Analytical and numerical solutions of pore formation in elastic food materials during dehydration.

In this paper, we describe a model for pore formation in food materials during drying. As a proxy for fruits and vegetables, we take a spherical hydrogel, with a stiff elastic skin, and a central cavity filled with air and water vapour. The model describes moisture transport coupled to large deformation mechanics. Both stress and chemical potential are derived from a free energy functional, following the framework developed by Suo and coworkers. We have compared Finite Volume and Finite Element implementations and analytical solutions with each other, and we show that they render similar solutions. The Finite Element solver has a larger range of numerical stability than the Finite Volume solver, and the analytical solution also has a limited range of validity. Since the Finite Element solver operates using the mathematically intricate weak form, we introduce the method in a tutorial manner for food scientists. Subsequently, we have explored the physics of the pore formation problem further with the Finite Element solver. We show that the presence of an elastic skin is a prerequisite for the growth of the central cavity. The elastic skin must have an elastic modulus of at least 10 times that of the hydrogel. An initial pore with 10% of the size of the gel can grow to 5 times its initial size. Such an increase in porosity has been reported in the literature on drying of vegetables, if a dense hard skin is formed, known as case hardening. We discuss that models as presented in this paper, where moisture transport is strongly coupled to large deformation mechanics, are required if one wants to describe pore/structure formation during drying and intensive heating (as baking and frying) of food materials from first principles.

Causal factors concerning the texture of French fries manufactured at industrial scale.

In this paper, we review the physical/chemical phenomena, contributing to the final texture of French fries, as occurs in the whole industrial production chain of frozen par-fried fries. Our discussion is organized following a multiscale hierarchy of these causal factors, where we distinguish the molecular, cellular, microstructural, and product levels. Using the same multiscale framework, we also discuss currently available theoretical knowledge, and experimental methods probing the relevant physical/chemical phenomena. We have identified knowledge gaps, and experimental methods are evaluated in terms of the effort and value of their results. With our overviews, we hope to give promising research directions such to arrive at a multiscale model, encompassing all causal factors relevant to the final texture. This multiscale model is the ultimate tool to evaluate process innovations for effects on final textural quality, which can be balanced against the impacts on sustainability and economics.

Hypotheses concerning structuring of extruded meat analogs.

In this paper, we review the physicochemical phenomena occurring during the structuring processes in the manufacturing of plant-based meat analogs via high-moisture-extrusion (HME). After the initial discussion on the input materials, we discuss the hypotheses behind the physics of the functional tasks that can be defined for HME. For these hypotheses, we have taken a broader view than only the scientific literature on plant-based meat analogs but incorporated also literature from soft matter physics and patent literature. Many of these hypotheses remain to be proven. Hence, we hope that this overview will inspire researchers to fill the still-open knowledge gaps concerning the multiscale structure of meat analogs.

Lattice Boltzmann model for freezing of French fries.

In this paper we present a Lattice Boltzmann model for food freezing, using the enthalpy method. Simulations are performed using the case study of freezing par-fried french fries. The action of par-frying leads to moisture removal from the crust region, which was treated via the initial conditions for the freezing model. Simulations show that under industrial-relevant freezing conditions, the crust region remains either unfrozen or only partially frozen. This result is important for the practical quality problem of dust, which is the phenomenon of fracturing of the crust during finish-frying. Next to the insight, the Lattice Boltzmann freezing model rendered for the case study of par-fried french fries, we pose that this freezing application is a comprehensive tutorial problem, via which food scientists can be conveniently introduced to the Lattice Boltzmann method. Commonly, the Lattice Boltzmann method has its value in solving complex fluid flow problems, but the complexity of these problems is possibly withholding food scientists to get familiar with the method. Our freezing is solved in 2D, and on a simple square lattice with only 5 particle velocities (a D2Q5 lattice). We hope via this simple tutorial problem, the Lattice Boltzmann method becomes more accessible.

Dust formation in French fries.

