Internal Diffusion Coefficients Research Articles

Modeling and optimization of production process of extruded protein textures in meat products technology

In the production of extruded protein textures, the method of multifaceted experimental planning was considered using the recurrence plan of the central composition. The work created a mathematical model of mass exchange in the extraction process layer to obtain the main factors of extraction kinetics (layer, solvent velocity, particles, and longitudinal mixing coefficient) to parameters (internal diffusion coefficients). Carasora protein concentrate was used as the object of the study. Carasora is a wonderful plant, which is used in various fields of production, as well as multifunctional food products in the form of fats, seeds, and proteins. Carasora provides not only rich protein, but also natural dietary fiber and healthy fatty acids, which makes carasora proteins useful for vegetarians and vegans. Because of these qualities, we plan to use pure extruded protein textures from carasora and have developed a mathematical model to find appropriate uses.

Semi-batch extraction of phenolic compounds from Rosmarinus officinalis: Kinetic study and dimensionless modeling

A transient and one-dimensional mathematical model with two partial differential equations is developed to simulate the extraction of de-oiled rosemary plant in a vertical fixed-bed reactor. The effect of the dimensionless numbers which appear in the final governing equations (Peclet and Damköhler numbers) is studied. The influence of solvent composition, solid particle size and temperature is also investigated. The process is controlled by internal diffusion effects, with the smallest particle size exhibiting the smallest internal diffusion coefficient. Among the different solvents, 80% ethanol shows the highest total phenolics recovery. The antiradical activity is also enhanced by increasing the temperature and the smaller particle size leads to an improvement in the extraction selectivity. Peclet number has a small effect on the results, while Damköhler number strongly affects the process. An increase in bed porosity causes a significant increase in the internal diffusion time.

Effect of Mass Fraction on Leaching Kinetics of Hydrophobic Ultraviolet Stabilizers in Low-Density Polyethylene.

The leaching kinetics of five hydrophobic ultraviolet (UV) stabilizers from low-density polyethylene (LDPE) (micro)fibers into water was evaluated in this study, with variation of the mass fraction (ω = 0.1-2.0 wt %) of the stabilizers. A one-dimensional convection-diffusion model for a cylindrical geometry, requiring partitioning between the LDPE fibers and water (KLDPEw) and the internal diffusion coefficients (DLDPE), was used to evaluate the leaching process and the leaching half-life of the target UV stabilizers at ω < 0.5 wt % (Case I). Diffusion through the aqueous boundary layer is the rate-determining step, and the leaching half-life is predicted to be very long (a few months to years) under unaffected conditions. When the UV stabilizers are supersaturated within LDPE fibers (i.e., ω > 0.5 wt %, Case II), the possible formation of a surficial crystal layer of the additives on the LDPE fiber extends the time scale for leaching compared to that in Case I due to the requirement of overcoming the crystallization energy. This study provides a fundamental understanding of the leaching profiles of plastic additives for assessing their potential chemical risks in aquatic environments; further studies under the relevant environmental conditions are required.

Sorption of ammonium by fibrous sorbent VION KN-1

The results of studies of the sorption extraction of ammonium ions from aqueous media by the fibrous sorbent VION KN-1 are presented. Weak acid ion exchange fiber. It has been established that the limiting step in the process of ammonium ion sorption is internal diffusion. The kinetic parameters of the sorption process are calculated, with the identification of a decrease in the half-sorption time and an increase in the internal diffusion coefficient. The applicability of the Langmuir and Freindlich models for describing the experimental isotherms of ammonium ion sorption by fiber has been studied. Certain constants and parameters. Through the appearance of regression coefficients, R2 showed that the Langmuir model better explores experimental data on the sorption of ammonium ions by a fibrous sorbent. A study of sorption in media was carried out. According to the curves of the dependence of the degree of extraction on the concentration and on the depth of the missed solution, it was found that with a decrease in concentration in the dynamic sorption mechanism, the reduction characteristics do not decrease, which makes their use reduced in the purification of dilute solutions containing ammonium ions. At a low concentration of ammonium ions in the initial solution, the degree of extraction is more than 93%. To predict the extraction of ammonium ions from wastewater, an increased concentration of neural packages of STATISTICA application programs was used. The input parameters for studying the neural network were chosen: the concentration of ammonium ions, the volume of the solution passed through the sorbent layer, and the weight of the sample of fibers. The output parameter is the degree of extraction of ammonium ions. The trained MPL-3-5-1 neural network has high coefficients of determination for the training, test and control samples, which gives a high estimate of the network performance and can predict the degree of extraction of ammonium ions by the fibrous sorbent VION KN-1..

