Fick's 2nd Law Research Articles

중성화와 염해를 고려한 콘크리트의 복합열화 예측

The most common deteriorating processes of concrete structures are carbonation and chloride ion ingress. Many concrete structures have been suffered from chloride ions diffusion or carbonation induced reinforcement corrosion damage and many studies have been done on it. However, those studies were confined mostly to the single deterioration of carbonation or chloride attack only, although actual environment is rather of combined conditions. In case of many in-situ concrete structures, deterioration happened more for the case of combined attack than the single case of carbonation or chloride attack. In this paper, chloride profiles of carbonated concrete is predicted by considering two layer composite model, which is based on Fick's 2nd law. From the experimental result on combined deterioration of chloride and carbonation, it was examined that high chloride concentration was built up to 3∼5 mm over depth from carbonation depth. The analytical modeling of chloride diffusion was suggested to depict the relative influence of the carbonation depth. The diffusion coefficients of carbonation concrete and uncarbonated concrete with elapsed time were considered in this modeling.

Moisture Diffusivity in Sponge Cake as Related to Porous Structure Evaluation and Moisture Content

ABSTRACT: Water diffusivity within sponge cake was determined at 5, 20, and 25 °C by identification from a water sorption kinetic and using a mathematical model based on Fick's 2nd law. Water diffusivity at 20 °C within sponge cake varied from 0.5 × 10‐10 m2/s to 7.5 × 10‐10 m2/s as a function of sponge cake moisture content. Influence of temperature on the concentration‐dependent diffusivity was investigated. The activation energy was found to vary with sponge cake moisture content from 84 to 128 kj/mole. Effective diffusivity variations were correlated with the changes in microstructure of the material that was observed by using environmental scanning electron microscopy. The level of porosity in the material played a dominant role in determining the effective diffusivity.

Phenanthrene sorption with heterogeneous organic matter in a landfill aquifer material

Phenanthrene was used as a model chemical to study the sorption properties of Canadian River Alluvium aquifer material. Both equilibrium and kinetic sorption processes were evaluated through batch studies. The bulk sample was divided into subsamples with varying properties such as particle size, organic content, equilibration time, etc. in order to determine the effect of these properties on resulting sorption parameters. The data have been interpreted and the effect of experimental variables was quantified using the Freundlich isotherm model and a numerical solution of Fick's 2nd law in porous media. Microscopic organic matter characterization proved to be a valuable tool for explaining the results. Different organic matter properties and sorption mechanisms were observed for each soil subsample. Samples containing coal particles presented high Koc values. Samples with organic matter dominated by organic coatings on quartz grains presented low Koc values and contained a high percentage of fast sorption sites. The numerical solution of Fick's 2nd law requires the addition of two terms (fast and slow) in order to fit the kinetics of these heterogeneous samples properly. These results thus demonstrate the need for soil organic matter characterization in order to predict and explain the sorption properties of a soil sample containing heterogeneous organic matter and also the difficulty and complexity of modeling sorption in such samples.

Coagulation rate studies of spinnable chitosan solutions

The coagulation properties of some mixtures of 5% chitosan in 2% aqueous acetic acid were investigated with the goal of determining the optimal coagulation conditions for the spinning of chitosan fibers. The chitosan was characterized and found to possess a deacetylation value of 84.9 ± 0.2%. Molecular weight of the chitosan was also measured; based on intrinsic viscosity, the Mv value was 7.73 × 105 g mol−1, and based on high-pressure liquid chromatography, the Mw value was 1.14 × 105 g mol−1. Solutions of 5% chitosan/2% acetic acid were prepared, filtered, and extruded through a large-diameter hole syringe into coagulation baths of varying composition that were all strongly basic in nature, at least a pH of 12 or greater. For each coagulant, time was varied from between 22 s and 2 minutes at room temperature. A second set of experiments was conducted where the temperature was varied from 20°C to 70°C at a constant time of 45 s. In a third set of experiments, using a 1M NaOH coagulant, different chitosans were also analyzed. Throughout all of the experiments, a distinct moving boundary between coagulated and uncoagulated polymer was observed within the cylindrical-shaped polymer fibers. Using a series of equations based on Fick's 2nd Law, a straight line relationship has been demonstrated between boundary motion and time and between boundary motion and temperature for each coagulant tested. The activation energy for each coagulant was also determined. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 66: 117–127, 1997

On the Joint Estimation of External Mass Transfer and Diffusion Coefficients Using Optimal and Heuristic Experimental Designs

Optimal experimental designs for maximum precision in the estimation of diffusivities (D) and mass transfer coefficients (Kc) for solute transport from/to a solid immersed in a fluid were determined. Diffusion in the solid was considered to lake place according to Fick's 2nd law. It was found that the optimal design was dependent on the Biol number. In the range of Biot numbers tested (0.1 lo 200). the firsl sampling time corresponded to values of fractional loss/uptake between 0.10 and 0.32. and the second sampling time corresponded to values of fractional loss/uptake between 0.67 and 0.82. Pseudo-experimental data were simulated by applying randomly generated errors following a normal distribution with 5% standard deviation to data calculated using given values of the model parameters, assuming both optimal and heuristic designs for which the sampling times corresponded to values of fractional loss/uptake from 0.30 to 0.95). The accuracy and precision of the estimates obtained by non-linear regression were compared Optimal designs were found to yield best results in terms of precision. It was concluded that the joint estimation of D and Kc should be avoided, particularly for very low Biot numbers, as even optimal designs are unable to yield good results; for largei Biot numbers die estimation of D was feasible, whereas the estimation of Kc was found to yield inaccurate values with large confidence intervals, in the whole range tested.

