Simultaneous chemical reaction and distillation of formaldehyde

The thesis is concerned with the development and testing of a mathematical model of a distillation process in which the components react chemically. The formaldehyde-methanol-water system was selected and only the reversible reactions between formaldehyde and water giving methylene glycol and between formaldehyde and methanol producing hemiformal were assumed to occur under the distillation conditions. Accordingly the system has been treated as a five component system. The vapour-liquid equilibrium calculations were performed by solving iteratively the thermodynamic relationships expressing the phase equilibria with the stoichiometric equations expressing the chemical equilibria. Using optimisation techniques, the Wilson single parameters and Henry's constants were calculated for binary systems containing formaldehyde which was assumed to be a supercritical component whilst Wilson binary parameters were calculated for the remaining binary systems. Thus the phase equilibria for the formaldehyde system could be calculated using these parameters and good accuracy was obtained when calculated values were compared with experimental values. The distillation process was modelled using the mass and energy balance equations together with the phase equilibria calculations. The plate efficiencies were obtained from a modified A.I.Ch.E. Bubble Tray method. The resulting equations were solved by an iterative plate to plate calculation based on the Newton Raphson method. Experiments were carried out in a 76mm I.D., eight sieve plate distillation column and the results were compared with the mathematical model calculations. Overall, good agreement was obtained but some discrepancies were observed in the concentration profiles and these may have been caused by the effect of limited physical property data and a limited understanding of the reactions mechanism. The model equations were solved in the form of modular computer programs. Although they were written to describe the steady state distillation with simultaneous chemical reaction of the formaldehyde system, the approach used may be of wider application.

Simultaneous biochemical reaction and separation in a continuous rotating annular chromatograph

The aim of this work has been to investigate the behaviour of a continuous rotating annular chromatograph (CRAC) under a combined biochemical reaction and separation duty. Two biochemical reactions have been employed, namely the inversion of sucrose to glucose and fructose in the presence of the enzyme invertase and the saccharification of liquefied starch to maltose and dextrin using the enzyme maltogenase. Simultaneous biochemical reaction and separation has been successfully carried out for the first time in a CRAC by inverting sucrose to fructose and glucose using the enzyme invertase and collecting continuously pure fractions of glucose and fructose from the base of the column. The CRAC was made of two concentric cylinders which form an annulus 140 cm long by 1.2 cm wide, giving an annular space of 14.5 dm3. The ion exchange resin used was an industrial grade calcium form Dowex 50W-X4 with a mean diameter of 150 microns. The mobile phase used was deionised and dearated water and contained the appropriate enzyme. The annular column was slowly rotated at speeds of up to 240°h-1 while the sucrose substrate was fed continuously through a stationary feed pipe to the top of the resin bed. A systematic investigation of the factors affecting the performance of the CRAC under simultaneous biochemical reaction and separation conditions was carried out by employing a factorial experimental procedure. The main factors affecting the performance of the system were found to be the feed rate, feed concentrations and eluent rate. Results from the experiments indicated that complete conversion could be achieved for feed concentrations of up to 50% w/v sucrose and at feed throughputs of up to 17.2 kg sucrose per m3 resin/h. The second enzymic reaction, namely the saccharification of liquefied starch to maltose employing the enzyme maltogenase has also been successfully carried out on a CRAC. Results from the experiments using soluble potato starch showed that conversions of up to 79% were obtained for a feed concentration of 15.5% w/v at a feed flowrate of 400 cm3/h. The product maltose obtained was over 95% pure. Mathematical modelling and computer simulation of the sucrose inversion system has been carried out. A finite difference method was used to solve the partial differential equations and the simulation results showed good agreement with the experimental results obtained.

Generalization of Ehrlich-Kjurkchiev Method for Multiple Roots of Algebraic Equations

In this paper a new method which is a generalization of the Ehrlich-Kjurkchiev method is developed. The method allows to find simultaneously all roots of the algebraic equation in the case when the roots are supposed to be multiple with known multiplicities. The offered generalization does not demand calculation of derivatives of order higher than first simultaneously keeping quaternary rate of convergence which makes this method suitable for application from practical point of view.