Kinetics of polyvinyl butyral (PVB) synthesis reaction catalyzed by deep eutectic solvent

AbstractIn this work, the kinetics of the polyvinyl butyral (PVB) synthesis reaction catalyzed by the deep eutectic solvents (DESs) at the low‐temperature stage was studied to control the particle size of PVB resin and optimize its synthesis process. The effects of stirring speed, the concentration of polyvinyl alcohol (PVA), catalyst dosage, and temperature on the synthesis reaction of PVB were investigated. The data obtained from kinetic experiments at 283.15–298.15 K were fitted with the shrinking core models, and the results showed that the model controlled by internal diffusion fitted well with the experimental data. The internal diffusion coefficient, DA, of n‐butanal in the product layer was further calculated by the obtained model parameters, and it was applied to predict the synthesis reaction of PVB at different concentrations of n‐butanal. The results indicated that the shrinking core model controlled by internal diffusion is suitable to describe the kinetics of the PVB synthesis reaction. DES played a dual role in catalysis and dispersion in the synthesis of PVB, and it was a green catalyst with good potential for PVB industrial applications.

Determination of the limiting stage of the adsorption kinetics of the dye “Methylene Blue” by the biomass of apricot pits

The paper presents the results of experimental studies to determine the limiting stage of the adsorption kinetics of the methylene blue dye by the biomass of the crushed peel of apricot pits. Morphological studies of the surface of the peel of apricot pits were carried out using a scanning electron microscope of the brand “TESCAN MIRA 3 LMU” (Czech Republic). Adsorption studies were carried out under static conditions by treating the biomass of the apricot pit peel with solutions of methylene blue of specified concentrations for a certain time. On the basis of the obtained data, the kinetic dependences were constructed and the necessary indicators were calculated. It was found that the sorption capacity of the apricot pit biomass under experimental conditions is 0.565 mmol/g. The results of the experiment were processed using the Microsoft office Excel software in the framework of the diffusion model, and an intradiffusion kinetic model of sorption was obtained. The constants of the intradiffusion kinetic model of sorption and the parameters of the internal diffusion coefficient are calculated, and the contribution of external diffusion to the adsorption process is determined. It is revealed that the adsorption process is limited by external diffusion.

Кинетические закономерности процесса водно-щелочного гидролиза березовой коры в СВЧ-поле

Birch bark consists of silver bark and bast. Silver bark contains up to 50 % of extractives and serves as a raw material for obtaining valuable biologically active substances (BAS), including betulin. A distinctive feature of the birch bark structure is a cross-linked polymer, suberin. Its monomers are suberic acids. They have found use in the production of lubricants, oils, insecticides, fungicides, polymers, polyesters, coatings, etc. A common method for extracting suberic acid salts from silver bark is exhaustive hydrolysis with an aqueous or water-alcohol solution of alkali (NaOH or KOH). We have proposed the activation of raw materials during hydrolysis by using an ultrahigh-frequency electromagnetic field (microwave hydrolysis). Isolation of suberin from silver bark is both a chemical and mass transfer process. Salts that are formed during hydrolysis of suberic acids diffuse to the surface of silver bark particles and pass into the hydrolysate. The limiting stage of mass transfer during birch bark hydrolysis is internal diffusion in the pores (mass conductivity). The anisotropy of the silver bark structure complicates the mathematical description of the mass transfer kinetics in the diffusion process. The process of internal diffusion during microwave hydrolysis is characterized by a steady regime starting from the 4th minute. The kinetics of this process and the effectiveness of diffusion in the tangential and longitudinal directions were determined. As the size of birch bark particles increases in both length (tangential direction) and width (longitudinal direction), the rate of the hydrolysis process and the degree of suberin isolation increase. Internal diffusion coefficients during microwave bark hydrolysis were determined. The highest value was obtained for fractions with a particle size of 3–4.5 mm (silver bark); the lowest – for fractions less than 1 mm (bast). The article shows that the small fraction (bast) should be separated and silver bark should be cut along the fiber in order to increase the yield of suberin after birch bark grinding.