In this study we report on the analysis of dust formation, a quality problem arising in the industrial processing of par-fried, frozen french fries. This dust constitutes fractured pieces broken off the crust during finish frying. We claim that this dust problem has many similarities with flaking arising during the final-baking of par-baked french baguettes, i.e. the two problems are governed by the same physical principles. Inspired by the hypotheses behind flaking, we have made an experimental design, where we have perturbed the operating conditions of an industrial processing line of french fries. The measured dust during finish frying is correlated with the physical properties of the crust, measured in the different unit operations of the industrial processing line, and the operating conditions. We have shown that dust is non-linearly correlated to 1) the moisture content of the crust as influenced by drying and par-frying, and 2) the freezing rate in the industrial tunnel freezer. Remarkably, the amount of dust decrease with the increase of frozen storage time, which we have explained via viscoelastic relaxation of locked-in stress - mediated by moisture migrating from core to crust. This decay is shown to be independent of pretreatments, which only determines its starting value. With the given relations industry can in principle control the dust problem, but these measures have to be weighed against their effects on other objectives of the industry.

Interactions in plasticizer mixtures used for sugar replacement.

In our quest for novel ingredients to be used in sugar replacement strategies, we have investigated the thermodynamics of polycarboxylic acids, such as citric acid. We have demonstrated the applicability of the Flory-Huggins (FH) theory to describe the thermodynamics of polycarboxylic acids solutions. Moreover, for citric acid we can describe the complete phase diagram with the theory. It shows that polycarboxylic acids have similar plasticizing and hygroscopic properties as sugars and polyols. Regarding mixtures of polycarboxylic acids and carbohydrates, the FH theory is able to describe a) the water activity of the mixtures, b) the solubility of ternary mixtures of acids and sugars, c) the lowering of the deliquescence point for binary mixtures of crystals, and d) the melting point depression in eutectic mixtures. Unexpectingly, our investigations show there is a strong non-zero FH interaction parameter between carboxylic acids and carbohydrates. In our prior sugar replacement strategy we have assumed zero interactions between plasticizers. Here, we will readdress this assumption. Carefull investigations of solid-liquid equilibrium of eutectic mixtures involving polycarboxylic acids and/or carbohydrates, shows nearly zero interaction in eutectic mixtures consisting only of two carbohydrates or two polycarboxylic acids. We now hold the hypothesis that there is strong non-zero interaction if the mixture contains plasticizers strongly differing in the amount of hydrogen bonding groups. This strong interaction explains why these mixtures, like polycarboxylic acids and carbohydrates, are excellent candidates as deep eutectic solvents. Furthermore, we conclude that polycarboxylic acids are useful additions to the toolbox of sugar replacers, albeit that there are some limitations to their amounts used.

Variations of the viscous properties of a sponge cake artificial bolus with some physiological parameters.

Artificial boluses were prepared from sponge cake by grinding the food to a given particle size and hydrating with artificial saliva. The shear viscosity of the artificial food bolus was then measured by capillary rheometry, and its variations with shear rate were studied as a function of four main factors: bolus water content, particle size, temperature and saliva viscosity. The flow curves can be fitted according to the Herschel-Bulkley model, which allows for the derivation of two main properties: yield stress and consistency. Saliva plasticizing coefficients are defined by the variations of these properties as a function of the water content. Their value, close to 12, is in good agreement with values obtained for molten starch (10 < α < 20). Particle size has little influence, whereas the effect of temperature and saliva viscosity is not monotonous. They underline the complexity of the structure of the bolus and the interplay between the saliva, acting as a lubricant and a swelling agent. Finally, the extensional viscosity of the artificial bolus is also determined by capillary rheometry, and it is shown to be of importance when comparing the viscous properties of the artificial bolus with those of real ones from literature.

Thermodynamic description of the chemical leavening in biscuits.

In this paper we describe the chemical reactions of leavening agents in baking biscuits on a sound thermodynamic basis. The model is part in a sequel targetted at physical understanding of biscuit baking with the purpose of reformulation of biscuits with respect to sucrose and sodium levels. The chemical leavening gases, CO2 and NH3, originate from the dissociation of sodium and ammonium bicarbonate. Next to water vapour, these produced gases create gas bubbles in the biscuit dough. The concentrations of the leavening agents and added salt lead to high ionic strength. Consequently, the activities of ions participating in the leavening reaction deviate strongly from ideality. The non-idealities are described using the Pitzer equations. The values of many parameters of the Pitzer model and equilibrium constants are obtained from the strong developed field of CO2 sequestering in ammonia solutions. The model describing the chemical reactions is coupled to a cell model describing the expansion of gas bubbles. Model simulations show that most of the produced gas originates from the bicarbonate, and the ammonium contributes significantly less. The functionality of ammonium as leavening agent is not quite clear, but it may help in reducing sodium levels.

