Couple Stress Sodium Alginate-Based Casson Nanofluid Analysis through Fick’s and Fourier’s Laws with Inclined Microchannel by Dolat Khan, Musawa Yahya Almusawa, Waleed Hamali, M. Ali Akbar

“…Applying Fourier’s and Fick’s laws to the time-fractional model makes the classical model dimensionally stable by generalization. …”
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Evaluation of effective diffusivity correlations for soybeans in thin layer drying by Felipe d'Avila, Rafael Maurício Urnau, Amanda Mansano Zanella Blauth, Marcos Flávio Pinto Moreira

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Modeling the Lithium Ion/Electrode Battery Interface Using Fick’s Second Law of Diffusion, the Laplace Transform, Charge Transfer Functions, and a [4, 4] Padé Approximant by John H. Summerfield, Charles N. Curtis

“…The model’s starting point is Fick’s second law of diffusion. The Laplace transform is used to move from time as the independent variable to frequency as the independent variable. …”
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Determination of thermophysical properties of cupuassu (Theobroma grandiflorum) dry almonds by Elisa Santana Cunha, Geovana Pires Araújo Lima, Jorge Henrique Oliveira Sales, Elizama Aguiar de Oliveira

Subjects: “…Fick’s model…”
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Laws of Gas Diffusion in Coal Particles: A Study Based on Experiment and Numerical Simulation by Yongjiang Hao, Xiaofeng Ji, Jiewen Pang

“…Comparative analysis between the numerically simulated outcomes and the assay results reveals that the simulation outcomes as per Darcy’s law match the experimental data better, while the simulated results by Fick’s law deviate greatly, which indicates that the methane flowing through coal particles is more in accordance with Darcy’s law.…”
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Numerical simulation of MHD Sakiadis flows of convectively heated thixotropic nanofluids in a porous medium using revised transport laws and Wakif-Buongiorno's model by A. Wakif

“…Due to the particular inability of Fourier's and Fick's laws in the realistic quantification of transfer processes that can occur certainly within a flowing biphasic mixture, on the one hand, and the explanation of the memory relaxation features of such a non-homogenous medium, on the other hand, the present scrutinization intends to propose a representative biphasic flow model to reveal the principal demeanors of convectively heated thixotropic nanofluids during their steady two-dimensional flows in the laminar regime over a stretching planar geometry in a Darcy-Forchheimer porous medium under the magnetic impact of an external electromagnetic device. …”
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Inertial Memory Effects in Molecular Transport Across Nanoporous Membranes by Slobodanka Galovic, Milena Čukić, Dalibor Chevizovich

“…In this work, we have derived two causal models as extensions of Fick’s second law, where causality is linked to the effects of inertial memory in the nanoporous membrane. …”
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Modelling of the Water Absorption Kinetics and Determination of the Water Diffusion Coefficient in the Pith of Raffia vinifera of Bandjoun, Cameroon by E. Tiaya Mbou, E. Njeugna, A. Kemajou, N. R. Tagne Sikame, D. Ndapeu

“…The result shows that the percentage of water absorption of the pith of Raffia vinifera increases from the periphery to the center in the radial position and from the base to the leaves in the longitudinal position. Fick’s second law was adopted for the study of the water diffusion. …”
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Anomalous Grain Boundary Diffusion: Fractional Calculus Approach by Renat T. Sibatov

“…Interpreting experimental data with the use of the classical Fisher model sometimes encounters contradictions that can be related to violation of Fick’s law. Here, we generalize the Fisher model to the case of non-Fickian (anomalous) diffusion ubiquitous in disordered materials. …”
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Modeling of Chloride Distribution in Cement-Based Materials with Neumann Boundary Condition by Qi Meng, Yan Zhang, Chun-jin Lin, Lin-hua Jiang, Da Chen

“…The nonstable transport of chloride in cement-based materials, including diffusion, convection, and chloride binding, is described as a general form of Fick’s law. Inspired by the heat transport of concrete, the second boundary condition called the Neumann boundary condition is considered in the chloride transport of concrete. …”
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Semianalytical Solutions to the Axisymmetric Free Strain Consolidation Problem of Unsaturated Soils under the Homogeneous and Mixed Boundary Conditions by Yuanchun Huang, Lei Wang, Sidong Shen