The relative importance of internal and external physical resistances to mass transfer for caffeine release from apple pectin tablets

The relative importance of the physical resistances to mass transfer have been explored by using halved 13 mm diameter apple-pectin tablets containing caffeine, in different external stirring environments within a beaker containing simulated gastric fluid. The effects of different external (outside of the tablets) mass-transfer resistances to the tablets created through two different stirrer types and stirrer speeds, and different internal (inside of the tablets) mass-transfer resistances created through different tablet concentrations and thicknesses, have been studied. These studies enable internal diffusion coefficients of caffeine through the apple pectin matrix to be estimated, as well as estimating the external mass-transfer coefficients from benzoic acid dissolution, which are in the range of 6.5 × 10-6 m/s – 2.4 × 10-5 m/s for the 0.6 mm thick tablets and 4.0 × 10-6 m/s – 1.6 × 10-5 m/s for the 7 mm thick tablets. The diffusion coefficients for different caffeine concentrations in the apple pectin half-tablets have also been calculated in this study. The diffusivity of caffeine in the 7 mm half-tablets with 1% caffeine through 99% pectin was around (1.8 ± 0.5) × 10-10 m2/s. This study points towards the development of multifilm mass-transfer theory for food digestion to create a more fundamentally based understanding of in-vitro digestion systems as an addition to the use of realistic in-vitro food digestion apparatus and give a better correlation between in-vitro and in-vivo digestion tests.

Modelling the dependence of the internal diffusion coefficient and hydrodynamic resistance on the structures and shapes of polymer membrane pores

Modelling the dependence of the internal diffusion coefficient and hydrodynamic resistance on the structures and shapes of polymer membrane pores

EPR Spectroscopy as an Efficient Tool for Investigations of Polyelectrolyte Multilayer Growth and Local Chain Dynamics.

The strong polycation poly(diallyldimethylammonium chloride) (PDADMAC) and the weak polyanion poly(ethylene-alt-maleic acid) (P(E-alt-MA)) were used to build polyelectrolyte multilayers (PEMs) up to 31 layers. A spin-label (SL) was covalently attached to the polyanion for studying the rotational dynamics of the polyacid backbone in a swollen state of the PEMs using continuous-wave (CW) electron paramagnetic resonance (EPR) spectroscopy. In the first step, the spin-labeled poly(ethylene-alt-maleic acid) (SL-P(E-alt-MA)) was used in every polyanion layer to monitor the PEMs growth by analyzing the integrated intensity of the spectra. The buildup was found to be pH-dependent resulting in PEM with different thicknesses. In the second step, SL-P(E-alt-MA) was selectively placed in a single polyanion layer to study the rotational dynamics of the polyacid backbone. The rotational diffusion coefficient of the polyacid backbone RS and the internal rotational diffusion coefficient of the SL attached to the polymer backbone RI were found to be higher at pH 5 than at pH 4, which is related to enhanced mobility.

Influence of Asphaltene polarity on wax deposition of waxy oils

Asphaltenes are the most polar components of crude oils. The influences of asphaltene polarity on the wax deposition were studied in this investigation using model waxy oils. Asphaltenes contained by a Venezuelan crude oil were fractionated into four subfractions of different polarity utilizing a liquid/liquid extraction technique and used to prepare asphaltene-containing waxy model oils. The mass, composition, dielectric characteristics and mechanical characteristics of the waxy deposits formed in the presence of asphaltene fractions of different polarity were characterized. It was found that the less polar asphaltenes in waxy oils lower the deposit mass but cause the wax content of the deposits to increase. In addition, the inner diffusion of longer n-alkanes and the outer diffusion of shorter n-alkanes are accelerated by the less polar asphaltenes. Furthermore, the waxy deposits formed with waxy oils containing less polar asphaltenes are enriched with less amount of asphaltene and present reduced internal effective diffusion coefficient as was characterized by NMR. Besides, the presence of less polar asphaltenes causes the radius of Nyquist diagram of waxy deposits to increase, indicating higher resistance. Eventually, rheological characteristics, such as gelation temperature and yield stress, suggest increased structural strength of waxy deposits formed in the presence of less polar asphaltenes.

