Search results for: Fick’s law

Authors: H. Namazi, H. T. N. Kuan

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Fick's first law relates the diffusive flux to the concentration field, by postulating that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient (spatial derivative). It is clear that the diffusion of flux cannot be instantaneous and should be some time delay in this propagation. But Fick’s first law doesn’t consider this delay which results in some errors especially when there is a considerable time delay in the process. In this paper, we introduce a time delay to Fick’s first law. By this modification, we consider that the diffusion of flux cannot be instantaneous. In order to verify this claim an application sample in fluid diffusion is discussed and the results of modified Fick’s first law, Fick’s first law and the experimental results are compared. The results of this comparison stand for the accuracy of the modified model. The modified model can be used in any application where the time delay has considerable value and neglecting its effect reflects in undesirable results.

Keywords: Fick's first law, flux, diffusion, time delay, modified Fick’s first law

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Authors: Abdul Hadi Bin Abdol Rahim, Alhassan Salami Tijani

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Hydrogen produced by means of polymer electrolyte membrane electrolyzer (PEME) is one of the most promising methods due to clean and renewable energy source. In the process, some energy loss due to mass transfer through a PEM is caused by diffusion, electro-osmotic drag, and the pressure difference between the cathode channel and anode channel. In PEME water molecules and ionic particles transferred between the electrodes from anode to cathode, Extensive mixing of the hydrogen and oxygen at anode channel due to gases cross-over must be avoided. In recent times the consciousness of safety issue in high pressure PEME where the oxygen mix with hydrogen at anode channel could create, explosive conditions have generated a lot of concern. In this paper, the steady state and simulation analysis of gases crossover in PEME on the temperature and pressure effect are presented. The simulations have been analysis in MATLAB based on the well-known Fick’s Law of molecular diffusion. The simulation results indicated that as temperature increases, there is a significant decrease in operating voltage.

Keywords: diffusion, gases crosover, steady state, Fick’s law

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Authors: N. Santatriniaina, J. Deseure, T. Q. Nguyen, H. Fontaine, C. Beitia, L. Rakotomanana

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Nowadays, with the increasing of the wafer's size and the decreasing of critical size of integrated circuit manufacturing in modern high-tech, microelectronics industry needs a maximum attention to challenge the contamination control. The move to 300 mm is accompanied by the use of Front Opening Unified Pods for wafer and his storage. In these pods an airborne cross contamination may occur between wafers and the pods. A predictive approach using modeling and computational methods is very powerful method to understand and qualify the AMCs cross contamination processes. This work investigates the required numerical tools which are employed in order to study the AMCs cross-contamination transfer phenomena between wafers and FOUPs. Numerical optimization and finite element formulation in transient analysis were established. Analytical solution of one dimensional problem was developed and the calibration process of physical constants was performed. The least square distance between the model (analytical 1D solution) and the experimental data are minimized. The behavior of the AMCs intransient analysis was determined. The model framework preserves the classical forms of the diffusion and convection-diffusion equations and yields to consistent form of the Fick's law. The adsorption process and the surface roughness effect were also traduced as a boundary condition using the switch condition Dirichlet to Neumann and the interface condition. The methodology is applied, first using the optimization methods with analytical solution to define physical constants, and second using finite element method including adsorption kinetic and the switch of Dirichlet to Neumann condition.

Keywords: AMCs, FOUP, cross-contamination, adsorption, diffusion, numerical analysis, wafers, Dirichlet to Neumann, finite elements methods, Fick’s law, optimization

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Authors: Salah Hamri, Tewfik Bouchaour, Ulrich Maschke

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The aim of this works is the study of swelling ratio of cross-linked polymer networks poly (2-hydroxyethyl methacrylate) (PHEMA). The system composed of erythrosine and Triethanolamine, in aqueous medium, is used as photo-initiator and 1,6-Hexanediol diacrylate as cross-linker. The analysis of UV-visible and infrared spectra, which were taken at different times during polymerization/cross linking, makes it possible to obtain useful information on the reaction mechanism. The swelling behavior was study by changing the nature of solvent, dye sensitizer (erythrosine, rose Bengal and eosin), and pH of the medium. The exploitation of experimental results using Fick diffusion model is also expected and shows a good correlation between theoretical and experimental results.

