Large amplitudes oscillatory shear (LAOS) behavior of egg white foams with apple pectins and xanthan gum

Food Research International 62 (2014) 299–307

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Large amplitudes oscillatory shear (LAOS) behavior of egg white foams with apple pectins and xanthan gum Paweł Ptaszek ⁎ Agriculture University in Krakow, Faculty of Food Technology, Department of Engineering and Machinery for Food Industry, ul. Balicka 122, 30-149 Kraków, Poland

a r t i c l e

i n f o

Article history: Received 28 September 2013 Accepted 1 March 2014 Available online 12 March 2014 Keywords: Foam Large amplitudes oscillatory shear LAOS Fourier transform rheology Hydrocolloids Protein

a b s t r a c t The study presents the results of research on non-linear rheological properties of foams based on egg white protein, xanthan gum and apple pectin of various levels of methylation. The rheological studies were carried out by means of large amplitude oscillatory shear (LAOS) and Fourier transform rheology (FTR) methods. The obtained foams revealed elastoviscoplastic properties. The analysis of the results allowed determination of yield stress, shear exponents and the Fourier spectra, which enabled estimation of the quantity and intensity of individual harmonics. The Lissajous patterns as well as coefficients of energy dissipation were also demonstrated. The foam containing solely egg white revealed the largest number of harmonics in the Fourier spectrum (17th), whereas supplementation with hydrocolloids induced a decrease in the amount of harmonics (9th). The image of the Fourier spectra was reflected by the Lissajous curves, which gradually acquired an ellipsoidal shape as the hydrocolloid concentration increased. The coefficient of energy dissipation in the function of the deformation amplitude demonstrated a sigmoid dependence and tended towards the value of approximately 0.8 for higher amplitudes. This indicated that the investigated foams were in a flow area. The statistical analysis (two/three-way ANOVA) of the abovementioned values showed that neither the level of methylation nor the pectin concentration in foam influences the yield stress. © 2014 Elsevier Ltd. All rights reserved.

Introduction Food foams Physicochemically, foams are gas–liquid systems where gas constitutes a disperse phase, while liquid is a continuous phase (Campbell & Mougeot, 1999). Foams are classified within a very wide group of the so-called soft matters. They show structural disorder and metastability (Sollich, 1998), which make them similar to glasses. The mechanisms within the systems are shaped by the temperature fluctuation-induced movements of chains which are not able to provoke a total relaxation of the structure. Due to the very long relaxation (slow relaxation modes), soft glassy material (SGM) theory may be applied for a description of the rheological phenomena which occur during shear of foams (Miyazaki, Wyss, Weitz, & Reichman, 2006; Sollich, 1998; Sollich, Lequeux, Hébraud, & Cates, 1997). The word “soft” was used here in order to emphasize the difference between the discussed systems and glasses in their ordinary meaning. The foams based on egg white protein or whey protein derivates constitute an important group of food foams (Campbell & Mougeot, 1999). However, the systems are unstable and they undergo disintegration over time. In order to prevent the disintegration various additives, ⁎ Tel.: +48 126624768; fax: +48 126624761. E-mail address: [email protected].

http://dx.doi.org/10.1016/j.foodres.2014.03.002 0963-9969/© 2014 Elsevier Ltd. All rights reserved.

such as monosaccharides and disaccharides and polysaccharides, are applied. The application of these additives allows for the shaping of the properties of foams in accordance with their technological purpose. The use of a specific polysaccharide is determined by the polysaccharide's molecular structure and by the ability of its interaction with a protein applied as a foam-forming agent. Pectin and xanthan gum are polyanion polysaccharides which are the most frequently used factors shaping mechanical properties of foams.

Hydrocolloids Pectin (P), a polysaccharide of plant origin (Ovodov, 2009; Yapo, 2011), is one of the constituents of the cell wall (from 2% to 35%). Pectin consists of a frame of (1 → 4) linked α-D-galacturonic acid units interrupted by single (1 → 2) linked α-L-rhamnose residue. The carboxyl groups of the galacturonic acid units are partly esterified by methanol. Pectin does not have a specific structure (Pérez, Mazeau, & du Penhoat, 2000) as it is dependent on the conditions of biosynthesis (Mohnen, 2008). “Smooth” molecules, i.e. without branching, and “hairy” molecules, i.e. branched, are the most frequent. Pectin adopts coil conformation of high elasticity, “worm-like”, in an aqueous solution; the highest elasticity was observed for “hairy” areas. The commercially available pectins are divided into two groups on the basis of their degree of esterification: high methoxyl pectin (HM), with a degree of methyl-

