Case of a Boltzmann gas leading to the Smoluchowski coagulation equation

A special model of a rarefied hard-sphere gas is considered. The hard-sphere particles undergo absolutely elastic collisions. It is assumed that particles can collide only if their nonzero velocities are orthogonal to each other. The model makes it possible to proceed from the Boltzmann equation to the Smoluchowski coagulation equation, where coagulation means that the kinetic energies of the colliding particles are added. A Monte Carlo scheme for simulation of the phenomenon is described, and the convergence of the simulation algorithm is proved. The convergence of numerical results to exact solutions of the Smoluchowski equation and to finite-difference solutions is tested.     

带有弹性碰撞的离散的凝结方程

带有弹性碰撞的离散的凝结方程是反映粒子增长动力学的数学模型，它刻划了这样一种粒子反应系统；系统中任意两个粒子碰撞后一定的概率或者凝结成为更大的粒子，或者发生弹性碰撞．本文研究了这一系统发生冻肢的可能性，并给出了一个充分条件．     

Rate of Convergence of a Stochastic Particle System for the Smoluchowski Coagulation Equation

By continuing the probabilistic approach of Deaconu et al. (2001), we derive a stochastic particle approximation for the Smoluchowski coagulation equations. A convergence result for this model is obtained. Under quite stringent hypothesis we obtain a central limit theorem associated with our convergence. In spite of these restrictive technical assumptions, the rate of convergence result is interesting because it is the first obtained in this direction and seems to hold numerically under weaker hypothesis. This result answers a question closely connected to the Open Problem 16 formulated by Aldous (1999).     

Hydride generation atomic fluorescence spectrometric determination of ultratraces of selenium and tellurium in cow milk

A sensitive procedure has been developed for selenium and tellurium determination in milk by hydride generation atomic fluorescence spectrometry (HG-AFS) after microwave-assisted sample digestion. The method provides sensitivity values of 1591 and 997 fluorescence units ng⁻¹ ml⁻¹ with detection limits of 0.005 and 0.015 ng ml⁻¹ for Se and Te, respectively. The application of the developed methodology to the analysis of cow milk samples of the Spanish market evidenced the presence of concentration ranges from 11.1 to 26.0 ng ml⁻¹ for Se, and from 1.04 to 9.7 ng ml⁻¹ for Te having found a good comparability with data obtained after dry-ashing of samples.     

Bound water measurements for aqueous protein solutions and food gels

The role of aqueous media in the stabilization of globular proteins and formation of gels was studied by absorption millimeter spectroscopy. This method allowed to measure bound water, the fraction of water which had decreased rotational mobility owing to the presence of solute. Hydration data for globular proteins were compared with data obtained previously for low-weight molecules and groups. It was found that rotational mobility of water molecules in the hydration shells of various kinds of solutes (groups) decreased in the following order: water structure breaking compounds>polar groups>unfolded proteins>globular proteins>non-polar groups. Time courses of the storage modulus were determined for the chemical acidification by glucono-δ-lactone (GDL) of milk samples prepared from skimmed milk powder (SMP). Gelation of unheated milk was a monotonous process that started at pH 4.9. Heat-treated milk from SMP (16 and 14 g per 100 ml) acidified by GDL (3 g per 100 ml) at 43 °C gave non-monotonous kinetics of gelation with two phases corresponding to the mechanisms induced by denatured whey proteins at pH>5 and by casein–casein interactions at pH 4.8–4.9. For heat-treated milk, measurement of bound water gave two stages of decrease in water mobility. Additional hydration of SMP during acidification gave 0.15–0.2 g and 0.8 g bound H₂O per gram of SMP for unheated and heat-treated milk, respectively.     

High-performance liquid chromatography with evaporative light-scattering detection for the determination of phospholipid classes in human milk,infant formulas and phospholipid sources of long-chain polyunsaturated fatty acids

We developed and validated a new high-performance liquid chromatographic method for the separation of phospholipid classes in human milk, infant formulas and phospholipidic sources of long-chain polyunsaturated fatty acids (LC-PUFAs) used in paediatric nutrition. Phosphatidylcholine, phosphatidylethanolamine, phosphatidylinositol, phosphatidylserine and sphingomyelin were separated in less than 25 min using an Extrasil silica column (150 x 4.0 mm I.D., 3-microm particle size) by isocratic elution with a mixture of isopropanol-hexane-water. Phospholipids were determined by an evaporative light-scattering detector. Several chromatographic conditions were assayed to optimise the method, whose suitability is shown by the detection limits, linearity ranges and precision rates obtained. The main advantages of the proposed method are its speed and the direct determination of the main phospholipids present in human milk, infant formulas and the phospholipid sources of LC-PUFAs used in paediatric nutrition.     