Keywords: cross-linker, photo-sensitizer, polymer network, swelling ratio

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Authors: Hassiba Benguergoura, Kamal Chanane, Sâad Moulay

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Pervaporation (PV), a membrane-based separation technology, has gained much attention because of its energy saving capability and low-cost, especially for separation of azeotropic or close-boiling liquid mixtures. There are two crucial issues for industrial application of pervaporation process. The first is developing membrane material and tailoring membrane structure to obtain high pervaporation performances. The second is modeling pervaporation transport to better understand of the above-mentioned structure–pervaporation relationship. Many models were proposed to predict the mass transfer process, among them, solution-diffusion model is most widely used in describing pervaporation transport including preferential sorption, diffusion and evaporation steps. For modeling pervaporation transport, the permeation flux, which depends on the solubility and diffusivity of components in the membrane, should be obtained first. Traditionally, the solubility was calculated according to the Flory–Huggins theory. Separation of the benzene (Bz)/cyclohexane (Cx) mixture is industrially significant. Numerous papers have been focused on the Bz/Cx system to assess the PV properties of membrane materials. Membranes with both high permeability and selectivity are desirable for practical application. Several new polymers have been prepared to get both high permeability and selectivity. Styrene-butadiene rubbers (SBR), dense membranes cross-linked by chloromethylation were used in the separation of benzene/cyclohexane mixtures. The impact of chloromethylation reaction as a new method of cross-linking SBR on the pervaporation performance have been reported. In contrast to the vulcanization with sulfur, the cross-linking takes places on styrene units of polymeric chains via a methylene bridge. The partial pervaporative (PV) fluxes of benzene/cyclohexane mixtures in styrene-butadiene rubber (SBR) were predicted using Fick's first law. The predicted partial fluxes and the PV separation factor agreed well with the experimental data by integrating Fick's law over the benzene concentration. The effects of feed concentration and operating temperature on the predicted permeation flux by this proposed model are investigated. The predicted permeation fluxes are in good agreement with experimental data at lower benzene concentration in feed, but at higher benzene concentration, the model overestimated permeation flux. The predicted and experimental permeation fluxes all increase with operating temperature increasing. Solvent sorption levels for benzene/ cyclohexane mixtures in a SBR membrane were determined experimentally. The results showed that the solvent sorption levels were strongly affected by the feed composition. The Flory- Huggins equation generates higher R-square coefficient for the sorption selectivity.

Keywords: benzene, cyclohexane, pervaporation, permeation, sorption modeling, SBR

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Authors: Rafeqah Raslan, Mastura AbdManaf, Junaidah Jai, Istikamah Subuki, Ana Najwa Mustapa

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The volatile citronella essential oil was encapsulated by simple coacervation and complex coacervation using gum Arabic and gelatin as wall material. Glutaraldehyde was used in the methodology as crosslinking agent. The citronella standard calibration graph was developed with R2 equal to 0.9523 for the accurate determination of encapsulation efficiency and release study. The release kinetic was analyzed based on Fick’s law of diffusion for polymeric system and linear graph of log fraction release over log time was constructed to determine the release rate constant, k and diffusion coefficient, n. Both coacervation methods in the present study produce encapsulation efficiency around 94%. The capsules morphology analysis supported the release kinetic mechanisms of produced capsules for both coacervation process.

Keywords: simple coacervation, complex coacervation, encapsulation efficiency, release kinetic study

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Authors: M. A. Khanday, Aasma Rafiq, Khalid Nazir

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This paper is an attempt to establish the mathematical models to understand the distribution of drug administration in the human body through oral and intravenous routes. Three models were formulated based on diffusion process using Fick’s principle and the law of mass action. The rate constants governing the law of mass action were used on the basis of the drug efficacy at different interfaces. The Laplace transform and eigenvalue methods were used to obtain the solution of the ordinary differential equations concerning the rate of change of concentration in different compartments viz. blood and tissue medium. The drug concentration in the different compartments has been computed using numerical parameters. The results illustrate the variation of drug concentration with respect to time using MATLAB software. It has been observed from the results that the drug concentration decreases in the first compartment and gradually increases in other subsequent compartments.

Keywords: Laplace transform, diffusion, eigenvalue method, mathematical model

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Authors: I. A. Simsek, S. N. Dogan, A. S. Kipcak, E. Morodor Derun, N. Tugrul

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In this study, the drying characteristics of shrimp are studied by using the traditional drying method of oven. Drying temperatures are selected between 60-80°C. Obtained experimental drying results are applied to eleven mathematical models of Alibas, Aghbashlo et al., Henderson and Pabis, Jena and Das, Lewis, Logaritmic, Midilli and Kucuk, Page, Parabolic, Wang and Singh and Weibull. The best model was selected as parabolic based on the highest coefficient of determination (R²) (0.999990 at 80°C) and the lowest χ² (0.000002 at 80°C), and the lowest root mean square error (RMSE) (0.000976 at 80°C) values are compared to other models. The effective moisture diffusivity (Deff) values were calculated using the Fick’s second law’s cylindrical coordinate approximation and are found between 6.61×10⁻⁸ and 6.66×10⁻⁷ m²/s. The activation energy (Ea) was calculated using modified form of Arrhenius equation and is found as 18.315 kW/kg.

