An Improvement of the Cell Diffusion Method for the Rapid Determination of Diffusion Constants in Gels or Foods

A diffusion cell was designed to study the apparent diffusion coefficient of solutes through foodstuffs. The mathematical model corresponding to the experimental setup did not assume quasi-steady state diffusion within the slice of food. It was used to obtain the effective diffusion coefficient of NaCl through 3% Agar gels. The results were compared to those obtained by using two agar gel cylinders at different concentrations. The diffusion coefficient of Cl^? in gel at 25°C was obtained with at least the same precision (D = 1.30 × 10^?9 m²/sec, S_D= 0.03 × 10^?9 m²/sec) within less than 110 min compared to a few hours with the two cylinder technique. With the mathematical model used to determine diffusion coefficients, the equilibrium ratio between solute concentration in solution and at the interface of foodstuff can be determined.     

Diffusion of organophosphorus insecticides in soils

Diffusion of disulfoton and dimethoate in a silt loam soil was studied over a range of concentrations and moisture contents. Apparent diffusion coefficients were calculated from the distribution of insecticide in a column of soil after diffusion from one half of the column to the other for a known time. The distribution was determined by slicing the column into narrow; sections using a specially constructed diffusion cylinder. Diffusion coefficients varied little with concentration for both insecticides, but increased rapidly with increasing moisture content for dimethoate from 3.31 × 10^?8 cm²/sec at 10% volumetric moisture content to 1.41 × 10^?6 cm²/sec at 43% moisture content. In contrast, for disulfoton which is more volatile, less soluble and more strongly sorbed than dimethoate, diffusion coefficients were smaller (2.83 × 10^?8 cm²/sec at 41% moisture content) but did not change much as the soil became drier (2.74 × 10^?8 cm²/sec at 8 % moisture content). The influence of partition between solid, solution and vapour phases in the soil and of the geometry of the pathway-through the soil pores on the apparent diffusion coefficient is discussed. The likely behaviour of other pesticides is considered in the light of these results.     

Mass transfer during osmotic dehydration of pineapple: considering Fickian diffusion in cubical configuration

Osmotic dehydration kinetics of pineapple cubes (15×15×15 mm³) was studied over a range of concentration (40-70°B) and temperature (30-50°C) of osmotic solution. The effective diffusion coefficients for water and solute diffusion were determined, considering pineapple as cubical configuration, assuming osmotic dehydration to be governed by Fickian diffusion. The effective diffusion coefficients for water as well as solute were empirically correlated with concentration and temperature of osmotic solution. A high degree of correlation was observed between predicted and experimental values of the effective diffusion coefficients of water (R²=0.99) as well as solute (R²=0.96).     

A SIMPLE METHOD TO DETERMINE DIFFUSION OF SODIUM IN THE EPIDERMIS OF GREEN OLIVES

The present study reports a simple method, both mathematical and experimental, to determine variable effective diffusion coefficients for sodium through the skins of olives. Skins removed from green olives, variety Arauco (also known as Criolla), were studied using a lye concentration of 2.25% (w/w) of NaOH at 20C. The diffusion of sodium was evaluated through fresh skins and previously alkali‐treated skins. The measured values of effective diffusion coefficients for untreated (fresh) olive skins increased two orders of magnitude during the processing time, from 10^?12 to 10^?10 m²/s. Whereas, the effective diffusion coefficients determined for previously treated olive skins were of the order of 10^?10 m²/s and increased very little with treatment time.     

Effect of Freezing on Diffusion of Ascorbic Acid during Water Heating of Potato Tissue

The effect of freezing on ascorbic acid losses during water heating of potato cylinders at 50°, 65° and 85°C was studied at different periods of time. Loss of ascorbic acid in frozen potato was mainly by diffusion and greater than for fresh potato. The estimated apparent diffusivities of ascorbic acid in frozen potato during water blanching were 13.64 × 10^-10 m²/sec at 50°C, 17.78 × 10^-10 m²/sec at 65°C and 20.30 × 10^-10 m²/sec at 80°C. The activation energy of the diffusion process was 3,007 cal/mol. Ascorbic acid aparent diffusion coefficients in potato tissue with pre-freezing treatment were between 80 and 90% of ascorbic acid diffusion coefficients in water in the 50–80°C range.     

