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This chapter provides an overview of the rheological characterization of tomato-based products, the importance of which is related to processing design, quality control, and sensory acceptance. First, we present some general principles of rheology, covering the fundamental concepts and rheological classification of fluid foods. Then, we discuss steady-state shear, time-dependent, and viscoelastic properties. Each of these is discussed separately, focusing on tomato products and presenting the equations generally used to model rheological behaviour and their respective parameters. In addition, some factors that influence rheological characteristics are presented, including the composition and characteristics of the product and the processing conditions.

Rheology is the science that studies the flow and deformations of materials when they are subjected to mechanical forces. Rheological study of food is necessary for the determination of engineering parameters, design of manufacturing machineries and unit operations, quality control and product development, definition of packaging and storage strategies, and more.1–3  Knowledge of rheological behavior is required all the way from manufacturing to product consumption. Consistency and mouthfeel are particularly valuable attributes in tomato products, highlighting the importance of rheology in sensory quality and consumer acceptance.

Fluid foods exhibit a wide variety of rheological behavior, ranging from Newtonian to time-dependent and viscoelastic.2  Since most tomato products are dispersions composed of suspended particles (pulp) and aqueous medium (serum), the content and characteristics of both phases play an important role in the complex rheology of tomato products. By causing structural and physicochemical changes in pulp and serum, food processing and its conditions consequently affect the rheological properties of the product as well.

In this chapter the principles of rheology, including the description of fundamental concepts and classification of fluids, are introduced. In addition, steady-state shear, time-dependent, and viscoelastic properties are described. Each is discussed separately, showing examples of tomato products and presenting the equations and their respective parameters usually employed to model the rheological behavior. Further, the influence of product composition, processing conditions, and operations on these properties is also discussed.

Rheology studies the deformation and flow of materials subjected to mechanical forces. Depending on the material characteristics and the mechanical events, different rheological properties are obtained. The determination of rheological properties of food is important because they are useful for studying food quality and for designing equipment and food processing. In addition, the rheological parameters are crucial for calculating unit operations that involve phenomena not only of momentum transfer, but also of heat and mass transfer.

The rheological properties are determined by studying the deformation of the material during the application of a stress (σ), or vice versa. The stress consists of applying a force (F) in a determined superficial area (A). Many types of stresses can be applied, depending on the food characteristics and processing, thus leading to different analyses.

For instance, in solid materials (Figure 1.1), normal stress (uniaxial compression or extension, where the applied force is perpendicular to the cross-section) or shear stress (where the applied force is parallel to the cross-section) can be applied. In fact, pure solid materials have elastic behavior, which means that when a stress applied to the solid is released, the solid recovers its shape from any deformation. However, “solid” foods do not behave either as a pure solid or as a pure fluid: they have an intermediate behavior known as viscoelastic behavior.

Figure 1.1

Types of stress (σ) applied to solids.6 

Figure 1.1

Types of stress (σ) applied to solids.6 

Close modal

The rheological properties of fluids are commonly evaluated by applying shear stress. Figure 1.2 illustrates an ideal experiment where a fluid sample is in contact with two parallel slabs of known area A separated by a distance dy. While one slab is fixed, the other one moves at constant velocity v due to an applied force F. The fluid layer close to the upper slab will move with the same velocity, while the fluid close to the lower slab will remain at rest. Therefore, when the steady-state condition is obtained, the fluid will move following a velocity profile in the x direction. In fact, the shear stress can be calculated by eqn (1.1), resulting in a fluid velocity gradient called shear rate (, eqn (1.2)).

formula
Equation 1.1
formula
Equation 1.2

The relation between the shear stress and the shear rate gives the information necessary to recognize the type of fluid and its behavior during processing. This is detailed in the following section.

Figure 1.2

Shear deformation of a fluid product. The fluid between two parallel slabs (dy) with area (A) is deformed by a shear stress due to an applied force (F). The velocity of the fluid that is close to the upper slab has a velocity (v), while the fluid close to the lower slab is at rest. This create a velocity gradient ().

Figure 1.2

Shear deformation of a fluid product. The fluid between two parallel slabs (dy) with area (A) is deformed by a shear stress due to an applied force (F). The velocity of the fluid that is close to the upper slab has a velocity (v), while the fluid close to the lower slab is at rest. This create a velocity gradient ().

Close modal

Fluid materials can be classified rheologically according to their flow behavior (Figure 1.3). First, a perfect fluid is one whose shear rate is linearly proportional to the shear stress and whose constant of proportionality is called viscosity (η), which represents the resistance of the fluid to flow. These fluids follow Newton's law (eqn (1.3)), so they are called Newtonian fluids. Example of Newtonian fluids are air, water, dilute solutions, oil, milk, clarified juices, and the juice serum.

σ=η · 
Equation 1.3
Figure 1.3

Classification of fluids according to their flow behavior.

Figure 1.3

Classification of fluids according to their flow behavior.

Close modal

However, most liquid foods do not follow Newton's law, due to structural changes during flow. They are known as non-Newtonian fluids, but depending on the fluid, they have different behaviors (Figure 1.3). These fluids can also be classified as time-independent or time-dependent non-Newtonian fluids. Time-dependent means that the fluid structure changes as the flow time increases. For instance, some particles of the fluid may aggregate to form bigger particles or may be destroyed to form smaller particles during flow, changing the rheological behavior as the fluid flows.3,4 

Time-independent non-Newtonian fluids can usually present four different behaviors: dilatant, pseudoplastic, Bingham, and Herschel–Bulkley (Figure 1.4). In most of these fluids, the “viscosity” is not a constant property in relation to the shear rate. This property is therefore known as apparent viscosity, as its value is a function of the shear rate.

Figure 1.4

Classification of fluids according to their shear stress/shear rate relationship.

Figure 1.4

Classification of fluids according to their shear stress/shear rate relationship.

Close modal

Dilatant fluids, or shear-thickening fluids, are characterized by an increase in apparent viscosity as the shear rate increases. Examples are concentrated suspensions of starch in water, crystalized honey, and suspensions of sand in water. This behavior is due to the collision of the suspended particles when the fluid is sheared, increasing the resistance to flow (i.e., causing an increase of the apparent viscosity).