The influence of the temperature increase rate on the accuracy of diffusion parameters estimated under non‐isothermal conditions

The accuracy of the diffusion parameters estimated under non‐isothermal conditions was studied using computer‐generated pseudo‐experimental points. The data sets were obtained from Fick's 2nd law and an Arrhenius‐type temperature dependence of the diffusivity. A normally distributed error was randomly attributed to the model data. The pseudo‐experimental points thus obtained were then fitted to the model equation, with non‐linear regression using the Simplex algorithm, yielding the estimates of the pre‐exponential factor and activation energy. Several linear temperature profiles were studied, from 0.014 to 16°C min−1. It was concluded that the accuracy of the parameters estimation depends on the temperature increase rate. The effects of the pre‐exponential factor, the activation energy, the range of temperature and the magnitude of the experimental error on the value of the temperature increase rate that led to maximum accuracy of the parameters estimates were also studied.

Effect of geometry on the effective moisture transfer diffusion coefficient

The effective moisture transfer diffusion coefficient ( D eff ) of ready-to-eat breakfast cereals (RTE) is determined either from an individual particle or a bulk of material in the literature. The D eff is assumed to be the same in both cases which can be dependent on the material thickness. In this study, the effect of bed depth of a bulk of two types of RTE cereal on D eff was investigated at several bed depths at 75% RH. Both linear and nonlinear solutions of Fick's 2nd Law were applied to determine D eff from the weight vs time data. The magnitude of D eff increased with an increase in bed depth. Since the captured air between the particles in the bulk volume contributed significantly to the moisture transfer in the system, the overall D eff of the system increased as the total volume of the captured air increased at higher bed depths. The relation was shown to have a square of the thickness dependence.

X-ray Microradiographic Determination of Diffusion Coefficients within Porous Media Based on Fick's 2nd Law: Theory and Error Analysis

A method based on Fick’s 2nd Law is described for the determination of local effective diffusion coefficients, within porous media, from X-ray absorption measurements. Numerical methods were used to simulate concentrations and corresponding X-ray absorption data during diffusion of an X-ray absorbing species within the fluid phase. Errors arising from X-ray counting statistics were investigated analytically and by Monte Carlo simulations. The influence of experimental conditions on errors is discussed.

Development of a gas diffusion probe for the determination of methane concentrations and diffusion characteristics in flooded paddy soil

A probe for the measurement of dissolved CH4 in anoxic methanogenic environments was developed. The probe was based on the diffusion of dissolved CH4 through a silicone membrane into a gas space at the end of the probe. This gas space was flushed with N2 and analyzed gas-chromatographically for CH4. The probe had a spatial resolution of < 1.3 mm, the detection limit was about 20 μM CH4, the precision of the measurement was 9%, and consecutive measurements could be made every 4 min. Memory effects after analysis of high CH4 concentrations could be avoided by flushing the probe with N2 between each measurement. The probe was sensitive for water movement and, therefore, was calibrated in an artificial sediment of glass beads (100 μm diam.) immersed by aqueous solutions of known CH4 concentrations. Sensitivity of the probe for changes in the sediment's porosity could not presently be excluded. The probe was used to measure vertical profiles of dissolved CH4 in microcosms of anoxic paddy soil. The vertical CH4 profiles measured with the probe compared fairly well with those measured after an extraction procedure. The profiles clearly showed that CH4 was produced in deeper layers and diffused upwards to be consumed in the oxic top 2 mm soil layers. The probe was also used to determine the diffusion coefficient of CH4 in an inactivated paddy soil microcosm using a set-up which allowed modelling of a measured CH4 concentration profile using Fick's 2nd law.

Freezing Influences Diffusion of Reducing Sugars in Carrot Cortex

ABSTRACTThe loss of reducing sugars from raw and previously frozen carrot cortex tissue immersed in warm water was studied as a function of temperature (40–100°C). Leaching was described as a diffusional mechanism by application of Fick's 2nd law. This approach successfully modeled losses from raw carrots at temperatures higher than 60°C. At low temperatures diffusion was much slower, due to a high resistence of the tissues to mass transfer, and Fick's 2nd law could not be applied. Previously frozen carrots showed a Fickian behaviour through the range of temperatures and diffusivities were much higher. Dependence of diffusivity on temperature followed an Arrhenius type equation for the two cases. However, the activation energy of pre‐frozen carrots was lower, indicating loss of sensitivity to temperature variations.

Solution of Fick's 2nd Law to the Problem of Diffusion in Composite Spherical Solids for Small Values of the Time

Solution of Fick's 2nd Law to the Problem of Diffusion in Composite Spherical Solids for Small Values of the Time

Solution for Fick's 2nd law with variable diffusivity in a multi-phase system

Solution for Fick's 2nd law with variable diffusivity in a multi-phase system

Studies on the Mechanism of Formation of Optically Active Substances in Living Organisms. Part I. General Consideration on the Stereospecificities of Enzymes and on the Possible Occurence of A New Supposed Enzyme

Anti-corrosion behaviour of rebar embedded in cement mortar containing chloride ions was investigated by electrochemical chloride extraction(ECE). of the initial chloride ions of the cement mortar was fixed to Friedel salts and the soluble chloride ions were successfully extracted by ECE method. Concentration profiles of the chloride ions were estimated by Fick's 2nd law with time and depth, and it was close to the real value. The corrosion potential increased to anodic direction after ECE test, and the corrosion of rebar was reduced as a result of AC impedance spectroscopy.