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P. Ptaszek / Food Research International 62 (2014) 299–307

esterification of de ≥ 50%, and low methoxyl pectin (LM), with a degree of methyl-esterification of de b 50% (Lopes da Silva & Rao, 2006). Xanthan gum is an extracellular polysaccharide produced by Xanthomonas campestris (Palaniraj & Jayaraman, 2011). Xanthan gum is an anionic polyelectrolyte with a β-(1 → 4)-D-glucopyranose glucan (as cellulose) backbone with side chains of -(3 → 1)-α- D mannopyranose-(2 → 1)-β- D -glucuronic acid-(4 → 1)-β-Dmannopyranose on alternating residues. Slightly less than half (~40%) of the terminal mannose residues are 4,6-pyruvated and the inner mannose is mostly 6-acetylated (that is, the side chains are mainly β-Dmannopyranosyl-(1 → 4)-(α-D-glucuronopyranosyl)-(1 → 2)-β-Dmannopyranoside-6-acetate-(1 → 3)). Some side chains may be missing. In a solution, xanthan gum adopts the conformation of a double helix (Morris, 2006). Due to their molecular structure and the presence of electrically loaded function groups, both pectin and XG, when combined with proteins, may form solid complexes (Lopes da Silva & Rao, 2006; Morris, 2006).

So far in the literature there are only the results of xanthan gum solution tests performed by means of LAOS (Carmona, Ramírez, Calero, & Muñoz, 2014), soy isolates with admixture of flaxseed gum (Bi, Li, Wang, Wang, & Adhikari, 2013), as well as for carrageenan gels (Hilliou, Wilhelm, Yamanoi, & Gonçalves, 2009). Also attempts to describe the rheological properties of dough were undertaken (Lefebvre, 2006; Ng & McKinley, 2008; Ng, McKinley, & Ewoldt, 2011), systems containing tapioca starch pastes and selected hydrocolloids (Fuongfuchat et al., 2012). All of the abovementioned works focused on the analysis of the non-linear properties of the tested systems during shear flow. The obtained results are consistent with those obtained by classical methods (flow curve, yield point). However, by combining in a single experiment research on the properties in the range of linear and non-linear deformations, LAOS and FTR techniques open a new approach to the cumulated research on the mechanical properties of food. Application of LAOS and FTR techniques requires a specific mathematical formalism. Such formalism was previously rarely encountered in food science. Unfortunately, it is necessary to determine the appropriate physical quantities, which then are easily given an appropriate physical interpretation. It will be discussed in the later part of this work.

Non-linear rheology Large amplitudes oscillatory shear (LAOS) and Fourier transform rheology (FTR) methods are now more often used as a tool for describing the rheological phenomena occurring in complex structural fluids such as molten polymers, polymer solutions, polymer blends, W/O and O/W emulsions and foam. This is because these systems exhibit a broad spectrum of rheological properties, from Newtonian viscosity, plasticity to viscoelasticity or elastic-viscoplasticity. Application of LAOS and FTR techniques allows one to assess the fundamental rheological properties (e.g., shear modulus or yield stress), as well as those that were previously unattainable (e.g. Fourier spectra analysis, geometric decomposition, Chebyshev coefficients) (Hyun et al., 2011). Also a number of completely new rheological quantities have been introduced, whose physical interpretation allows better understanding of the phenomena occurring during the flow. All of these quantities can be derived as a result of only one experiment. Information about the rheological properties of the tested material obtained in this way is complete and characterizes it in terms of non-linear shear flow. Due to the possibility of structurally complex material testing, LAOS and FTR techniques can be an excellent tool for the analysis of food rheological properties. These methods are starting to be introduced into the canon of rheological testing of food (Melito, Daubert, & Foegeding, 2012). They can be used at the phase of designing a new food product, where the information about the behavior of the product in the case of large values of deformation (and more generally the movement) is essential. In the case of large (non-linear) deformations it is also possible to make deductions about the behavior of the product in the mouth during chewing. For this reason, LAOS and FTR methods can be used for example for preselection of food additives responsible for the shaping of product structure. Through the interpretation of LAOS experimental results, it is possible to indicate the additives responsible for shaping of the viscous, elastic and plastic properties of finished products, and also to investigate the interaction of a selected structure forming additives. LAOS technique is a convenient and inexpensive tool, because of performing only one type of experiment, providing virtually full information about the rheological properties of the additive.

