Prediction of the freezing point of multicomponent liquid refrigerant solutions

The freezing point is one of the most critical properties required to complete the mathematical formulation related to the transport phenomena involved in the immersion chilling and freezing (ICF) of foods. Unfortunately, data for ternary and higher order systems are scarce. The aim of this work was to verify the validity of an excess Gibbs energy model for predicting the freezing point of multicomponent mixtures of electrolytes and non-electrolytes, considering the processing conditions used in immersion chilling and freezing of foods. The extended UNIQUAC model was used. Data obtained from literature corresponding to freezing points of the ternary systems: NaCl-KCl-H₂O, NaCl-CaCl₂-H₂O, NaCl-MgCl₂-H₂O and NaCl-EtOH-H₂O, were compared with predicted values. The model accuracy was satisfactory, the highest absolute deviation being smaller than 1.71 °C for the 378 data compared.     

Interaction between copper chloride and caffeine as seen by diffusion at 25 °C and 37 °C

A Taylor dispersion method is used to measure ternary mutual diffusion coefficients (D₁₁, D₂₂, D₁₂ and D₂₁) for aqueous solutions of CuCl₂ (1) + caffeine (2) + H₂O-(3) at 25 °C and 37 °C at carrier concentrations from (0.000 to 0.020 mol dm⁻³), for each solute, respectively. The results are compared with these obtained for the binary systems, that is, CuCl₂ (1) + H₂O (2) and caffeine (1) + H₂O (2), also reported here. From these data it is possible to make conclusions about the influence of the caffeine solutes in diffusion of copper chloride.     

Ternary diffusion coefficients of nickel chloride plus theophylline plus water at 298.15 K

Ternary mutual diffusion coefficients (D₁₁, D₂₂, D₁₂ and D₂₁) for aqueous solutions containing nickel chloride and theophylline (THP), at T = 298.15 K, and at different carrier concentrations were measured by using the Taylor technique. The results are compared with those obtained for the binary systems H₂O–NiCl₂ and H₂O–theophylline, already published. These data permit us to have a better understanding of the structure of this ternary system and its thermodynamic behaviour. For example, it is possible to take conclusions about the influence of this electrolyte in diffusion of THP, and to estimate some parameters, such as the number of moles of each component transported per mole of the other component driven by its own concentration gradient.     

PFG-NMR self-diffusion in casein dispersions: Effects of probe size and protein aggregate size

The self-diffusion coefficients of different molecular weight PEGs (Polyethylene glycol) and casein particles were measured, using a pulsed-gradient nuclear magnetic resonance technique (PFG-NMR), in native phosphocaseinate (NPC) and sodium caseinate (SC) dispersions where caseins are not structured into micelles. The dependence of the PEG self-diffusion coefficient on the PEG size, casein concentration, the size and the mobility of casein obstacle particles are reported. Wide differences in the PEG diffusion coefficients were found according to the casein particle structure. The greatest reduction in diffusion coefficients was found in sodium caseinate suspensions. Moreover, sodium caseinate aggregates were found to diffuse more slowly than casein micelles for casein concentrations >9 g/100 g H₂O. Experimental PEG and casein diffusion findings were analyzed using two appropriate diffusion models: the Rouse model and the Speedy model, respectively. According to the Speedy model, caseins behave as hard spheres below the close packing limit (10 g/100 g H₂O for SC (Farrer & Lips, 1999) and 15 g/100 g H₂O for NPC (Bouchoux et al., 2009)) and as soft particles above this limit. Our results provided a consistent picture of the effects of diffusant mass, the dynamics of the host material and of the importance of the casein structure in determining the diffusion behavior of probes in these systems.     

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.     

Determination of aroma compound diffusion in model food systems: Comparison of macroscopic and microscopic methodologies

Diffusion properties at macroscopic and microscopic scales for three aroma compounds (in solution and gel systems) were characterized using three different methodologies: the diffusion cell and the Volatile Air Stripping Kinetic methods for the determination of apparent diffusion coefficients and the pulsed-field-gradient Nuclear Magnetic Resonance method for the determination of self-diffusion coefficients. The accuracy of the methods was established by comparing ethyl hexanoate diffusion coefficient in water or D₂O solution and in 1%-agar gel system at 25 and 30 °C. The robustness of the three methodologies was also investigated in 1%-iota-carrageenan system with different NaCl content leading to gel strengthening.     

Development of a Mathematical Model for MAP Systems Applied to Nonrespiring Foods

ABSTRACT A mathematical model for gas diffusion processes in MAP systems was built. The model was applied to MAP systems containing CO₂, O₂, and N₂ with nonrespiring foods. The validation study was done with gelatin, and simulation trials were carried out utilizing Hake (Merluccius australis) fillets. Experimental results confirmed the proposed mathematical model and its numerical solution. The prediction errors obtained in the validation study were under 5%; the same was true with the simulation trials whose errors were always lower than 5%. Both the simulation trials and validation study demonstrated that MAP systems reach equilibrium after a short period of time if film permeability is low.     