Kinetics and thermodynamics of water extraction of foxtail millet polysaccharides

In order to understand the mechanism of the extraction process of polysaccharides from foxtail millet by hot water, the extraction was carried out for studying the kinetics and thermodynamics of extraction process. After the appropriate stirring rate and liquid material ratio was selected through preliminary experiment, the changes of polysaccharides mass concentration in the extract liquor with extraction temperature and extraction time were measured. The experimental data were fitted by the first-order model. The kinetics and thermodynamics parameters were calculated. The results showed that the appropriate stirring rate and liquid material ratio was 150 r/min, 20.0 mL/g respectively. The greater extraction rate and higher equilibrium mass concentration could be obtained under higher extraction temperature. The extraction process accorded with the first-order dynamics model. The apparent activation energy of process was 12.03 kJ/mol under study conditions. The internal diffusion coefficient was increased with increasing temperature in the range of 7.84×10-10 - 1.29×10-9 m2/min. The half-life was decreased from 25.2 min to 3.9 min as temperature increased. The Gibbs free energies were all less than zero, the enthalpy change was 31.96 kJ/mol and the entropy change was 120.3 J/(mol·K) in process. The polysaccharides extraction process was a spontaneous, endothermic and entropy increases process.

Mass transfer coefficient and effective internal diffusion coefficient for coke solution loss reaction with non-equimolar diffusion

The mass transfer process of coke solution loss reaction (Ccoke + CO2 = 2CO) was rather complex due to coke porous structure and non-equimolar diffusion. However, non-equimolar diffusion in the external and internal diffusion process was often neglected in the study of coke solution loss reaction. This study has treated the mass transfer coefficient and effective internal diffusion coefficient as the object with the effect of non-equimolar diffusion. The experiments of metallurgical coke gasification with CO2 in the temperature range of 1100–1300 °C and at atmospheric pressure were carried out. When the weight-loss rate of coke reached 25%, the experiments were stopped. The calculated results showed that, after modification, mass transfer coefficients were decreased markedly, and they were changing over time during the coke gasification, from 1100 °C to 1300 °C, the deviation of correction was 38.89%, 37.94%, 36.96%, 35.99% and 35.61% individually. Effective internal diffusion coefficients were modified from 2D curves to 3D surface, they were increased not only with weight-loss rate, but also decreased with radius at each temperature. Kinetic parameters were also significantly affected, especially the activation energy, which increased from 213.41 to 232.02 kJ/mol. Finally the controlling steps at different temperatures were analyzed by comparing the effectiveness factor, which was approximately 0.7, 0.5, 0.4, 0.35 and 0.28 in the temperature range of 1100–1300 °C, the conclusion could be drawn that the controlling steps maintained stable at each temperature with non-equimolar diffusion.

Diffusion of IFRS using innovation diffusion models

PurposeThis study aims to examine the diffusion pattern of International Financial Reporting Standards (IFRS) into the countries and identifies the channels of diffusion.Design/methodology/approachData includes 98 countries that made a public commitment to IFRS adoption from 2000 to 2016. Adoptee countries are categorized based on Rogers’ adopter categorizations to understand country characteristics. Innovation diffusion models such as internal influence, external influence and bass diffusion that explain diffusion patterns are applied to the cumulative adoption of IFRS. Coefficients of internal and external diffusion are obtained using the models to explain the mode of diffusion pattern of IFRS. Further tests are done to identify the best model that explains IFRS diffusion.FindingsFindings show that IFRS diffusion is a result of external influence through vertical communication from a centralized body (IASB) and internal influence due to imitation and interpersonal communication between countries. Imitation effect among the countries has a stronger effect on the IFRS adoption compared to the communication obtained from IASB.Practical implicationsFindings obtained can help standards-setting bodies, organizations and countries to understand the potential future of adopters and non-adopters. It facilitates the standard-setting bodies to manage IFRS diffusion by implementing measures to spread the word on the benefits of IFRS.Originality/valueThe study generates value by modeling a successive increase in the number of IFRS adoptee countries using empirical methods and identifies the reasons for the diffusion life cycle of IFRS.

A new modified walnut shell by grafting l‐aspartic acid: Synthesis and kinetics

AbstractA new modified walnut shell was prepared by grafting l‐aspartic acid (ASP) to walnut shell (WNS) in the hydrochloric acid solution (1.0 M). The effects of stirring speed, particle size, solid‐liquid ratio, temperature, and modifying agent concentration on grafting yield were studied. The grafting process conditions were optimized, and the grafting yield of WNS reached ∼14 wt%. The kinetics of the grafting reaction was investigated in the temperature range of 348‐368 K. A three‐step hypothesis was proposed to describe the grafting process: The ASP molecules diffuse to the out surface of WNS through the liquid film, then attend to the internal surface and react with WNS. The shrinking core models with different controlling steps were used to fit the kinetic data of the grafting process, and the results showed that the model controlled by a product layer fitted well with the experimental data. The internal diffusion coefficient DA of ASP in WNS has been calculated, and it was applied to predict the grafting yield at different ASP concentrations by a shrinking core model. The results showed that the shrinking core model controlled by internal diffusion is suitable.

