Home About us Contact
|
Home About us Contact | ||
|
|
||
Fick's Law (fick + law)
Selected AbstractsThe mathematical modelling of the osmotic dehydration of shark fillets at different brine temperaturesINTERNATIONAL JOURNAL OF FOOD SCIENCE & TECHNOLOGY, Issue 4 2006Saheeda Mujaffar Summary The effect of brine temperature (20, 30, 40 and 50 °C) on the osmotic drying behaviour of shark slabs (10 × 5 × 1 cm) in saturated (100°) brine was investigated. The parameters investigated were weight reduction, water loss, salt gain and water activity. Salt uptake and moisture data were analysed using various mathematical solutions based on Fick's Law of Diffusion and the effective diffusion coefficients were predicted after considering the process variables. The expressions presented by Azuara et al. (1992), based on the model presented by Crank (1975), were successfully used to predict the equilibrium point and to calculate diffusion coefficients at not only the initial stages of dehydration, but also at different times during the osmotic process. [source] Estimating diesel degradation rates from N2, O2 and CO2 concentration versus depth data in a loamy sandEUROPEAN JOURNAL OF SOIL SCIENCE, Issue 1 2007J. Van De Steene Summary The degradation rate of the pollutant is often an important parameter for designing and maintaining an active treatment system or for determining the rate of natural attenuation. A quasi-steady-state gas transport model based on Fick's law with a correction term for advective flux, for estimating diesel degradation rates from N2, O2 and CO2 concentration versus depth data, was evaluated in a laboratory column study. A loamy sand was spiked with diesel fuel at 0, 1000, 5000 and 10 000 mg kg,1 soil (dry weight basis) and incubated for 15 weeks. Soil gas was sampled weekly at 6 selected depths in the columns and analysed for O2, CO2 and N2 concentrations. The agreement between the measured and the modelled concentrations was good for the untreated soil (R2= 0.60) and very good for the soil spiked with 1000 mg kg,1 (R2= 0.96) and 5000 mg kg,1 (R2= 0.97). Oxygen consumption ranged from ,0.15 to ,2.25 mol O2 m,3 soil day,1 and CO2 production ranged from 0.20 to 2.07 mol CO2 m,3 soil day,1. A significantly greater mean O2 consumption (P < 0.001) and CO2 production (P < 0.005) over time was observed for the soils spiked with diesel compared with the untreated soil, which suggests biodegradation of the diesel substrate. Diesel degradation rates calculated from respiration data were 1.5,2.1 times less than the change in total petroleum hydrocarbon content. The inability of this study to correlate respiration data to actual changes in diesel concentration could be explained by volatilization, long-term sorption of diesel hydrocarbons to organic matter and incorporation of diesel hydrocarbons into microbial biomass, aspects of which require further investigation. [source] Pristine New Zealand forest soil is a strong methane sinkGLOBAL CHANGE BIOLOGY, Issue 1 2004Sally J. Price Abstract Methanotrophic bacteria oxidize methane (CH4) in forest soils that cover ,30% of Earth's land surface. The first measurements for a pristine Southern Hemisphere forest are reported here. Soil CH4 oxidation rate averaged 10.5±0.6 kg CH4 ha,1 yr,1, with the greatest rates in dry warm soil (up to 17 kg CH4 ha,1 yr,1). Methanotrophic activity was concentrated beneath the organic horizon at 50,100 mm depth. Water content was the principal regulator of (r2=0.88) from the most common value of field capacity to less than half of this when the soil was driest. Multiple linear regression analysis showed that soil temperature was not very influential. However, inverse co-variability confounded the separation of soil water and temperature effects in situ. Fick's law explained the role of water content in regulating gas diffusion and substrate supply to the methanotrophs and the importance of pore size distribution and tortuosity. This analysis also showed that the chambers used in the study did not affect the oxidation rate measurements. The soil was always a net sink for atmospheric CH4 and no net CH4 (or nitrous oxide, N2O) emissions were measured over the 17-month long study. For New Zealand, national-scale extrapolation of our data suggested the potential to offset 13% of CH4 emissions from ca. 90 M ruminant animals. Our average was about 6.5 times higher than rates reported for most Northern Hemisphere forest soils. This very high was attributed to the lack of anthropogenic disturbance for at least 3000,5000 years and the low rate of atmospheric nitrogen deposition. Our truly baseline data could represent a valid preagricultural, preindustrial estimate of the soil sink for temperate latitudes. [source] Generalized Diffusion Tensor Imaging (GDTI): A Method for Characterizing and