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## Arrhenius-type Equation (arrhenius-type + equation)
## Selected Abstracts## A novel self-consistent Nývlt-like equation for metastable zone width determined by the polythermal method CRYSTAL RESEARCH AND TECHNOLOGY, Issue 3 2009K. SangwalAbstract Using a power-law relation between three-dimensional nucleation rate J and dimensionless supersaturation ratio S, and the theory of regular solutions to describe the temperature dependence of solubility, a novel Nývlt-like equation of metastable zone width of solution relating maximum supercooling ,Tmax with cooling rate R is proposed in the form: ln(,Tmax/T0) = , + , lnR, with intercept , = {(1,m)/m }ln(,Hs/RGTlim) + (1/m)ln(f/KT0) and slope , = 1/m. Here T0 is the initial saturation temperature of solution in a cooling experiment, ,Hs is the heat of dissolution, RG is the gas constant, Tlim is the temperature of appearance of first nuclei, m is the nucleation order, and K is a new nucleation constant connected with the factor f defined as the number of particles per unit volume. It was found that the value of the term , for a system at saturation temperature T0 is essentially determined by the constant m and the factor f. The value of the factor f for a solute,solvent system at initial saturation temperature T0 is determined by solute concentration c0. Analysis of the experiment data for four different solute-water systems according to the above equation revealed that: (1) the values of , and m for a system at a given temperature depend on the method of detection of metstable zone width, and (2) the value of slope , = 1/m for a system is practically a temperature-independent constant characteristic of the system, but the value of , increases with an increase in saturation temperature T0, following an Arrhenius-type equation with an activation energy Esat. The results showed, among others, that solubility of a solute is an important factor that determines the value of the nucleation order m and the activation energy Esat for diffusion. In general, the lower the solubility of a solute in a given solvent, the higher is the value of m and lower is the value of Esat. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## DEHYDRATION CHARACTERISTICS OF PAPAYA (CARICA PUBENSCENS): DETERMINATION OF EQUILIBRIUM MOISTURE CONTENT AND DIFFUSION COEFFICIENT JOURNAL OF FOOD PROCESS ENGINEERING, Issue 5 2009R. LEMUS-MONDACAABSTRACT This study determined the drying kinetics behavior of papaya at different temperatures (40, 50, 60, 70 and 80C). Desorption isotherms were determined at 5, 20 and 50C over a relative humidity range of 10,95%. The Guggenheim, Anderson and de Boer models were found to be suitable for description of the sorption data. The samples reached equilibrium moisture of 0.10 ± 0.01 g water/g dry matter. Fick's second law model was used to calculate the effective diffusivity (6.25,24.32 × 10 - 10 m2/s). In addition, experimental data were fitted by means of seven mathematical models. The kinetic parameters and the diffusion coefficient were temperature-dependent and were evaluated by an Arrhenius-type equation. The modified Page model obtained the best-fit quality on experimental data according to statistical tests applied. PRACTICAL APPLICATIONS The main utility of this study is the application of both different empirical models and the diffusional model in tropical fruits' dehydration, which can be considered a basis for a very accurate estimation of drying time and the optimization of the same process. Two newly mathematical models are proposed in this study, through which a good fit on the data of experimental moisture content was achieved. The study of drying of papaya cultivated in Chile engages a great technological interest, because this product is widely used in the development of different products such as candying, canning, juice, syrup and marmalade. In addition, papayas cultivated in Chile, along with other tropical fruits cultivated in Brazil, Colombia and the Caribbean, have become especially important in the exportations of these countries. The major markets for these products include the U.S.A., the European Community and Asia. [source] ## RHEOLOGICAL BEHAVIOR OF POMEGRANATE (PUNICA GRANATUM L.) JUICE AND CONCENTRATE JOURNAL OF TEXTURE STUDIES, Issue 1 2005N ALTANABSTRACT The rheological behavior of pomegranate juice (Punica granatum L.), prepared from fresh pomegranates, was studied as a function of solids concentration in the range 17.5,75°Brix at 10,55C, using a controlled stress rheometer. Concentration methods did not influence flow behavior. There were no significant differences (P > 0.05) between viscosity and activation energy values for the pomegranate juices concentrated by different methods. The juices exhibited Newtonian behavior regardless of the concentration method. The effect of temperature was described by an Arrhenius-type equation with an activation energy in the range 5.34,32.2 kJ/mol depending on concentration. An exponential model described better the effect of the soluble solids on the viscosity and Eavalues. A simple equation was proposed for describing the combined effect of temperature and soluble solids content on the juice viscosity. [source] ## RHEOLOGICAL BEHAVIOUR OF CLARIFIED MANGO JUICE CONCENTRATES JOURNAL OF TEXTURE STUDIES, Issue 3 2000NGASEPPAM IBOYAIMA SINGHABSTRACT The rheological behaviour of clarified mango juice was measured at temperatures 15,85C and concentrations 15,66 °Brix, using a rotoviscometer. Mango juice free of pectin and pulp behaves as a Newtonian fluid. The effect of temperature can be described by an Arrhenius-type equation. The activation energy for viscous flow was in the range of 1.64,8.44 kcal/g-mol, depending on the concentration. The effect of concentration was modelled better by an exponential relationship than a power-law relationship. Simple equations are proposed for describing the combined effect of temperature and soluble solids content on the juice viscosity. [source] ## Kinetic Modeling of Breweryapos;s Spent Grain Autohydrolysis BIOTECHNOLOGY PROGRESS, Issue 1 2005Florbela CarvalheiroIsothermal autohydrolysis treatments of breweryapos;s spent grain were used as a method for hemicellulose solubilization and xylo-oligosaccharides production. The time course of the concentrations of residual hemicelluloses (made up of xylan and arabinan) and reaction products were determined in experiments carried out at temperatures in the range from 150 to 190 °C using liquid-to-solid ratios of 8 and 10 g/g. To model the experimental findings concerning to breweryapos;s spent grain autohydrolysis several kinetic models based on sequential pseudo-homogeneous first-order reactions were tested. Xylan and arabinan were assumed to yield oligosaccharides, monosaccharides (xylose or arabinose), furfural, and other decomposition products in consecutive reaction steps. The models proposed provide a satisfactory interpretation of the hydrolytic conversion of xylan and arabinan. An additional model merging the two proposed models for xylan and arabinan degradation assuming that furfural was formed from both pentoses was developed and the results obtained are discussed. The dependence of the calculated kinetic coefficients on temperature was established using Arrhenius-type equations. [source] |