The aim The aim of the study is a comprehensive LAOS and FTR analysis of rheological properties of foams obtained on the base of egg white protein, xanthan gum and apple pectins. The influence of the molecular mass and pectin's esterification level on the properties of the obtained foams will be analyzed. Materials and methods Materials Commercially available egg white protein (Ovopol, Poland) and the food additives xanthan gum (XG, Hortimex, Poland) and apple pectins of various methylation levels (Pektowin Jaslo, Poland) were used as investigated materials. The protein content in egg white calculated by the method of Kjeldahl was 83.87 ± 0.10%. The molecular masses of polysaccharides were chromatographically determined according to the method of Lukasiewicz and Kowalski (2012). The level of pectin methylation (de) was established according to Bochek, Zabivalova, and Petropavlovskii (2001). All DE measurements were made in triplicate. Table 1 presents molecular characteristics of the polysaccharides used in the study. Foam preparation The bases for foams were prepared in the relation of 9:1 (water: dry mass). The dry mass was composed of egg white protein and/or one or two hydrocolloids. Table 2 shows the proportions of dry mass used in the production of the investigated foams. The prepared foams were placed in a planetary mixer (FCM Stalgast, Poland) and whipped at 300 rpm. Foams were prepared in a container (20 L capacity) using a wire whip agitator with a changing diameter from 100 to 200 mm. Both the container and the rotor were supplied by the producer. Initial volume of all mixtures subjected to foaming was 2 L. Within the

Table 1 Molecular characteristics of polysaccharides.

Mn, g·mol−1 Mw, g·mol−1 Pd de, %

P1

P2

P3

XG

(0.88 ± 0.05) · 105 (7.6 ± 0.06) · 105 8.6 ± 1.2 67 ± 3

(0.81 ± 0.03) · 105 (15.76 ± 0.80) · 105 19.2 ± 3.1 59 ± 5

(0.86 ± 0.01) · 105 (16.04 ± 0.50) · 105 18.0 ± 2.9 50 ± 2

(0.022 ± 0.001) · 105 (19.60 ± 0.90) · 105 871 ± 40 –

P. Ptaszek / Food Research International 62 (2014) 299–307 Table 2 Concentration of egg white (w/w) in studied foams as a function of hydrocolloid concentration (w/w). XG Pi

0% 9.1% 8.8% 8.5% 8.2%

0% 0.3% 0.6% 0.9%

0.3% 8.8% 8.6% 8.2% 7.9%

0.6% 8.5% 8.2% 7.9% 7.6%

0.9% 8.2% 7.9% 7.6% 7.3%

301

into the measuring position. This manner of selection of a measurement sensor guarantees the lack of artifacts when making measurements with the use of large deformation amplitudes. The appropriate rheological measurements were made in triplicate at 23 °C. All time series obtained during the measurements were composed of 15 periods of which the last 6 periods were analyzed. Analysis of rheological properties

i = 1,2,3.

preliminary tests, the whipping time of 120 s was chosen. This time was based on the volume fraction of gas phase (ϕ) measurements. The criterion was set as maximum gas volume fraction during whipping. The basic properties of the produced foams are presented in Table 3. The detailed analysis of the physical and morphological properties of the foams will be shown in a separate publication which is presently in preparation.

The measurement concept based on the LAOS technique is analogous to the measurements which employ the application of small amplitudes within the range of linear viscoelasticity. The concept consists in subjecting the investigated material to the time-variable strain. Due to the ease of its analysis, most commonly it is a sinusoidal signal which adopts the following form (Hyun et al., 2011): γðωt Þ ¼ γ0 sinðωt Þ:

ð1Þ

For the shear stress the response can be expressed with the help of the following harmonic function:

Rheological measurements All rheological measurements were carried out with the help of an RS6000 rheometer (Haake, Germany) equipped with a system of cone– plate geometry (din = 35 mm, angle 2°) at the frequency of f = 1 Hz. The proper rheological studies were preceded by multiple tests in order to eliminate a slip of the investigated material on the sensor's walls. The preliminary studies included tests which used serrated sensors of plate–plate type, flat sensors of plate–plate type and the same sensors with abrasive paper of high gradation (3000) attached to the sensor. Experiments with the system of plate–cone type were also conducted. The successive step in the research was to select a measurement gap as this parameter plays a key role during analyses of dispersed systems. The set of sensors and the size of the measurement gap were empirically selected in the course of the tests. 95% reproducibility of the results was accepted as a criterion. This led to the elimination of both the corrugated and flat sensors of plate–plate type. The best results were acquired for the sensor of plate–plate type with abrasive paper attached and for the sensor of plate–cone type. As the sensor of plate–cone type was found to be easy in operation, it was decided to apply this system in combination with the measurement gap of 1 mm. This selection was also dictated by negligible damage of foam after lowering the sensor

τðt; ω; γ0 Þ ¼ γ0 

Xh

i ′ ″ Gn ðω; γ0 Þ  sinðnωt Þ þ Gn ðω; γ0 Þ  cosðnωt Þ : ð2Þ

nodd

In the case of small strains there is only one harmonic present and, hence, G′1 and G″1 become real (G′) and imaginary (G″) parts of the complex spring modulus (G* = G′ + jG″), well known from the studies of linear viscoelasticity. As high values of deformation amplitudes are applied, a larger number of harmonics are observed which are typical of the non-linear response of the material. The analysis of the results was arranged into two parts. The first part comprised the analysis of the dependencies of G′ and G″ moduli in the function of amplitude. The second part referred directly to the analysis of time series. Analysis of G′ and G″ Knowing the values of G′ and G″ as the function of amplitude, the shear modulus (G0) can be determined according to the following dependence: ′