Web-based Simultaneous Equation Solver

* This work has been supported by NIMP, University of Plovdiv under contract No MU-1.

Simultaneous determination of B-Group vitamins in enriched cookies

The objective of this research was to determine the levels of enrichment of vitamins B1, B2, B6 and B3 in different types and brands of enriched cookies. The chromatographic separation was performed in a C18 column with gradient elution and UV detection at 254 and 287 nm. The results show that only 5 of the 24 brands evaluated are in accordance with the Brazilian legislation with respect to the vitamin content declared on the labels. However, consumption of approximately 100-150 g of most of the brands supplies the recommended dietary intake for children and adults of the vitamins evaluated.

Bond strength of a pit-and-fissure sealant associated to etch-and-rinse and self-etching adhesive systems to saliva-contaminated enamel: individual vs. simultaneous light curing

This study evaluated in vitro the shear bond strength (SBS) of a resin-based pit-and-fissure sealant [Fluroshield (F), Dentsply/Caulk] associated with either an etch-and-rinse [Adper Single Bond 2 (SB), 3M/ESPE] or a self-etching adhesive system [Clearfil S3 Bond (S3), Kuraray Co., Ltd.] to saliva-contaminated enamel, comparing two curing protocols: individual light curing of the adhesive system and the sealant or simultaneous curing of both materials. Mesial and distal enamel surfaces from 45 sound third molars were randomly assigned to 6 groups (n=15), according to the bonding technique: I - F was applied to 37% phosphoric acid etched enamel. The other groups were contaminated with fresh human saliva (0.01 mL; 10 s) after acid etching: II - SB and F were light cured separately; III - SB and F were light cured together; IV - S3 and F were light cured separately; V - S3 and F were light cured simultaneously; VI - F was applied to saliva-contaminated, acid-etched enamel without an intermediate bonding agent layer. SBS was tested to failure in a universal testing machine at 0.5 mm/min. Data were analyzed by one-way ANOVA and Fisher's test (α=0.05).The debonded specimens were examined with a stereomicroscope to assess the failure modes. Three representative specimens from each group were observed under scanning electron microscopy for a qualitative analysis. Mean SBS in MPa were: I-12.28 (±4.29); II-8.57 (±3.19); III-7.97 (±2.16); IV-12.56 (±3.11); V-11.45 (±3.77); and VI-7.47 (±1.99). In conclusion, individual or simultaneous curing of the intermediate bonding agent layer and the resin sealant did not seem to affect bond strength to saliva-contaminated enamel. S3/F presented significantly higher SBS than the that of the groups treated with SB etch-and-rinse adhesive system and similar SBS to that of the control group, in which the sealant was applied under ideal dry, noncontaminated conditions.

Production and body composition traits of broilers in relation to breast weight evaluated by path analysis

Breast weight has great economic importance in poultry industry, and may be associated with other variables. This work aimed to estimate phenotypic correlations between performance (live body weight at 7 and 28 days, and at slaughter, and depth of the breast muscle measured by ultrasonography), carcass (eviscerated body weight and leg weight) and body composition (heart, liver and abdominal fat weight) traits in a broiler line, and quantify the direct and indirect influence of these traits on breast weight. Path analysis was used by expanding the matrix of partial correlation in coefficients which give the direct influence of one trait on another, regardless the effect of the other traits. The simultaneous maintenance of live body weight at slaughter and eviscerated body weight in the matrix of correlations might be harmful for statistical analysis involving systems of normal equations, like path analysis, due to the observed multicollinearity. The live body weight at slaughter and the depth of the breast muscle as measured by ultrasonography directly affected breast weight and were identified as the most responsible factors for the magnitude of the correlation coefficients obtained between the studied traits and breast weight. Individual pre-selection for these traits could favor an increased breast weight in the future reproducer candidates of this line if the broilers' environmental conditions and housing are maintained, since the live body weight at slaughter and the depth of breast muscle measured by ultrasonography were directly related to breast weight.