Keywords: activation energy, drying, effective moisture diffusivity, modelling, oven, shrimp

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Authors: Asma A. Parlin, K. Nakamura, N. Watanabe, T. Komai

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Understanding the effective diffusion of benzene vapor in the soil-atmosphere interface is important as an intrusion of benzene into the atmosphere from the soil is largely driven by diffusion. To analyze the vertical one dimensional effective diffusion of benzene vapor in porous medium with high water content, diffusion experiments were conducted in soil columns using Andosol soil and Toyoura silica sand with different water content; for soil water content was from 0 to 30 wt.% and for sand it was from 0.06 to 10 wt.%. In soil, a linear relation was found between water content and effective diffusion coefficient while the effective diffusion coefficient didn’t change in the sand with increasing water. A numerical transport model following unsteady-state approaches based on Fick’s second law was used to match the required time for a steady state of the gas phase concentration profile of benzene to the experimentally measured concentration profile gas phase in the column. The result highlighted that both the water content and porosity might increase vertical diffusion of benzene vapor in soil.

Keywords: benzene vapor-phase, effective diffusion, subsurface soil medium, unsteady state

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Authors: Brahim Dennai, Abdelhak Bentaleb, Rachid Khelfaoui, Asma Abdenbi

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The diffusion flux given by the Fick’s law characterizethe mixing rate. A passive mixing strategy is proposed to enhance mixing of two fluids through perturbed jet low. A numerical study of passive mixers has been presented. This paper is focused on the modeling of a micro-injection systems composed of passive amplifier without mechanical part. The micro-system modeling is based on geometrical oscillators form. An asymmetric micro-oscillator design based on a monostable fluidic amplifier is proposed. The characteristic size of the channels is generally about a few hundred of microns. The numerical results indicate that the mixing performance can be as high as 99 % within a typical mixing chamber of 0.20 mm diameter inlet and 2.0 mm distance of nozzle - spliter. In addition, the results confirm that self-rotation in the circular mixer significantly enhances the mixing performance. The novel micro mixing method presented in this study provides a simple solution to mixing problems in microsystem for application in chemistry.

Keywords: micro oscillator, modeling, micro mixture, diffusion, size effect, chemical equation

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Authors: Ritesh Watharkar, Sourabh Chakraborty, Brijesh Srivastava

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Reduction of water from the fruits and vegetables using different drying techniques is widely employed to prolong the shelf life of these food commodities. Heat transfer occurs inside the sample by conduction and mass transfer takes place by diffusion in accordance with temperature and moisture concentration gradient respectively during drying. This study was undertaken to study and model the thin layer drying behavior of Bhimkol pulp. The drying was conducted in a tray drier at 500c temperature with 5, 10 and 15 % concentrations of added maltodextrin. The drying experiments were performed at 5mm thickness of the thin layer and the constant air velocity of 0.5 m/s.Drying data were fitted to different thin layer drying models found in the literature. Comparison of fitted models was based on highest R2(0.9917), lowest RMSE (0.03201), and lowest SSE (0.01537) revealed Middle equation as the best-fitted model for thin layer drying with 10% concentration of maltodextrin. The effective diffusivity was estimated based on the solution of Fick’s law of diffusion which is found in the range of 3.0396 x10-09 to 5.0661 x 10-09. There was a reduction in drying time with the addition of maltodextrin as compare to the raw pulp.

Keywords: Bhimkol, diffusivity, maltodextrine, Midilli model

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Authors: Weiyao Zhu, Qian Qi, Ming Yue, Dongxu Ma

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Due to the nano-micro pore structures and the massive multi-stage multi-cluster hydraulic fracturing in shale gas reservoirs, the multi-scale seepage flows are much more complicated than in most other conventional reservoirs, and are crucial for the economic development of shale gas. In this study, a new multi-scale non-linear flow model was established and simplified, based on different diffusion and slip correction coefficients. Due to the fact that different flow laws existed between the fracture network and matrix zone, a three-zone composite model was proposed. Then, according to the conformal transformation combined with the law of equivalent percolation resistance, the productivity equation of a horizontal fractured well, with consideration given to diffusion, slip, desorption, and absorption, was built. Also, an analytic solution was derived, and the interference of the multi-cluster fractures was analyzed. The results indicated that the diffusion of the shale gas was mainly in the transition and Fick diffusion regions. The matrix permeability was found to be influenced by slippage and diffusion, which was determined by the pore pressure and diameter according to the Knudsen number. It was determined that, with the increased half-lengths of the fracture clusters, flow conductivity of the fractures, and permeability of the fracture network, the productivity of the fractured well also increased. Meanwhile, with the increased number of fractures, the distance between the fractures decreased, and the productivity slowly increased due to the mutual interference of the fractures. In regard to the fractured horizontal wells, the free gas was found to majorly contribute to the productivity, while the contribution of the desorption increased with the increased pressure differences.