Modeling of internal diffusion mass transfer during filtration drying of capillary-porous material

The article presents the results of theoretical and experimental studies on the determination of the coefficients of internal diffusion of moisture from capillary-porous materials of plant origin during filtration drying, in particular, beet pulp, a by-product of sugar production. A model based on the solution of the internal diffusion differential equation with the

Diffusion in Binary Aqueous Solutions of Alcohols by Molecular Simulation

Based on the molecular dynamics method, the calculations for diffusion coefficients were carried out in binary aqueous solutions of three alcohols: ethanol, isopropanol, and tert-butanol. The intermolecular potential TIP4P/2005 was used for water; and five force fields were analyzed for the alcohols. The force fields providing the best accuracy of calculation were identified based on a comparison of the calculated self-diffusion coefficients of pure alcohols with the experimental data for internal (Einstein) diffusion coefficients of alcohols in solutions. The temperature and concentration dependences of the interdiffusion coefficients were determined using Darken’s Equation. Transport (Fickian) diffusion coefficients were calculated using a thermodynamic factor determined by the non-random two-liquid (NRTL) and Willson models. It was demonstrated that for adequate reproduction of the experimental data when calculating the transport diffusion coefficients, the thermodynamic factor has to be 0.64. Simple approximations were obtained, providing satisfactory accuracy in calculating the concentration and temperature dependences of the transport diffusion coefficients in the studied mixtures.

Diffusion of Resveratrol in Silica Alcogels.

The trans-resveratrol (RSV)-loaded silica aerogel (RLSA) was prepared by the sol-gel method, adding the drug during the aging process, solvent replacement and freeze drying. A series of characterizations showed that RSV stays in the silica aerogel in two ways. First, RSV precipitates due to minimal solubility in water during the solvent replacement process. After freeze drying, the solvent evaporates and the RSV recrystallizes. It can be seen from scanning electron microscope (SEM) and transmission electron microscope (TEM) images that the recrystallized RSV with micron-sized long rod-shaped is integrated with the dense silica network skeleton. Second, from small-angle X-ray scattering (SAXS) results, a portion of the RSV molecules is not crystallized and the size is extremely small. This can be attached to the primary and secondary particles of silica to enhance its network structure and inhibit shrinkage, which is why the volume and pore size of RLSA is larger. In addition, the diffusion of RSV in silica alcogel was studied by a one-dimensional model. The apparent diffusion coefficients of inward diffusion, outward diffusion and internal diffusion were calculated by fitting the time- and position-dependent concentration data. It was found that the outward diffusion coefficient (5.25 × 10−10 m2/s) is larger than the inward (2.93 × 10−10 m2/s), which is probably due to the interface effect. The diffusion coefficients obtained for different concentrations in the same process (inward diffusion) are found to be different. This suggests that the apparent diffusion coefficient obtained is affected by molecular adsorption.

Correlations between kinetic and thermodynamic parameters of the extraction of tobacco leaves

The correlations between thermodynamic and kinetic parameters in the extraction of tobacco leaves (solid – liquid system) were determined. The values of the parameters internal molecular diffusion coefficient, activation energy and entropy were used in the calculation procedure presented in the study, with regard to the extraction process of leaves of three types of tobacco (Virginia, Burley and Oriental), carried out with 50% ethanol as a solvent at different temperatures (20, 30, 40, 50, 60 and 70°C) and duration (10, 20, 30, 40, 50 and 60 min). On the basis of the Arrhenius law the effective diffusion coefficient in solid – liquid system and the reaction rate constant of the three types of tobacco were computed.

Effect of Temperature on the Kinetics of the Sorption of Strontium Cations by a Sorbent Based on Titanium Phosphate

Kinetics of the sorption of strontium ions from model solutions on an inorganic sorbent based on titanium phosphate is studied. Experimental dependences describing the ion exchange kinetics are obtained that represent three exchange mechanisms: exchange on surfaces, ion diffusion into the bulk of the sorbent, and a heterogeneous ion exchange reaction to form a new phase. The internal diffusion coefficients, ion exchange rate constants, and apparent activation energies for internal and external diffusion are determined.