In contrast, pseudoplastic fluids, or shear-thinning fluids, present an opposite behavior: as the shear rate is increased, the apparent viscosity is reduced. This behavior is caused by the alignment of the suspended particles due to the flow when they are subjected to shear. For instance, when these fluids are at rest, they seem to be very consistent; however, their consistency is reduced when the container they are in is shaken. Familiar examples of such fluids are fruit purées, mayonnaise, mustard, and ketchup.

These two first fluids (dilatant and pseudoplastic) can be mathematically described by eqn (1.4), known as the Ostwald–de Waele model or power law model. In this equation k represents the consistency coefficient and n represents the flow behavior index. For Newtonian fluids n=1, for dilatant fluids n>1, and for pseudoplastic fluids n<1.

σ=k · n
Equation 1.4

There are other types of fluids that need a minimum shear stress to start to flow. This minimum shear stress is known as yield stress (σ0). The presence of yield stress is characteristic of multiphase materials such as fruit pulps and juices, which are formed by particles in suspension (cells, cellular wall, fibers) in an aqueous solution of sugars, proteins, soluble polysaccharides, and minerals (the serum phase).5  After the application of a shear stress higher than the yield stress, the fluid flows. When flowing, some fluids (including some juices) behave similarly to Newtonian fluids; these are known as Bingham plastic fluids. On the other hand, if after the application of the yield stress the fluid behaves similarly to a pseudoplastic fluid, the fluid is called a Herschel–Bulkley fluid. The most common mathematical model used to describe fluids with a yield stress is the Herschel–Bulkley model (eqn (1.5)). Note that this model can be used as a general model for describing all the previously described fluid behaviors:

σ=σ0+k · n
Equation 1.5

The characterization of time-dependent non-Newtonian fluids is important for understanding possible changes during processing. There are two common fluid behaviors: fluids whose consistency (apparent viscosity) is reduced over the shearing time, known as thixotropic fluids, and others whose consistency is increased over the shearing time, known as rheopectic fluids. Rheopectic behavior is characterized by the reorganization of the fluid structure during flow and it is unusual to find in food products. Thixotropic behavior, on the other hand, is characterized by the rupture and disaggregation of suspended particles and molecules in the food. Therefore, the stress is reduced as the flow time passes. This behavior is very common in foods such as fruit derivatives, tomato products being a typical example.

Most food does not behave either as an ideal fluid (with pure viscous behavior, described by Newton's law) or as an ideal solid (with pure elastic behavior, described by Hooke's law). Food products have an behavior intermediate between these two ideals, thus being classified as viscoelastic products. The viscoelastic properties of a food are important in studying the product stability, the properties of which can be correlated with the structure to explain the product changes during processing. Assessing the viscoelastic properties of food can be carried out by methods such as the dynamic oscillatory procedure or creep and recovery procedure.6 

The dynamic oscillatory procedure consists of applying a sinusoidal shear stress with a determined amplitude within the linear behavior (<5%).7  Three parameters are involved during the procedure, where one of them is kept constant, another is varied, and the third is measured: shear stress (σ), strain (γ), and oscillatory frequency (ω).3  In most cases, an oscillatory movement is applied to the product, and the strain is measured as response. Depending on the phase difference (δ) between the input and output (Figure 1.5), the viscoelastic properties are determined. When there is no phase difference between the strain and the stress sinusoids, it means that the product behaves as a pure elastic solid; when the phase difference is 90°, it means that the product behaves as a pure viscous fluid. If the phase difference is between 0° and 90°, this means that the product has viscoelastic behavior.

Figure 1.5

Stress–strain response of a pure elastic product, a viscoelastic product, and a pure viscous product. Note that depending on the phase difference, the viscoelastic behavior of the product can be determined.1,2 

Figure 1.5

Stress–strain response of a pure elastic product, a viscoelastic product, and a pure viscous product. Note that depending on the phase difference, the viscoelastic behavior of the product can be determined.1,2 

Close modal

Consequently, viscoelastic products can be described by eqn (1.6). This equation introduces the parameters G′ and G″. The parameter G′ is known as the storage modulus and describes the elastic behavior of the product (eqn (1.7)). G″ is the loss modulus and describes the viscous behavior of the product (eqn (1.8)).

formula
Equation 1.6
formula
Equation 1.7
formula
Equation 1.8

In addition, other viscoelastic parameters can be obtained from this procedure: the complex modulus (G*, (eqn (1.9)) and the complex viscosity (η*, eqn (1.10)), which represent the overall resistant of the product to flow:6 

formula
Equation 1.9
formula
Equation 1.10

Another frequently used procedure to determine the viscoelastic properties of food is the creep-compliance procedure. This consists of applying an instantaneous stress (σ) to the product, which is then kept constant for a period of time when the strain change (γ) is measured. Then, the stress is released, and the recovery behavior of the product is observed. When compliance (J, the inverse of the modulus of elasticity) against time is plotted (eqn (1.11)), a creep-recovery profile similar to Figure 1.6A is obtained.1  This method combines fundamental mechanical models (Figure 1.6B) to describe the viscoelastic properties: Hooke's elasticity model (represented by a spring), Newton's viscosity model (represented by a dashpot), and their combinations.

Figure 1.6

(A) Typical creep-recovery profile of viscoelastic products. (B) Most-used mechanical models to describe viscoelasticity of food.3,6,9 

Figure 1.6

(A) Typical creep-recovery profile of viscoelastic products. (B) Most-used mechanical models to describe viscoelasticity of food.3,6,9 

Close modal

Some of the most commonly used models to describe viscoelastic behavior are the Maxwell model, which combines a spring and a dashpot placed in series; the Kelvin–Voigt model, which combines a spring and a dashpot placed in parallel; and the Burger model, which combines a Maxwell body and a Kelvin–Voigt body in series. All these models make it possible to isolate the elastic and viscous contribution of a viscoelastic product, being a very interesting approach for studying these products. The Burger model is the most complete and best describes the viscoelastic complexity of foods (eqn (1.12)). Its parameters are useful to isolate viscous and elastic behavior: G0 and η0 refer to the instantaneous elastic modulus and viscosity component associated with the Maxwell spring, G1 refers to the retarded elastic modulus associated with the Kelvin–Voigt body, and η1 is the viscosity component associated with the retarded elasticity of the Kelvin–Voigt body.