Imaging Diffusion Anisotropy Caused by Non-Gaussian DiffusionISRAEL JOURNAL OF CHEMISTRY, Issue 1-2 2003Chunlei Liu For non-Gaussian distributed random displacement, which is common in restricted diffusion, a second-order diffusion tensor is incapable of fully characterizing the diffusion process. The insufficiency of a second-order tensor is evident in the limited capability of diffusion tensor imaging (DTI) in resolving multiple fiber orientations within one voxel of human white matter. A generalized diffusion tensor imaging (GDTI) method was recently proposed to solve this problem by generalizing Fick's law to a higher-order partial differential equation (PDE). The relationship between the higher-order tensor coefficients of the PDE and the higher-order cumulants of the random displacement can be derived. The statistical property of the diffusion process was fully characterized via the higher-order tensor coefficients by reconstructing the probability density function (PDF) of the molecular random displacement. Those higher-order tensor coefficients can be measured using conventional diffusion-weighted imaging or spectroscopy techniques. Simulations demonstrated that this method was capable of quantitatively characterizing non-Gaussian diffusion and accurately resolving multiple fiber orientations. It can be shown that this method is consistent with the q-space approach. The second-order approximation of GDTI was shown to be DTI. [source] Preparation and optimization of 2,4-D loaded cellulose derivatives microspheres by solvent evaporation techniqueJOURNAL OF APPLIED POLYMER SCIENCE, Issue 4 2007Z. El Bahri Abstract Controlled release herbicide formulations were prepared by microencapsulation using solvent evaporation technique. 2,4-D was chosen as core material, which was microencapsulated in two cellulose derivatives as matrices: cellulose acetate butyrate butyryl (CAB) and ethylcellulose (EC). The work is intended to produce systems containing the herbicide to reduce its risks by dermal contact, evaporation, or degradation and to control the release of the active agent. The microspheres loaded by 2,4-D were characterized by scanning electron microscopy and infrared spectroscopy. We have obtained microparticles in the range of D32 of 42,277 ,m with CAB and 88,744 ,m with EC by varying the process parameters. The drug entrapment was improved by controlling certain factors such as polymer/solvent ratio, pH of continuous phase, and organic phase solvent. The drug release was established in deionized water at pH = 5.5 and 25°C and the 2,4-D concentrations were estimated by UV analysis. The release data were analyzed according to Fick's law and the results demonstrate that the release rate can be controlled by modifying the process parameters. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 2742,2751, 2007 [source] Simple models for evaluating effects of small leaks on the gas barrier properties of food packagesPACKAGING TECHNOLOGY AND SCIENCE, Issue 2 2003Donghwan Chung Abstract A detailed theoretical analysis and calculations were made for providing a simple and explicit means to evaluate the effects of small leaks on the barrier properties of food packages. Small leaks, such as pinholes and channel leaks, were approximated as cylindrical pores with diameters of 50,300,,m. The first part of the current study proposes a simple mathematical model based on Fick's law of diffusion, which accounts for both the gas leakage across small leaks and the gas permeation across package walls. The model uses an effective permeability that depends on leak dimensions, type of diffusing gas, type of packaging material and gas conditions around the leak ends. In the second part of the study, three practical cases are presented to illustrate the application of the proposed model in examining the significance of leaks. These demonstrate in a simple and explicit manner that for LDPE packages: (a) leaks affect the oxygen transfer more than the water vapour transfer; (b) leak effects are more significant at lower storage temperatures; and (c) that for high gas barrier packages, the effect of leaks is very important and should not be neglected. The model can be also used to arrive at conclusions about the significance of leaks in other packaging situations (e.g. other than LDPE packaging materials) and to correct the shelf-life estimation of gas- and water vapour-sensitive foods for errors from package leaks. Copyright © 2003 John Wiley & Sons, Ltd. [source] Water absorption behavior of different types of organophilic montmorillonite-filled polyamide 6/polypropylene nanocompositesPOLYMER COMPOSITES, Issue 2 2010Kusmono The water absorption behavior of different types of organophilic montmorillonite (OMMT)-filled polyamide 6/polypropylene nanocomposites with and without