G0 ¼ lim G ðγ0 Þ:

ð3Þ

γ0 →0

Table 3 Density (ρ, kg·m−3) and volume fraction of gas phase (ϕ) of egg white and hydrocolloid foams. XG

0% 0.3%

P1 P2 P3

0.6%

P1 P2 P3

0.9%

P1 P2 P3

0%

0.3%

0.6%

0.9%

ρ = 54 ± 15 ϕ = 0.95 ± 0.02 ρ = 112 ± 2 ϕ = 0.89 ± 0.01 ρ = 117 ± 2 ϕ = 0.89 ± 0.01 ρ = 118 ± 1 ϕ = 0.89 ± 0.01 ρ = 133 ± 3 ϕ = 0.87 ± 0.01 ρ = 144 ± 1 ϕ = 0.86 ± 0.01 ρ = 131 ± 2 ϕ = 0.87 ± 0.01 ρ = 145 ± 2 ϕ = 0.86 ± 0.01 ρ = 160 ± 1 ϕ = 0.85 ± 0.01 ρ = 149 ± 3 ϕ = 0.85 ± 0.01

ρ = 115 ± 15 ϕ = 0.90 ± 0.01 ρ = 127 ± 2 ϕ = 0.88 ± 0.01 ρ = 140 ± 1 ϕ = 0.87 ± 0.01 ρ = 134 ± 2 ϕ = 0.87 ± 0.01 ρ = 146 ± 2 ϕ = 0.86 ± 0.01 ρ = 153 ± 21 ϕ = 0.85 ± 0.01 ρ = 158 ± 2 ϕ = 0.84 ± 0.01 ρ = 151 ± 1 ϕ = 0.85 ± 0.01 ρ = 163 ± 3 ϕ = 0.85 ± 0.01 ρ = 152 ± 2 ϕ = 0.85 ± 0.01

ρ = 126 ± 1 ϕ = 0.87 ± 0.01 ρ = 114 ± 1 ϕ = 0.90 ± 0.01 ρ = 117 ± 2 ϕ = 0.88 ± 0.01 ρ = 114 ± 2 ϕ = 0.89 ± 0.01 ρ = 121 ± 1 ϕ = 0.89 ± 0.01 ρ = 144 ± 2 ϕ = 0.86 ± 0.01 ρ = 130 ± 3 ϕ = 0.87 ± 0.01 ρ = 131 ± 1 ϕ = 0.88 ± 0.01 ρ = 149 ± 2 ϕ = 0.86 ± 0.01 ρ = 147 ± 2 ϕ = 0.86 ± 0.01

ρ = 133 ± 2 ϕ = 0.89 ± 0.01 ρ = 112 ± 1 ϕ = 0.88 ± 0.01 ρ = 121 ± 1 ϕ = 0.88 ± 0.01 ρ = 122 ± 1 ϕ = 0.87 ± 0.01 ρ = 130 ± 1 ϕ = 0.88 ± 0.01 ρ = 137 ± 1 ϕ = 0.86 ± 0.01 ρ = 133 ± 2 ϕ = 0.87 ± 0.01 ρ = 147 ± 2 ϕ = 0.85 ± 0.01 ρ = 152 ± 2 ϕ = 0.86 ± 0.01 ρ = 144 ± 3 ϕ = 0.86 ± 0.01

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P. Ptaszek / Food Research International 62 (2014) 299–307

In the non-linear area, the analysis of the shear exponents was carried out (Miyazaki et al., 2006), hence: G′γ0

−β

and G″γ0

−δ

:

ð4Þ

The yield stress (τ0) was determined as an intersection point of β with the value of G0 in the coordinate system log–log. The G′ ~ γ − 0 value τ0 was counted on the base of the dependence τ0 = γ0|G*| (Marze, Guillermic, & Saint-Jalmes, 2009; Rouyer, Cohen-Addad, & Höhler, 2005). The analysis of the relation of the shear exponents β and δ plays an essential role in the investigation of the properties of the SGM systems. The values of β and δ are one of the criteria of the phenomenological estimation of the investigated system's metastability. The criteria were proposed by Miyazaki et al. (2006) and are as follows: 1. The peak present on the G″ curve is located in the range of amplitudes varying from 10−2 to 10°. 2. The peak is visible for that frequency for which the response of the material is elastic G′ N G″. β δ and G″ ~ γ− 3. The relation of the exponent β/δ (G′ ~ γ− 0 0 ) should equal to 2 for the highest values of the deformation amplitudes. Time series analysis In order to confirm the presence of the higher harmonics, the signal acquired in the experiment is subjected to a discrete Fourier transformation and, consequently, the signal's spectrum is obtained. The spectrum provides information on the presence and participation of individual harmonics in the analyzed phenomenon. However, the intensity of the discrete Fourier spectrum is dependent on the number of the periods of the analyzed signal. Therefore, the postulate of the signal intensity normalization against the signal intensity of the first harmonic (fundamental frequency) was introduced to the analysis of the harmonic components: I n=1 ≡

