A mathematical model of the effect of pH and food matrix composition on fluid transport into foods: An application in gastric digestion and cheese brining

The question of bioaccessibility of nutrients within a food matrix has become of increasing interest in the fields of nutrition and food science as bioaccessibility is the precursor to bioavailability. By analyzing the propagation of the wetting front of acidic water in raw carrot core and Edam cheese as model systems, we show that the diffusion of the acidic water is dependent on the pH of the gastric fluid and the food matrix. In addition, we demonstrate that the diffusion of NaCl during cheese brining is also dependent upon the concentration of the NaCl. This demonstrates that Fickian diffusion, along with a concentration dependent diffusion coefficient, is a valid model for describing concentration profiles in multiple food systems.Utilizing the diffusion rates found at various pH levels (1.50, 2.00, 3.50, 4.30, 5.25 and 7.00), we developed a model to describe the measured non-linear rate of soluble solid loss during digestion at various constant pH levels. Additionally, we have developed a model to predict the likely rate of soluble solid loss during digestion in the stomach where pH decreases with time. This model can be used to help understand and optimize the relationship between food structure/composition and food degradation in the human stomach, which may help in the development of novel foods with desired functionality.     

An absorption model for the thickness effect in hydrophilic films

The permeability parameters for moisture transmission through hydrophilic films are well known to be thickness dependent, this effect appearing in permeability studies based on diffusion models. In our model we assume that, besides diffusion, some of the water vapour of the diffusion flux is removed by the hydrophilic components of the films. This water is immobilized and becomes hydration water of the hydrophilic molecules. This paper describes a diffusion–adsorption model, with thickness‐independent parameters, which explains this phenomenon.     

Oscillatory water sorption dynamics of bread crust

Step-wise and oscillatory gravimetric sorption experiments were used to study the equilibrium and dynamic water sorption behavior of bread crust. Water uptake kinetics is strongly related to crispness retention of composite products consisting of a dry crispy part and a more humid and soft part. We show that oscillatory sorption experiments of bread crusts could be very well described by a Fickian diffusion model. Many essential features, such as the shape of the oscillatory sorption curves, and the dependency of water sorption rates on time, time-interval between successive step-wise changes in relative humidity, and particle size are understood now to a great detail.     

Modeling water sorption dynamics of cellular solid food systems using free volume theory

Water sorption and dynamical properties of bread crust were studied using gravimetric sorption experiments. Water uptake and loss were measured while relative humidity (RH) was step-wise in- or decreased. Experimental results were compared with Fickian diffusion models and empirical models like the exponential and power-law model. From comparison of experimental sorption curves and the power-law model for short times it followed for all bread crust that the diffusional coefficient n is close to one. It turned out that this is not due to so-called case II diffusion and water transport that is limited by relaxation of the solid material but due to the fact that RH did not instantaneously but gradually increased to the set value.Sorption curves of isotherm experiments could be best described by the Fickian diffusion model for low RH and by the exponential model for large RH. Transport rates depend on moisture content and show a maximum around RH = 0.7, corresponding to a water mass fraction ω₁ = 0.12. Diffusion rates could be well described by free volume theory up to the maximum, but this theory could not explain the strong decrease at higher ω₁. Indications for a local glass-rubber transition at room temperature were found near a water mass fraction ω₁ ≈ 0.09. This corresponds very well to the start of the crisp–non-crisp transition as measured by a sensory panel, but not to the glass-rubber transition at ω₁ ≈ 0.12 as measured by other techniques like Differential Scanning Calorimetry. So it seems that more than one glass-rubber like transitions may be important to describe the properties of heterogeneous cellular food systems.     

New methods to assess water diffusion in amorphous matrices during storage and drying

Water diffusion coefficient is an important parameter for food processing and stability, strongly influenced by the composition and the physical state of the matrix (amorphous glassy or rubbery/crystalline). In this study, two different methods to assess water diffusion in amorphous matrices were compared. First, an automatic sorption device was used to measure the water sorption kinetics of powders of maltodextrin DE21 and DE47 with defined shapes when equilibrating at different air relative humidity (0–60% at 25 °C). Calculation of water diffusion coefficients was done according to Crank’s and Weibull’s models, and it was not possible when powders undergo glass transition. In the second part of the study a thin film dryer was used to assess the drying kinetics of aqueous solutions of maltodextrin (DE 6-12-29-40). The Yamamoto’s model allowed calculating water diffusion as a function of water content and temperature, above and below glass transition temperature.     

