Journal articles: 'Fick's first law'

1

Slyusarenko, E. M., and V. S. Soldatov. "Description of Interdiffusion Processes in Multicomponent Systems by the First Fick's Law." physica status solidi (b) 154, no. 2 (1989): 475–82. http://dx.doi.org/10.1002/pssb.2221540207.

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Straub, D., R. Graue, F. Heitmeir, P. Nebendahl, and Th K. Wurst. "Fick's First Law Correction by an exact solution of the boltzmann equation." Propellants, Explosives, Pyrotechnics 12, no. 3 (1987): 105–12. http://dx.doi.org/10.1002/prep.19870120310.

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Zhou, Larissa, Kendra Nyberg, and Amy C. Rowat. "Understanding diffusion theory and Fick's law through food and cooking." Advances in Physiology Education 39, no. 3 (2015): 192–97. http://dx.doi.org/10.1152/advan.00133.2014.

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Diffusion is critical to physiological processes ranging from gas exchange across alveoli to transport within individual cells. In the classroom, however, it can be challenging to convey the concept of diffusion on the microscopic scale. In this article, we present a series of three exercises that use food and cooking to illustrate diffusion theory and Fick's first law. These exercises are part of a 10-wk undergraduate course that uses food and cooking to teach fundamental concepts in physiology and biophysics to students, including nonscience majors. Consistent demonstration of practical applications in a classroom setting has the potential to fundamentally change how students view the role of science in their lives (15).

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Gornshteyn, B. J. "Fick's First Law of Diffusion and Binary Gas Separation by Hollow-Fiber Asymmetric Membrane." Canadian Journal of Chemical Engineering 81, no. 1 (2008): 139–46. http://dx.doi.org/10.1002/cjce.5450810118.

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Lavery, Paul S., Carolyn E. Oldham, and Marco Ghisalberti. "The use of Fick's First Law for predicting porewater nutrient fluxes under diffusive conditions." Hydrological Processes 15, no. 13 (2001): 2435–51. http://dx.doi.org/10.1002/hyp.297.

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Robischon, Marcel. "Surface-Area-to-Volume Ratios, Fluid Dynamics & Gas Diffusion: Four Frogs & Their Oxygen Flux." American Biology Teacher 79, no. 1 (2017): 64–67. http://dx.doi.org/10.1525/abt.2017.79.1.64.

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Processes of diffusion of oxygen can be described in a formalized and simplified manner in formulas such as Fick's laws of diffusion. For a sound understanding of the interconnections of anatomical structure, biological function, and environmental factors in a living system, however, real-life case studies need to be employed to explore what is captured in the equation and what is not, and which other structures and behaviors may play a role in respiratory physiology. I use four anuran examples to illustrate, starting with Fick's first law, respiratory processes as influenced by surface-area-to-volume ratio and turbulence in the surrounding medium.

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Denny Kamaruddin, H. "Some observations about the application of Fick's first law for membrane separation of multicomponent mixtures." Journal of Membrane Science 135, no. 2 (1997): 147–59. http://dx.doi.org/10.1016/s0376-7388(97)00142-7.

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Belova, I. V., M. J. Brown, and G. E. Murch †. "Computer simulation of the phenomenological transport coefficient in the lattice gas and Fick's First Law." Philosophical Magazine 85, no. 14 (2005): 1495–506. http://dx.doi.org/10.1080/14786430500036637.

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PERRIAT, P., and B. GILLOT. "A model for coupled diffusion reactions in MnZn ferrites. Generalization of the Fick's first law." Solid State Ionics 67, no. 1-2 (1993): 35–43. http://dx.doi.org/10.1016/0167-2738(93)90306-n.

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Ujihara, Toru, Kozo Fujiwara, Gen Sazaki, Noritaka Usami, and Kazuo Nakajima. "New method for measurement of interdiffusion coefficient in high temperature solutions based on Fick's first law." Journal of Crystal Growth 241, no. 3 (2002): 387–94. http://dx.doi.org/10.1016/s0022-0248(02)01316-7.

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Jordan, P. M. "Growth, decay and bifurcation of shock amplitudes under the type-II flux law." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2087 (2007): 2783–98. http://dx.doi.org/10.1098/rspa.2007.1895.

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By replacing Fick's diffusion law with Green and Nagdhi's type-II flux law, a hyperbolic counterpart to the classical Fisher–KPP equation is obtained. In this article, an analytical study of this partial differential equation is presented with an emphasis on shock and related kinematic wave phenomena. First, an exact travelling wave solution (TWS) is derived and examined. Then, using singular surface theory, exact amplitude expressions for both shock and acceleration waves are obtained. In addition, the issue of shock stability is addressed and the limitations of the model are noted. It is shown that discontinuity (i.e. shock) formation in the TWS occurs only when the propagation speed, which must exceed the characteristic speed, tends to the latter. It is also shown that the shock amplitude equation undergoes a transcritical bifurcation. Lastly, numerical simulations of acceleration waves in a simple model problem are presented.

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Housaindokht, Mohammad R., Mahmood Bahrololoom, Shirin Tarighatpoor, and Ali A. Mossavi-Movahedi. "An approach based on diffusion to study ligand-macromolecule interaction." Acta Biochimica Polonica 49, no. 3 (2002): 703–7. http://dx.doi.org/10.18388/abp.2002_3779.

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A new approach has been developed to study binding of a ligand to a macromolecule based on the diffusion process. In terms of the Fick's first law, the concentration of free ligand in the presence of a protein can be determined by the measurement of those ligands which are diffused out. This method is applied to the study of binding of methyl-orange to lysozyme in phosphate buffer of pH 6.2, at 30 degrees C. The binding isotherm was determined initially, followed by application of the Hill equation to the data obtained, then binding constant and binding capacity were estimated.

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Checamarev, Gerardo, Maria I. Yeannes, Alicia E. Bevilacqua, and Maria R. Casales. "Mass Transfer During Osmotic Dehydration of Chub Mackerel Cylinders in Ternary Solution." Journal of Food Research 3, no. 5 (2014): 49. http://dx.doi.org/10.5539/jfr.v3n5p49.