In : I1

ð5Þ

The normalization condition (Eq. (5)) enables a convenient, relative comparison of the intensities of individual harmonics. The most frequently applied method of estimation of the rheological non-linear properties based on In/1 (n = 3) can be expressed by the following quotation: Q≡

I3=1 γ20

allowed calculation of the In/1 and Q parameters according to Eqs. (5) and (6). Projection of forcing function and the response of the material onto the phase plane (γ,τ) resulted in obtaining the Lissajous pattern, on whose basis the amount of dissipated energy per cycle was estimated according to Eq. (7). The area integral in Eq. (7) was calculated numerically by the 4th order Newton–Cotes method. Statistical analysis A classical Student's t-test was applied for the statistical analysis. The hypothesis system was as follows: H0: β/δ = 2, H1: β/δ ≠ 2 (further explanations in the text). Calculations were carried out with the help of R software (R Core Team, 2012). Additionally, two-way and three-way analyses of variance (two-way, three-way ANOVA) against the type of pectin, its content in foam and the concentration of xanthan gum were carried out. R software was applied in the calculations. The successive analysis was conducted by the HSD Tukey's test. All calculations were made at the significance level of p = 0.05. Results and discussion

:

ð6Þ

The dissipation coefficient, defined by Eq. (7), constitutes another important parameter which is used in determining the amount of the dissipated energy (Ewoldt, Winter, Maxey, & McKinley, 2010):

φ≡

Fig. 1. Concept of determination of energy dissipation coefficient (φ).

∮ τðωt Þ  dγðωt Þ Ed ¼H : ðEd Þpp 4  γmax  τmax

ð7Þ

γmax means the amplitude of the strain applied (γ0) whereas τmax is equal to the highest value of stress. The magnitude φ in Eq. (7) is interpreted as a relation of the amount of energy dissipated by the studied material in one cycle to the amount of dissipated energy which would be produced if the investigated material was a pure plastic system. The concept of the parameter φ is shown in Fig. 1. The integral in Eq. (7) represents the area of the Lissajous figure, obtained by projecting the time course of γ(ωt) and τ(ωt) on the phase plane (γ, τ). Analysis of the time series relied on the determination of the Fourier transform with the help of the FFT (fast Fourier transform) method. This

The behavior of the complex spring modulus (G* = G′ + jG″) in the function of deformation amplitude (γ0) was first to be analyzed. The courses of both the real (G′) and imaginary (G″) parts of the analyzed modulus in the function of deformation amplitude appear in the background in the attached video materials (mov. 1,2,3). All analyzed foams have a typical range of linear viscoelasticity which is manifested by a parallel course of the moduli against the γ0 axis where G′ N G″. In the non-linear area, one can initially observe a typical equalization of the values of G′ and G″, and then the G′ value becomes lower than that of G″. This phenomenon is evidence that foams lose their ability to store energy in their structure in favor of energy dissipation due to the presence of the inner friction strength (the flow begins). The presence of large values of deformation causes the saturation of foam with mechanical energy. Next, it leads to the dissipation of energy through the occurrence of the flow. The majority of the analyzed systems displayed a characteristic maximum on the G″ curve, located in the area where G′ and G″ intersect. Pure white egg protein foams did not demonstrate such behavior (if such a maximum exists, it must be comparable with experimental noise). Supplementation of foam with solely XG causes appearance of