An Extension of the Invariance Principle for a Class of Differential Equations with Finite Delay

An extension of the uniform invariance principle for ordinary differential equations with finite delay is developed. The uniform invariance principle allows the derivative of the auxiliary scalar function V to be positive in some bounded sets of the state space while the classical invariance principle assumes that. V <= 0. As a consequence, the uniform invariance principle can deal with a larger class of problems. The main difficulty to prove an invariance principle for functional differential equations is the fact that flows are defined on an infinite dimensional space and, in such spaces, bounded solutions may not be precompact. This difficulty is overcome by imposing the vector field taking bounded sets into bounded sets.

EXISTENCE RESULTS FOR NEUTRAL INTEGRO-DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY

In this paper we discuss the existence of mild, strict and classical solutions for a class of abstract integro-differential equations in Banach spaces. Some applications to ordinary and partial integro-differential equations are considered.

GLOBAL SOLUTIONS FOR ABSTRACT FUNCTIONAL DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

In this paper we study the existence of global solutions for a class of abstract functional differential equation with nonlocal conditions. An application is considered.

Weighted S-Asymptotically omega-Periodic Solutions of a Class of Fractional Differential Equations

We study the existence of weighted S-asymptotically omega-periodic mild solutions for a class of abstract fractional differential equations of the form u' = partial derivative (alpha vertical bar 1)Au + f(t, u), 1 < alpha < 2, where A is a linear sectorial operator of negative type.

EXISTENCE RESULTS FOR ABSTRACT NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper we discuss the existence of solutions for a class of abstract partial neutral functional differential equations.

SOLITON SOLUTIONS TO SYSTEMS OF COUPLED SCHRODINGER EQUATIONS OF HAMILTONIAN TYPE

We study the existence of positive solutions of Hamiltonian-type systems of second-order elliptic PDE in the whole space. The systems depend on a small parameter and involve a potential having a global well structure. We use dual variational methods, a mountain-pass type approach and Fourier analysis to prove positive solutions exist for sufficiently small values of the parameter.

LOCAL WELL POSEDNESS, ASYMPTOTIC BEHAVIOR AND ASYMPTOTIC BOOTSTRAPPING FOR A CLASS OF SEMILINEAR EVOLUTION EQUATIONS OF THE SECOND ORDER IN TIME

A class of semilinear evolution equations of the second order in time of the form u(tt)+Au+mu Au(t)+Au(tt) = f(u) is considered, where -A is the Dirichlet Laplacian, 92 is a smooth bounded domain in R(N) and f is an element of C(1) (R, R). A local well posedness result is proved in the Banach spaces W(0)(1,p)(Omega)xW(0)(1,P)(Omega) when f satisfies appropriate critical growth conditions. In the Hilbert setting, if f satisfies all additional dissipativeness condition, the nonlinear Semigroup of global solutions is shown to possess a gradient-like attractor. Existence and regularity of the global attractor are also investigated following the unified semigroup approach, bootstrapping and the interpolation-extrapolation techniques.

Theory of small-signal ac response of a dielectric liquid containing two groups of ions

The analysis of Macdonald for electrolytes is generalized to the case in which two groups of ions are present. We assume that the electrolyte can be considered as a dispersion of ions in a dielectric liquid, and that the ionic recombination can be neglected. We present the differential equations governing the ionic redistribution when the liquid is subjected to an external electric field, describing the simultaneous diffusion of the two groups of ions in the presence of their own space charge fields. We investigate the influence of the ions on the impedance spectroscopy of an electrolytic cell. In the analysis, we assume that each group of ions have equal mobility, the electrodes perfectly block and that the adsorption phenomena can be neglected. In this framework, it is shown that the real part of the electrical impedance of the cell has a frequency dependence presenting two plateaux, related to a type of ambipolar and free diffusion coefficients. The importance of the considered problem on the ionic characterization performed by means of the impedance spectroscopy technique was discussed. (c) 2008 American Institute of Physics.