Determination of Sorbic Acid Diffusivity in Edible Wheat Gluten and Lipid Based Films

Edible films using wheat gluten as the structural matrix with or without different lipid components and pure lipid films were tested for sorbic acid retention properties. A diffusion mechanism following Fick's first law was identified. An experimental procedure was developed for determining the diffusivity coefficient of sorbic acid in edible films immersed in an aqueous medium. The effect of film composition and temperature was investigated. The diffusion coefficient of sorbic acid in a gluten based film was 7.6 × 10^?12 m²/sec. The addition of a lipid component such as acetylated monoglyceride led to a 50% reduction in diffusivity. In a pure lipid film such as beeswax the diffusion coefficient of sorbic acid was 2.7 × 10 ^?16m ²/sec. The effect of temperature could be described by an Arrhenius type model, with activation energy ranging from 30.0 to 39.8 kJ/mole.     

Diffusion of Sucrose in Osmo-Dehydrofrozen Apple

Apple parallelepipeds were dewatered by osmosis in sucrose solution at 30°C for 3 h, and at 70°C for 1 h. Dewatered material was air-frozen at ?12, ?20, and ?35°C and stored for 1, 3, and 6 months. After a prescribed time of storage, cryoscopic temperature, amount of non-frozen water, and effective diffusion coefficients were calculated based on sucrose concentration profiles in the frozen material. In frozen, osmotically dewatered apple, mass transfer was very slow. After 6 months of storage, large concentration gradients still occurred in the frozen material. Effective diffusion coefficients, based on sucrose concentration expressed as percent of the total mass of the sample, were statistically not dependent on storage temperature. They were dependent on sucrose concentration and varied from 2·10^?14 m²/s, at high sucrose concentration, to 5·10^?11 m²/s, at low sucrose concentration. On the other hand, effective diffusion coefficients, based on the sucrose concentration in non-frozen water, were dependent on storage temperature and sucrose concentration as well. They were from 1·10^?15 m²/s to 2·10^?12 m²/s.     

Diffusivity of potassium sorbate in κ-carrageenan based antimicrobial film

The diffusion of potassium sorbate incorporated into κ-carrageenan based antimicrobial film was measured at 5 s intervals using a diffusion cell. The kinetics of potassium sorbate release followed Fick's law of diffusion, as shown by diffusional exponent characteristic n-value and high correlation coefficients between experimental and theoretical data. The effects of solution pH at the film surface (3.8, 5.2 and 7.0) and temperature (5, 25 and 40 °C) on diffusion were investigated. Diffusion was found to be unaffected by adjacent solution pH in the range of values tested, but a decrease in temperature from 40 to 5 °C resulted in a reduction of diffusion coefficients from 4.24×10⁻¹³ to 1.29×10⁻¹³ m²/s at pH 5.2.     

Sorption and diffusion properties of volatile phenols into cork

The sorption and diffusion properties of seven common volatile phenols in hydro-alcoholic medium placed in contact with natural cork were investigated to determine the influence of cork closures on the concentration of these compounds in wine. Weighted cork samples were immersed in model wine solutions containing selected concentrations of each compound and were sampled over time. Sorption coefficients ranged between 125 and 306 mg of aroma compound per kg of cork, while diffusion coefficients varied from 0.8 to 4.1 × 10⁻¹¹ m²/s. Sorption isotherms of guaiacol and 4-propylguaiacol, respectively, the lowest and highest sorbed compounds of an homologous series of guaiacol, accurately fit Henry’s model. Hydrophobicity of aroma compounds seems to be a determining factor in both diffusion and sorption. This could indicate a preferential pathway for diffusion through suberin, the more hydrophobic constituent of cork.     