Preventing Moisture Transfer in a Composite Food Using Edible Films: Experimental and Mathematical Study

ABSTRACT: Water barrier properties of various edible films: acetylated monoglycerides (AMG), dark chocolate (DC), and wheat gluten (WG) were evaluated through water sorption isotherm, diffusivity, and permeability measurements. Diffusivity and sorption isotherm were then used in a mathematical model for predicting moisture transfer evolution in composite foods. It was successfully validated in agar gel/sponge-cake systems with the studied films at the interface. Using model predictions and relevant permeability measurement comparisons, AMG appeared to be the most efficient water vapor barrier films. Acetylation of monoglycerides seemed to be favorable to improve their water vapor transfer resistance mainly by reducing water solubility and despite a slight increase of water vapor diffusivity.     

Relations between sensorial crispness and molecular mobility of model bread crust and its main components as measured by PTA,DSC and NMR

Consumer appreciation of brittle cellular foods, like bread crusts, depends on textural properties such as crispness. This crispy character is lost above a certain water activity. It is not known what exactly is happening in these crusts when water enters. So is it unclear whether it is the change in the starch or the gluten that initiates the loss of crispness with ageing time. In this paper the effect of water on the glass transition of model bread crusts was studied using two complementary techniques: phase transition analysis (PTA) and temperature modulated differential scanning calorimetry (TMDSC). The mobility of water was studied with nuclear magnetic resonance (NMR). The results were compared with sensory data. Bread crusts prepared with different types of flour were tested to evaluate the effect of flour composition on the crispness of model crusts equilibrated at different relative humidities. In addition the single flour components starch and gluten were studied. Sensory crispness scores decreased with increasing a_w from 0.55 upwards. At a_w 0.70 sensory crispness was completely lost. Both DSC and PTA showed a transition point at an a_w of 0.70–0.75. NMR gave a transition point in the mobility of the protons of water at a_w 0.58. This supports the hypothesis that loss of crispness starts as a result of processes at a molecular level, before the macroscopic glass transition. This also suggests that the presence of water that is not directly attached to the solid matrix causes the loss of crispness at low a_w. At higher a_w increased mobility of the macromolecules will start to play a role. NMR experiments with the separate flour components indicate that the T₂ transition point in starch samples occurs at a lower RH than for gluten. This could imply that starch loses crispness at lower a_w than gluten. Increased mobility of small components and side chains might induce increased energy dissipation upon deformation of the material resulting in less available energy for fracture propagation and with that in a less crispy product.     

Osmotic Dehydration Behavior of Red Paprika (Capsicum Annuum L.)

ABSTRACT: Osmotic dehydration of red paprika was studied using a combined sucrose (5 to 45 g/100 g) and sodium chloride (0 to 15 g/100g) solution. The effective diffusion coefficients for water and solute were determined using the slope method based on the Fickian diffusion model. The effects of concentration of sucrose, sodium chloride and their complex interaction on water and solute diffusion coefficients as well as on equilibrium moisture and solid contents were studied using central composite rotatable design of experiments. The graphical optimization showed that at optimum conditions (sucrose concentration and sodium chloride concentration were 21.86 g/100 g and 2.02 g/100 g, respectively), the following criteria were achieved: water diffusion coefficient (D_ew) 0.80 × 10⁻⁹ m²/s, solid diffusion coefficient (D_es 0.82 × 10⁻⁹ m²/s, equilibrium moisture content (m∞) 6.85 kg/kg, and equilibrium solid content (s∞) 2.00 kg/kg.     

Water interactions and microstructure of chitosan-methylcellulose composite films as affected by ionic concentration

Edible films based on high molecular weight chitosan (CH) and methylcellulose (MC) were obtained by mixing different ratios (0:1, 0.5:1.5, 1.0:1.0, 1.5:0.5 and 1:0) of the biopolymers in two solvent conditions (0.95 and 6.85 mmol of ions per g polymer). In order to characterize the dry films, water sorption isotherms, water vapour permeability and film microstructure were evaluated. Water vapour permeability of CH-MC composite films was significantly affected by both the CH-MC ratio and the ionic concentration in the matrix. This can be attributed to the influence of ions on polymer chain packaging during the film formation and their role in the water uptake capacity of the films which affects the water transport properties.     