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In the analysis, design and optimization of an osmotic dehydration process is important to know the kinetic of water loss and solutes gain. In this study, the mass transfer during osmotic dehydration of chub mackerel (Scomber japonicus) cylinders in ternary solution glycerol/salt/water was analyzed. The models of Zugarramurdi &amp; Lupín and Azuara were used to describe mass transfer and to estimate equilibrium values. The radial effective diffusion coefficient was estimated using the analytical solution of Fick's second law. Diffusion coefficients were determined for a finite cylinder, for an infinite cylinder considering only the first term of the series and considering higher order terms of the series. The profiles of water and solutes during the osmotic dehydration were calculated by using the estimated water and solutes diffusivities. According to the results obtained, using three terms in the analytical solution of the Fick's second law is appropriate to determine the diffusion coefficients. The diffusion coefficient for infinite cylinder were 2.63×10-6, 4.11×10-6 and 4.25×10-6 cm2/s for water loss, salt and glycerol gain respectively. For a finite cylinder these values were 2.30×10-6, 3.67×10-6 and 3.78×10-6 cm2/s respectively. All the models proposed were in agreement with experimental data for solutes gain ((0.967&lt;R2adj&lt;0.986); (0.0016&lt;RMSE&lt;0.039) and (4.17&lt;P&lt;10.0)). The model based on the solution of Fick’s Law for an infinite cylinder with higher order terms was the best fit for water loss and solutes gain. The equilibrium values estimated with Azuara model agree with the experimental (0&lt;relative error&lt;9.8). Water and solute distributions as a function of time and location in the radial direction were plotted.

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Hairch, Y., and A. El Afif. "Permeation of Toluene into (Polypropylene/Acrylonitrile-co-butadiene Rubber) immiscible blend." MATEC Web of Conferences 286 (2019): 08001. http://dx.doi.org/10.1051/matecconf/201928608001.

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This study examines the unsteady permeation process of a solvent through a mixture of two immiscible polymers with a complex dividing interface. The mathematical model consists of three nonlinear PDEs that incorporate the coupling arising between mass transport and the dynamic changes of the blend internal structure. In addition to the solvent mass fraction c, we choose, as additional state variables, the conformation tensor m to characterize the macromolecular chains while the embedded interface is described by a scalar Q and a traceless second-order tensor q respectively for the size and shape anisotropy of the area. We extend the Fick's first law by two new non-Fickian terms. Among the obtained results, we present the transient permeation mass flux profiles of toluene through PP/NBR blend system at different compositions and predict the corresponding time lag.

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Gu, Xiao Zhi, Kai Ning Chen, Wei Huang, Xiang Bai, and Cheng Xin Fan. "The Influence of Emergent Macrophytes on Porewater PO₄^3- Distribution and Physic Transport in the Estuary Wetlands." Advanced Materials Research 610-613 (December 2012): 2683–87. http://dx.doi.org/10.4028/www.scientific.net/amr.610-613.2683.

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Emergent macrophytes growth and development are believed to play an important role in nutrients physical transport processes and biogeochemical cycles. In the present study, a high-resolution in-situ sampling technology (Porewater equilibrators, Peepers) was employed to obtain vertical porewater PO43- profiles from the vegetated and the non-vegetated sediments, and accurately quantify benthic flux across sediment-water interface by Fick's first law applying porewater profiles of peepers, and coupled with core sediments incubation experiments as comparison. In addition, to distinguish benthic organism contribution to measured apparent benthic flux, we used HgCl2 (0.5% by weight) to suppress bottom fauna activity during the experiment. The results showed that porewater PO43- concentrations were far lower in vegetated than in the non-vegetated sediments, and also significantly lower in overlying water than in porewater. Whereas, porewater PO43- distribution fluctuated sharply at the upper sediments and kept an approximative constant below 8cm depth. Additionally, the average molecular diffusion flux applying Fick's first law fluctuated slightly within the range of 0.004 to 0.018 mg m-2 d-1(i.e., PO43- from porewater diffused into overlying water), which was higher in typha latifolia site, but lower in zizania latifolia site. PO43- average apparent diffusion flux based on core sediments incubation experiments varied between 1.03 and 6.78 mg m-2 d-1, and an opposite pattern was observed with respect to emergent macrophyte effects, as the PO43- flux at phragmites australis site was low (only 19% of control), but reached as high as 126% of the control in typha latifolia site. In unsterilized treatments (i.e., benthic organism participation), PO43- average net fluxes were lower up to an order of magnitude and more variable compared with those in sterilized treatments. Our results highlighted emergent macrophytes (e.g., phragmites australis) in estuary wetlands could efficiently relieved release risk from sediments, and reduce dissolved reactive phosphorus diffusion physical barrier crossed sediment-water interface by adding porosity in surface sediment.

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Han, Sang Hun, and Woo Sun Park. "Reliability Assessment of Corrosion Initiation of Harbor Concrete Structure Using FOSM." Key Engineering Materials 385-387 (July 2008): 621–24. http://dx.doi.org/10.4028/www.scientific.net/kem.385-387.621.

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Due to the uncertainty of variables in durability model, the probabilistic approach is increasing. Monte Carlo Simulation (MCS) is an easily accessible method, but requires a lot of repeated operations. This paper evaluated the effectiveness of First Order Second Moment method (FOSM), which is more convenient and time saving method than MCS, to predict the corrosion initiation in harbor concrete structure. Mean Value First Order Second Moment method (MV FOSM) and Advanced First Order Second Moment method (AFOSM) are applied to the error function solution of Fick's second law modeling chloride diffusion. Reliability index and failure probability based on MV FOSM and AFOSM are compared with the results by MCS. The comparison showed that AFOSM and MCS predict similar reliability indexes and MV FOSM underestimates the probability of corrosion initiation by chloride attack. Also, the sensitivity of variables in durability model to failure probability was evaluated on the basis of AFOSM. The results showed that AFOSM is a simple and efficient method to estimate the possibility of corrosion initiation in harbor concrete structures.

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17

Knee, Michael. "Rapid Measurement of Diffusion of Gas Through the Skin of Apple Fruits." HortScience 26, no. 7 (1991): 885–87. http://dx.doi.org/10.21273/hortsci.26.7.885.

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A method was devised for measuring the resistance to gaseous diffusion of bulky plant organs, such as apple (Malus domestica Borkh.) fruits, in which the skin is the major barrier to diffusion. An individual fruit was incubated in a sealed container in the presence of a measured concentration of ethane for a certain time (usually 20 min). The fruit was then transferred to another, similar container. The ethane concentration that diffused into the new container was measured after an equal time (usually 20 min). An expression relating resistance to the measured ethane concentrations was derived from Fick's First Law of diffusion. An estimate of the internal volume of the fruit, accessible to ethane, was also necessary. The method was tested on several fruits of various apple cultivars. Longer incubation periods are necessary for apples with high diffusive resistance.

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Chen, Ping, Feng Zhang, Lei Zhang, et al. "Uptake of Photosensitizer 2-Devinyl-2-(1-methoxylethyl) Chlorinfin Human Breast Cancer Cells: A Diffusion Kinetics Study." International Journal of Photoenergy 2012 (2012): 1–8. http://dx.doi.org/10.1155/2012/192380.