P. Ptaszek / Food Research International 62 (2014) 299–307

the aforementioned maximum and the area of the linear viscoelasticity becomes narrow, whereas supplementation with a single pectin (Pi = 1,2,3) also leads to the occurrence of a maximum whose value increases as the pectin concentration grows. However, in the case of pectins, the area of linear viscoelasticity does not become smaller. Upon supplementation of foams with both XG and Pi (i = 1,2,3), one can observe a shift towards the right side of the linear viscoelasticity limit, followed by a moderate formation of a maximum on the G″ curve. For these systems, the points of the G′ and G″ intersection and the location of the maximum on the G″ curve lie within the amplitude values γ0 ranging from 1 to 10. Table 1 summarizes the values of the β and δ exponents which are present in Eq. (2). The positive values of the exponents indicate that the analyzed foams are shear thinned. Table 4 also displays both the ratio of β to δ and the analysis of the significance of the values obtained against number 2 (Miyazaki et al., 2006). As demonstrated in Table 4, the value of the quotient of β/δ is significantly different than 2 in foams produced from pure white egg protein. Consequently, the foam obtained from pure egg white protein does not meet the requirements of metastability. Supplementation with XG only causes that a visible peak appears in the range of γ from 10−1 to 1, in which the requirement of G′ N G″ is met and the relation β/δ is 2 (Table 4). This means that the systems containing XG can be classified as metastable and their behavior can be analyzed according to the SGM theory (Miyazaki et al., 2006; Sollich, 1998; Sollich et al., 1997). The foams obtained on the base of protein and 0.3% wt pectins reveal properties which are similar to those of Table 4 Rheological parameters of analyzed foams. XG

0

0.3

β/δ τ0, Pa G″max, Pa G0, Pa β/δ

τ0, Pa

G″max, Pa

G0, Pa

0.6

β/δ

τ0, Pa

G″max, Pa

G0, Pa

0.9

β/δ

τ0, Pa

G″max, Pa

G0, Pa

a

P1 P2 P3 P1 P2 P3 P1 P2 P3 P1 P2 P3 P1 P2 P3 P1 P2 P3 P1 P2 P3 P1 P2 P3 P1 P2 P3 P1 P2 P3 P1 P2 P3 P1 P2 P3

0

0.3

2.68 ± 0.03a 125 ± 6 – 404 ± 12 2.88 ± 0.03a 2.52 ± 0.04a 2.33 ± 0.03a 100 ± 6 65 ± 2 53 ± 3 91 ± 1 43 ± 3 37 ± 4 425 ± 6 184 ± 8 174 ± 4 2.42 ± 0.06a 2.18 ± 0.01a 1.82 ± 0.02a 85 ± 1 34 ± 3 21 ± 1 92 ± 4 29 ± 1 41 ± 3 417 ± 13 184 ± 9 170 ± 6 2.05 ± 0.02 1.96 ± 0.01 1.96 ± 0.01 28 ± 1 24 ± 3 21 ± 1 81 ± 4 41 ± 2 38 ± 3 343 ± 23 163 ± 10 155 ± 12

1.94 21 63 250 2.27 2.24 1.95 23 39 20 76 25 27 280 112 112 2.14 2.24 2.10 11 24 27 69 33 27 236 138 118 2.09 2.26 2.21 7 46 45 80 25 34 236 111 138

0.6 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.02 3 7 16 0.01a 0.02a 0.01 1 1 2 3 1 2 9 4 2 0.03a 0.05a 0.03 1 2 2 3 2 2 6 4 3 0.03 0.02a 0.04a 1 3 2 2 3 2 16 9 7

2.02 27 60 218 2.24 2.15 2.02 27 70 45 51 27 27 201 209 120 2.39 2.22 2.19 32 78 58 52 27 25 203 127 110 2.52 2.38 2.21 29 79 80 54 25 29 198 113 131

0.9 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.01 2 4 20 0.04a 0.02a 0.05 2 1 1 3 2 1 4 7 6 0.02a 0.02a 0.03a 1 1 2 1 1 2 12 13 9 0.06a 0.04a 0.07a 3 2 1 3 1 3 7 6 3

Significant difference (Student t-test H0: β / δ = 2, H1: β / δ ≠ 2).

2.00 ± 0.02 38 ± 4 72 ± 5 265 ± 17 2.29 ± 0.07a 2.20 ± 0.02a 2.25 ± 0.03a 51 ± 3 89 ± 2 74 ± 1 58 ± 2 26 ± 1 22 ± 1 237 ± 6 119 ± 3 100 ± 4 2.36 ± 0.04a 2.26 ± 0.03a 2.22 ± 0.01a 68 ± 1 83 ± 2 78 ± 2 77 ± 6 26 ± 1 27 ± 2 332 ± 6 122 ± 3 123 ± 2 2.48 ± 0.04a 2.38 ± 0.02a 2.24 ± 0.05a 57 ± 1 83 ± 3 88 ± 3 67 ± 1 27 ± 1 30 ± 2 273 ± 10 139 ± 8 147 ± 9

