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Law Model (law + model)
Kinds of Law Model Selected AbstractsRelease of potassium sorbate from active films of sodium alginate crosslinked with calcium chloridePACKAGING TECHNOLOGY AND SCIENCE, Issue 6 2009E. M. Zactiti Abstract The release of potassium sorbate from alginate films was evaluated considering different active agent concentrations in the film and three levels of alginate crosslinking. The mechanism involved in the diffusional process was investigated using the Power Law Model. The results indicated that potassium sorbate diffusion in alginate films has characteristics of Fickian and non-Fickian behaviour. Effective diffusion coefficients obtained using the solution in series derived from Fick's Second Law are close to values obtained by the short-time solution, indicating that the influence of swelling on effective diffusivity, although perceptible, is small, allowing the use of an average effective diffusivity. The values of effective diffusivity found indicate that alginate films have a potential use as systems for release of active substances. Copyright © 2009 John Wiley & Sons, Ltd. [source] Mobility of shear thinning viscous drops in a shear Newtonian carrying flow using DR-BEMINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2009M. Giraldo Abstract The study of drop behaviour has attracted great interest in the last years due to its importance in different industrial and biological systems. Most available works focus on Newtonian drops, excluding some very important applications such as polymer mixing. Simulations of non-Newtonian drops have had only limited study, mostly in time-dependent rheologies or simple flow cases. This work presents a boundary-only formulation based on the dual reciprocity method to model the motion and deformation of non-Newtonian shear thinning drops due to a shear Newtonian unbounded carrying flow. Pair-wise interactions at low Reynolds number between two viscous shear thinning non-Newtonian drops are numerically simulated in order to obtain mobility magnitudes under linear shear flow of different strengths. Separation of the drops in the direction perpendicular to the imposed flow field at high capillary number (small surface tension) and low viscosity ratio was favoured by shear thinning, increasing in magnitude as the capillary number increases and the viscous ratio decreases. Higher values of this separation occur at higher values of the viscosity ratio when compared with the case of Newtonian drops. In order to obtain a good physical description of the non-Newtonian drop behaviour, while maintaining good computational performance, the non-Newtonian viscosity is made to obey the truncated power law model. Copyright © 2008 John Wiley & Sons, Ltd. [source] Effect of milk source on the rheological properties of yogurt during the gelation processINTERNATIONAL JOURNAL OF DAIRY TECHNOLOGY, Issue 3 2001R Y Jumah This paper presents research on the effect of milk source on the rheological properties of curd during the gelation process of yogurt. The highest value for viscosity was exhibited by ovine milk, followed by caprine, bovine and camel milks. For bovine, ovine and caprine milk, three different transient viscosity stages were identified and described by mathematical expressions, whereas camel milk showed no significant variation in viscosity during gelation. The chemical composition of milk, namely total solids and protein content, has a major effect on the rheological properties of curd. A power law model allows the determination of the flow behaviour index and the consistency coefficient of curd made from different milk sources. [source] Optimisation study of gum extraction from Basil seeds (Ocimum basilicum L.)INTERNATIONAL JOURNAL OF FOOD SCIENCE & TECHNOLOGY, Issue 9 2009Seyed M. A. Razavi Summary Basil seed (Ocimum basilicum L.) is cultivated in large quantities in different regions of Iran. This seed has reasonable amounts of gum with good functional properties which is comparable with commercial food hydrocolloids. A central composite rotatable design was applied to evaluate the effects of temperature, pH and water/seed ratio on the yield, apparent viscosity and protein content of water-extracted Basil seed gum. All of the variables significantly (P < 0.05) affected the extraction yield, whereas the effect of water/seed ratio on apparent viscosity and the effects of pH and water/seed ratio on protein content were not significant (P > 0.05). Numerical optimisation determined the optimum extraction conditions based on the highest yield and viscosity and the lowest protein content as being temperature 68.71 °C, pH 8.09 and water/seed ratio 65.98:1. Power law model well described non-Newtonian pseudoplastic behaviour of BSG. Flow behaviour index (n) and consistency index (K) of 1% crude and pure BSG samples were 0.306, 0.283 and 17.46, 20.22 Pa sn, respectively. [source] Spinning of protein fibres from blue squat lobster (Cervimunida jhoni) industry by-productsINTERNATIONAL JOURNAL OF FOOD SCIENCE & TECHNOLOGY, Issue 6 2007Mario Pérez-Won Summary The fresh whole crustaceans by-products from blue squat lobster (Cervimunida