formula
Equation 1.11
formula
Equation 1.12

For more detailed information about rheology concepts and analysis, the reader may consult the following references: Ahmed et al.,8  Augusto and Vitali,3  Ibarz and Barbosa-Canovas,9  Rao,2  Rao and Steffe,6  Singh and Heldman,10  and Steffe.1 

A steady flow curve (shear stress as a function of shear rate) is a valuable way to characterize the rheological behavior of fluids and this information is very useful in various industrial applications.1  The steady-state shear properties are related to the product flow behavior. From an engineering standpoint, these properties are important for the design of machinery such as fillers, pumps, and impellers and the design of several unit operations, including fluid moving, mixing, and heat transfer processes.1,11,12 

As already discussed, from flow curves and use of rheological models, the behavior of fluids can be classified as Newtonian or non-Newtonian. The latter can be divided into four categories: pseudoplastic (shear-thinning), dilatant (shear-thickening), Bingham, and Herschel–Bulkley. Different flow models have been employed to describe properties under steady-shear over wide ranges of shear rates. For tomato products, the power law model (eqn (1.4)) and, when yield stress is considered, the Herschel–Bulkley model (eqn (1.5)) have been extensively used. In addition, other models, such as Casson, Carreau, and Falguera–Ibarz, have also been employed. Table 1.1 presents the equations of these models and some examples of tomato-based products in which the successful use of these models has been reported.

Table 1.1

Rheological models commonly used to describe the flow behavior of tomato products.a

ModelEquationTomato productReference
Power law σ=Kn Concentrate, paste, ketchup, purée, sauce, juice 12–18  
Herschel–Bulkley σ=σ0+Kn Paste, purée, pulp, concentrate, ketchup, juice 14, 17, 19–23  
Casson σ0.5=σ0C0.5+Kc0.5 Concentrate, paste, ketchup 11, 14, 18, 21, 24  
Carreau  Paste, ketchup 25  
Falguera–Ibarz ηa=η+(η0η)k Juice 26, 27  
ModelEquationTomato productReference
Power law σ=Kn Concentrate, paste, ketchup, purée, sauce, juice 12–18  
Herschel–Bulkley σ=σ0+Kn Paste, purée, pulp, concentrate, ketchup, juice 14, 17, 19–23  
Casson σ0.5=σ0C0.5+Kc0.5 Concentrate, paste, ketchup 11, 14, 18, 21, 24  
Carreau  Paste, ketchup 25  
Falguera–Ibarz ηa=η+(η0η)k Juice 26, 27  
a

Yield stress (σ0), consistency coefficient (K), flow behavior index (n), Casson yield stress (σ0C), Casson viscosity (KC2), apparent viscosity (ηa), apparent zero-shear viscosity or initial viscosity (η0), time constant (λc), exponents (N and k), equilibrium viscosity (η).

In general, tomato-based products are characterized as pseudoplastic fluids (0<n<1) or as pseudoplastic fluids with yield stress, i.e., Herschel–Bulkley fluids (0<n < 1, σ0>0). However, the magnitudes of flow properties and even fluid rheological classification may vary depending on the type of product as well as on various other factors including composition (e.g., solids content, particle size and presence of additives) and processing conditions (e.g., temperature and unit operation).

Each type of tomato product has its own compositional characteristics, which results in different rheological behavior. The flow behavior index of the power law model varies from about 0.2 for tomato paste and ketchup (pseudoplastic behavior) to almost 1 for tomato serum (nearly Newtonian behavior), at room temperature.17,24,28  In the flow curves presented in the Figure 1.7, the differences in shear stress values of each type of tomato product are clear.17,21,26,29  Tomato juice presents low shear stress values and a yield stress lower than 1 Pa.26  In contrast, tomato pastes exhibit much greater shear stresses and a yield stress of 43 Pa.21  Higher stress values are typical of concentrated suspensions, such as tomato paste; lower values are characteristic of diluted suspensions, such as tomato juice. The presence and magnitude of yield stress has been related to the characteristics of the particles and their structural network, the interparticle interactions, and the balance of internal and external forces.30 

Figure 1.7

Flow curves of tomato paste (23 °C, modelled by the Herschel–Bulkley equation, data from Dervisoglu and Kokini21 ), ketchup (25 °C, modelled by the Herschel–Bulkley equation, data from Koocheki et al.17 ), tomato sauce (25 °C, modelled by the power law equation, data from Diantom et al.29 ), and tomato juice (20 °C, modelled by the Herschel–Bulkley equation, data from Augusto et al.26 ).

Figure 1.7

Flow curves of tomato paste (23 °C, modelled by the Herschel–Bulkley equation, data from Dervisoglu and Kokini21 ), ketchup (25 °C, modelled by the Herschel–Bulkley equation, data from Koocheki et al.17 ), tomato sauce (25 °C, modelled by the power law equation, data from Diantom et al.29 ), and tomato juice (20 °C, modelled by the Herschel–Bulkley equation, data from Augusto et al.26 ).

Close modal

Like other fruit- and vegetable-based products, most tomato products are dispersions consisting of particles (pulp) suspended in a continuous phase containing soluble components (colloidal serum). The pulp is basically composed of cell wall material (cellulose, lignin, hemicellulose) and water-insoluble pectic materials,30,31  while the serum is composed of low and high molecular weight solutes, such as pectic substances, sugars, salts, and organic acids.28  Both serum and pulp, including their interactions with each other, contribute to the rheological properties of the product.

The insoluble solids of the pulp generally play a more dominant role than the soluble solids of the serum.20,23  The serum phase seems to alter the formation of product structure and particle network when at rest, but its influence may be less significant when the tomato suspension is subjected to shear conditions.22 

Several studies showed that flow properties are strongly affected by the amount of suspended particles. The relationship between rheological parameters (apparent viscosity, yield stress, consistency coefficient) and solids (total solids, insoluble solids, and pulp content) have been described using power law or exponential functions.20,28,30,32  For example, eqn (1.13) presents the relationship between viscosity of tomato serum (ηserum), pulp content (Cpulp) and apparent viscosity at shear rate of 100 s−1 () in tomato concentrates:28 

η100=ηserum+A(Cpulp)B
Equation 1.13

Generally, a higher solids concentration decreases the flow behavior index and increases the consistency coefficient, apparent viscosity, and yield stress. This effect is illustrated in Figure 1.8, which presents the relationship between insoluble solids content and yield stress for tomato concentrates before and after homogenization at 9 MPa.