A Method for the Determination of Diffusion Coefficients of Food Components in Low- and Intermediate Moisture Systems

A simple set-up to measure translational diffusion of components in low moisture systems is described. The tracer technique was tested on the diffusion of ¹⁴C-labeled tripalmitin and palmitic acid in a model system containing paraffin oil, microcrystalline cellulose and gum arabic. Different methods to evaluate the apparent diffusion coefficients from the experimental diffusion curve were compared. Good results were obtained using a curve-fitting procedure based on the sum of least squares. The technique appears to be suitable for measuring diffusion coefficients up to 10^?9 cm²/sec. The procedure offers the possibility to quantify the mobility of chemical components in dried foodstuffs in order to elucidate the mechanisms and kinetics of reactions occurring during storage.     

Numerical modelling of conjugate heat and mass transfer during hydrofluidisation food freezing in different water solutions

A novel method of hydrofluidisation food freezing is numerically investigated in this paper. This technique is based on freezing small food products in a liquid medium under highly turbulent flow conditions when the heat transfer coefficient is higher than 1 000 W⋅m⁻²⋅K⁻¹, which depends on the operating and flow conditions. A numerical model was developed to characterise the freezing process in terms of the heat transfer and diffusion of liquid solution components into the food product. The study investigates the freezing process of spherical samples in binary solutions of ethanol (30%) and glycerol (40%) and ternary solution of ethanol and glucose (15%/25%). The developed model was employed to determine the concentration of the liquid solution in food samples and to quantify the effect of sample size, heat transfer coefficient, solution temperature and concentration on the process. The food sample size varied from 5 to 30 mm, and the heat transfer coefficients varied from 1 000 to 4 000 W⋅ m⁻²⋅ K⁻¹. The results confirm that a freezing time of 15 min for 30 mm diameter samples or less than 1 min for 5 mm diameter samples can be achieved with the hydrofluidisation method. The solution uptake was influenced by the solution type, sample size and process parameters and varied from 8.9 to 35 g of solute per kg of product for ethanol-glucose and glycerol solutions, respectively. This paper quantifies the advantages and possible limitations of hydrofluidisation, which has not yet been entirely studied, especially in terms of the mass absorption of different solutes.     

Mass transport analysis in perforation-mediated modified atmosphere packaging of strawberries

A space-and-time dependent mathematical model was developed to predict O₂, CO₂, N₂ and H₂O concentration in perforation-mediated polymeric packages during cold-storage of strawberries. The numerical solution of the corresponding mathematical model was obtained by applying the finite element method (FEM). The problem was solved in a domain corresponding to the headspace of a package augmented by the total void spaces of the contained bulk produce and for realistic boundary conditions. Transport of O₂, CO₂, N₂ and H₂O was modelled based on Maxwell–Stefan equations for gas transport through packaging’s headspace and on Fick’s law for diffusion through the micro-perforated packaging. The model predictions were tested against published experimental data of O₂ and CO₂ concentrations in modified atmosphere packaging storage of strawberries and the agreement is satisfactory. As for reaching the recommended in the literature gases concentrations for strawberry storage, the model predictions revealed that the tested micro-perforated polypropylene packaging combined with the adopted storage conditions are marginally adequate. To this end, the theoretical findings are suggestive of improvements, in terms of material properties, especially with regard to the permeability of the polymeric packaging film.     

Dual mode diffusion and sorption of sodium chloride in pre-cooked egg white

The concentration profiles of NaCl by the one-dimensional diffusion in pre-cooked EW (egg white) were obtained at 5-80 °C. D's (Fick's diffusion coefficients) estimated at respective concentrations of NaCl in EW showed peaks at a certain NaCl concentration in the substrate. The peak became prominently high with the increase in temperature. These variations were interpreted in terms of the dual mode sorption and diffusion theory, which was successfully applied to the diffusion behavior of NaCl in Japanese radish. In EW, the water swollen protein phase coexists with the dispersed liquid water phase. It is in the former phase where the diffusion rate in EW is determined via the dual mode mechanism. By applying the theory, thermodynamic diffusion coefficients, D_T(p), of the partitioned species at respective temperatures were found to be smaller than those, D_T(L), of the Langmuir sorption species. The variations of D with peaks were interpreted with these two D_T's and equilibrium parameters of the two species. The sorption isotherms of NaCl by EW were found to be slightly convex upward at low NaCl concentrations, which were successfully interpreted by considering the two phases mentioned above and the equilibrium parameters for the partitioned and Langmuir species.     

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.     

Transport phenomena in immersion-cooled apples

The effect of immersion chilling and freezing (ICF) process parameters (solution temperature, concentration and composition, initial food temperature) on heat and mass transfer was studied on apple cylinders dipped into a sodium chloride aqueous solution, with particular emphasis on the unsteady-state period (first hour of treatment). Food behaviour was characterized for various thermal processes; the levels of salt impregnation in chilling and supercooling conditions, at 2 °C and −10 °C, respectively, were similar (3% i.m. after 1 h of processing) and much higher than in freezing at −17.8 °C (0.6% initial mass for the same processing time). Further control of solute entrance in freezing conditions could be achieved through food surface treatments, including precoating with cold water before ICF; use of a complex immersion solution containing a high molecular weight of solute; quick freezing of the outer food layer. Above all, the frozen water fraction inside the food was found to be an important factor governing solute entrance in freezing conditions.     