Nutritional parameters of commercially available milk samples by FTIR and chemometric techniques

A chemometric study on the prediction of the main nutritional aspects of milk has been carried out by using fourier transform infrared spectroscopy (FTIR) attenuated total reflectance (ATR) measurements of commercially available milk samples of different types. Whole, semi and skimmed milks, enriched or not with calcium, vitamins or modified by alteration of lipid or sugar composition were considered. After evaluating different strategies for data acquisition and ATR cleaning between samples, hierarchical cluster analysis (HCA) was carried out for classification of samples in order to choose the calibration set. The prediction capabilities of partial least squares (PLS) data treatment were evaluated in order to obtain information about total fat, total protein, total carbohydrates (CH), calories and calcium. On using the mean square error of cross-validation and prediction as control variables, a critical evaluation were made about the calibration set to be used, the spectral range to be considered and the data treatment (PLS-1 or PLS-2) to be performed. By selecting a calibration set of 33 samples the properties of 48 samples were predicted with relative precision of triplicates of 0.062, 0.040 and 0.039% w/v for total fat, protein and carbohydrates, and 0.66 kcal/100 ml for calories, and 2.1 mg of Ca/100 ml. The mean difference (d_x−y) between predicted and actual values and standard deviation of mean differences (s_x−y), were of 0.06 (0.38), 0.03 (0.18) and −0.15 (0.41), being s_x−y values between brackets, for total fat, proteins and carbohydrates, 0.06 (3.8) kcal/100 ml for calories and −4.5 (9) mg/100 ml for calcium.The sensitivity and selectivity of the methodology developed were evaluated on terms of the net analyte signal. Selectivity factors ranging from 2 to 7.6% have been calculated for the five parameters considered.     

Topographical properties of polymer films deposited in capillaries for electrophoretic separations of large organic molecules

Topography and thickness of hydrophilic polymer coatings of fused-silica capillaries for capillary electrophoresis (CE) were investigated using atomic force microscopy (AFM), scanning electron microscopy (SEM), and profilometry. Three hydrogels, poly(2-hydroxyethyl methacrylate) [poly(HEMA)], poly(diethylene glycol monomethacrylate) [poly(DEGMA)], and poly(triethylene glycol monomethacrylate) [poly(TEGMA)], were deposited using two procedures, either by simple physical sorption of the polymers, or by derivatization of the capillary wall surface with glycidyl methacrylate (EPMA) followed by polymerization of the appropriate monomers. The performance of the modified capillaries was tested under CE conditions (decrease in the electroosmotic flow, EOF dependence on pH, separation of milk and standard proteins). It has been found that the most important property of the polymer coating is its thickness, whereas its topography and the degree of its hydrophobicity are less significant. Film deposition by physical adsorption is preferable to polymerization on the derivatized surface.     

Multicommutation as an environmentally friendly analytical tool in the hydride generation atomic fluorescence determination of tellurium in milk

The aim of this study is to show the advantages of the emerging multicommutation methodology based on the use of solenoid valves for Te determination in milk by hydride generation atomic fluorescence spectrometry (HG-AFS). The delivery of a series of alternating sequential insertions of small volumes of samples and reagents gives rise to new hydrodynamic processes and exciting analytical potentials by controlling the time of flow through the on/off-switched solenoid valves. This drastically reduces the reagent consumption by a factor of 4 and the generation of effluents (590 mL h^–1 instead of 750 mL h^–1 generated by the continuous-mode measurement) and also provides an improvement in the laboratory productivity by an increase of the sample throughput (85 h^–1 compared to 20 h^–1 found in the continuous mode). So, multicommutation is an environmentally and economically sustainable alternative to the methodology based on continuous measurements. The multicommutation-based method developed was applied to tellurium determination in commercially available milk samples; a calibration range of 0.0–0.5 ng mL^–1 and a detection limit of 0.20 ng L^–1 with average relative standard deviation of 2.1% were found. Comparable results were obtained for a series of samples using both continuous and multicommutation HG-AFS modes.     

Glass and polymeric membrane electrodes for the measurement of pH in milk and cheese

While there is a considerable interest in the food industry in determining various analytes using ion-selective electrodes (ISEs), only few reports describe their use for direct measurements in food. In this study, the suitability of glass electrodes and ionophore-based solvent polymeric ISEs for the determination of pH in Process cheese, Cheddar cheese and milk was investigated. The liquid junction potential between a 3 M KCl bridge electrolyte and diluted as well as undiluted Process cheese was found to be negligible. Reference electrodes with ceramic plug and sleeve-type junctions performed well, although precautions needed to be taken to prevent plugging at the junctions. While the protein rennet casein posed no problems in pH measurements, the extraction of neutral lipophilic compounds or hydrophobic peptides into solvent polymeric membranes was evident, resulting in some loss of selectivity for monovalent cations upon exposure to cheese. However, it was found that ISEs based on tridodecylamine (R₃N) as ionophore and o-nitrophenyl octyl ether (oNPOE) as plasticizer can be used to accurately measure the pH of milk and, after desensitization of the electrodes in a cheese emulsion, of diluted Process cheese. Since pH measurements with a glass electrode showed that emulsions of cheese moderately diluted to a cheese content of 70% have the same pH as undiluted cheeses, it is possible to determine the pH in cheese with ionophore-based ISEs. R₃N membranes also performed well in undiluted milk.