Accelerated Mass Transfer During Osmotic Dehydration of High Intensity Electrical Field Pulse Pretreated Carrots

High intensity electrical field pulse (0.22 to 1.60 kV/cm) pretreatment was tested to accelerate the osmotic dehydration of carrot. Applied energy in the range of 0.04 to 2.25 kJ/kg, increased cell disintegration index in the range of 0.09 to 0.84 with < 1 °C rise in the product temperature. The effective diffusion coefficients of water and solute, determined using a Fickian diffusion model, increased exponentially with electric field strength according to D = A exp(-B/E). The rise in effective diffusion coefficient may be attributed to an increase in cell wall permeability, facilitating transport of water and solute. Such increase was evidenced by cell disintegration index and softening of product.     

Agglomeration of durum wheat semolina: Thermodynamic approaches for hydration properties measurements

In the manufacturing process of pasta or couscous, durum wheat semolina agglomeration comprises successive steps, in particular a wetting and hydration stage. In this step, interactions between water molecules and semolina grains contribute to the agglomeration properties. Hydration properties of semolina have been recognised to play an important role in agglomeration.The hydration properties of semolina have been characterised using various methods which can be divided into 2 groups according to the water addition: liquid or vapour. Several parameters can be used to describe hydration properties and hydration mechanisms, such as: water sorption capacity, hydration kinetics, diffusion of water within the solid (swelling, dissolution, solid-water affinity and thermodynamic properties).In this study, sorption isotherms and diffusion coefficients have been determined by gravimetric method in specific conditions. The immersion enthalpy of the semolina and its main sub-components, starch and gluten have been measured by mixing micro-calorimetry. Hydration thermodynamic properties, Gibbs free energy, enthalpy and entropy, were calculated from these experimental data. It was found that hydration by vapour or liquid water is an exothermic reaction.The determined diffusion coefficient was used to estimate the stabilisation time of water within the solid. Being high at low relative humidity, the diffusion coefficient decreases during progressive saturation of solid sites. Sorption energy and solid-water affinity yield information about the type of interaction between water molecules and solid sites. The drop in the sorption energy during the increase in water content can be attributed to a decrease in solid-water interactions. The hydration energy of durum wheat semolina in vapour or liquid water was found to be low. This corresponds to the energy input needed to generate contact between water and grain surface and for mixture homogenisation.     

Oil Migration in 2-Component Confectionery Systems

ABSTRACT:  Oil migration from high oil content centers into chocolate coatings results in product quality changes. The objective of this study was to monitor and model peanut oil migration in 2-layer systems of increasing phase complexity. Three 2-layer systems were prepared: peanut oil/cocoa butter; peanut butter paste/cocoa butter; and peanut butter paste/chocolate. Magnetic resonance imaging was used to measure liquid oil signal as a function of position over a storage time of 193 days at 25 °C. The 3 types of samples exhibited appreciably different patterns of oil migration. The peanut oil/cocoa butter samples had mass transfer typical of oil being absorbed into a liquid/solid region. The peanut butter paste/cocoa butter magnetic resonance profiles were characterized by mass transfer with a partition coefficient greater than unity. The peanut butter paste/chocolate samples exhibited a time-dependent peanut oil concentration at the interface between the chocolate and peanut butter paste. The spatial and temporal experimental data of the peanut butter paste/chocolate samples were modeled using a Fickian diffusion model, fitting for the effective diffusivity. Values of the diffusivity for the 6 chocolate formulations ranged from 1.10 to 2.01 × 10⁻¹³ m²/s, with no statistically significant differences.     