Keywords: multi-scale, fracture network, composite model, productivity

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Authors: Albana Hasimi, Edlira Tako, Elvin Çomo, Partizan Malkaj, Blerina Papajani, Ledjan Malaj, Mirela Ndrita

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Many endeavors have been exerted during the last years for developing new artificial polymeric membranes which fulfill the demanded conditions for biomedical uses. One of the most tested polymers is Poly(vinyl alcohol) [PVA]. Ours groups, is based on the possibility of using PVA for personal protective equipment against covid. In them, we explore the possibility of modifying the properties of the polymer by adding Montmorillonite [MMT]. Heat-treatment above the glass transition temperature are used to improve mechanical properties mainly by increasing the crystallinity of the polymer, which acts as a physical network. Temperature-Modulated Differential Scanning Calorimetry (TMDSC) measurements indicated that the presence of 0.5% MMT in PVA causes a higher Tg value and shaped peak of crystallinity. Decomposition is observed at two of the melting points of the crystals during heating 25-240oC and overlap of the recrystallization ridges during cooling 240-25oC. This is indicative of the presence of two types (quality or structure ) of polymer crystals. On the other hand, some indication of improvement of the quality of the crystals by heat-treatment is given by the distinct non-reversing contribution to melting. Data on sorption and transport of water in polyvinyl alcohol films: PVA pure and PVA/MMT matrix, modified by thermal treatment, are presented. The thermal treatment has aftereffect the films become more rigid, and because of this, the water uptake is significantly lower in membranes. That is indicates by analysis of the resulting water uptake kinetics. The presence 0.5% w/w of MMT has no significant impact on the properties of PVA membranes. Water uptake kinetics deviates from Fick’s law due to slow relaxation of glassy polymer matrix for all membranes category.

Keywords: crystallinity, montmorillonite, nanocomposite, poly (vinyl alcohol)

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Authors: Ayobami Solomon Popoola

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Yam is majorly a carbohydrate food grown in most parts of the world. It could be boiled, fried or roasted for consumption in a variety of ways. Blanching is an established heat pre-treatment given to fruits and vegetables prior to further processing such as dehydration, canning, freezing etc. Losses of soluble solids during blanching has been a great problem because a reasonable quantity of the water-soluble nutrients are inevitably leached into the blanching water. Without blanching, the high residual levels of reducing sugars after extended storage produce a dark, bitter-tasting product because of the Maillard reactions of reducing sugars at frying temperature. Measurement and prediction of such losses are necessary for economic efficiency in production and to establish the level of effluent treatment of the blanching water. This paper aims at resolving this problem by investigating the effects of cube size and temperature on the rate of diffusional losses of reducing sugars and total sugars during hot water blanching of water-yam. The study was carried out using four temperature levels (65, 70, 80 and 90 °C) and two cubes sizes (0.02 m³ and 0.03 m³) at 4 times intervals (5, 10, 15 and 20 mins) respectively. Obtained data were fitted into Fick’s non-steady equation from which diffusion coefficients (Da) were obtained. The Da values were subsequently fitted into Arrhenius plot to obtain activation energies (Ea-values) for diffusional losses. The diffusion co-efficient were independent of cube size and time but highly temperature dependent. The diffusion coefficients were ≥ 1.0 ×10⁻⁹ m²s⁻¹ for reducing sugars and ≥ 5.0 × 10⁻⁹ m²s⁻¹ for total sugars. The Ea values ranged between 68.2 to 73.9 KJmol⁻¹ and 7.2 to 14.30 KJmol⁻¹ for reducing sugars and total sugars losses respectively. Predictive equations for estimating amount of reducing sugars and total sugars with blanching time of water-yam at various temperatures were also presented. The equation could be valuable in process design and optimization. However, amount of other soluble solids that might have leached into the water along with reducing and total sugars during blanching was not investigated in the study.

Keywords: blanching, kinetics, sugar losses, water yam

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Authors: Ben Nadler

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Cell adhesion plays a vital role in many cell activities. The motivation to model cell adhesion is to study important biological processes, such as cell spreading, cell aggregation, tissue formation, and cell adhesion, which are very challenging to study by experimental methods alone. This study provides important insight into cell adhesion, which can lead to improve regenerative medicine and tissue formation techniques. In this presentation the biological cells adhesion is mediated by receptors–ligands binding and the diffusivity of the receptor on the cell membrane surface. The ability of receptors to diffuse on the cell membrane surface yields a very unique and complicated adhesion mechanism, which is exclusive to cells. The phospholipid bilayer, which is the main component in the cell membrane, shows fluid-like behavior associated with the molecules’ diffusivity. The biological cell is modeled as a fluid-like membrane with negligible bending stiffness enclosing the cytoplasm fluid. The in-plane mechanical behavior of the cell membrane is assumed to depend only on the area change, which is motivated by the fluidity of the phospholipid bilayer. In addition, the presence of receptors influences on the local mechanical properties of the cell membrane is accounted for by including stress-free area change, which depends on the receptor density. Based on the physical properties of the receptors and ligands the attraction between the receptors and ligands is modeled as a charged-nonpolar which is a noncovalent interaction. Such interaction is a short-range type, which decays fast with distance. The mobility of the receptor on the cell membrane is modeled using the diffusion equation and Fick’s law is used to model the receptor–receptor interactions. The resultant interaction force, which includes receptor–ligand and receptor–receptor interaction, is decomposed into tangential part, which governs the receptor diffusion, and normal part, which governs the cell deformation and adhesion. The formulation of the governing equations and numerical simulations will be presented. Analysis of the adhesion characteristic and properties are discussed. The roles of various thermomechanical properties of the cell, receptors and ligands on the cell adhesion are investigated.