jhoni) were minced and the protein was solubilised with 0.1 m of NaOH. Then the solution was centrifuged and the supernatant was precipitated using 0.1 m of HCl. The dope was prepared with 4% of protein, solid NaOH and coadjutant (sodium alginate or carragenan). The dope was extruded through the trial-spinning machine and the fibre was formed. The results showed that the best condition of protein extraction was 90 min and pH 12.5 when 58.4% of protein from whole crustacean by-products could be extracted. The protein isolate was obtained at pH 4.0. The best fibres were obtained when the ratios protein/NaOH, and protein/coadjutant were 10:1 and 1:1 respectively. Rheological measurements of all dopes exhibited non-Newtonian behaviour and the experimental data were described by the power law model. The consistency index (k) of the dopes containing carragenan seem to be a parameter to evaluate dope spinnability. [source] Studies in transesterification of ethylene carbonate to dimethyl carbonate over Amberlyst A-21 catalystJOURNAL OF CHEMICAL TECHNOLOGY & BIOTECHNOLOGY, Issue 1 2006Shekhar M Dhuri Abstract Transesterification of ethylene carbonate (EC) with methanol (MeOH) was studied in a slurry reactor using various homogeneous and heterogeneous, acidic as well as basic, catalysts. Among all catalysts studied, the weakly basic anion-exchange resin Amberlyst A-21 gave more than 95% selectivity towards dimethyl carbonate (based on EC converted). Using this Amberlyst A-21 as a catalyst, the kinetics for the transesterification reaction was studied in the range of temperature from 363 to 393 K, varying catalyst loading from 11.24 to 44.97 kg m,3 and the molar ratio MeOH:EC being varied between 4:1 and 16:1. The initial rate data were analysed using a power law model to aid process design. Copyright © 2005 Society of Chemical Industry [source] Effect of floc concentration on the rheology of a ferric flocJOURNAL OF CHEMICAL TECHNOLOGY & BIOTECHNOLOGY, Issue 2 2004Wendy AM McMinn Abstract The primary interest of this work is to determine the effect of floc concentration on ferric floc particle interactions and hence, rheology. In accordance with established theory, ferric floc viscosity exhibits a non-linear increase with solids content, with the viscosity increasing sharply above a concentration of 12 000 ppm. Shear effectively breaks down floc structure, and thus reduces viscosity, the extent of which is independent of solids content. The effect of shear is also observed to diminish over time and can be adequately characterised by a power law model. Addition of aluminium nitrate to ferric floc increases the quantity of water bound within the floc, and thus produces suspensions which are more viscous in nature. Copyright © 2003 Society of Chemical Industry [source] DEHYDRATION CHARACTERISTICS OF PAPAYA (CARICA PUBENSCENS): DETERMINATION OF EQUILIBRIUM MOISTURE CONTENT AND DIFFUSION COEFFICIENTJOURNAL OF FOOD PROCESS ENGINEERING, Issue 5 2009R. LEMUS-MONDACA ABSTRACT 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 PROPERTIES OF SET YOGURT AS INFLUENCED BY INCUBATION TEMPERATURE AND HOMOGENIZATIONJOURNAL OF FOOD QUALITY, Issue 5 2002R.R. SHAKER The effect of incubation temperature and homogenization on the rheological nature of yogurt curd during gelation was investigated in this study. Our results indicated that the optimum incubation temperature for acid development was 45C. The minimum viscosity was observed at 40C while the maximum viscosity was at 48C. Our results also indicated that incubation temperature affected yogurt viscosity during the gelation process while homogenization had no significant effect. Increasing the incubation temperature decreased the flow behavior index and increased the consistency coefficient; homogenization increased the flow behavior index and decreased the consistency coefficient as described by a power law model. [source] Microbial Inactivation Kinetics during High-Pressure Carbon Dioxide Treatment: Nonlinear Model for the Combined Effect of Temperature and Pressure in Apple JuiceJOURNAL OF FOOD SCIENCE, Issue 8 2008G. Ferrentino ABSTRACT:, Isobaric and isothermal semi-logarithmic survival curves of natural microflora in apple juice treated with high-pressure carbon dioxide at 7, 13, and 16 MPa pressures and 35, 50, and 60 °C temperatures were fitted with a nonlinear equation to find the values of the coefficient b(P ), b(T ), n(P ), and n(T ). Profiles of the model parameters were obtained as a function of pressure and temperature. The model fitted with good agreement (R2 > 0.945), the survival curves. An empirical equation was proposed to describe the combined effects of pressure and temperature. The equation, derived from a power law model, was written in the form: . The proposed model fitted the experimental data well. At 7 MPa and 50 and 60 °C, 13 MPa and 35 and 60 °C, 16 MPa and 35 °C, the model provided log10 reduction residual values (observed value , fitted value) lower than 0.284 showing a good agreement between the experimental and the predicted survival levels. [source] Laser monitoring of non-Newtonian liquids during dip coatingAICHE JOURNAL, Issue 12 2009Alexandre F. Michels Abstract Dip coated films, widely used in the coating industry, are usually measured by capacitive methods with micrometric precision. In this work, interferometric determination of thickness evolution in real time, for the first time to our best knowledge, is applied to volatile non-Newtonian liquids with several viscosities and distinct dip withdrawing speeds. Thickness evolution during the process depends on time as predicted by a power law model. Comparison with measured results (uncertainty of ± 0.007 ,m) showed very good agreement after initial steps of the process. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source] RHEOLOGICAL BEHAVIOR AND TIME-DEPENDENT CHARACTERIZATION OF ICE CREAM MIX WITH DIFFERENT SALEP CONTENTJOURNAL OF TEXTURE STUDIES, Issue 3 2005S. KU ABSTRACT The effect of salep concentration on the rheological characteristics of ice cream mixes (0.5,1.5% salep content), prepared from nonfat cow's milk and sugar, was studied using a controlled stress rheometer. The flow curves and time-dependent flow properties of the ice cream mixes were assessed at different temperatures. The ice cream mixes' samples showed slightly thixotropic behavior, which was reduced as the salep content decreased. The forward and backward measurements of the flow curves of ice cream mixes were modeled with the power law model. The ice cream mixes showed pseudoplastic flow behavior after destruction of the thixotropic structure. In mixes that were first presheared at a high shear rate flow properties could also be described by the power law model. The second-order structural kinetic, first-order stress decay and Weltman models were applied to model the time-dependent flow properties of the ice cream mixes. Among these, the first-order stress decay model was found to fit well the experimental data. [source] Theoretical and visual study of bubble dynamics in foam injection moldingPOLYMER ENGINEERING & SCIENCE, Issue 3 2010Mehdi Mahmoodi This article presents an experimental observation and a theoretical prediction of bubble dynamics in foam injection molding process with a main focus on the cell collapse phenomenon under pressure. Using a visualizing setup, cell growth behavior under a nonisothermal condition was monitored. In conjunction with the growth behavior, dynamics of cell collapse under different pressures and the effect of growing time on collapse behavior and final cell size were studied. Theoretical simulation of bubble behavior included power law model, which predicted bubble dynamics during foaming process. The results show that collapse phenomenon strongly depends on both exerted holding pressure and growth time. The presented model can also give a reasonable prediction of growth and collapse of cells and could give insight to control of cell size in injection foaming process. POLYM. ENG. SCI., 2010. © 2009 Society of Plastics Engineers [source] Flexural creep of all-polypropylene composites: Model analysisPOLYMER ENGINEERING & SCIENCE, Issue 5 2008K. Banik In this article, simple viscoelastic and empirical models are presented to predict and analyze the flexural creep behavior of all-poly(propylene) (all-PP) composites. Results of the successful application of these models to the actual creep behavior of unidirectional (UD) and cross-ply (CP) all-PP composites tested by short-term flexural creep measurements over a temperature range of 20,80°C are presented. Analysis of the momentary creep behavior of all-PP composites with different tape lay-ups are made to understand their deformation mechanism. Further to the main theme of the article, an interesting discrepancy while predicting the long-term creep behavior of these composites based on the time-temperature superposition (TTS) principle and Findley power law model is visualized which has also been illustrated here. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers [source] CFD simulation of non-Newtonian fluid flow in anaerobic digestersBIOTECHNOLOGY & BIOENGINEERING, Issue 3 2008Binxin Wu Abstract A general mathematical model that predicts the flow fields in a mixed-flow anaerobic digester was developed. In this model, the liquid manure was assumed to be a non-Newtonian fluid, and the flow governed by the continuity, momentum, and k-, standard turbulence equations, and non-Newtonian power law model. The commercial computational fluid dynamics (CFD) software, Fluent, was applied to simulate the flow fields of lab-scale, scale-up, and pilot-scale anaerobic digesters. The simulation results were validated against the experimental data from literature. The flow patterns were qualitatively compared for Newtonian and non-Newtonian fluids flow in a lab-scale digester. Numerical simulations were performed to predict the flow fields in scale-up and pilot-scale anaerobic digesters with different water pump power inputs and different total solid concentration (TS) in the liquid manure. The optimal power inputs were determined for the pilot-scale anaerobic digester. Some measures for reducing dead and low velocity zones were proposed based upon the CFD simulation results. Biotechnol. Bioeng. 2008;99: 700,711. © 2007 Wiley Periodicals, Inc. [source] | |||||||||||||||||||||||||