Understanding functionality of sucrose in cake for reformulation purposes.

We review the functionality of sucrose during the manufacture of cakes from the perspective of sugar replacement. Besides providing sweetness, sucrose has important functionalities concerning structure formation. These functionalities also need to be mimicked in reformulated cakes. First, we review the hypotheses, concerning the development of structure and texture of cakes during manufacturing, which are conveniently summarized in a qualitative way using the Complex Dispersed Systems methodology. Subsequently, we represent the changes of the state of the cake during manufacturing in a supplemented state diagram, which indicates the important phase transitions occurring during baking. From the analysis, we have learned that sucrose act both as a plasticizer and as a humectant, modifying the phase transitions of biopolymers, dough viscosity, and water activity. If sugar replacers exactly mimick this behavior of sucrose, similar textures in reformulated cakes can be obtained. Physical theories exist for characterizing the plasticizing and hygroscopic behavior of sugars and their replacers. We have shown that the starch gelatinization and egg white denaturation can be predicted by the volumetric density of hydrogen bonds present in the solvent, consisting of water, sugar or its replacers, such as polyols or amino-acids.

Physical chemistry of gastric digestion of proteins gels.

In this paper, we present the rich physics and chemistry of the gastric digestion of protein gels. Knowledge of this matter is important for the development of sustainable protein foods that are based on novel proteins sources like plant proteins or insects. Their digestibility is an important question in the design of these new protein foods. As polyelectrolyte gels, they can undergo volume changes upon shifts in pH or ionic strengths, as protein gels experience when entering the gastric environment. We show that these volume changes can be modelled using the Flory-Rehner theory, combined with Gibbs-Donnan theory accounting for the distribution of electrolytes over gel and bath. In-vitro experiments of soy protein gels in simulated gastric fluid indeed show intricate swelling behaviour, at first the gels show swelling but at longer times they shrink again. Simulations performed with the Flory-Rehner/Gibbs-Donnan theory reproduce qualitatively similar behaviour. In the final part of the paper, we discuss how the model must be extended to model realistic conditions existing in the in-vivo gastric environment.

Dextrose equivalence of maltodextrins determines particle morphology development during single sessile droplet drying.

Particle morphology development during spray drying is critical to powder properties. The aim of this study was to investigate whether the dextrose equivalence (DE) of maltodextrins can be used as an indicator for the final particle morphology. Maltodextrins were characterized on glass transition temperature (Tg) and viscosity, where low DE-value maltodextrins exhibited higher Tg and viscosity than high DE maltodextrins (≥21). A new custom-built sessile single droplet dryer was used to analyse morphology development of minute maltodextrin droplets (R0 ~ 100 µm) at 60 °C and 90 °C. Droplets with low DE showed early skin formation (2-5 s) and developed smoothly shaped particles with large cavities. Rheology on low DE maltodextrin films at dry matter of 82% (w/w) suggested that drying droplets acquired elasticity after locking providing resistance against surface compression. After locking morphology development is probably halted as the glassy state is approached. On the contrary, rheology on high DE maltodextrin (≥21) films at dry matter of 93% (w/w) suggested that drying droplets with high DE developed viscous skins, which are susceptible to surface deformations, leading to wrinkling, folding or creasing particle morphologies. The results demonstrated that DE-value may be used as an indicator for particle morphology development when interpreted in view of the process conditions.

Understanding functionality of sucrose in biscuits for reformulation purposes.

We review the functionality of sucrose during the manufacture of biscuits from the perspective of sugar replacement. Besides to providing sweetness, sucrose has important functionalities concerning structure and texture formation. These functionalities also need to be mimicked in reformulated biscuits. First, we review the hypotheses concerning the development of structure and texture of biscuits during manufacturing, which are conveniently summarized in a qualitative way using the Complex Dispersed Systems methodology. Subsequently, we represent the changes of the state of the biscuit during manufacturing in the supplemented state diagram, which indicates the important phase transitions occurring during mixing and baking. We propose that when reformulated biscuits follow similar paths in the state diagram, similar structures and textures can be obtained. Physical theories exist for predicting these phase transitions for existing sucrose-rich biscuits and also reformulated biscuits containing extensive sweeteners as sugar replacers. More accurate predictions of structure and texture can be eventually obtained if they are combined with computational models, including heat and moisture transfer.