compatibilizers (maleated PP or PP- g -MA and maleated styrene-ethylene/butylene-styrene or SEBS- g -MA) was evaluated. Four different types of OMMT, i.e., dodecylamine-modified MMT (D-MMT), 12 aminolauric acid-modified MMT (A-MMT), stearylamine-modified MMT (S-MMT), and commercial organo-MMT (C-MMT) were used as reinforcement. The water absorption response of the nanocomposites was studied and analyzed by tensile test and morphology assessment by scanning electron microscopy (SEM). The kinetics of water absorption of the nanocomposites conforms to Fick's law. The Mm and D are dependent on the types of OMMT and compatibilizers. The equilibrium water content and diffusivity of PA6/PP blend were increased by the addition of OMMT but decreased in the presence of compatibilizers. On water absorption, both strength and stiffness of the nanocomposites were drastically decreased, but the ductility was remarkably increased. Both PP- g -MA and SEBS- g -MA played an effective role as compatibilizers for the nanocomposites. This was manifested by their higher retention ability in strength and stiffness (in the wet and re-dried states), reduced the equilibrium water content, and diffusivity of the nanocomposites. POLYM. COMPOS., 2010. © 2009 Society of Plastics Engineers [source] Soret Diffusion and Non-Ideal Dufour Conduction in Macroporous Catalysts with Exothermic Chemical Reaction at Large Intrapellet Damköhler NumbersTHE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 3 2007Laurence A. Belfiore Abstract The adiabatic temperature rise in catalytic pellets is predicted from a modified version of the Prater equation. Onsager reciprocal relations for coupled heat and mass transfer are violated in an analysis of thermal diffusion in macroporous catalysts with exothermic chemical reaction when Dufour conduction (i.e., the diffusion-thermo effect) is neglected. In this contribution, Dufour conduction is analyzed for both ideal and non-ideal pseudo-binary gas mixtures that simulate the production of methanol from carbon monoxide and hydrogen. In the diffusion-controlled regime at large intrapellet Damköhler numbers where intermolecular collisions provide the dominant resistance to mass transfer within the catalytic pores, temperatures in the catalytic core could be much greater than predictions based on the original Prater equation when the Prater number exceeds 0.30. The molecular flux of thermal energy includes Fourier's law, the interdiffusional flux, and Dufour conduction. Diffusional mass flux includes Fick's law and the Soret effect. All physicochemical properties of the reactive gas mixture exhibit temperature dependence. There is essentially no difference between maximum intrapellet temperature predictions that include or neglect ideal Dufour conduction when external catalytic surface temperatures range from 300-400 K and thermal diffusion enhances the flux of "smaller" reactants toward the centre of the catalyst. For "large-molecule reactants" that participate in exothermic reactions, thermal diffusion opposes Fick's law and Dufour conduction opposes Fourier's law. Under these conditions, it is demonstrated that core temperatures are overestimated by neglecting both off-diagonal coupling mechanisms (i.e., Soret diffusion and Dufour conduction). Prater numbers greater than unity and unrealistically high gas pressures are required to distinguish between maximum intrapellet temperatures for ideal and real gas simulations, where the latter consider two-body interactions for Lennard-Jones molecules in the virial equation of state. On prédit l'augmentation de la température adiabatique dans les pastilles catalytiques à partir d'une version modifiée de l'équation de Prater. Les relations réciproques d'Onsager pour le transfert de chaleur et de matière couplé sont violées dans une analyse de la diffusion thermique dans les catalyseurs macroporeux avec réaction chimique exothermique lorsque la conduction de Dufour (p.ex., l'effet de thermo-diffusion) est négligée. Dans cet article, on analyse la conduction de Dufour pour des mélanges de gaz pseudo-binaires idéaux et non idéaux qui simulent la production de méthanol à partir d'oxyde de carbone et d'hydrogène. Dans le régime à diffusion contrôlée à grand nombre de Damköhler entre les pastilles pour lesquels les collisions entre les molécules fournit la résistance dominante au transfert de matière à l'intérieur des pores catalytiques, les températures dans le noyau catalytique pourraient être bien plus grandes que les prédictions basées sur l'équation de Prater originale lorsque le nombre de Prater excède 0,30. Le flux moléculaire de l'énergie thermique inclut la loi de Fourier, le flux interdiffusionnel, et la conduction de Dufour. Le flux massique diffusionnel inclut la loi de Fick et l'effet Soret. Toutes les propriétés