Keywords: cell adhesion, cell membrane, receptor-ligand interaction, receptor diffusion

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Authors: Eusèbe Gnonlonfoun, Xavier Framboisier, Michel Fick, Emmanuel Rondags

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Pathogenic fungi represent a generic problem for cereals, including barley, as they can produce a number of thermostable toxic metabolites such as mycotoxins that contaminate plants and food products, leading to serious health issues for humans and animals and causing significant losses in global food production. In addition, mycotoxins represent a significant technological concern for the malting and brewing industries, as they may affect the quality and safety of raw materials (barley and malt) and final products (beer). Moreover, this situation is worsening due to the highly variable climatic conditions that favor microbial development and the societal desire to reduce the use of phytosanitary products, including fungicides. In this complex environmental, regulatory and economic context for the French barley-malt-beer industry, this project aims to develop an innovative biocontrol process by using technological bacteria, isolated from infection-resistant barley cultures, that are able to reduce the development of spoilage fungi and the associated mycotoxin production. The experimental approach consists of i) coculturing bacterial and pathogenic fungal strains in solid and liquid media to access the growth kinetics of these microorganisms and to evaluate the impact of these bacteria on fungal growth and mycotoxin production; then ii) the results will be used to carry out a micro-malting process in order to develop the aforementioned process, and iii) the technological and sanitary properties of the generated barley malts will finally be evaluated in order to validate the biocontrol process developed. The process is expected to make it possible to guarantee, with controlled costs, an irreproachable hygienic and technological quality of the malt, despite the increasingly complex and variable conditions for barley production. Thus, the results will not only make it possible to maintain the dominant world position of the French barley-malt chain but will also allow it to conquer emerging markets, mainly in Africa and Asia. The use of this process will also contribute to the reduction of the use of phytosanitary products in the field for barley production while reducing the level of contamination of malting plant effluents. Its environmental impact would therefore be significant, especially considering that barley is the fourth most-produced cereal in the world.

Keywords: barley, pathogenic fungi, mycotoxins, malting, bacterial biocontrol

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Authors: Sibashish Baksi, Ujjaini Sarkar, Sudeshna Saha

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In the present study, hydrolysis of Pinus roxburghi wood powder was carried out with Viscozyme, and kinetics of the hydrolysis has been investigated. Finely ground sawdust is submerged into 2% aqueous peroxide solution (pH=11.5) and pretreated through autoclaving, probe sonication, and alkaline peroxide pretreatment. Afterward, the pretreated material is subjected to hydrolysis. A chain of experiments was executed with delignified biomass (50 g/l) and varying enzyme concentrations (24.2–60.5 g/l). In the present study, 14.32 g/l of glucose, along with 7.35 g/l of xylose, have been recovered with a viscozyme concentration of 48.8 g/l and the same condition was treated as optimum condition. Additionally, thermal deactivation of viscozyme has been investigated and found to be gradually decreasing with escalated enzyme loading from 48.4 g/l (dissociation constant= 0.05 h⁻¹) to 60.5 g/l (dissociation constant= 0.02 h⁻¹). The hydrolysis reaction is a pseudo first-order reaction, and therefore, the rate of the hydrolysis can be expressed as a fractal-like kinetic equation that communicates between the product concentration and hydrolytic time t. It is seen that the value of rate constant (K) increases from 0.008 to 0.017 with augmented enzyme concentration from 24.2 g/l to 60.5 g/l. Greater value of K is associated with stronger enzyme binding capacity of the substrate mass. However, escalated concentration of supplied enzyme ensures improved interaction with more substrate molecules resulting in an enhanced de-polymerization of the polymeric sugar chains per unit time which eventually modifies the physiochemical structure of biomass. All fractal dimensions are in between 0 and 1. Lower the value of fractal dimension, more easily the biomass get hydrolyzed. It can be seen that with increased enzyme concentration from 24.2 g/l to 48.4 g/l, the values of fractal dimension go down from 0.1 to 0.044. This indicates that the presence of more enzyme molecules can more easily hydrolyze the substrate. However, an increased value has been observed with a further increment of enzyme concentration to 60.5g/l because of diffusional limitation. It is evident that the hydrolysis reaction system is a heterogeneous organization, and the product formation rate depends strongly on the enzyme diffusion resistances caused by the rate-limiting structures of the substrate-enzyme complex. Value of the rate constant increases from 1.061 to 2.610 with escalated enzyme concentration from 24.2 to 48.4 g/l. As the rate constant is proportional to Fick’s diffusion coefficient, it can be assumed that with a higher concentration of enzyme, a larger amount of enzyme mass dM diffuses into the substrate through the surface dF per unit time dt. Therefore, a higher rate constant value is associated with a faster diffusion of enzyme into the substrate. Regression analysis of time curves with various enzyme concentrations shows that diffusion resistant constant increases from 0.3 to 0.51 for the first two enzyme concentrations and again decreases with enzyme concentration of 60.5 g/l. During diffusion in a differential scale, the enzyme also experiences a greater resistance during diffusion of larger dM through dF in dt.