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The kinetics of photosensitizer 2-devinyl-2-(1-methoxylethyl) chlorinf(CPD4) uptake in MCF-7 human breast cancer cells is described by a diffusion kinetics model and experimentally investigated using laser scanning confocal microscopy (LSCM). CPD4 permeated into MCF-7 cells with increasing incubation time, which was followed by its binding to cell organelles. Subcellular distribution study revealed that CPD4 was primarily localized on the mitochondria and membranes, supporting that the mode of transmembrane transport was diffusion. A kinetics model describing CPD4 passing through the plasma membrane of MCF-7 cells was proposed based on Fick's first law of diffusion. The kinetics of cellular uptake of CPD4 was studied by three-dimensional LSCM. By fitting the experimental data using the above model, important cellular uptake and distribution parameters were obtained, which are of clinical significance in photodynamic therapy.

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Curran, M. "Gas Movements in the Roots of Avicennia marina (Forsk.) Vierh." Functional Plant Biology 12, no. 2 (1985): 97. http://dx.doi.org/10.1071/pp9850097.

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Apparatus for the determination of the rates of oxygen diffusion through excised portions of the root system of Avicennia marina is described. The diffusive resistances of portions of the horizontal root system are measured and the results compared with the values predicted by simple formulations of Fick's first law of diffusion. Predictions of oxygen diffusion rates made without making allowance for respiration or tortuosity are in close agreement with the measured values and thus it is concluded that the horizontal root system is a highly efficient means of oxygen transport. The diffusive resistances of a selection of pneumatophores are also measured and the effect of epiphytic algae is assessed. Structural studies of both horizontal roots and pneumatophores help to explain the ease with which gas moves within the root system, which is compared in conceptual terms with a series of open tubes.

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Pai, T. Y., C. F. Ouyang, Y. C. Liao, and H. G. Leu. "Qxygen transfer in gravity flow sewers." Water Science and Technology 42, no. 3-4 (2000): 417–22. http://dx.doi.org/10.2166/wst.2000.0412.

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Oxygen diffused to water in gravity sewer pipes was studied in a 21 m long, 0.15 m diameter model sewer. At first, the sodium sulfide was added into the clean water to deoxygenate, then the pump was started to recirculate the water and the deoxygenated water was reaerated. The dissolved oxygen microelectrode was installed to measure the dissolved oxygen concentrations varied with flow velocity, time and depth. The dissolved oxygen concentration profiles were constructed and observed. The partial differential equation diffusion model that considered Fick's law including the molecular diffusion term and eddy diffusion term were derived. The analytic solution of the partial differential equation was used to determine the diffusivities by the method of nonlinear regression. The diffusivity values for the oxygen transfer was found to be a function of molecular diffusion, eddy diffusion and flow velocity.

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Kassab, Fuad, Ricardo Paulino Marques, and Francisco Lacaz-Vieira. "Modeling Tight Junction Dynamics and Oscillations." Journal of General Physiology 120, no. 2 (2002): 237–47. http://dx.doi.org/10.1085/jgp.20028604.

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Tight junction (TJ) permeability responds to changes of extracellular Ca2+ concentration. This can be gauged through changes of the transepithelial electrical conductance (G) determined in the absence of apical Na+. The early events of TJ dynamics were evaluated by the fast Ca2+ switch assay (FCSA) (Lacaz-Vieira, 2000), which consists of opening the TJs by removing basal calcium (Ca2+bl) and closing by returning Ca2+bl to normal values. Oscillations of TJ permeability were observed when Ca2+bl is removed in the presence of apical calcium (Ca2+ap) and were interpreted as resulting from oscillations of a feedback control loop which involves: (a) a sensor (the Ca2+ binding sites of zonula adhaerens), (b) a control unit (the cell signaling machinery), and (c) an effector (the TJs). A mathematical model to explain the dynamical behavior of the TJs and oscillations was developed. The extracellular route (ER), which comprises the paracellular space in series with the submucosal interstitial fluid, was modeled as a continuous aqueous medium having the TJ as a controlled barrier located at its apical end. The ER was approximated as a linear array of cells. The most apical cell is separated from the apical solution by the TJ and this cell bears the Ca2+ binding sites of zonula adhaerens that control the TJs. According to the model, the control unit receives information from the Ca2+ binding sites and delivers a signal that regulates the TJ barrier. Ca2+ moves along the ER according to one-dimensional diffusion following Fick's second law. Across the TJ, Ca2+ diffusion follows Fick's first law. Our first approach was to simulate the experimental results in a semiquantitative way. The model tested against experiment results performed in the frog urinary bladder adequately predicts the responses obtained in different experimental conditions, such as: (a) TJ opening and closing in a FCSA, (b) opening by the presence of apical Ca2+ and attainment of a new steady-state, (c) the escape phase which follows the halt of TJ opening induced by apical Ca2+, (d) the oscillations of TJ permeability, and (e) the effect of Ca2+ap concentration on the frequency of oscillations.

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Amendola, Mariângela, and Marlene R. Queiroz. "Mathematical methodologies for calculating the mass diffusion coefficient of bananas during drying." Revista Brasileira de Engenharia Agrícola e Ambiental 11, no. 6 (2007): 623–27. http://dx.doi.org/10.1590/s1415-43662007000600011.

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In this work two mathematical methodologies to solve the diffusion differential equation related to the banana drying process were used in order to obtain the mass diffusion coefficient value. A simplified mathematical model was considered that was based on Fick's Law, with initial and boundary conditions according to the experimental procedure carried out for banana drying. The first methodology was performed by using an approximation of the analytical solution and the second by using the numerical simulation according to the implicit scheme of the finite difference method. The calculation was carried out by looking for the minimal value of the norm calculated between the experimental data and the theoretical results obtained using different values of the diffusion coefficient. The algorithms associated with these methodologies were implemented with Matlab. The values of the diffusion coefficient according to the first and second methodologies were 1.65 x 10-6 [m² h-1] and 1.58 x 10-6 [m² h-1] respectively, with the associated minimal residual values of 0.0269 and 0.0257.

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Kim, Yun Hae, Sung Won Yoon, Jin Woo Lee, Jin Cheol Ha, and Ri Ichi Murakami. "Effect of Moisture Absorption and Fiber Ply Orientation for Artificial Hip Joint on the Mechanical Properties of Carbon/PEEK Composites." Advanced Materials Research 774-776 (September 2013): 1326–35. http://dx.doi.org/10.4028/www.scientific.net/amr.774-776.1326.