Figure 1.8

Yield stress as a power law function of the insoluble solid content at 20 °C in non-homogenized and homogenized (at 9 MPa) tomato concentrates prepared from the dilution of hot-break tomato paste.Data from Bayod et al.30 

Figure 1.8

Yield stress as a power law function of the insoluble solid content at 20 °C in non-homogenized and homogenized (at 9 MPa) tomato concentrates prepared from the dilution of hot-break tomato paste.Data from Bayod et al.30 

Close modal

The rheological behavior of tomato products is also closely related to constituents that do not originate from the fruit. For instance, different ingredients (additives), such as hydrocolloids (polysaccharides and proteins), are extensively used by the food industry in various tomato products such as ketchups and sauces. This practice is often intended to improve the texture and stability of the products. The effect of some typical hydrocolloids on consistency and behavior index of tomato sauce and ketchup are presented in Figure 1.9. Each ingredient interacts with the components of the product in a distinct way and results in different rheological modifications. Therefore, certain additives and formulations may be selected during the product design, depending on the desired rheological characteristics and specific applications.

Figure 1.9

Consistency coefficient (bars) and flow behavior index (dots) at 25 °C of tomato sauce and ketchup without addition of hydrocolloids (control) and with 1% of addition of guar, carboxy methyl cellulose (CMC), and xanthan gum.Data from Diantom et al.29  and Koocheki et al.17 

Figure 1.9

Consistency coefficient (bars) and flow behavior index (dots) at 25 °C of tomato sauce and ketchup without addition of hydrocolloids (control) and with 1% of addition of guar, carboxy methyl cellulose (CMC), and xanthan gum.Data from Diantom et al.29  and Koocheki et al.17 

Close modal

Since food products are subjected to different temperatures during processing, storage, and consumption, the temperature dependence of rheological properties is very important. In general, the effect of temperature on the parameters of rheological models, including viscosity, apparent viscosity, yield stress, and consistency index, can be modelled according to an Arrhenius model (eqn (1.14)):

formula
Equation 1.14

where A is the parameter of rheological models, A0 is a constant, Ea is the activation energy, R is the gas constant, and T is the temperature. The apparent viscosity and consistency coefficient of tomato products usually decrease with increasing temperature. The effect of temperature on the power law consistency coefficient of ketchup is shown in Figure 1.10. It can be described by an Arrhenius relationship with values of activation energy of around 2 kcal mol−1.18  Higher temperatures represent a higher level of internal energy, with greater distance between molecules, which facilitates molecular movement and vibration, leading to a lower consistency coefficient.3 

Figure 1.10

Effect of hot-break and cold-break processing on the power law consistency coefficient of ketchup at different temperatures.Data from Rani and Bains.18 

Figure 1.10

Effect of hot-break and cold-break processing on the power law consistency coefficient of ketchup at different temperatures.Data from Rani and Bains.18 

Close modal

Besides the temperature, the processing steps and unit operations to which the product is submitted also have a great influence on rheological properties. By causing changes in particle characteristics of the suspension and serum viscosity, some operations such as homogenization end up affecting the flow behavior of the tomato product. In Figure 1.8, higher yield stresses are shown in homogenized tomato concentrates than in non-homogenized ones. Although homogenization decreases the viscosity of fruit juice serum, the yield stress and apparent viscosity of tomato dispersions (serum+pulp) are generally increased.27,30,33  After homogenization, the tomato particles are disrupted, resulting in small fragments with irregular shape (less spherical), different particle network and size distribution, and release of cell material into the continuous phase. As a consequence, both particle–particle and particle–serum interactions are improved. And further, depending on process parameters, such as homogenization pressure, these changes occur to different extents.27,33,34 

Another interesting operation to highlight is the preheating treatment, also known as breaking. Here, temperature is once again a parameter under discussion. The processing of tomato at higher break temperatures results in tomato products with higher viscosity and consistency.16,18 Figure 1.10 shows the consistency coefficients of ketchup produced from hot-break and cold-break treated tomatoes. Higher consistency can be explained by the changes in the product microstructure and also by the greater degree of enzyme inactivation and thus less degradation of pectin.

For time-dependent fluids, apparent viscosity and shear stress depend not only on shear rate, but also on the duration of shearing. The assessment of rheological parameters with time of shearing makes it possible to establish relationships between structure and flow in food suspensions, including most tomato products.35,36  It is noteworthy that in steady-state shear experiments a preshearing process is generally carried out prior to the measurements precisely to avoid measuring the time-dependent behavior. The time-dependence of rheological properties is related to internal structural changes and the balance between structural breakdown due to shear and reorganization due to particle attractive forces. Based on that, two behaviors can be found: thixotropic and rheopectic.

The increase in apparent viscosity with time at a fixed shear rate, characteristic of rheopectic fluids, is related to aggregation and reorganization of the internal structure.26,37  Most food products present thixotropic behavior; rheopecticity, a dilatant (shear-thickening) behavior, is less common in foods in general.26  Thixotropy is related to the breakdown of interparticle interactions when the product is subjected to shearing, which results in the decay of shear stress and apparent viscosity with time.26  Thus, in thixotropic fluids, the resistance to deformation decreases along the time of shearing.12 

Two models are frequently used for describing time-dependent flow in tomato products: the Figoni–Shoemaker model (eqn (1.15)) and the Weltman model (eqn (1.16)).36,38  In these equations, σe is the equilibrium shear stress, σ0 is the initial shear stress, A is a parameter related to initial shear stress, B and kFS are related to the stress variation with time and t is the shearing time:26 

σ=σe+(σ0σe) · exp(−kFS · t)
Equation 1.15
σ=A−B · ln t
Equation 1.16

Tomato juice sheared at constant shear rate (in the range of 50 to 500 s−1) for 1000 s exhibited thixotropic behavior, which was well described by both models.26  The parameters σe, σ0, and kFS showed a tendency to increase with shear rate, which is expected since tomato juice exhibits a Herschel–Bulkley nature, as mentioned in the previous section. The shear stress decay with time modelled by the Figoni–Shoemaker equation and the increase of its parameters as a function of shear rate is shown in Figure 1.11. Additionally, the values of parameter A from the Weltman model also tended to increase with shear rate for tomato juice. A similar tendency of A was observed in ketchup sheared for 60 min at shear rates ranging from 5 to 35 s−1, whose behavior was also found to be thixotropic and well described by both models.35 

Figure 1.11

Time-dependence of tomato juice shear stress modelled by the Figoni–Shoemaker equation.Reproduced from ref. 26 with permission from Springer Nature, Copyright 2012.