Keywords: viscozyme, glucose, fractal kinetics, thermal deactivation

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Authors: Caiyun Liu, A. Hernandez-Manas, N. Grimi, E. Vorobiev

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Drying is one of the most used methods for food preservation, which extend shelf life of food and makes their transportation, storage and packaging easier and more economic. The commonly dried method is hot air drying. However, its disadvantages are low energy efficiency and long drying times. Because of the high temperature during the hot air drying, the undesirable changes in pigments, vitamins and flavoring agents occur which result in degradation of the quality parameters of the product. Drying process can also cause shrinkage, case hardening, dark color, browning, loss of nutrients and others. Recently, new processes were developed in order to avoid these problems. For example, the application of pulsed electric field provokes cell membrane permeabilisation, which increases the drying kinetics and moisture diffusion coefficient. Microwave drying technology has also several advantages over conventional hot air drying, such as higher drying rates and thermal efficiency, shorter drying time, significantly improved product quality and nutritional value. Rehydration kinetics of dried product is a very important characteristic of dried products. Current research has indicated that the rehydration ratio and the coefficient of rehydration are dependent on the processing conditions of drying. The present study compares the efficiency of two processes (1: room temperature air drying, 2: microwave/air drying) in terms of drying rate, product quality and rehydration ratio. In this work, potato slices (≈2.2g) with a thickness of 2 mm and diameter of 33mm were placed in the microwave chamber and dried. Drying kinetics and drying rates of different methods were determined. The process parameters included inlet air velocity (1 m/s, 1.5 m/s, 2 m/s) and microwave power (50 W, 100 W, 200 W and 250 W) were studied. The evolution of temperature during microwave drying was measured. The drying power had a strong effect on drying rate, and the microwave-air drying resulted in 93% decrease in the drying time when the air velocity was 2 m/s and the power of microwave was 250 W. Based on Lewis model, drying rate constants (kDR) were determined. It was observed an increase from kDR=0.0002 s-1 to kDR=0.0032 s-1 of air velocity of 2 m/s and microwave/air (at 2m/s and 250W) respectively. The effective moisture diffusivity was calculated by using Fick's law. The results show an increase of effective moisture diffusivity from 7.52×10-11 to 2.64×10-9 m2.s-1 for air velocity of 2 m/s and microwave/air (at 2m/s and 250W) respectively. The temperature of the potato slices increased for higher microwaves power, but decreased for higher air velocity. The rehydration ratio, defined as the weight of the the sample after rehydration per the weight of dried sample, was determined at different water temperatures (25℃, 50℃, 75℃). The rehydration ratio increased with the water temperature and reached its maximum at the following conditions: 200 W for the microwave power, 2 m/s for the air velocity and 75°C for the water temperature. The present study shows the interest of microwave drying for the food preservation.

Keywords: drying, microwave, potato, rehydration

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Authors: Lei Li, Ming M. Chai, Xiao X. Lu, Jia W. Wang

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The mixing process of two liquid layers in a cylindrical container includes the upper liquid with higher density rushing into the lower liquid with lighter density, the lower liquid rising into the upper liquid, meanwhile the two liquid layers having interactions with each other, forming vortices, spreading or dispersing in others, entraining or mixing with others. It is a complex process constituted of flow instability, turbulent mixing and other multiscale physical phenomena and having a fast evolution velocity. In order to explore the mechanism of the process and make further investigations, some experiments about the interfacial instability and mixing behavior between two liquid layers bounded in different volumes are carried out, applying the planar laser induced fluorescence (PLIF) and the high speed camera (HSC) techniques. According to the results, the evolution of interfacial instability between immiscible liquid develops faster than theoretical rate given by the Rayleigh-Taylor Instability (RTI) theory. It is reasonable to conjecture that some mechanisms except the RTI play key roles in the mixture process of two liquid layers. From the results, it is shown that the invading velocity of the upper liquid into the lower liquid does not depend on the upper liquid's volume (height). Comparing to the cases that the upper and lower containers are of identical diameter, in the case that the lower liquid volume increases to larger geometric space, the upper liquid spreads and expands into the lower liquid more quickly during the evolution of interfacial instability, indicating that the container wall has important influence on the mixing process. In the experiments of miscible liquid layers’ mixing, the diffusion time and pattern of the liquid interfacial mixing also does not depend on the upper liquid's volumes, and when the lower liquid volume increases to larger geometric space, the action of the bounded wall on the liquid falling and rising flow will decrease, and the liquid interfacial mixing effects will also attenuate. Therefore, it is also concluded that the volume weight of upper heavier liquid is not the reason of the fast interfacial instability evolution between the two liquid layers and the bounded wall action is limited to the unstable and mixing flow. The numerical simulations of the immiscible liquid layers’ interfacial instability flow using the VOF method show the typical flow pattern agree with the experiments. However the calculated instability development is much slower than the experimental measurement. The numerical simulation of the miscible liquids’ mixing, which applying Fick’s diffusion law to the components’ transport equation, shows a much faster mixing rate than the experiments on the liquids’ interface at the initial stage. It can be presumed that the interfacial tension plays an important role in the interfacial instability between the two liquid layers bounded in finite volume.