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The purpose of this study is to determine the correct estimation of the mechanical property between epoxy resin and PEEK sheet as the composites and its validity has been tested with the alternative materials of the metal-based materials for artificial hip joint. Moreover, this work evaluated the mechanical properties according to the moisture absorption and the fractured surfaces of Carbon/Epoxy and Carbon/PEEKcomposites were also evaluated. First, the specimens for the Carbon/PEEK and Carbon/Epoxy composites manufactured with the ASTM standard. The specimens immersed in distilled water at 37°C during 100 days and the coefficient of moisture was measured in according tothe Fick's law. In addition, this work evaluated the fracture energy according to the fiber ply orientation. As a result, the coefficient ofmoisture-absorption of Carbon/PEEK composites was the lowest because the interface coherence with the fiber and resin are the most strong. Also, the fracture energy of the Carbon/PEEK composites was more excellent than the Carbon/Epoxy composites.

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Nogueira, C. G., E. D. Leonel, and H. B. Coda. "Reliability algorithms applied to reinforced concrete structures durability assessment." Revista IBRACON de Estruturas e Materiais 5, no. 4 (2012): 440–50. http://dx.doi.org/10.1590/s1983-41952012000400003.

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This paper addresses the analysis of probabilistic corrosion time initiation in reinforced concrete structures exposed to ions chloride penetration. Structural durability is an important criterion which must be evaluated in every type of structure, especially when these structures are constructed in aggressive atmospheres. Considering reinforced concrete members, chloride diffusion process is widely used to evaluate the durability. Therefore, at modelling this phenomenon, corrosion of reinforcements can be better estimated and prevented. These processes begin when a threshold level of chlorides concentration is reached at the steel bars of reinforcements. Despite the robustness of several models proposed in the literature, deterministic approaches fail to predict accurately the corrosion time initiation due to the inherently randomness observed in this process. In this regard, the durability can be more realistically represented using probabilistic approaches. A probabilistic analysis of ions chloride penetration is presented in this paper. The ions chloride penetration is simulated using the Fick's second law of diffusion. This law represents the chloride diffusion process, considering time dependent effects. The probability of failure is calculated using Monte Carlo simulation and the First Order Reliability Method (FORM) with a direct coupling approach. Some examples are considered in order to study these phenomena and a simplified method is proposed to determine optimal values for concrete cover.

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JOUBERT, H. D., J. J. TERBLANS, and H. C. SWART. "EFFECT OF SLOW HEATING AND COOLING ON THE INTERDIFFUSION OF THIN FILMS." Surface Review and Letters 14, no. 04 (2007): 703–7. http://dx.doi.org/10.1142/s0218625x07009967.

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Interdiffusion parameters are often extracted from depth profiles of the interface of annealed thin films by measuring the annealing time of the sample as well as the distance over which interdiffusion took place. The annealing time is usually taken as the time from the moment the sample enters the oven to the exact moment the sample is removed from the oven. However, diffusion does not start and stop at these points, as the temperature of the sample does not change instantaneously. Any calculation performed with the instantaneous and therefore erroneous time will result in incorrect diffusion parameters extracted from the depth profiles. The influence of the extended heating period is studied by solving Fick's second law numerically and employing three distinct heating profiles in the calculations, namely instantaneous, actual, and linear. The results indicate a clear difference between the first two calculated depth profiles. Using these calculations and some experimental results, a method that employs linear heating and cooling of a sample is proposed for studying the interdiffusion of fast diffusing elements (with low activation energies).

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Martinez, A. Rodriguez, F. Sobron Grañón, F. Rull Pérez, A. C. Prieto Colorado, and And H. G. M. Edwards. "Mass Diffusion Transport Studies of Lithium Sulfate in Aqueous Solutions Using Raman Spectroscopy." Applied Spectroscopy 49, no. 8 (1995): 1131–36. http://dx.doi.org/10.1366/0003702953964930.

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The diffusivity coefficients of lithium sulfate solutions in water and water and silica gels over the concentration range 0.2 to 2.5 molal have been measured for the first time with micro-Raman spectroscopy for a horizontal-tube capillary, conventional 90° Raman scattering for a narrow-bore vertical-tube system, and FT-Raman spectroscopy for the gels. Data were obtained for axial concentration profiles as function of the distance and for time elapse at fixed positions on the tube axis with the use of integrated intensity measurements of the v1 (SO4) symmetric stretching band at 980 cm−1. The use of computer model calculations to fit the experimental data yielded values of DA = 0.4 × 10−5 cm2 s−1 for the vertical system and 0.3 × 10−5 cm−2 s−1 for the gel system. Discrepancies observed for the horizontal system have been ascribed to the presence of convective flow. A convective flow rate of 5.10−2 cm h−1 was calculated in this case with the use of computer simulation and used in the fitting of the experimental data through a general form of the second Fick's law. Under these conditions, a DA value of 0.2 × 10−5 cm2 s−1 was obtained.

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Nicholson, Ronald V., Robert W. Gillham, John A. Cherry, and Eric J. Reardon. "Reduction of acid generation in mine tailings through the use of moisture-retaining cover layers as oxygen barriers." Canadian Geotechnical Journal 26, no. 1 (1989): 1–8. http://dx.doi.org/10.1139/t89-001.

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Acid production in sulphidic tailings can cause severe degradation of water quality in both subsurface and surface systems. The availability of gaseous oxygen and the rate of diffusion of oxygen through the open pore spaces in the upper zone of the tailings are the critical factors controlling the rate of acid generation. Acid generation can be reduced by applying a fine-grained, nonreactive cover layer to the tailings surface. The key process involves moisture retention by capillary forces so that near-saturated conditions can be maintained even when the cover layer occurs at several metres above the water table. Textured layering of fine over coarse materials improves moisture retention in the fine layer when infiltration exceeds evapotranspiration. The application of such a cover layer can theoretically reduce oxygen diffusion coefficients and rates of acid generation by up to four orders of magnitude. This can represent a substantial difference in the potential treatment costs of tailings seepage. Simplified calculations based on Fick's first law can be applied to preliminary laboratory measurements of diffusion characteristics of potential cover materials to evaluate their effectiveness in decreasing acidification. These concepts and methods provide an initial evaluation before field-scale testing of cover performance. Key words: pyrite oxidation, tailings, remediation, covers, acid generation, oxygen diffusion.

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Purnaditya, Ngakan Putu, Herr Soeryantono, and Dwinanti Rika Marthanty. "Proposing mathematical model for seawater intrusion phenomena in the coastal aquifer." MATEC Web of Conferences 197 (2018): 10003. http://dx.doi.org/10.1051/matecconf/201819710003.