Figure 1.11

Time-dependence of tomato juice shear stress modelled by the Figoni–Shoemaker equation.Reproduced from ref. 26 with permission from Springer Nature, Copyright 2012.

Close modal

Most tomato products are dispersions composed of suspended insoluble particles (pulp) and aqueous medium (serum). Because of the complex nature and microscale heterogeneity of these dispersions, tomato products may exhibit different behaviors. Their time-dependent rheology depends on their composition and any conditions to which they have been submitted, such as previous shear and thermal history, temperature, time of shearing, and shear rate.

Although thixotropic behavior is more common, some tomato products may also present rheopecticity under certain conditions. For instance, unlike the exclusive thixotropic behavior of tomato juice found by Augusto et al.26  and Tiziani and Vodovotz,37  De Kee et al.39  reported an initial increase (rheopecticity) followed by a decrease in viscosity (thixotropy) of tomato juice with time of shearing at shear rates between 41 and 549 s−1. Abu-Jdayil et al.12  observed that tomato paste showed a thixotropic behavior at low shear rates (2.20 and 6.12 s−1) and a rheopectic behavior at high shear rates (28.38 and 79.02 s−1), regardless of temperature, as illustrated in Figure 1.12. Similar results involving the transition of thixotropic to rheopectic behavior depending on shear rate were also reported for tomato juice with added soy protein isolate.37 

Figure 1.12

Effect of shear rate (2.20 and 79.02 s−1) and temperature (20 and 50 °C) on time-dependence of tomato paste shear stress modelled by the Weltman equation.Data from Abu-Jdayil et al.12 

Figure 1.12

Effect of shear rate (2.20 and 79.02 s−1) and temperature (20 and 50 °C) on time-dependence of tomato paste shear stress modelled by the Weltman equation.Data from Abu-Jdayil et al.12 

Close modal

Other tomato products presented different behaviors. While tomato paste presented both rheopectic and thixotropic behaviors, tomato concentrates, obtained from dilution of the tomato paste in water, presented a slight time-dependence.12  In contrast, tomato powder solutions with the same solids content as paste and concentrates, obtained from the dispersion of spray-dried tomato powder in water, showed a time-independent rheological behavior.12  This is attributed to the fact that the tomato powder was subjected to a different thermal and mechanical history during processing, causing hydrolysis of components, resulting in structural changes and different rheological behavior.12 

Since time-dependence is closely related to the product structure and interparticle interactions, the attributes of the suspended particles are important in determining the time-dependent rheological behavior. Thus, the unit operations and process conditions that can structurally modify the particles, serum, and their interactions are relevant factors. By reducing the diameter of the suspended particles, operations such as homogenization increase the particle surface area and interaction forces. The smaller particles tend to aggregate, forming a network, which in turn explains the increase of thixotropy observed in homogenized tomato juice.27 

The viscoelastic properties of whole tomato fruit and many tomato products have been widely studied in the literature. The viscoelastic properties are important for better understanding the product behavior during processing, storage, and consumption, as well as for monitoring the tomato fruit damage or the changes during ripening or storage conditions.

Tomato products such as tomato pastes, tomato sauces, and tomato juice are viscoelastic materials, even at concentrations of 4–5%.25,26,40,41  The dynamic oscillatory shear procedure has generally been used to describe the viscoelastic properties of tomato products, using different dynamic parameters, such as G′, G″, G*, and η*. At low frequency (ω), the G′ values were always higher than those of G″,1  and the tan(δ)=(G′′/G′) had lower values, indicating that elastic properties rather than viscous properties predominate in tomato products.19  Tomato products can therefore be classified as weak gels.

As already mentioned, tomato products are composed of a dispersed phase (solids, structuring component) and a continuous phase (serum, highly viscous fluid). The continuous and dispersed phases contribute to a complex network structure, where the difference in the product's structure is indicated by the force required to separate the solids from the serum.24  Therefore, again, the network force is important and contributes to rheological properties. The volume fraction, particle concentration, size, distribution, and morphology (surface/shape) should be taken into consideration as well.22,42,43 

At higher pulp content or particle concentration, tomato products have a more pronounced gel characteristic (larger G′ values). A higher G′ modulus is observed with an increase in tomato paste concentration and particle volume fraction (ϕ) (Figure 1.13).

Figure 1.13

(A) Changes in the particle volume fraction (ϕ) and in the storage/elastic modulus (G′, at ω=1 Hz) for 10, 30 and 40% tomato paste suspensions. Data from Bayod and Tornberg.43  (B) G′ modulus (at =0.1 rad s−1) as function of tomato pulp content (%) of reconstituted suspensions (RS) of tomato purée homogenized at 20 MPa with particle size expressed as the mean of area-based diameter (D[3,2] µm); curves represent the power law model fits (G′=g(pulp%)n.Reproduced from ref. 22 with permission from Springer Nature, Copyright 2013.

Figure 1.13

(A) Changes in the particle volume fraction (ϕ) and in the storage/elastic modulus (G′, at ω=1 Hz) for 10, 30 and 40% tomato paste suspensions. Data from Bayod and Tornberg.43  (B) G′ modulus (at =0.1 rad s−1) as function of tomato pulp content (%) of reconstituted suspensions (RS) of tomato purée homogenized at 20 MPa with particle size expressed as the mean of area-based diameter (D[3,2] µm); curves represent the power law model fits (G′=g(pulp%)n.Reproduced from ref. 22 with permission from Springer Nature, Copyright 2013.