Keywords: interfacial instability and mixing, two liquid layers, Planar Laser Induced Fluorescence (PLIF), High Speed Camera (HSC), interfacial energy and tension, Cahn-Hilliard Navier-Stokes (CHNS) equations

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Authors: Davide Gotti, Milan Prodanovic, Sergio Pinilla, David Muñoz-Torrero

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Since its proposal, the Doyle-Fuller-Newman (DFN) lithium-ion battery model has gained popularity in the electrochemical field. In fact, this model provides the user with theoretical support for designing the lithium-ion battery parameters, such as the material particle or the diffusion coefficient adjustment direction. However, the model is mathematically complex as it is composed of several partial differential equations (PDEs) such as Fick’s law of diffusion, the MacInnes and Ohm’s equations, among other phenomena. Thus, to efficiently use the model in a time-domain simulation environment, the selection of the discretization technique is of a pivotal importance. There are several numerical methods available in the literature that can be used to carry out this task. In this study, a comparison between the explicit Euler, Crank-Nicolson, and Chebyshev discretization methods is proposed. These three methods are compared in terms of accuracy, stability, and computational times. Firstly, the explicit Euler discretization technique is analyzed. This method is straightforward to implement and is computationally fast. In this work, the accuracy of the method and its stability properties are shown for the electrolyte diffusion partial differential equation. Subsequently, the Crank-Nicolson method is considered. It represents a combination of the implicit and explicit Euler methods that has the advantage of being of the second order in time and is intrinsically stable, thus overcoming the disadvantages of the simpler Euler explicit method. As shown in the full paper, the Crank-Nicolson method provides accurate results when applied to the DFN model. Its stability does not depend on the integration time step, thus it is feasible for both short- and long-term tests. This last remark is particularly important as this discretization technique would allow the user to implement parameter estimation and optimization techniques such as system or genetic parameter identification methods using this model. Finally, the Chebyshev discretization technique is implemented in the DFN model. This discretization method features swift convergence properties and, as other spectral methods used to solve differential equations, achieves the same accuracy with a smaller number of discretization nodes. However, as shown in the literature, these methods are not suitable for handling sharp gradients, which are common during the first instants of the charge and discharge phases of the battery. The numerical results obtained and presented in this study aim to provide the guidelines on how to select the adequate discretization technique for the DFN model according to the type of application to be performed, highlighting the pros and cons of the three methods. Specifically, the non-eligibility of the simple Euler method for longterm tests will be presented. Afterwards, the Crank-Nicolson and the Chebyshev discretization methods will be compared in terms of accuracy and computational times under a wide range of battery operating scenarios. These include both long-term simulations for aging tests, and short- and mid-term battery charge/discharge cycles, typically relevant in battery applications like grid primary frequency and inertia control and electrical vehicle breaking and acceleration.

Keywords: Doyle-Fuller-Newman battery model, partial differential equations, discretization, numerical methods

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Authors: Salvatore Brischetto, Domenico Cesare

Abstract:

Major improvements in future aircraft and spacecraft could be those dependent on an increasing use of conventional and unconventional multilayered structures embedding composite materials, functionally graded materials, piezoelectric or piezomagnetic materials, and soft foam or honeycomb cores. Layers made of such materials can be combined in different ways to obtain structures that are able to fulfill several structural requirements. The next generation of aircraft and spacecraft will be manufactured as multilayered structures under the action of a combination of two or more physical fields. In multifield problems for multilayered structures, several physical fields (thermal, hygroscopic, electric and magnetic ones) interact each other with different levels of influence and importance. An exact 3D shell model is here proposed for these types of analyses. This model is based on a coupled system including 3D equilibrium equations, 3D Fourier heat conduction equation, 3D Fick diffusion equation and electric and magnetic divergence equations. The set of partial differential equations of second order in z is written using a mixed curvilinear orthogonal reference system valid for spherical and cylindrical shell panels, cylinders and plates. The order of partial differential equations is reduced to the first one thanks to the redoubling of the number of variables. The solution in the thickness z direction is obtained by means of the exponential matrix method and the correct imposition of interlaminar continuity conditions in terms of displacements, transverse stresses, electric and magnetic potentials, temperature, moisture content and transverse normal multifield fluxes. The investigated structures have simply supported sides in order to obtain a closed form solution in the in-plane directions. Moreover, a layerwise approach is proposed which allows a 3D correct description of multilayered anisotropic structures subjected to field loads. Several results will be proposed in tabular and graphical formto evaluate displacements, stresses and strains when mechanical loads, temperature gradients, moisture content gradients, electric potentials and magnetic potentials are applied at the external surfaces of the structures in steady-state conditions. In the case of inclusions of piezoelectric and piezomagnetic layers in the multilayered structures, so called smart structures are obtained. In this case, a free vibration analysis in open and closed circuit configurations and a static analysis for sensor and actuator applications will be proposed. The proposed results will be useful to better understand the physical and structural behaviour of multilayered advanced composite structures in the case of multifield interactions. Moreover, these analytical results could be used as reference solutions for those scientists interested in the development of 3D and 2D numerical shell/plate models based, for example, on the finite element approach or on the differential quadrature methodology. The correct impositions of boundary geometrical and load conditions, interlaminar continuity conditions and the zigzag behaviour description due to transverse anisotropy will be also discussed and verified.

Keywords: composite structures, 3D shell model, stress analysis, multifield loads, exponential matrix method, layer wise approach

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Authors: Wiam El Kheir, Anais Dumais, Maude Beaudoin, Bernard Marcos, Nick Virgilio, Benoit Paquette, Nathalie Faucheux, Marc-Antoine Lauzon

Abstract:

The high infiltrative pattern of glioblastoma multiforme cells (GBM) is the main cause responsible for the actual standard treatments failure. The tumor high heterogeneity, the interstitial fluid flow (IFF) and chemokines guides GBM cells migration in the brain parenchyma resulting in tumor recurrence. Drug delivery systems emerged as an alternative approach to develop effective treatments for the disease. Some recent studies have proposed to harness the effect CXC-lchemokine-ligand-12 to direct and control the cancer cell migration through delivery system. However, the dynamics of the brain environment on the delivery system remains poorly understood. Nanoparticles (NPs) and hydrogels are known as good carriers for the encapsulation of different agents and control their release. We studied the release of CXCL12 (free or loaded into NPs) from an alginate-based hydrogel under static and indirect perfusion (IP) conditions. Under static conditions, the main phenomena driving CXCL12 release from the hydrogel was diffusion with the presence of strong interactions between the positively charged CXCL12 and the negatively charge alginate. CXCL12 release profiles were independent from the initial mass loadings. Afterwards, we demonstrated that the release could tuned by loading CXCL12 into Alginate/Chitosan-Nanoparticles (Alg/Chit-NPs) and embedded them into alginate-hydrogel. The initial burst release was substantially attenuated and the overall cumulative release percentages of 21%, 16% and 7% were observed for initial mass loadings of 0.07, 0.13 and 0.26 µg, respectively, suggesting stronger electrostatic interactions. Results were mathematically modeled based on Fick’s second law of diffusion framework developed previously to estimate the effective diffusion coefficient (Deff) and the mass transfer coefficient. Embedding the CXCL12 into NPs decreased the Deff an order of magnitude, which was coherent with experimental data. Thereafter, we developed an in-vitro 3D model that takes into consideration the convective contribution of the brain IFF to study CXCL12 release in an in-vitro microenvironment that mimics as faithfully as possible the human brain. From is unique design, the model also allowed us to understand the effect of IP on CXCL12 release in respect to time and space. Four flow rates (0.5, 3, 6.5 and 10 µL/min) which may increase CXCL12 release in-vivo depending on the tumor location were assessed. Under IP, cumulative percentages varying between 4.5-7.3%, 23-58.5%, 77.8-92.5% and 89.2-95.9% were released for the three initial mass loadings of 0.08, 0.16 and 0.33 µg, respectively. As the flow rate increase, IP culture conditions resulted in a higher release of CXCL12 compared to static conditions as the convection contribution became the main driving mass transport phenomena. Further, depending on the flow rate, IP had a direct impact on CXCL12 distribution within the simulated brain tissue, which illustrates the importance of developing such 3D in-vitro models to assess the efficiency of a delivery system targeting the brain. In future work, using this very model, we aim to understand the impact of the different phenomenon occurring on GBM cell behaviors in response to the resulting chemokine gradient subjected to various flow while allowing them to express their invasive characteristics in an in-vitro microenvironment that mimics the in-vivo brain parenchyma.

Keywords: 3D culture system, chemokines gradient, glioblastoma multiforme, kinetic release, mathematical modeling

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