DETERMINATION OF VARIABLE DIFFUSION OF SODIUM DURING DEBITTERING OF GREEN OLIVES

Time‐variable average effective diffusion coefficients of sodium in the skin and flesh were determined using Macroscopic Mass Balances from experimental data obtained during debittering of green olives, variety Arauco at temperatures of 15, 20 and 25C and lye concentrations of 1.50, 2.25 and 3.00% of NaOH. The effective diffusion coefficient of sodium increased with treatment time at both surfaces of the skin, while it varied very little within the flesh, and in many cases, remained almost constant during the debittering process. In general, the diffusion coefficients determined in the present study were within an order of magnitude of 10^?10 m²/s for the flesh during most of the treatment time, while for the skin, they were of the order of 10^?12 m²/s for the initial treatment times. Macroscopic mass balances are a simple mathematical method that can be used in lieu of more common numerical techniques, to evaluate variable diffusion coefficients providing accuracy and greater detail of the whole phenomena.     

Diffusion of calcium gluconate in aqueous solutions of lactose at 298.15 K

Binary mutual diffusion coefficients (interdiffusion coefficients) of calcium gluconate (C₁₂H₂₂CaO₁₄) in water at 298.15 K and at concentrations between 0.001 and 0.0500 mol dm⁻³ have been measured, using a Taylor dispersion method. These data are discussed on the basis of the Onsager-Fuoss model. Based on these data, the equivalent conductance at infinitesimal concentration of the gluconate ion in the studied solutions has been estimated. Through the same technique, ternary mutual diffusion coefficients (D₁₁, D₂₂, D₁₂ and D₂₁) for aqueous solutions containing calcium gluconate and lactose, at T = 298.15 K, and at different carrier concentrations, were also measured. These data permit us to have a better understanding of the structure of these systems and the thermodynamic behaviour of calcium gluconate in different media.     

Apparent coefficient of diffusion of carbon dioxide through samples of cereals and rapeseed

The apparent diffusion coefficients of carbon dioxide (CO₂) through rapeseed, wheat, maize and oats were determined in the laboratory using a specially designed cylindrical diffusion apparatus. The diffusion coefficient was not affected significantly (P > 0.05) by the direction of CO₂ flow in relation to force of gravity. The effect of compaction of wheat (38–42% porosity) on diffusion coefficient was not significant (P > 0.05). Coefficient of diffusion, however, decreased with increasing moisture content of wheat. At 10°C the mean diffusion coefficients of CO₂ through stored seeds were: rapeseed at 8% moisture content, 2.8; wheat at 13% moisture content, 3.5; maize at 14% moisture content, 3.0; and oats at 14.5% moisture content, 3.9 mm²/s.     

MOISTURE TRANSFER PROPERTIES of WILD RICE

Working isotherms for processed wild rice and desorption isotherms for unprocessed wild rice were determined at temperatures ranging from 10 to 43.5°C. the constants for the Guggenheim-Anderson-DeBoer (GAB), Day and Nelson, Chen and Clayton and modified Halsey equations were determined by using a nonlinear optimization technique. the GAB equation showed extremely good fit to the experimental data (less than 5% error). the diffusion coefficients for moisture transport in both broken and whole processed wild rice and for unprocessed wild rice samples were determined at room temperature. the processed broken wild rice kernels had an effective diffusion coefficient of 2.66 × 10^?9 m²/h, whereas the effective diffusion coefficient was 7.08 × 10^?10m²/h for the processed whole wild rice kernels. Unprocessed wild rice had moderate effective diffusivity (1.4 × 10^?9 m²/h). These results predicted quite well the equilibrium water activities and time to equilibrium of wild rice-white rice mixtures using both analytical methods and the finite element method. the transfer of moisture to or from packaged wild rice was also illustrated for different distribution systems.     