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Seawater intrusion is one of groundwater quality problem which in this problem, the mixing between freshwater and saltwater in the coastal aquifer occurs. Mathematical modelling can be formulated to describe the mechanism of this phenomena. The main objective of this research is to develop the mathematical model of groundwater flow and solute transport that applicable to seawater intrusion mechanism. This mechanism is arranged as a differential equation and distinguished into 3 equations. The first equation is groundwater flow equation in dependent-density. It means that the density of groundwater (ρ) changes in spatial and temporal domain due freshwater and seawater are mixed in the coastal aquifer. The second equation is solute transport. Like as groundwater flow equation, in solute transport equation there is a change of solute concentration (С) in the spatial and temporal domain. The last equation is the relationship between groundwater density (ρ) and solute concentration (С). Special case for the third equation, in which this equation is adopted from USGS Seawat model. The first equation and second equation are governed by Eulerian mass conservation law. The main theoretical consideration of governing groundwater flow equation is such as fluid and porous matrix compressibility theory, Darcy's law for groundwater in motion theory and some properties of soil. In other hands, solute transport is involving advection transport and hydrodynamic dispersion transport. Hydrodynamic dispersion is arranged by diffusion Fick's law and dispersion in porous media theory and it depends on transversal and longitudinal dispersivity. Using Jacob Bear's theory which states that fluid density as temperature, concentration and pressure function, authors obtain three primary variables in this model. Those variables follow fluid density (ρ), total head (h) and concentration (С). In this model, isotropic and isobar condition is considered, hence fluid density (ρ) is a function of concentration (С) only. Finally, from this research, authors wish this mathematical model is applicable to modelling, describing and predicting seawater intrusion phenomena theoretically.

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Lv, Junchen, Yuan Chi, Changzhong Zhao, Yi Zhang, and Hailin Mu. "Experimental study of the supercritical CO 2 diffusion coefficient in porous media under reservoir conditions." Royal Society Open Science 6, no. 6 (2019): 181902. http://dx.doi.org/10.1098/rsos.181902.

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Reliable measurement of the CO 2 diffusion coefficient in consolidated oil-saturated porous media is critical for the design and performance of CO 2 -enhanced oil recovery (EOR) and carbon capture and storage (CCS) projects. A thorough experimental investigation of the supercritical CO 2 diffusion in n -decane-saturated Berea cores with permeabilities of 50 and 100 mD was conducted in this study at elevated pressure (10–25 MPa) and temperature (333.15–373.15 K), which simulated actual reservoir conditions. The supercritical CO 2 diffusion coefficients in the Berea cores were calculated by a model appropriate for diffusion in porous media based on Fick's Law. The results show that the supercritical CO 2 diffusion coefficient increases as the pressure, temperature and permeability increase. The supercritical CO 2 diffusion coefficient first increases slowly at 10 MPa and then grows significantly with increasing pressure. The impact of the pressure decreases at elevated temperature. The effect of permeability remains steady despite the temperature change during the experiments. The effect of gas state and porous media on the supercritical CO 2 diffusion coefficient was further discussed by comparing the results of this study with previous study. Based on the experimental results, an empirical correlation for supercritical CO 2 diffusion coefficient in n -decane-saturated porous media was developed. The experimental results contribute to the study of supercritical CO 2 diffusion in compact porous media.

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Goodman, B. E., J. L. Anderson, and J. W. Clemens. "Evidence for regulation of sodium transport from airspace to vascular space by cAMP." American Journal of Physiology-Lung Cellular and Molecular Physiology 257, no. 2 (1989): L86—L93. http://dx.doi.org/10.1152/ajplung.1989.257.2.l86.

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Evidence has been accumulating that regulation of the rate of solute and fluid removal from the alveolar spaces may play an important role in the prevention and/or resolution of alveolar pulmonary edema. In this study, the isolated perfused rat lung was used to investigate the effects of an adenosine 3',5'-cyclic monophosphate (cAMP) analogue or a phosphodiesterase inhibitor on active sodium transport from airspace to vascular space. Three tracers were instilled into the airways of isolated Krebs-Ringer bicarbonate solution (KRB)-perfused rat lungs. The appearance of tracers in the single-pass perfusate was measured, and the apparent permeability-surface area products (PS) were calculated for each tracer at each sample time based on Fick's first law of diffusion. After steady-state PS values had been reached, a cAMP analogue or phosphodiesterase inhibitor was added to the perfusate. Both agents caused significant increases in the PS for 22Na. In another group of experiments, a cAMP analogue was added to the perfusate, followed by the subsequent addition of a sodium transport inhibitor and the resultant large decrease in the PS for 22Na. These data are consistent with the regulation of active sodium transport across the intact mammalian alveolar epithelium by a cAMP-mediated process leading to removal of sodium from the alveolar spaces, with anions and water following passively.

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Ruggeri, Tommaso. "Multi-temperature mixture of fluids." Theoretical and Applied Mechanics 36, no. 3 (2009): 207–38. http://dx.doi.org/10.2298/tam0903207r.

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We present a survey on some recent results concerning the different models of a mixture of compressible fluids. In particular we discuss the most realistic case of a mixture when each constituent has its own temperature (MT) and we first compare the solutions of this model with the one with a unique common temperature (ST ). In the case of Eulerian fluids it will be shown that the corresponding (ST ) differential system is a principal subsystem of the (MT) one. Global behavior of smooth solutions for large time for both systems will also be discussed through the application of the Shizuta-Kawashima condition. Then we introduce the concept of the average temperature of mixture based upon the consideration that the internal energy of the mixture is the same as in the case of a single-temperature mixture. As a consequence, it is shown that the entropy of the mixture reaches a local maximum in equilibrium. Through the procedure of Maxwellian iteration a new constitutive equation for non-equilibrium temperatures of constituents is obtained in a classical limit, together with the Fick's law for the diffusion flux. Finally, to justify the Maxwellian iteration, we present for dissipative fluids a possible approach of a classical theory of mixture with multi-temperature and we prove that the differences of temperatures between the constituents imply the existence of a new dynamical pressure even if the fluids have a zero bulk viscosity.

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Randsoe, Thomas, and Ole Hyldegaard. "Effect of oxygen breathing on micro oxygen bubbles in nitrogen-depleted rat adipose tissue at sea level and 25 kPa altitude exposures." Journal of Applied Physiology 113, no. 3 (2012): 426–33. http://dx.doi.org/10.1152/japplphysiol.00193.2012.