Close modal

Compared to reconstituted suspensions in water, original tomato purées have larger G′ and G″ values, which is attributed to the serum phase.22  Using creep-compliance experiments, the effect of soluble solids concentration (°Brix) in the serum was evidenced. At higher °Brix content, the magnitudes of instantaneous elastic modulus and the storage modulus also increased.44  In addition, after high-pressure homogenization (HPH) processing of tomato juice, elastic and viscous behaviors were increased (i.e., lower compliance (J(t)) values during creep-recovery procedure). This was attributed to disruption of suspended particles during processing and the development of a stronger internal structure.45  In fact, these rheological changes are also reflected in other physical properties of the tomato juice, such as increasing the physical stability by reducing the pulp sedimentation.34 

The effect of particle size is difficult to interpret, since, at the same time, the network structure, particle shape distribution, surface, and deformability contribute to the observed viscoelastic behavior.22,43  For example, Moelants et al.22  found that the storage modulus G′ does not decrease or increase proportionally with the particle size after the homogenization process. In contrast, Figure 1.14 shows that the smaller the particle size, the higher the viscoelastic properties.

Figure 1.14

(A) Particle size distribution (PSD). (B) Complex modulus (G*) as a function of oscillatory frequency (ω) for tomato juice (4.5 °Brix) processed with HPH at 0 MPa and 150 MPa.Data from Augusto et al.27  and Augusto et al.53 

Figure 1.14

(A) Particle size distribution (PSD). (B) Complex modulus (G*) as a function of oscillatory frequency (ω) for tomato juice (4.5 °Brix) processed with HPH at 0 MPa and 150 MPa.Data from Augusto et al.27  and Augusto et al.53 

Close modal

The viscoelastic properties can also be modified by the addition of different additives, such as protein or fiber. The addition of soy protein (1%) to tomato juice reduced the serum separation and increased the water-holding capacity, increasing the dynamic modulus values.37  However, the addition of soy germ (1.5%) endowed higher temperature stability to tomato juice than the addition of soy protein.46  Additionally, using tomato by-products, the viscoelastic modulus can also be modified. The addition of tomato slurry to tomato paste samples favored the increase of the plateau modulus, while the elastic modulus increased with the increase of total solids using tomato pomace.47,48 

Tomato products are typically the result of crushing, pulping, thermal processing, dilution, and homogenization of the fruit.15  The resulting enzyme activity, particle characteristics, and final mixture composition determines the product's stability and rheology. Thermal processes (such as hot/cold break, concentration, and pasteurization) imply modifications of structure and components that result in different viscoelastic responses of tomato products.

The effect of temperature is dependent on the initial particle concentration, tomato variety, and screen size opening.40,49,50  Industrial tomato processing is usually performed by hot break (85–90 °C) or cold break (<70 °C).51  Concentration by evaporation is still the most conventional concentration method.52 

At higher temperatures, or with an increase in temperature, the following effects are promoted, which increase the viscoelastic parameters of tomato products:

  • inactivation of pectic enzymes (principally polygalacturonase and pectin methylesterase)40,50,51 

  • increase of water-soluble pectin fractions and increase of water-insoluble solid fraction40,49,50 

  • breaking of non-covalent bonds between dispersed tomato particle clusters and surrounding pectin network.49 

At low temperatures (≤65 °C), pectic enzymes are active during processing.40,41  Pectin methylesterase decreases the esterification degree of the pectins and polygalacturonase transforms them into smaller soluble compounds, influencing the charge of the cell wall and decreasing cell-to-cell adhesion. Consequently, the product's viscoelasticity decreases.40  For example, the loss and storage moduli for tomato paste and tomato ketchup processed at high temperatures are higher than those of similar products processed at low temperature (Figure 1.15).50 

Figure 1.15

Influence of breaking temperature on evolution of storage (G′) and loss moduli (G″) with oscillatory frequency at 25 °C. (A) Tomato ketchup obtained from tomato paste processed at break temperature of 85 °C and 65 °C and 1.5 mm screen size, manufactured from tomato variety H-282.50  (B) Tomato paste samples processed at break temperature of 80 °C and 65 °C, manufactured from tomato variety 140-C.Reproduced from ref. 40 with permission from John Wiley and Sons, Copyright © 2002 Society of Chemical Industry.

Figure 1.15

Influence of breaking temperature on evolution of storage (G′) and loss moduli (G″) with oscillatory frequency at 25 °C. (A) Tomato ketchup obtained from tomato paste processed at break temperature of 85 °C and 65 °C and 1.5 mm screen size, manufactured from tomato variety H-282.50  (B) Tomato paste samples processed at break temperature of 80 °C and 65 °C, manufactured from tomato variety 140-C.Reproduced from ref. 40 with permission from John Wiley and Sons, Copyright © 2002 Society of Chemical Industry.

Close modal

Another processing related to changes in viscoelastic properties is homogenization. The viscoelastic properties during the homogenization process can be increased or decreased depending mainly on the degree of homogenization and on the initial particle concentration. As observed on Figure 1.13A, a higher homogenization degree of tomato purée resulted in a reduced storage modulus.22  In the same manner, Tan and Kerr15  observed a decrease in the storage and loss moduli due to smaller particles and less entanglement. In contrast, Bayod and Tornberg43  and Lopez-Sanchez et al.42  observed that after homogenization, at low tomato paste concentrations (<40%) the storage modulus increases. However, at 40% tomato paste suspension, the modulus is almost constant, reflecting the strength of the particle network formed.

On the other hand, Bayod et al.25  evaluated different tomato pastes processed into ketchup after dilution and homogenization. Although the phase angle (δ) shows no differences between the pastes and ketchups, the viscoelastic parameters (G′, G″, and η*) of the pastes and the corresponding ketchup are not directly proportional. This indicates that the changes in structure induced by processing might be governed by other product properties, composition, and the networks formed.

Although HPH technology reduces the serum phase viscosity by cleaving its components, HPH increased the tomato juice storage (G′) and loss (G″) moduli.33,53  As observed in Figure 1.14B, the complex modulus (G*) increases with the HPH at 150 MPa. This indicates that a higher value of HPH results in smaller suspended particles (Figure 1.14A), with greater surface area, which contributed to strong interparticle interactions.