小米挤压膨化产品的吸湿动力学研究

挤压膨化食品极易从周围环境中吸收水分,导致脆性丧失;对吸湿动力学过程的了解有助于选定合适的包装材料和存储环境。将4种形态的小米挤压膨化产品在不同温度、相对湿度下吸湿,并对吸湿过程进行模拟分析。与扩散模型、Peleg模型相比,Weibull模型最能预测小米挤压膨化产品的吸湿行为。根据Weibull模型,同一温度下,初始吸湿速率随相对湿度增大而近似线性增大。同一相对湿度下,总体吸湿速率随温度升高呈近似线性增大。温度越低、相对湿度越高,平衡水分越高。不同样品间的平衡水分差异较小,而吸湿速度差异明显,尤其在低温—低相对湿度条件时。外层气孔结构的差异可能是样品间初始吸湿速率差异的主要原因。     

Effect of colloidal properties of oil-in-water emulsions on ethanol liquid–vapour partition

Ethanol vapour–liquid partition was studied in oil-in-water emulsified model systems prepared with two different emulsifiers (β-lactoglobulin (β-Lg) and Tween 20) and 2% w/w of ethanol at varying oil quantity (10–75% w/w). The role of some structural and physical properties of the emulsified system on the thermodynamic equilibrium of ethanol in the vapour phase was studied by dispersion degree, interfacial area and viscosity evaluations. Results of the ethanol vapour pressure (P_e) of emulsified systems are discussed on the basis of those obtained in hydro-alcoholic models having composition similar to that of the aqueous phase.Composition and structural characteristics of emulsified model systems resulted to affect liquid–vapour partition of ethanol. In particular, oil content affected P_e as a consequence of the variation of both the oil/water weight ratio and the physical properties of the dispersed state. The lower P_e and partition coefficient (K_e) values of emulsified systems as compared with those of aqueous models at similar ethanol concentration could be attributed mainly to ethanol adsorption/retention phenomena taking place during emulsification process at interfacial level. This result is the consequence of the surface free energy of ethanol which leads it to easily to adsorb at interfaces of phases characterised by different polarity (water–air, oil–water). The presence of Tween 20 and β-Lg in aqueous systems, and in particular the former one, significantly increased the volatility of ethanol. On the contrary, their use in the preparation of the emulsified systems resulted to influence the ethanol liquid–vapour partition only at oil concentration above 40% w/w, even if they affected their structural properties and, in turn, their viscosity. Taking into account the marked effects of the presence of ethanol itself on the structural and rheological properties of the emulsified system, results of the present study could be of interest in the development and optimisation of new formulated emulsified foods and beverages containing this alcohol as well as their stability and sensorial acceptability.     

Removal of polycyclic aromatic hydrocarbons from water by migration into polyethylene

Water was spiked with three polycyclic aromatic hydrocarbons (PAHs) and filled into a steel diffusion chamber. Low-density polyethylene sheet combined of five polyethylene foils was used as a partition in the chamber. Depth of PAHs migration into the sheet was followed for 143 h, using high performance liquid chromatography with selective fluorimetric detection after extraction of PAHs from the foils peeled off. On the basis of the results obtained, the process of PAHs migration into PE was characterised as a one-dimensional diffusion into polyethylene bulk. The diffusion coefficients were calculated for individual compounds using the second Fick law. It was concluded that PAHs are primarily adsorbed on the polyethylene surface with subsequent migration into bulk polymer. Transportation of PAHs through the bulk can be described satisfactorily by Fickian laws of diffusion and is consistent with the theory of the depth adsorption of PAHs in polyethylene.     

Transport parameters for aroma compounds through i-carrageenan and sodium alginate-based edible films

In an effort to produce more environmentally friendly materials, renewable and biodegradable biopolymers have been investigated as coating materials. Edible films obtained from i-carrageenan and sodium alginates have good mechanical characteristics, are emulsion stabilizers, and decrease oxygen transfer. The addition of lipids to form emulsified films decreases the water vapour transfer and could be used to encapsulate active substances or aroma compounds. The aim of this work was to measure permeability, sorption and diffusion coefficient of the n-hexanal and D-limonene aroma compounds through emulsified (wf) and non-emulsified (wof) i-carrageenan and sodium alginate-based films to finally compare with estimated permeability calculated from sorption and diffusion coefficients. Sorption results are mainly governed by the physico-chemical characteristics of the aroma compound. The diffusion coefficient presents a strong dependence on the molecular size of the aroma compound. Differences found in permeability determinations are mainly due to the sorption process which modifies the film structure.     