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The standard treatment of altitude decompression sickness (aDCS) caused by nitrogen bubble formation is oxygen breathing and recompression. However, micro air bubbles (containing 79% nitrogen), injected into adipose tissue, grow and stabilize at 25 kPa regardless of continued oxygen breathing and the tissue nitrogen pressure. To quantify the contribution of oxygen to bubble growth at altitude, micro oxygen bubbles (containing 0% nitrogen) were injected into the adipose tissue of rats depleted from nitrogen by means of preoxygenation (fraction of inspired oxygen = 1.0; 100%) and the bubbles studied at 101.3 kPa (sea level) or at 25 kPa altitude exposures during continued oxygen breathing. In keeping with previous observations and bubble kinetic models, we hypothesize that oxygen breathing may contribute to oxygen bubble growth at altitude. Anesthetized rats were exposed to 3 h of oxygen prebreathing at 101.3 kPa (sea level). Micro oxygen bubbles of 500-800 nl were then injected into the exposed abdominal adipose tissue. The oxygen bubbles were studied for up to 3.5 h during continued oxygen breathing at either 101.3 or 25 kPa ambient pressures. At 101.3 kPa, all bubbles shrank consistently until they disappeared from view at a net disappearance rate (0.02 mm2 × min−1) significantly faster than for similar bubbles at 25 kPa altitude (0.01 mm2 × min−1). At 25 kPa, most bubbles initially grew for 2–40 min, after which they shrank and disappeared. Four bubbles did not disappear while at 25 kPa. The results support bubble kinetic models based on Fick's first law of diffusion, Boyles law, and the oxygen window effect, predicting that oxygen contributes more to bubble volume and growth during hypobaric conditions. As the effect of oxygen increases, the lower the ambient pressure. The results indicate that recompression is instrumental in the treatment of aDCS.

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33

Barbanti, A., MC Bergamini, F. Frascari, S. Miserocchi, M. Ratta, and G. Rosso. "Diagenetic processes and nutrient fluxes at the sediment-water interface, northern Adriatic Sea, Italy." Marine and Freshwater Research 46, no. 1 (1995): 55. http://dx.doi.org/10.1071/mf9950055.

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Early diagenetic processes that control pore-water chemistry and nutrient fluxes at the sediment-water interface were studied in late summer 1989 and spring 1990 at four sites influenced by fine sediments of the Po River. Parameters on the solid fraction (grain size and C, N and P) and pore- water profiles of SO42-, NO3-, NH3, alkalinity, PO43-, Fe, Mn, Ca and Mg were determined. Data interpretation was supported by application of kinetic and stoichiometric modelling. Nutrient fluxes were calculated by Fick's first law. In the prodelta station the pore-water profiles showed large depletion in SO42- ions, jointly with the increase with depth of alkalinity, NH3 and PO43- concentrations, thus indicating anaerobic decomposition of organic matter, mainly due to bacterial sulfate reduction. At the other three sites the results were completely different. Nutrient concentrations in pore water were one order of magnitude lower. The peaks of alkalinity, NH3 and PO43- values near the interface and the constant presence of SO42- ions indicate aerobic decomposition of organic matter in the uppermost sediment. Nutrient fluxes showed much higher values in the prodelta station, whereas fluxes in the remaining stations decreased southward. In addition, seasonal variations produced higher summertime fluxes. The clear-cut difference in diagenetic processes as a function of the distance from the main Po River mouth can be explained by the rapid burial of sediments rich in organic matter and inorganic compounds in the prodelta station. At the other stations, the lower sedimentation rate and more efficient bioturbation and resuspension processes cause a prolonged exposure of sediments to aerobic metabolization reactions before burial.

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Aoki, Koichi. "Simulation for memory effect of Fick’s first law." Journal of Chemical Sciences 121, no. 5 (2009): 601–5. http://dx.doi.org/10.1007/s12039-009-0073-0.

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Wang, W. W., X. Jiang, B. H. Zheng, et al. "Composition, mineralization potential and release risk of nitrogen in the sediments of Keluke Lake, a Tibetan Plateau freshwater lake in China." Royal Society Open Science 5, no. 9 (2018): 180612. http://dx.doi.org/10.1098/rsos.180612.

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The lakes distributed in the Tibetan Plateau constitute a lake group with the highest altitude, largest lakes and largest area in the world and are important in global climate and environmental effects. Freshwater lakes in the Tibetan Plateau possess high ecological values and high vulnerability. The migration and transformation of nitrogen in sediments are critical to lake ecosystems, but information on sedimentary nitrogen in the freshwater lakes in the Tibetan Plateau is limited. A case study was conducted in Keluke Lake, China, to reveal the effects of sedimentary nitrogen on water quality in plateau freshwater lakes. Nitrogen speciation, mineralization potential and release flux were analysed through a sequential extraction method, waterlogged incubation experiment and Fick's first diffusion law, respectively. The content of total nitrogen (TN) was 1295.75–6151.69 mg kg −1 , and 94.2% of TN was organic nitrogen (ON). The contents of three nitrogen fractions were in the order of hydrolysable nitrogen > residual nitrogen > exchangeable nitrogen. Ammonia nitrogen ( N H 4 + − N ) was the main mineralization product, and hydrolysable ON was the most significant contributor. The sediments showed a great mineralization potential, with a potentially mineralizable nitrogen value of 408.76 mg N kg −1 of sediment, that was mainly affected by hydrolysable ammonium nitrogen. The N H 4 + − N diffusion flux ranged from 24.14 to 148.75 mg m −2 d −1 , and the sediments served as an internal nitrogen source. Nitrogen release from sediments was considerably influenced by exchangeable ammonia nitrogen. The sediments in Keluke Lake pose a potential nitrogen release risk and threaten the water quality of the lake. The total content, speciation, mineralization of ON and the release flux at sediment–water interface should be considered comprehensively to evaluate the effects of nitrogen in sediments to water quality.

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Wiaux, F., M. Vanclooster, and K. Van Oost. "Vertical partitioning and controlling factors of gradient-based soil carbon dioxide fluxes in two contrasted soil profiles along a loamy hillslope." Biogeosciences 12, no. 15 (2015): 4637–49. http://dx.doi.org/10.5194/bg-12-4637-2015.

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Abstract. In this study we aim to elucidate the role of physical conditions and gas transfer mechanism along soil profiles in the decomposition and storage of soil organic carbon (OC) in subsoil layers. We use a qualitative approach showing the temporal evolution and the vertical profile description of CO2 fluxes and abiotic variables. We assessed soil CO2 fluxes throughout two contrasted soil profiles (i.e. summit and footslope positions) along a hillslope in the central loess belt of Belgium. We measured the time series of soil temperature, soil moisture and CO2 concentration at different depths in the soil profiles for two periods of 6 months. We then calculated the CO2 flux at different depths using Fick's diffusion law and horizon specific diffusivity coefficients. The calculated fluxes allowed assessing the contribution of different soil layers to surface CO2 fluxes. We constrained the soil gas diffusivity coefficients using direct observations of soil surface CO2 fluxes from chamber-based measurements and obtained a good prediction power of soil surface CO2 fluxes with an R2 of 92 %. We observed that the temporal evolution of soil CO2 emissions at the summit position is mainly controlled by temperature. In contrast, at the footslope, we found that long periods of CO2 accumulation in the subsoil alternates with short peaks of important CO2 release. This was related to the high water filled pore space that limits the transfer of CO2 along the soil profile at this slope position. Furthermore, the results show that approximately 90 to 95 % of the surface CO2 fluxes originate from the first 10 cm of the soil profile at the footslope. This indicates that soil OC in this depositional context can be stabilized at depth, i.e. below 10 cm. This study highlights the need to consider soil physical properties and their dynamics when assessing and modeling soil CO2 emissions. Finally, changes in the physical environment of depositional soils (e.g. longer dry periods) may affect the long-term stability of the large stock of easily decomposable OC that is currently stored in these environments.

