sampling electrothermal atomization atomic absorption spectrometry (SS-ETAAS) were characterized by means of blank measurements and--for the first time--by means of the calibration curve method, where a calibration near the range of these limits (limit of decision, detection and quantification) was performed. The limit of decision as derived from blank measurements was calculated according to the 3sigma-criterion to be 0.003 and 0.019 ng for Cd and Pb, respectively. For Pb and Cd a roughly three-fold increase of these limits was observed when the calibration method according to DIN 32 645 was applied. When solid reference material was used, only a slight increase could be observed. The analytical limits were 2 to 20 times lower than reported for sample decomposition methods. The blank measurement and conventional calibration curve method, however, do not account for factors relating to solid sampling such as sample mass and matrix. Therefore, the calibration curve model was applied to data derived from comparisons between direct solid sampling ETAAS and a compound reference method (ETAAS following sample homogenization and digestion). The observed analytical limits were not found to be substantially increased if enough samples with low element contents were available for calibration. Coupling of the calibration curve model with the comparison of methods included real test samples and thus the relevant maximum sample mass and analyte content in the range of the lower analytical limits. As validation procedures frequently include comparisons of methods, the present approach might prove to be of some general interest for the characterization of analytical quality in rapid methods.     

Calibration — A multidimensional approach

Analytical calibration, in its entirety, comprises both qualitative and quantitative analysis and has to be considered, therefore, from a multidimensional point of view. The relationships must be characterised between the presence of certain analytes and typical signal patterns (e.g. at certain wavelengths) on the one hand and between the amount of given analytes and signal intensities on the other. It is useful to take a three dimensional model as the basis for the classical quantitative analysis and calibration. The relationships between the signal intensity and the true concentration of reference materials used for calibration and the concentration to be estimated in real analytical samples spread a three dimensional function whose corresponding two dimensional projections represent the common calibration function, the analytical evaluation function and the recovery function, which is important for validation (testing the accuracy). Under certain conditions the three dimensional model can be simplified to the common two dimensional one. Multivariate calibration relates to multidimensionality in analytical problems and data sets in principle. Multicomponent analysis and multisignal evaluation are characterized and illustrated by special applications.     

Characterization of the selectivity of a phenytoin imprinted polymer

The selectivity of analytical methods based on molecularly imprinted polymers (MIPs) is due to the preferential adsorption of the analyte(s) as compared to other substances (interferences). This paper shows the theoretical and practical difficulties, which have to be considered and solved when real samples need to be analysed in a wide range of analyte and interferant concentrations. It is shown that the estimation of interference effects requires either many measurements or a realistic model of the adsorption equilibrium in mixed solutions of the analyte and the interferences. Examples are shown for positive (cooperative) interference effects, for better experimental design and interpretation of binary isotherm measurements and for establishing the chemical model of interference from selectivity measurements. The usual MIP model consisting of a cavity, which closely fits the shape of the template from all sides, appears unsuitable for this MIP, and it is replaced with a more realistic, more open model. The applicability of the results to using non-imprinted polymers as selective sorbents and to screening drug candidates is also shown.     

Specific Versus Non-specific Response in Exponential Molecular Amplification from Cross-Catalysis: Modeling the Influence of Background Amplifications on the Analytical Performances

Molecule based signal amplifications relying on an autocatalytic process may represent an ideal strategy for the development of ultrasensitive analytical or bioanalytical assays, the main reason being the exponential nature of the amplification. However, to take full advantage of such amplification rates, high stability of the starting co-reactants is required in order to avoid any undesirable background amplification. Here, on the basis of a simple kinetic model of cross-catalysis including a certain degree of intrinsic instability of co-reactants, we highlight the key parameters governing the analytical response of the system and discuss the analytical performances that are expected from a given kinetic set. In particular, we show how the detection limit is directly related to the relative instability of reactants within each catalytic loop. The model is validated with an experimental dataset and is intended to serve as a guide in the design and optimization of autocatalytic molecular-based amplification systems with improved analytical performances.     

A model study of the laser-induced stabilization of a collision complex

The possibility of stabilizing a collision complex by stimulated emmission with coherent radiation is explored for a model. three-atom system. The lifetimes of several resonance states of this system were obtained previously and are used in a simple two-level model to describe the interaction of radiation with a resonance state and a true bound state. For the case where the energy difference between the two levels is time independent, simple, analytical expressions are used to obtain the time-dependent transition probability. Numerical solutions are obtained for the more realistic case where this energy difference is time dependent. For both cases, a substantial transition probability for stabilization is calculated for moderate laser intensities (e.g. 8.1 kW/cm² for an assumed dipole matrix element of 0.01 D).     

Solution of mathematical models of flow systems used in analytical chemistry and process analysis in the case of slug and time injection

Simple relationships for reducing the analytical solutions obtained when using distributed- and lumped-parameter models for slug and time injection to the mathematically less complicated and better investigated solutions for step- or delta-function inputs have been derived. They allow considerable simplification and substantial economy in computational time if numerical integration is performed. Examples are presented with hydraulic models frequently used in flow-injection analysis, chromatography and process analysis (e.g., the axially dispersed plug flow model, the convective diffusion equation, the ideally mixed tank model and the tanks-in-series model).     

Comprehensive Assessment of Flow and Other Analytical Methods Dedicated to the Determination of Zinc in Water

An original strategy to evaluate analytical procedures is proposed and applied to verify if the flow-based methods, generally favorable in terms of green chemistry, are competitive when their evaluation also relies on other criteria. To this end, eight methods for the determination of zinc in waters, including four flow-based ones, were compared and the Red–Green–Blue (RGB) model was exploited. This model takes into account several features related to the general quality of an analytical method, namely, its analytical efficiency, compliance with the green analytical chemistry, as well as practical and economic usefulness. Amongst the investigated methods, the best was the flow-based spectrofluorimetric one, and a negative example was that one involving a flow module, ICP ionization and MS detection, which was very good in analytical terms, but worse in relation to other aspects, which significantly limits its overall potential. Good assessments were also noted for non-flow electrochemical methods, which attract attention with a high degree of balance of features and, therefore, high versatility. The original attempt to confront several worldwide accepted analytical strategies, although to some extent subjective and with limitations, provides interesting information and indications, establishing a novel direction towards the development and evaluation of analytical methods.