Diffusion of carbon dioxide through grain bulks

The diffusion coefficient of carbon dioxide (CO₂) through grain bulks was determined using a transient method with the following variables: (1) grain bulk (wheat, barley, and canola); (2) moisture content (m.c.) (dry, damp, and wet conditions); (3) temperature (5°C, 15°C, 25°C, and 40°C); (4) direction of gas flow (upwards, downwards, and horizontal); (5) porosity (two levels for each grain bulk); (6) grain kernel orientation (vertical and horizontal); (7) initial concentration in the gas chamber (20%, 40%, and 60%); and (8) dockage (0%, 4%, 8%, and 12%). The diffusion coefficients of CO₂ through wheat bulks ranged from 5.9×10⁻⁶ to 7.6×10⁻⁶ m² s⁻¹, through barley bulks from 5.1×10⁻⁶ to 8.4×10⁻⁶ m² s⁻¹, and through canola bulks from 3.7×10⁻⁶ to 5.3×10⁻⁶ m² s⁻¹ for the test conditions studied.Increasing the m.c. decreased diffusion coefficients. An increase in temperature generally increased the diffusion coefficient of CO₂. Diffusion in the downward direction resulted in higher diffusion coefficients. No significant difference in diffusion coefficients was observed between the upward and horizontal directions of flow. An increase in porosity resulted in higher diffusion coefficients. The upward diffusion coefficient of CO₂ was higher for vertical grain kernel orientation than for horizontal kernel orientation for wheat and barley but for canola, the difference between the two kernel orientations was not significant. There was no significant difference in diffusion coefficients for different initial gas concentrations. The diffusion coefficient increased linearly as the dockage was increased.The amount of CO₂ absorbed by barley and canola increased with an increase in m.c. in polynomial fashion. There was no significant difference in the sorption of CO₂ by barley and canola when the temperature of the grain was changed from 15°C to 40°C.     

Chemical and Physical Treatment Effects on Solid-Liquid Extraction of Apple Tissue

Various experimental treatments have been selectively applied to apple tissue in an effort to determine whether a solid-liquid extraction process could be utilized for manufacturing single strength beverage juice. Vacuum impregnation of enzymatic and chemical solutions showed a positive effect on accelerating the rate of diffusion in the tissues studied. The greatest overall effect on increasing the rate of diffusion was caused by a pretreatment with radio-frequency energy. Observed diffusion coefficients were 4.11 × 10^-6 cm²/sec with this treatment, as compared to 1.20 × 10^-6 cm²/sec for the control group of samples. Pretreatment techniques are suggested to enhance the rate of diffusion in apple tissue that may be of commercial value.     

Development of an in-house method for the incorporation of model migrants in polyethylene films and determination of diffusion constants in food

Two methods were tested and compared for the additivation of low density polyethylene (LDPE). The aim was to obtain highly contaminated plastic films to enable the study of migration (diffusion and partition phenomena). One of the methods involved immersion of low density polyethylene (LDPE) films in a concentrated solution of the selected substances. The other method involved achieving close contact of plastic films with a polyethylene wax contaminated with the selected compounds. The PE-wax method provided better results as regards the final concentration and homogeneity of the contaminants in the plastic films (deviations between replicates for each plastic film was lower than 10% for both migrants tested). This method was therefore considered suitable for preparing a homogeneous additive release system. Finally, to test the applicability of the method, concentration profiles were studied in chocolate spread placed in contact with the contaminated films, and diffusion coefficients were estimated in this foodstuff. Estimated diffusion coefficients were 4.6 × 10⁻⁰⁷ cm²/s for DPBD and 3.2 × 10⁻⁰⁷ cm²/s for triclosan in the same conditions.     

Prediction of pH Change in Processed Acidified Turnips

The acetic acid uptake by turnips was studied during an acidification process in containers. The process was successfully described by a Fickian diffusion, using a correlation for the buffer effect. Diffusion coefficients (0.629 to 3.99 × 10^-9 m²/sec) and partition coefficients (0.8 to 1.1) were obtained by optimization of the fit between experimental and theoretical values, using the simplex method. The partition coefficient did not show an evident dependence on temperature, while diffusivity followed an Arrhenius type behavior. The relationship between acid concentration and pH was described using a cubic model with parameters independent of temperature. Results showed that the combination of these models describing the acid diffusion into the food and the buffering effects of the food allowed accurate prediction of pH evolution in the acidification process.     