Theoretical investigation of the swelling of polysaccharide microgels in sugar solutions.

In this paper, we explain the increased swelling of crosslinked polysaccharide microgels by the increase of sugar concentration using a modified Flory-Rehner theory. This theory is validated via the investigation of the swelling of dextran microgels in sugar solutions, which can be viewed as a model system for crosslinked starch in sugar solution and custard. An essential part of our modified theory is that starch perceives the sugar solution as an effective solvent rendering a certain hydrogen bond density. Our simulations show that the often experimentally observed maximum in swelling of starch at 20% sugar concentration is probably due to the fact that equilibrium is not reached within practical time scales. Also, we discuss the use of our theory as a tool in sugar reformulation issues of custard. From simulation results one can produce a state diagram showing which formulations render a creamy, space-filling network.

Predicting the solubility of mixtures of sugars and their replacers using the Flory-Huggins theory.

In this paper we investigate whether the Flory-Huggins theory can describe the thermodynamics of solutions of simple carbohydrates, like sugars and polyols. In particular, we focus on the description of the solubility of the carbohydrates in water. This is investigated for both binary and ternary mixtures, having two types of these carbohydrates. This research question arises especially in the case of bakery products, where one seeks to replace sucrose with other simple carbohydrates - which are often polyols. Based on the model parameters obtained from fitting the theory to the experimental data of binary solutions, we show that the theory can predict (a) solubility data for ternary mixtures, over a broad range of concentrations and temperatures, and (b) the deliquescence point of binary mixtures of carbohydrate crystals as a function of temperature. The theory can even be applied to carbohydrates, which form hydrate crystals. Together with our earlier theories on the thermodynamics of complex food mixtures, we have now a complete thermodynamic framework to describe the phase and state transitions of food materials as confectionery and bakery products, where the question of sucrose replacement is urgent.

Filler functionality in edible solid foams.

We review the functionality of particulate ingredients in edible brittle foams, such as expanded starchy snacks. In food science and industry there is not a complete awareness of the full functionality of these filler ingredients, which can be fibers, proteins, starch granules and whole grains. But, we show that much can be learned about that from the field of synthetic polymeric foams with (nano)fillers. For edible brittle foams the enhancement of mechanical strength by filler ingredients is less relevant compared to the additional functionalities such as 1) the promotion of bubble nucleation and 2) cell opening-which are much more relevant for the snack texture. The survey of particulate ingredients added to snack formulations shows that they cannot be viewed as inert fillers, because of their strong hygroscopic properties. Hence, these fillers will compete with starch for water, and that will modify the glass transition and boiling point, which are important factors for snack expansion. Filler properties can be modified via extrusion, but it is better if that processing step is decoupled from the subsequent processing steps as mixing and expansion. Several filler ingredients are also added because of their nutritional value, but can have adverse effect on snack expansion. These adverse effects can be reduced if the increase of nutritional value is decoupled from other filler functionality via compartmentalization using micropellets.

Hyperelastic models for hydration of cellular tissue.

In this paper we present hyperelastic models for swelling elastic shells, due to pressurization of the internal cavity. These shells serve as model systems for cells having cell walls, as can be found in bacteria, plants and fungi. The pressurized internal cavity represents the cell vacuole with intact membrane at a certain turgor pressure, and the elastic shell represents the hydrated cell wall. At pressurization the elastic shell undergoes inhomogeneous deformation. Its deformation is governed by a strain energy function. Using the scaling law of Cloizeaux for the osmotic pressure, we obtain approximate analytical expressions of the cell volume versus turgor pressure - which are quite comparable to numerical solutions of the problem. Subsequently, we have simulated the swelling of shells - where the cell wall material is embedded with microfibrils, leading to strain hardening and anisotropic cell expansion. The purpose of our investigations is to elucidate the contribution of cell membrane integrity and turgor to the water holding capacity (hydration) of plant foods. We conclude with a discussion of the impact of this work on the hydration of food material, and other fields like plant science and the soft matter physics of responsive gels.