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Fatykhov, Y. A., M. V. Shumanova, and V. A. Shumanov. "The mechanism of mass transfer in the process of fish salting." Proceedings of the Voronezh State University of Engineering Technologies 81, no. 1 (2019): 42–46. http://dx.doi.org/10.20914/2310-1202-2019-1-42-46.

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The process of fish salting is based on patterns associated with the diffusion of salt in the fish tissue and the diffusion-osmotic transfer of water from the tissues of fish to the brine or in the opposite direction. Atlantic herring is an object of research. The character of the spatial-temporal distribution of salt within the product (herring) was established. As a method of experimental research was used a modern method of non-destructive testing, called photon correlation spectroscopy. The theoretical model of the process was obtained on the basis of the second Fick's law as a solution of a differential equation by the method of separation of variables. The qualitative nature of the mathematical model is interpreted as an exponential approach to the equilibrium value of salt concentration in the process of fish salting. Experimental dependences of the diffusion coefficient on the depth of salt penetration into the muscle tissue of fish were obtained. The mass transfer rate of salt in the first stage of the salting process is about 3·10-4 mm/s. The experimental value of the mass transfer rate is compared with the theoretical value of the proposed model. A satisfactory coincidence is obtained. The qualitative character of the advancement of the salt critical concentration (8.0%) in the form of a front has been established. This is consistent with the theory of P.B. Crean. The causes associated with the apparent increase in the diffusion coefficient at the second stage of the fish salting process are analyzed, which have been noted by many researchers. The expediency of using the effective diffusion coefficient in studies was expressed, which to a greater extent corresponds to the actual course of the process of mass transfer of salt and moisture. It is noted that the most recognized modern theoretical and empirical models of the process of salting fish are models that reflect an exponential approach to the equilibrium of substances involved in the process The acceptability of using the empirical model of salting fish Zugarramurdi and Lupine was confirmed as qualitatively corresponding to the theoretical model proposed in the article..

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Moustafine, R. I., V. V. Budnikov, S. G. Abdullina, Sh F. Nasibullin, and R. A. Saleev. "Polycomplex Carrier for Buccal Mucoadhesion Delivery of Metronidazole." Drug development & registration 9, no. 2 (2020): 83–90. http://dx.doi.org/10.33380/2305-2066-2020-9-2-83-90.

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Introduction. One of the well-known requirements for buccal drug delivery systems is the demonstration of mucoadhesive properties of the carrier, ensuring retention on the mucosa for a long time with the gradual release of the included drug. It should be noted that one of the advantages of buccal systems compared with oral ones is the absence of the «first pass effect» through the liver.Aim. To carry out a physicochemical and pharmaceutical research of the interpolyelectrolyte complex (IPEC), obtained on the basis of pharmaceutically acceptable polymers – Eudragit® EPO and Noveon® AA-1, in comparison with the physical mixture and individual polymers, as a mucoadhesive delivery system of metronidazole for the treatment of periodontal diseases.Materials and methods. Obtained on the basis of a pair of pharmaceutical polymers (Eudragit® EPO and Noveon® AA-1), two IPEC samples were characterized by elemental analysis, FTIR spectroscopy, and modulated temperature differential scanning calorimetry (mDSC) in comparison with individual polymers and their physical mixtures. The study of swelling ability, bioadhesion and release was carried out in a medium simulating artificial salivary fluid (pH 7.0) at a temperature of 37 ± 0.1 °C. Mucoadhesion of polymer samples and IPEC was studied using a TA.XTplus texture analyzer (Stable Micro Systems, UK). The release of metronidazole (MD) from matrices based on the developed IPEC was studied on a CE 7Smart USP 4 apparatus (Sotax, Switzerland) using the Flow Trough Cell method at a speed a flow of 20 ml/min in an open cycle within 5 hours. The amount of released MD was estimated by UV spectrophotometry on a Lambda 25 instrument (PerkinElmer, USA) at a wavelength of 319 nm.Results and discussion. As a result of studies on the physicochemical and pharmaceutical properties, there was selected the optimal composition of a polycomplex carrier (IPEC 2) based on Eudragit® EPO and Noveon® AA-1, which is characterized by the required bioadhesive properties and the ability of providing controlled release of drug from the tablet matrix (with weight ratio MD/IPEC-2 1:0.5) in conditions mimicking oral cavity environment, which provides the necessary mode of buccal delivery of metronidazole in accordance with Fick's law of diffusion.Conclusion. IPEC 2 is a perspective for use as carrier for buccal controlled delivery of metronidazole.

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ERDELYI, Z. "On the ?rationalisation? of Fick?s first law." Scripta Materialia 49, no. 6 (2003): 613–17. http://dx.doi.org/10.1016/s1359-6462(03)00353-1.

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Pg Sulaiman, D. N. H., H. Suhaimi, and N. Shamsuddin. "Estimating glucose diffusion coefficient of membranes for tissue engineering applications using Fick’s First Law." IOP Conference Series: Materials Science and Engineering 991 (December 22, 2020): 012103. http://dx.doi.org/10.1088/1757-899x/991/1/012103.

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41

Bauer, Wolfgang R., and Walter Nadler. "Stationary flow, first passage times, and macroscopic Fick’s first diffusion law: Application to flow enhancement by particle trapping." Journal of Chemical Physics 122, no. 24 (2005): 244904. http://dx.doi.org/10.1063/1.1940056.

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Hou, Zhi Hong, and Shi Yong Luo. "Simulation and Computation of Diffusion in Solids." Applied Mechanics and Materials 182-183 (June 2012): 933–36. http://dx.doi.org/10.4028/www.scientific.net/amm.182-183.933.