Viscoelastic properties, using compression tests, make it possible to describe and/or predict the structural changes of fresh tomato fruits, which are susceptible to damage during harvesting, packaging, storage, transport, and sale in markets. Microscale damage (failure of cells) is manifested as the macro-scale deterioration of a whole fruit. Therefore, some authors have studied viscoelastic characteristics at multiple scales: single cells, tissues, and the whole tomato fruit.54–56 

Changes in the tomato fruit during ripening and during storage at different temperatures can be monitored by the study of its viscoelastic properties.57–59  Unripe tomatoes show more elastic characteristics, related to higher firmness and lower deformation ratio, than ripe ones.59  Furthermore, using the Kelvin–Voigt model, it was observed that the pericarp tissue of non-chilled or prechilled tomato fruits are more fluid (i.e., less elastic) than those of chilled fruit. The instantaneous elastic modulus (G0) of non-chilled fruit decreases gradually with the storage time, while chilled fruit maintain almost constant G0 values during storage time.57 

Therefore, in higher damage conditions, storage time, or ripening stage, the strain response (γ) at an applied instantaneous stress (σ) to the product is higher, and there is a loss of recovery properties, resulting in different compliance results (eqn (1.11)), as observed in Figure 1.16. Consequently, these viscoelastic parameters can be used for maturity classification or for quality monitoring of tomatoes.

Figure 1.16

Representation of a creep-recovery profile (compliance (inverse of the modulus of elasticity, J) against time) showing the different viscoelastic behavior for tomatoes during ripening, storage under refrigeration, or storage at room temperature. Based on results reported by Jackman and Stanley57  and Sirisomboon et al.59 

Figure 1.16

Representation of a creep-recovery profile (compliance (inverse of the modulus of elasticity, J) against time) showing the different viscoelastic behavior for tomatoes during ripening, storage under refrigeration, or storage at room temperature. Based on results reported by Jackman and Stanley57  and Sirisomboon et al.59 

Close modal

Tomato-based products exhibit complex rheology, which requires a detailed study of steady-state shear as well as time-dependent and viscoelastic behaviors. Because most tomato products are dispersions composed of suspended particles (pulp) dispersed in an aqueous medium (serum), the flow and deformation of these products are closely related to particle and serum characteristics as well as product structure. Rheological properties depend on both particle–particle and particle–serum interactions. Consequently, processing conditions that affect these interactions in some way are also responsible for causing changes in the rheological characteristics. Hence, studies and predictions of the rheological behaviors depending on composition and processing are relevant and essential for optimization of processes, equipment, and products.

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Figures & Tables

Figure 1.1

Types of stress (σ) applied to solids.6 

Figure 1.1

Types of stress (σ) applied to solids.6 

Close modal
Figure 1.2

Shear deformation of a fluid product. The fluid between two parallel slabs (dy) with area (A) is deformed by a shear stress due to an applied force (F). The velocity of the fluid that is close to the upper slab has a velocity (v), while the fluid close to the lower slab is at rest. This create a velocity gradient ().

Figure 1.2

Shear deformation of a fluid product. The fluid between two parallel slabs (dy) with area (A) is deformed by a shear stress due to an applied force (F). The velocity of the fluid that is close to the upper slab has a velocity (v), while the fluid close to the lower slab is at rest. This create a velocity gradient ().

Close modal
Figure 1.3

Classification of fluids according to their flow behavior.

Figure 1.3

Classification of fluids according to their flow behavior.

Close modal
Figure 1.4

Classification of fluids according to their shear stress/shear rate relationship.

Figure 1.4

Classification of fluids according to their shear stress/shear rate relationship.

Close modal
Figure 1.5

Stress–strain response of a pure elastic product, a viscoelastic product, and a pure viscous product. Note that depending on the phase difference, the viscoelastic behavior of the product can be determined.1,2 

Figure 1.5

Stress–strain response of a pure elastic product, a viscoelastic product, and a pure viscous product. Note that depending on the phase difference, the viscoelastic behavior of the product can be determined.1,2 

Close modal
Figure 1.6

(A) Typical creep-recovery profile of viscoelastic products. (B) Most-used mechanical models to describe viscoelasticity of food.3,6,9 

Figure 1.6

(A) Typical creep-recovery profile of viscoelastic products. (B) Most-used mechanical models to describe viscoelasticity of food.3,6,9 

Close modal
Figure 1.7

Flow curves of tomato paste (23 °C, modelled by the Herschel–Bulkley equation, data from Dervisoglu and Kokini21 ), ketchup (25 °C, modelled by the Herschel–Bulkley equation, data from Koocheki et al.17 ), tomato sauce (25 °C, modelled by the power law equation, data from Diantom et al.29 ), and tomato juice (20 °C, modelled by the Herschel–Bulkley equation, data from Augusto et al.26 ).

Figure 1.7

Flow curves of tomato paste (23 °C, modelled by the Herschel–Bulkley equation, data from Dervisoglu and Kokini21 ), ketchup (25 °C, modelled by the Herschel–Bulkley equation, data from Koocheki et al.17 ), tomato sauce (25 °C, modelled by the power law equation, data from Diantom et al.29 ), and tomato juice (20 °C, modelled by the Herschel–Bulkley equation, data from Augusto et al.26 ).

Close modal
Figure 1.8

Yield stress as a power law function of the insoluble solid content at 20 °C in non-homogenized and homogenized (at 9 MPa) tomato concentrates prepared from the dilution of hot-break tomato paste.Data from Bayod et al.30 

Figure 1.8

Yield stress as a power law function of the insoluble solid content at 20 °C in non-homogenized and homogenized (at 9 MPa) tomato concentrates prepared from the dilution of hot-break tomato paste.Data from Bayod et al.30 

Close modal
Figure 1.9

Consistency coefficient (bars) and flow behavior index (dots) at 25 °C of tomato sauce and ketchup without addition of hydrocolloids (control) and with 1% of addition of guar, carboxy methyl cellulose (CMC), and xanthan gum.Data from Diantom et al.29  and Koocheki et al.17 

Figure 1.9

Consistency coefficient (bars) and flow behavior index (dots) at 25 °C of tomato sauce and ketchup without addition of hydrocolloids (control) and with 1% of addition of guar, carboxy methyl cellulose (CMC), and xanthan gum.Data from Diantom et al.29  and Koocheki et al.17 

Close modal
Figure 1.10

Effect of hot-break and cold-break processing on the power law consistency coefficient of ketchup at different temperatures.Data from Rani and Bains.18 

Figure 1.10

Effect of hot-break and cold-break processing on the power law consistency coefficient of ketchup at different temperatures.Data from Rani and Bains.18 

Close modal
Figure 1.11

Time-dependence of tomato juice shear stress modelled by the Figoni–Shoemaker equation.Reproduced from ref. 26 with permission from Springer Nature, Copyright 2012.