Effects of salt on the expansion of starchy snacks: a multiscale analysis.

We investigate the effect of salt on the expansion of starchy snacks during frying by means of a multiscale simulation model. This model has been developed earlier for starchy snacks without salt. The simulation results are analysed by means of the supplemented state diagram. We have found that the optimal expansion for salty snacks occurs under the same conditions as for snacks without salt. This occurs at the moisture content where the 4 bar boiling line intersects the critical isoviscosity line of 1 MPa s. Salt is shown to influence both the boiling line and the critical isoviscosity line, via a change of the glass transition. The optimal moisture content for salty snacks is lower than that of unsalted snacks. We view our findings as important for reformulations of starchy snacks with lower salt levels. Furthermore, the presented tools of the multiscale simulations and supplemented state diagram can generally be used for reformulation problems in structured foods.

Multiscale analysis of structure development in expanded starch snacks.

In this paper we perform a multiscale analysis of the food structuring process of the expansion of starchy snack foods like keropok, which obtains a solid foam structure. In particular, we want to investigate the validity of the hypothesis of Kokini and coworkers, that expansion is optimal at the moisture content, where the glass transition and the boiling line intersect. In our analysis we make use of several tools, (1) time scale analysis from the field of physical transport phenomena, (2) the scale separation map (SSM) developed within a multiscale simulation framework of complex automata, (3) the supplemented state diagram (SSD), depicting phase transition and glass transition lines, and (4) a multiscale simulation model for the bubble expansion. Results of the time scale analysis are plotted in the SSD, and give insight into the dominant physical processes involved in expansion. Furthermore, the results of the time scale analysis are used to construct the SSM, which has aided us in the construction of the multiscale simulation model. Simulation results are plotted in the SSD. This clearly shows that the hypothesis of Kokini is qualitatively true, but has to be refined. Our results show that bubble expansion is optimal for moisture content, where the boiling line for gas pressure of 4 bars intersects the isoviscosity line of the critical viscosity 10(6) Pa.s, which runs parallel to the glass transition line.

Mesoscale models of dispersions stabilized by surfactants and colloids.

In this paper we discuss and give an outlook on numerical models describing dispersions, stabilized by surfactants and colloidal particles. Examples of these dispersions are foams and emulsions. In particular, we focus on the potential of the diffuse interface models based on a free energy approach, which describe dispersions with the surface-active agent soluble in one of the bulk phases. The free energy approach renders thermodynamic consistent models with realistic sorption isotherms and adsorption kinetics. The free energy approach is attractive because of its ability to describe highly complex dispersions, such as emulsions stabilized by ionic surfactants, or surfactant mixtures and dispersions with surfactant micelles. We have classified existing numerical methods into classes, using either a Eulerian or a Lagrangian representation for fluid and for the surfactant/colloid. A Eulerian representation gives a more coarse-grained, mean field description of the surface-active agent, while a Lagrangian representation can deal with steric effects and larger complexity concerning geometry and (amphiphilic) wetting properties of colloids and surfactants. However, the similarity between the description of wetting properties of both Eulerian and Lagrangian models allows for the development of hybrid Eulerian/Lagrangian models having advantages of both representations.

Predictions of glass transition temperature for hydrogen bonding biomaterials.

We show that the glass transition of a multitude of mixtures containing hydrogen bonding materials correlates strongly with the effective number of hydroxyl groups per molecule, which are available for intermolecular hydrogen bonding. This correlation is in compliance with the topological constraint theory, wherein the intermolecular hydrogen bonds constrain the mobility of the hydrogen bonded network. The finding that the glass transition relates to hydrogen bonding rather than free volume agrees with our recent finding that there is little difference in free volume among carbohydrates and polysaccharides. For binary and ternary mixtures of sugars, polyols, or biopolymers with water, our correlation states that the glass transition temperature is linear with the inverse of the number of effective hydroxyl groups per molecule. Only for dry biopolymer/sugar or sugar/polyol mixtures do we find deviations due to nonideal mixing, imposed by microheterogeneity.