303

foams containing protein only and they do not easily fall within the classification as SGM systems. The foams are characterized by a descending value of β/δ in the function of the methylation level and this value considerably differs from 2 (Table 4). With the following increase in the pectin concentration (0.6% wt) the curve G′ shifts towards lower values of the deformation amplitude; the observed γ0 range is located in the range previously proposed by Miyazaki et al. (2006) but the value β/δ still remains distinctly different from 2. The systems containing 0.9% pectin meet all three requirements, presented above, and therefore they can be phenomenologically classified as SGM. Relaxation phenomena occur very slowly in such systems (Sollich, 1998; Sollich et al., 1997). From a practical point of view this means that the foam classified as SGM will maintain a given shape for a long time. Also, the degradation of such foam will occur in a long time period. The properties of XG and pectin based foams are dependent on the level of pectin methylation. The value of β/δ undergoes changes, and solely in a few cases, for the pectin P3, it takes the value of 2. The variance analysis (three-way ANOVA, Table 5) revealed that the methylation level significantly influences the value of the relation of the exponents (β/δ). The effect of the interaction between pectins and XG was also observed. Further analysis based on the two-way ANOVA (Table 6) showed that only P1 pectin has an influence on the value of β/δ. Supplementation with XG, however, significantly influenced the relation of the exponents of the systems containing P1 and P2; still, a system with P3 did not show such behavior. Moreover, the interaction of pectin with XG in all three cases was confirmed (Table 3). In Tables 7 and 8, the results of the significance are displayed in pairs for comparison purposes. For β/δ, an effect of “saturation” of XG against pectin can be observed. In the case of P1, all values significantly differ from one another, whereas in the case of P2 only two values are different. Due to the fact that the variance analysis had not shown any considerable influence of XG on the β/δ values, measurements for P3 were not carried out (Table 6). This phenomenon has been also documented in the video materials (mov 1,2,3). The viscoelasticity range is subjected to a visible increase. The intersection point of G′(γ0) with G″(γ0) and the peak on the curve G″ are located beyond the value of γ0 = 1. The yield stress (τ0) is another important parameter, determined on the basis of G′(γ0) and G″(γ0). The values of τ0 are presented in Table 4. The highest value of τ0 = 125 Pa was observed for the foam obtained from egg white protein only. Supplementation with solely XG decreases the value of τ0 almost two- or three-fold. The reduction of the yield stress value also occurs in the systems containing pectins and it depends on the methylation level of pectin (Table 4, column I). For instance, the value τ0 for the lowest P1 concentration is 100 Pa, whereas for the highest concentration the value is more than two-fold lower. In the case of foams with P2, at first the yield stress decreases two-fold in comparison to egg white-based foam, and further changes become less and less salient. The relation of the yield stress value to pectin concentration in P3 containing foams is qualitatively similar. As demonstrated in Table 5, xanthan gum has a significant influence on the yield stress and the pectin-XG interaction is visible. The two-way ANOVA analysis (Table 6) showed that pectin concentration has no impact on τ0. However, it was demonstrated that XG has an evident influence on the formation of τ0. The interaction between pectin and xanthan gum is manifested by the increase of the value of τ0 along with the increase Table 5 Results of three-way ANOVA for β/δ and τ0 — influence of XG and pectin (P) de and concentration. Three-way ANOVA

β/δ τ0 a

Pde

Pc

XGc

a

a

a

–

–

a

Significant difference.

Pde:Pc – –

Pde:XGc

Pc:XGc

Pde:Pc:XGc

– –

a

– –

a

304

P. Ptaszek / Food Research International 62 (2014) 299–307

of the XG concentration in foam (additional information is included in Table 4; analysis against lines). Table 7 displays the results of the in-pair comparison of the influence of specific XG concentrations on the yield stress value. In the case of the P1 containing system, the only observed similarity relates to the concentrations of 0.3% wt of XG and 0.6% wt of XG. The pair comparison for P2 and P3 revealed that the systems show the same growing dependence of τ0 on XG content, which may be interpreted as an increase of the systems' elasticity. Fig. 2a and b depicts Fourier spectra of the selected foams. In the case of foam produced on the base of egg white protein, the number of harmonics visibly increases as the amplitude of deformations grows. This is an indication of a very complex response of the material to the applied deformation within the non-linear range. The third and fifth harmonics reach the maximum level. Similar behavior was observed by Hyun, Nam, Wilhellm, Ahn, and Lee (2006) in the case of a weak gel of synthetic polymers. Supplementation with XG causes a visible decrease in the number of the observed harmonics and their intensity. Also, evident maxima are absent in the courses of individual harmonics. Some pectins reveal an even greater effect of suppression. Higher harmonics (11ω–19ω) disappear within the range of the observed deformation amplitudes. Fig. 2a and b presents the influence of the supplementation with both XG and Pi (i = 1,2,3); it can be seen that the addition of both hydrocolloids markedly suppresses higher harmonics. A remarkable effect is ascribed here only to the harmonics ranging from 3ω to 9ω. A change in XG level at a constant pectin concentration also leads to the disappearance of the higher harmonics. This indicates that as the amount of the hydrocolloid increases, the response of the material to the applied deformation becomes less complicated (in terms of the structure of the Fourier spectrum). As shown in Fig. 1, for the ideal plastic systems, the Lissajous figure has a rectangular shape. This means that the system response to an applied strain is a square wave. Fourier transformation of such a signal results in a very complex spectrum. The phenomenon of occurrence of a large number of harmonics can be explained by the characteristics for egg protein foam plasticity. In the real case discussed in this work, foams with a low level of hydrocolloids show not only purely plastic properties but also viscoelastic. It causes that the calculated Lissajous figures are similar to a rectangle, which means that the Fourier transform will also contain a large number of higher harmonics. Such foams will exhibit strong nonlinear properties, and this will be their characteristic feature. It should be stressed that the quantity and intensity of higher harmonics in the Fourier spectrum should be interpreted as the measure of nonlinearity of the material response. In the analyzed cases, a great number of harmonics observed for the foam containing egg white protein only means that the response is close to plasticity, which confirms the analysis of Lissajous figures (Fig. 1, mov. 1,2,3); the obtained