physicochimiques du mélange de gaz réactif montre une dépendance thermique. Il n'y a essentiellement pas de différence entre les prédictions des températures maximales entre les pastilles qui incluent ou négligent la conduction de Dufour idéale quand les températures de surface catalytiques externes sont comprises entre 300 et 400 K; la diffusion thermique améliore le flux des réactifs «plus petits» vers le centre du catalyseur. Pour les «réactifs composés de grandes molécules» qui participent aux réactions exothermiques, la diffusion thermique s'oppose à la loi de Fick et la conduction de Dufour à la loi de Fourier. Dans ces conditions, il est démontré que les températures de noyau sont surestimées en négligeant les deux mécanismes de couplage hors-diagonales (c.à-d. la diffusion de Soret et la conduction de Dufour). Des nombres de Prater plus grands que l'unité et des pressions de gaz élevées peu réalistes sont nécessaires pour distinguer les températures maximales entre les pastilles entre les simulations de gaz idéales et réelles, en considérant pour ces dernières les interactions à deux corps pour les molécules de Lennard-Jones dans l'équation d'état du viriel. [source] Electronic Speckle Pattern Interferometry: A Tool for Determining Diffusion and Partition Coefficients for Proteins in GelsBIOTECHNOLOGY PROGRESS, Issue 6 2002David Karlsson The aim of this study was to demonstrate electronic speckle pattern interferometry (ESPI) as a powerful tool in determining diffusion coefficients and partition coefficients for proteins in gels. ESPI employs a CCD camera instead of a holographic plate as in conventional holographic interferometry. This gives the advantage of being able to choose the reference state freely. If a hologram at the reference state is taken and compared to a hologram during the diffusion process, an interferometric picture can be generated that describes the refraction index gradients and thus the concentration gradients in the gel as well as in the liquid. MATLAB is then used to fit Fick's law to the experimental data to obtain the diffusion coefficients in gel and liquid. The partition coefficient is obtained from the same experiment from the flux condition at the interface between gel and liquid. This makes the comparison between the different diffusants more reliable than when the measurements are performed in separate experiments. The diffusion and partitioning coefficients of lysozyme, BSA, and IgG in 4% agarose gel at pH 5.6 and in 0.1 M NaCl have been determined. In the gel the diffusion coefficients were 11.2 ± 1.6, 4.8 ± 0.6, and 3.0 ± 0.3 m2/s for lysozyme, BSA, and IgG, respectively. The partition coefficients were determined to be 0.65 ± 0.04, 0.44 ± 0.06, and 0.51 ± 0.04 for lysozyme, BSA, and IgG, respectively. The current study shows that ESPI is easy to use and gives diffusion coefficients and partition coefficients for proteins with sufficient accuracy from the same experiment. [source] Physical foundations, models, and methods of diffusion magnetic resonance imaging of the brain: A reviewCONCEPTS IN MAGNETIC RESONANCE, Issue 5 2007Ludovico Minati Abstract The foundations and characteristics of models and methods used in diffusion magnetic resonance imaging, with particular reference to in vivo brain imaging, are reviewed. The first section introduces Fick's laws, propagators, and the relationship between tissue microstructure and the statistical properties of diffusion of water molecules. The second section introduces the diffusion-weighted signal in terms of diffusion of magnetization (Bloch,Torrey equation) and of spin-bearing particles (cumulant expansion). The third section is dedicated to the rank-2 tensor model, the bb -matrix, and the derivation of indexes of anisotropy and shape. The fourth section introduces diffusion in multiple compartments: Gaussian mixture models, relationship between fiber layout, displacement probability and diffusivity, and effect of the b -value. The fifth section is devoted to higher-order generalizations of the tensor model: singular value decompositions (SVD), representation of angular diffusivity patterns and derivation of generalized anisotropy (GA) and scaled entropy (SE), and modeling of non-Gaussian diffusion by means of series expansion of Fick's laws. The sixth section covers spherical harmonic decomposition (SHD) and determination of fiber orientation by means of spherical deconvolution. The seventh section presents the Fourier relationship between signal and displacement probability (Q -space imaging, QSI, or diffusion-spectrum imaging, DSI), and reconstruction of orientation-distribution functions (ODF) by means of the Funk,Radon transform (Q -ball imaging, QBI). © 2007 Wiley Periodicals, Inc. Concepts Magn Reson Part A 30A: 278,307, 2007. [source] | ||||||||||||||||