“…In this paper, the governing equations of water and air in the polar coordinate were given according to two stress state variables theory of unsaturated soils, Darcy’s law, and Fick’s law under the axisymmetric condition. …”
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Numerical analysis of sodium diffusion in aluminum electrolysis cathode carbon blocks based on a microstructure multi-factor corrected model. by Chenglong Gong, Tianqi Xu, Huarong Qi, Yan Li

“…A random aggregate model was implemented in Python and imported into finite element software to simulate sodium diffusion using Fick's second law. Results indicate that increased porosity, higher temperatures, reduced binding effects, increased current density, and higher molecular ratios enhance sodium infiltration, reducing diffusion resistance and increasing the diffusion coefficient. …”
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Production Analysis for Fractured Vertical Well in Coal Seam Reservoirs with Stimulated Reservoir Volume by Chen Li

“…Based on the dual-porosity flowing mechanism, combined with the Langmuir adsorb equation, Fick diffusion law, and Darcy law, a mathematical model considering diffusion in matrix and transport in natural fracture system is established, using spherical matrix to describe the transient steady-state sorption, and using cubic matrix to describe the pseudosteady-state sorption. …”
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Chloride Penetration in Coastal Concrete Structures: Field Investigation and Model Development by Weidong Zhuo, Quanzhe Yan, Zhengxian Yang, Shaohong Lin, Kaiqi Lin, Fuqiang He

“…Field measurements of 42 in-service reinforced concrete bridges in coastal environments of Southeast China, covering a wide range of service year, span length, and concrete mixture, were carried out to investigate the chloride penetration. 323 sets of chloride measurement data were collected in total and then analysed to optimize the parameters involved in the common chloride diffusion model derived based on Fick’s second law. A modified chloride diffusion model was then proposed, taking into consideration a range of influencing factors including ambient temperature, relative humidity, stress state, carbon dioxide, chloride binding, and ageing. …”
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A Gas Seepage Modeling Study for Mitigating Gas Accumulation Risk in Upper Protective Coal Seam Mining Process by Cun Zhang, Lei Zhang, Mingxue Li, Chen Wang

“…These equations have been developed by using Fick’s second law of diffusion and Darcy’s flow law. …”
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Evaluation Technique of Chloride Penetration Using Apparent Diffusion Coefficient and Neural Network Algorithm by Yun-Yong Kim, Byung-Jae Lee, Seung-Jun Kwon

“…Considering time-dependent diffusion coefficient based on Fick’s 2nd Law and NNA (neural network algorithm), analysis technique for chloride penetration is proposed. …”
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Influence of Pore Structure on Chloride Penetration in Cement Pastes Subject to Wetting-Drying Cycles by Honglei Chang, Zhiwu Zuo, Mingyue Qu, Fei Wang, Zhi Ge, Jian Liu

“…In such cases, the chloride diffusion coefficient (D) obtained through directly fitting the standard error function of Fick’s second law is no longer accurate. The more reliable D obtained by the method proposed by Andrade is employed in this research to investigate the influence of pore structure on chloride penetration rate of pastes. …”
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Yttria stabilized zirconia membrane stability in molten fluoride fluxes for low-carbon magnesium production by the SOM process by Milshtein J., Gratz E., Pati S., Powell A.C., Pal U.

“…The diffusion process was modeled using a numerical approach with an analytic solution to Fick’s second law. These modeling and experimental methods allowed for the determination of the optimum YF3 concentration in the flux to minimize yttria diffusion and improve membrane stability. …”
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Modelling the Mass Transfer Kinetics of Battered and Breaded Fish Nuggets during Deep-Fat Frying at Different Frying Temperatures by Wei Zhang, Jiwang Chen, Yi Yue, Zhenzhou Zhu, E Liao, Wenshui Xia

“…The results showed that Fick’s second law of diffusion and the first-order kinetic model could well describe the kinetics of moisture loss and fat absorption of the crust, respectively. …”
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Design and Fabrication of a High Performance Microfluidic Chip for Blood Plasma Separation: Modelling and Prediction of System Behaviour via CFD Method by Hossein Amini, Amin Sokhansanj, Mohammad Akrami, Ismaeil Haririan

“…This led to the higher movement of whole blood, including plasma. Fick’s law of diffusion was validated for this diffusion transfer, the Navier–Stokes equation was used for the momentum balance, and the Laplace equation was utilized for the dynamics of the mesh. …”
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