Mass Transfer Modelling During Osmotic Dehydration of Jumbo Squid (Dosidicus gigas): Influence of Temperature on Diffusion Coefficients and Kinetic Parameters

Mathematical modelling was used to study the effect of process temperature on moisture and salt mass transfer during osmotic dehydration (OD) of jumbo squid with 6% (w v ⁻¹) NaCl at 75, 85 and 95 °C. The diffusion coefficients for moisture and salt increased with temperature. Based on an Arrhenius-type equation, activation energy values of 62.45 kJ mol⁻¹ and 52.14 kJ mol⁻¹ for moisture and salt, respectively, were estimated. Simulations of mass transfer for both components were performed according to Newton, Henderson and Pabis, Page, Weibull and logarithmic mathematical expressions. The influence of drying temperature on the kinetic parameters was also studied. Based on statistical tests, the Weibull and logarithmic models were the most suitable to describe the mass transfer phenomena during OD of jumbo squid.     

Modeling calcium and water intake in threshed corn grain during thermo-alkaline treatment

A mathematical model describing simultaneous solvent diffusion and gelatinization of starch was used to explain the water and calcium absorption in threshed corn grains during the thermo-alkaline treatment. A computer-aided nonlinear optimization technique was used to find the effective diffusion coefficients and the reaction rate constants of water and calcium in threshed corn grains at boiling temperature (92.5 ± 0.3 °C). The mathematical model shows good correlation between measured and predicted values of water and calcium intake. It is concluded that the cooking process is limited by the reaction of starch components with water and calcium. The effective diffusion coefficient for water varied between 1.18 × 10⁻¹⁰ and 1.45 × 10⁻¹⁰ m²/s and for calcium between 8.55 × 10⁻¹⁰and 16.77 × 10⁻¹⁰ m²/s. The diffusion of water and calcium in threshed corn was produced with a reaction rate constants in the range of 6.83 × 10⁻⁴ to 10.4 × 10⁻⁴ s⁻¹ for water and 2.7 × 10⁻⁵–7.6 × 10⁻⁵ s⁻¹ for calcium. According to these effective diffusion coefficient values the diffusive process seems to be slower for water than for calcium. However, the reaction rate constant values are approximately 10 times higher for water than for calcium which may indicate that a higher amount of solvent was linked in the water diffusion process due to the gelatinization. Low concentration of Ca(OH)₂ such as 0.10% did not significantly affect the water diffusion of threshed corn during the cooking process.     

Diffusion of Acetic and Propionic Acids from Chitosan-based Antimicrobial Packaging Films

The diffusion of acetic or propionic acids from thin (44 to 54 μm) chitosan‐based antimicrobial packaging films in which they were incorporated was measured after immersion of the films in water, and the effects of pH (5.7, 6.4, or 7.0) and temperature (4 °C, 10 °C, or 24 °C) on diffusion were investigated. The kinetics of acetic‐ and propionic‐acid release deviated from the Fickian model of diffusion. Diffusion was found to be unaffected by pH in the range of values tested, but a decrease in temperature from 24 °C to 4 °C resulted in a reduction of diffusion coefficients from 2.59 × 10^?12 m².s^?1 to 1.19 × 10^?12 m².s^?1 for acetic acid and from 1.87 × 10^?12 m².s^?1 to 0.91 × 10^?12 m².s^?1 for propionic acid. The effect of temperature on diffusion was well (r² > 0.9785) described by an Arrhenius‐type model with activation energies of 27.19 J.mole^?1 (acetic) and 24.27 J.mole^?1 (propionic). Incorporation of lauric acid or essential oils (cinnamaldehyde or eugenol) into the chitosan film at the time of preparation produced a subsequent reduction in the diffusion of acetic or propionic acid, and maximum effects were obtained with lauric acid and cinnamaldehyde incorporated to final concentrations of 1.0% and 0.5% (w/w), respectively.