Alternative fatty food simulants for migration testing of polymeric food contact materials.

The amounts of substances migrating from plastics into foodstuffs with high fat contents are in most cases higher than in foodstuffs with water contents. This increase in migration commonly is due to the higher solubility of the migrating organic compounds in fat compared to water. The increase in migration is not necessarily due to an increase in the substance's diffusion coefficient due to interactions between the fat and the plastic as is often assumed. Ethanol is a good simulant for fatty foods because it has little interaction with many plastics, e.g. polyolefins, migrants are readily soluble in it, and because it is easy to work with analytically. The utilizable limits of ethanol and ethanol/water mixtures as food simulants are developed from the physical background of diffusion. The use of ethanol and ethanol/water mixtures is supported by published experimental migration results.     

The importance of glassy biopolymer components in food

The glassy state is not just important in low moisture and frozen foods, where it influences the physical and chemical stability and the crispness of some foodstuffs: glassy biopolymer components affect the physical properties of most food systems and low moisture biological systems. Glassy foods are not always fragile and crispy in texture. Therefore, the relationship between mechanical behaviour and molecular dynamics in low-moisture biopolymer systems will be considered. Vitrification of a macromolecular system only requires a mutual fixation of a certain proportion of the chain segments. The higher the rigidity of the chains, the lower the number of the chain segments which must be mutually fixed to vitrify the system. Mechanical stress can help the thermal movement to re-activate the motion of mutually fixed segments and involves a long deformation of glassy material. The stress required to effect long deformation presumably increases up to the strength of the material as the temperature decreases from the glass transition to the temperatures of brittleness (crispness). Vitrification of a loaded viscoelastic system results in an accumulation of mechanical energy (memory effect), which can be released (elastic recovery) above the glass transition temperature due to heating and or addition of a plasticizer. The effects of memory and elastic recovery could be of particular importance for producing foodstuffs which change their form, e.g. self-stirring dry foods and drinks on re-hydration in hot water. The importance of glassy biopolymer ingredients from the viewpoint of food formulation and processing is discussed.     

In vivo stratum corneum over-hydration and water diffusion coefficient measurements using opto-thermal radiometry and TEWL Instruments

Skin over-hydration is a common problem that affects many people who wear incontinence pads or diapers. The aim of this study is to develop a new method for stratum corneum (SC) over-hydration and SC water diffusion coefficient measurements using opto-thermal transient emission radiometry (OTTER) and evaporimetry. With OTTER, we can measure the SC surface hydration and hydration gradient. With evaporimetry, we can measure the time-dependent evaporative drying curves of water vapour flux density (WVFD). The combination of hydration results and WVFD results can yield information on the SC water diffusion coefficient and how it depends on the SC surface hydration level. The results show that SC water diffusion coefficient is non-linearly proportional to the SC surface hydration level. The results also show strong correlations between evaporative drying flux measured using the Evaporimeter and surface hydration estimated from OTTER measurements.     

Sensory Crispness of Crispy Rolls: Effect of Formulation, Storage Conditions, and Water Distribution in the Crust

ABSTRACT:  Crispness is an important sensory quality parameter that strongly influences the acceptability of cellular solid foods such as the crust of many types of breads. Crispness of the bread crust depends particularly on its water content. In this study, the relationship between sensory crispness of crispy rolls and the average water content of the crust was studied for different bread formulations (control, amylase, glucose-oxidase, and protease) and storage conditions (40% and 80% RH). From the different formulations used, only protease treatment increased the crispness of the crust and its retention at both storage conditions. The positive effect of the protease treatment was due to a lower water content of the crust of these breads compared to the other formulations. The relationship between sensory attributes, formulation, and storage conditions was found to be dominated by the dependence on storage conditions. When combining data for low and high humidity storage it showed that crusts with equal water contents could exhibit different scores for crispness. The results led to the hypothesis that a gradient of water content exists within the crust. At high humidity, the crust will take up water from both crumb and environment and a relative smaller gradient of water will exist within the crust. At low humidity on the other hand, the crust will take up water from the crumb only, resulting in a larger gradient of water within the crust.