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.     

Estimation of Heat and Mass Transfer Coefficients During Air-Freezing of Cucumber

Freezing of foods involves coupled heat and mass transfer. It is essential to optimally design the freezing equipment and maximise the efficiency of the freezing process. Therefore, it is necessary to estimate the heat and mass transfer coefficients. In this study, the surface heat and mass transfer coefficients were estimated employing the Hilbert equation as well as the corresponding thermal and diffusive boundary layers during freezing of unpeeled cucumber at low air temperatures (?10 to??18 and??25°C). The estimated mean heat transfer coefficients ranged from 10.99 W m^?2 K^?1 for 0.5 m s^?1 up to 40.07 W m^?2 K^?1 for 5.0 m s^?1. The respective mass transfer coefficients ranged from 8.98 up to 32.40 m s^?1. The estimated heat transfer coefficients were compared with the respective ones calculated from Dincer and Dincer and Cengeli during air-cooling (22 to 2°C) of unpeeled cucumbers of similar size as well as other agricultural cylindrical products.     

液体浸渍冷冻对鲟鱼贮藏过程中品质的影响

研究新兴低温冻结技术液体浸渍冷冻对鲟鱼贮藏期品质的影响,分析比较液体浸渍冷冻和传统空气冷冻处理后的鲟鱼在贮藏期的品质变化,并对多个指标进行了检测分析。结果表明,液体浸渍冷冻处理的鲟鱼冷冻速率是传统空气冷冻的12.47倍,经过液体浸渍冷冻的鲟鱼其肌纤维受到的破坏较空气冷冻小,贮藏过程中鲟鱼的回复性与L*值均较空气冷冻高(P0.05),二者挥发性盐基氮值和过氧化值的变化趋势也具有显著性差异(P0.05)。因此,液体浸渍冷冻能够更好地保持鲟鱼原有的品质,可在鲟鱼贮藏保鲜过程中加以利用。     

Solubility of sodium and potassium iodates in saturated salt solutions

The determination of the solubilities of KIO₃ and NaIO₃ in saturated NaCl solution at 0, 10, 20 °C were carried out in two ternary systems KIO₃–NaCl–H₂O and NaIO₃–NaCl–H₂O. Saturated KIO₃ and NaIO₃ solutions were prepared and NaCl was added to saturation. Iodate concentrations were measured using standardized sodium thiosulphate. The solubilities of KIO₃ and NaIO₃ are temperature sensitive over the range 0 °C to 20 °C (unlike NaCl). Iodate solubility was much lower in saturated NaCl than that of deionised water. In saturated NaCl at 10 °C, for example, NaIO₃ was 19% and KIO₃ was 15% the solubility of that found in deionised water at the same temperature.     

浸渍式快速冻结技术的研究现状及发展前景

浸渍式快速冻结是一种高效的冷冻加工方式,以其冻结速度快、耗能少、产品质量好等优点展现出可观的发展前景。阐述了浸渍式快速冻结的原理及特点,分析了浸渍式快速冻结在食品加工工业中的应用以及存在的问题,综述了浸渍式快速冻结的未来发展趋势。     

Ethylene production,respiration and gas exchange modelling in modified atmosphere packaging for banana fruits

A mathematical model was developed from experimental measurements to describe the evolution of the O₂, CO₂ and ethylene in a modified atmosphere packaging system for Cavendish bananas. The respiration and ethylene production in the fruits were experimentally obtained from a closed system method and then represented by Michaelis–Menten equations of enzyme kinetics. The gas transfer through the packaging was described by a Fick's diffusion equation, and the temperature dependence was represented based on the Arrhenius law. The model was validated by packaging the fruit in perforated bags of polypropylene and low density polyethylene at 12 °C for a period of 8 days. With the developed model it was possible to satisfactorily describe the experimental evolution of the gas content in the headspace of the packages, obtaining coefficients of determination (R²) of 0.93 for the O₂ levels, 0.90–0.91 for the CO₂ levels, and 0.89–0.93 for the ethylene levels.     

Thermophysical Properties of SweetPotato Puree at Freezing and Refrigeration Temperatures

The thermophysical properties (initial freezing point, unfreezable water, enthalpy of freezing, and specific heat) of alginate-restructured sweet potato (SP) puree at freezing and refrigeration temperatures were determined using differential scanning calorimetry. Restructuring of SP puree increased the amount of unfreezable (bound) water in the puree from 0.44 g H₂O/g solids to about 0.56 g H₂O/g solids and reduced the freezing point from ?2.5 to ?3.2°C. During freezing (or melting), the specific heat increased from about 1.9 to 90 kJ/kg. After freezing, the specific heats of restructured and nonrestructured SP puree were respectively 3.695 and 3.404 kJ/kg. Between 358 and 403 kJ/kg of heat have to be removed when SP puree (at 20°C) is to be frozen to ?40°C.