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A computation software on diffusion computation in solids was developed. The software includes two sub-modules of “database management system (DBMS)” and "Evaluation & prediction". The “DBMS” deals with the diffusion coefficients gathered from reported documents and the data evaluated according to some rules, besides, it can provide users with retrieval of diffusion coefficients. Based on the solutions to the Fick’s first law and the Fick’s second law in the four typical critical conditions, the "Evaluation & prediction" sub-module gives the predication of concentration distribution after diffusion process in solids or computation for diffusion coefficient.

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Tapia-Hernández, Marcos, Belén Cerda-Mendoza, and Esteban Parra-Valencia. "Medical records: the first challenge in health care." Medwave 16, no. 10 (2016): e6601-e6601. http://dx.doi.org/10.5867/medwave.2016.10.6601.

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Luo, Shi Yong, Wen Cai Xu, Li Xia Huo, Xin Lin Zhang, and Jia Yun Zhang. "A Computer Software on Diffusion in Solid." Advanced Materials Research 267 (June 2011): 410–13. http://dx.doi.org/10.4028/www.scientific.net/amr.267.410.

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A computer software on solid/solid reaction kinetics, KinPreSSR, is one of subsystems in the software, Intellectualized Database Management System on Kinetics of Metallurgy (IDMSKM). KinPreSSR is a Windows application developed using Visual C++ and FoxPro, and includes two main modules, “DIFFUSION” and “REACTION”. The ‘DIFFUSION’ module includes two sub-modules of “database management system (DBMS)” and "Evaluation & prediction". The “DBMS” deals with the diffusion coefficients gathered from reported documents and the data evaluated according to some rules, besides, it can provide users with retrieval of diffusion coefficients. Based on the solutions to the Fick’s first law and the Fick’s second law in the four typical critical conditions, the "Evaluation & prediction" sub-module gives the predication of concentration distribution after diffusion process in solids or computation for diffusion coefficient.

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45

Liu, Ruixue, Huiguang Yin, Lianying Zhang, Bing Li, and Xianbiao Mao. "Model for the Patterns of Salt-Spray-Induced Chloride Corrosion in Concretes under Coupling Action of Cyclic Loading and Salt Spray Corrosion." Processes 7, no. 2 (2019): 84. http://dx.doi.org/10.3390/pr7020084.

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In this study, the patterns of chloride ion erosion of unsaturated concrete subjected to the coupling action of cyclic loading and salt spray corrosion were experimentally studied, and Fick’s Second Law was used to fit the variation patterns of chloride concentration to obtain the chloride diffusion coefficient. Accordingly, we have established a mathematical model that describes chloride transport in unsaturated concrete and accounts for the effects of gas flow, water migration, convection diffusion, and capillary action. This model is composed of three equations—the gas flow equation, the solution flow equation, and the solute convection–diffusion equation. The COMSOL numerical analysis software was subsequently used to obtain solutions for this model, based on parameters such as porosity and the chloride diffusion coefficient. Subsequently, the saturation, relative permeability, and the chloride ion concentration during the first corrosion cycle were analyzed. The numerical results were consistent with the experimental values and were therefore superior to the values obtained using Fick’s Second Law.

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Chandra-ambhorn, Somrerk, Thammaporn Thublaor, and Celine Pascal. "CHAPTER 1 Thermodynamics and Kinetics of the High Temperature Oxidation of Stainless Steels." Solid State Phenomena 300 (February 2020): 1–24. http://dx.doi.org/10.4028/www.scientific.net/ssp.300.1.

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This chapter introduces stainless steels and their classification for the high temperature applications. The enabling theories for the high temperature corrosion i.e. thermodynamics and kinetics are further addressed. The basic concept of thermodynamics is given and the stability of the formation of thermal oxide on stainless steel is exemplified. Types of defect in the oxide and Fick’s first law for the diffusion of defect though the oxide are introduced. Oxidation kinetics is explained with the emphasis on the derivation of the parabolic rate law.

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Fiedler, Thomas, Andreas Öchsner, Nilindu Muthubandara, Irina V. Belova, and Graeme E. Murch. "Calculation of the Effective Thermal Conductivity in Composites Using Finite Element and Monte Carlo Methods." Materials Science Forum 553 (August 2007): 51–56. http://dx.doi.org/10.4028/www.scientific.net/msf.553.51.

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In this paper, the Finite Element and lattice Monte Carlo methods are used to calculate the effective thermal conductivity of two models of a composite: circular and square inclusions arranged in a square planar arrangement. A new lattice Monte Carlo method based around Fick’s First Law is also presented. Excellent agreement is found between these quite different methods. It is also shown that the results are in excellent agreement with the century-old Maxwell Equation.

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Ujihara, Toru, Kozo Fujiwara, Gen Sazaki, Noritaka Usami, and Kazuo Nakajima. "Evaluation of the diffusion coefficients in liquid GaGe binary alloys using a novel method based on Fick’s first law." Journal of Non-Crystalline Solids 312-314 (October 2002): 196–202. http://dx.doi.org/10.1016/s0022-3093(02)01696-4.

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Luo, Shi Yong, Wen Cai Xu, Zun Zhong Liu, and Jia Yun Zhang. "A Computation Software on Diffusion and Solid State Reactions Kinetics." Advanced Materials Research 148-149 (October 2010): 316–21. http://dx.doi.org/10.4028/www.scientific.net/amr.148-149.316.

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A computer software on solid/solid reaction kinetics, KinPreSSR, is one of subsystems in the software, Intellectualized Database Management System on Kinetics of Metallurgy (IDMSKM). KinPreSSR is a Windows application developed using Visual C++ and FoxPro, and includes two main modules, “DIFFUSION” and “REACTION”. KinPreSSR deals with the kinetics on the diffusion in solid state as well as solid/solid reactions. In the ‘REACTION’ module, the system has organized the commonly recognized kinetic models, parameters and employed both numerical and graphical methods for data analyses. The proper combination between the kinetic contents and the analytical methods enables users to use KinPreSSR for the evaluation and prediction of solid/solid reactions interested. The ‘DIFFUSION’ module includes two sub-modules of “database management system (DBMS)” and "Evaluation & prediction". The “DBMS” deals with the diffusion coefficients gathered from reported documents and the data evaluated according to some rules, besides, it can provide users with retrieval of diffusion coefficients. Based on the solutions to the Fick’s first law and the Fick’s second law in the four typical critical conditions, the "Evaluation & prediction" sub-module gives the predication of concentration distribution after diffusion process in solids or computation for diffusion coefficient.

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Ye, Jingyi, Huiyi Wu, Chuanli Huang, et al. "Comparisons of in vitro Fick’s first law, lipolysis, and in vivo rat models for oral absorption on BCS II drugs in SNEDDS." International Journal of Nanomedicine Volume 14 (July 2019): 5623–36. http://dx.doi.org/10.2147/ijn.s203911.

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Journal articles on the topic 'Fick's first law'

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