Figure 1.11

Time-dependence of tomato juice shear stress modelled by the Figoni–Shoemaker equation.Reproduced from ref. 26 with permission from Springer Nature, Copyright 2012.

Close modal
Figure 1.12

Effect of shear rate (2.20 and 79.02 s−1) and temperature (20 and 50 °C) on time-dependence of tomato paste shear stress modelled by the Weltman equation.Data from Abu-Jdayil et al.12 

Figure 1.12

Effect of shear rate (2.20 and 79.02 s−1) and temperature (20 and 50 °C) on time-dependence of tomato paste shear stress modelled by the Weltman equation.Data from Abu-Jdayil et al.12 

Close modal
Figure 1.13

(A) Changes in the particle volume fraction (ϕ) and in the storage/elastic modulus (G′, at ω=1 Hz) for 10, 30 and 40% tomato paste suspensions. Data from Bayod and Tornberg.43  (B) G′ modulus (at =0.1 rad s−1) as function of tomato pulp content (%) of reconstituted suspensions (RS) of tomato purée homogenized at 20 MPa with particle size expressed as the mean of area-based diameter (D[3,2] µm); curves represent the power law model fits (G′=g(pulp%)n.Reproduced from ref. 22 with permission from Springer Nature, Copyright 2013.

Figure 1.13

(A) Changes in the particle volume fraction (ϕ) and in the storage/elastic modulus (G′, at ω=1 Hz) for 10, 30 and 40% tomato paste suspensions. Data from Bayod and Tornberg.43  (B) G′ modulus (at =0.1 rad s−1) as function of tomato pulp content (%) of reconstituted suspensions (RS) of tomato purée homogenized at 20 MPa with particle size expressed as the mean of area-based diameter (D[3,2] µm); curves represent the power law model fits (G′=g(pulp%)n.Reproduced from ref. 22 with permission from Springer Nature, Copyright 2013.

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Figure 1.14

(A) Particle size distribution (PSD). (B) Complex modulus (G*) as a function of oscillatory frequency (ω) for tomato juice (4.5 °Brix) processed with HPH at 0 MPa and 150 MPa.Data from Augusto et al.27  and Augusto et al.53 

Figure 1.14

(A) Particle size distribution (PSD). (B) Complex modulus (G*) as a function of oscillatory frequency (ω) for tomato juice (4.5 °Brix) processed with HPH at 0 MPa and 150 MPa.Data from Augusto et al.27  and Augusto et al.53 

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Figure 1.15

Influence of breaking temperature on evolution of storage (G′) and loss moduli (G″) with oscillatory frequency at 25 °C. (A) Tomato ketchup obtained from tomato paste processed at break temperature of 85 °C and 65 °C and 1.5 mm screen size, manufactured from tomato variety H-282.50  (B) Tomato paste samples processed at break temperature of 80 °C and 65 °C, manufactured from tomato variety 140-C.Reproduced from ref. 40 with permission from John Wiley and Sons, Copyright © 2002 Society of Chemical Industry.

Figure 1.15

Influence of breaking temperature on evolution of storage (G′) and loss moduli (G″) with oscillatory frequency at 25 °C. (A) Tomato ketchup obtained from tomato paste processed at break temperature of 85 °C and 65 °C and 1.5 mm screen size, manufactured from tomato variety H-282.50  (B) Tomato paste samples processed at break temperature of 80 °C and 65 °C, manufactured from tomato variety 140-C.Reproduced from ref. 40 with permission from John Wiley and Sons, Copyright © 2002 Society of Chemical Industry.

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Figure 1.16

Representation of a creep-recovery profile (compliance (inverse of the modulus of elasticity, J) against time) showing the different viscoelastic behavior for tomatoes during ripening, storage under refrigeration, or storage at room temperature. Based on results reported by Jackman and Stanley57  and Sirisomboon et al.59 

Figure 1.16

Representation of a creep-recovery profile (compliance (inverse of the modulus of elasticity, J) against time) showing the different viscoelastic behavior for tomatoes during ripening, storage under refrigeration, or storage at room temperature. Based on results reported by Jackman and Stanley57  and Sirisomboon et al.59 

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Table 1.1

Rheological models commonly used to describe the flow behavior of tomato products.a

ModelEquationTomato productReference
Power law σ=Kn Concentrate, paste, ketchup, purée, sauce, juice 12–18  
Herschel–Bulkley σ=σ0+Kn Paste, purée, pulp, concentrate, ketchup, juice 14, 17, 19–23  
Casson σ0.5=σ0C0.5+Kc0.5 Concentrate, paste, ketchup 11, 14, 18, 21, 24  
Carreau  Paste, ketchup 25  
Falguera–Ibarz ηa=η+(η0η)k Juice 26, 27  
ModelEquationTomato productReference
Power law σ=Kn Concentrate, paste, ketchup, purée, sauce, juice 12–18  
Herschel–Bulkley σ=σ0+Kn Paste, purée, pulp, concentrate, ketchup, juice 14, 17, 19–23  
Casson σ0.5=σ0C0.5+Kc0.5 Concentrate, paste, ketchup 11, 14, 18, 21, 24  
Carreau  Paste, ketchup 25  
Falguera–Ibarz ηa=η+(η0η)k Juice 26, 27  
a

Yield stress (σ0), consistency coefficient (K), flow behavior index (n), Casson yield stress (σ0C), Casson viscosity (KC2), apparent viscosity (ηa), apparent zero-shear viscosity or initial viscosity (η0), time constant (λc), exponents (N and k), equilibrium viscosity (η).

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