shape is closer to a rectangle. Supplementation of XG causes the suppression of harmonics above 3ω. The response of such a foam is also nonlinear (due to the presence of 3ω) but closer to the response of a material with viscous properties, as is confirmed by the shape of the obtained Lissajous figures (Fig. 1, mov. 1,2,3), which become ellipsoidal. The changes in the behavior of the third harmonic are partially visible in Fig. 3. The figure displays dependencies Q(γ0). As far as the low values of γ0 are concerned, the values of the Q parameter should be considered solely demonstratively as the values refer to the linear range and the value of the third harmonic is very low or equal to zero. Interpretable values are obtained for the non-linear area. One may assume that the interpretable values of Q of the studied systems begin for the amplitudes located to the right side of the vertical lines in Fig. 3. The lines represent amplitudes for which the yield stresses were (τ0) determined. In the case of foam containing egg white protein only, firstly, a maximum appears in the course of Q(γ0), then the curve suddenly descends. The foams containing XG only (line I) show analogous behavior with the exception that the maximum slowly disappears as the concentration of the hydrocolloid increases. An opposite situation is observed for the foams containing Pi (i = 1,2,3; column I). The aforementioned maximum increases as the pectin concentration grows. Subsequently, the values of Q become lower. The systems which contain egg white protein, XG and Pi (i = 1,2,3) demonstrate variable behavior in the course of Q(γ0), depending on the pectin methylation level. In the case of the foams with XG and P1, the dependence is illustrated by a line, which, initially, gradually descends within the range of the average amplitudes to rapidly fall as the dependence reaches high values of γ0. The maximum is reached only for the foams containing a combination of 0.3% wt XG and 0.3% wt P1 or 0.3% wt XG and 0.6% wt P1. The discussed behavior is particularly visible in the attached video materials (mov. 1,2,3). The presented Lissajous figures, initially in the observed scale, narrow down to a point due to the low deformation amplitude (this phenomenon is visible in the linear range of viscoelasticity). Then, the area of the figure undergoes a considerable enlargement which indicates that the system dissipates an increasing amount of mechanical energy in a single period. The complexity of the Lissajous curves is dependent on the complex system's answer to the sinusoidal variable deformation. The complexity stems from the existence of several harmonics which are present in the response of the material, which is directly manifested by the complexity of the Fourier spectrum mentioned above. The first row represents a system consisting of pure egg white protein supplemented with XG only. The displayed Lissajous figures undergo a visible evolution as the XG concentration in the foam grows. The figure describing the properties of the egg white proteinconsisting foam acquires the most complex shape within the range of the non-linear deformation. Supplementation with XG leads to a gradual smoothing of the figure. However, supplementation with solely pectin Pi (i = 1,2,3) has a different influence on the discussed phenomena. Initially, supplementation with pectins (first column) does not cause a smoothing of the Lissajous figure and its longitudinal shape remains. It is only after pectin Pi (i = 1,2,3) reaches the concentration of 0.9% wt that a figure, similar in shape and area to the figure representing foam supplemented with 0.3% wt XG, is obtained. Supplementation with both Pi (i = 1,2,3) and XG induced the Lissajous figures to manifest a shape similar to an ellipse. Furthermore,

Table 7 Pairwise comparison — influence of XG.

Table 8 Pairwise comparison — influence of P1.

Table 6 Results of two-way ANOVA for β/δ and τ0 — influence of XG and pectin concentration. Two-way ANOVA

β/δ τ0 a

XGP1

P1:XG

a

a

a

–

a

a

P2

XGP2

P2:XG

P3

– –

a

a

a

a

– –

XGP3

P3:XG

–

a

a

a

Significant difference.

XG

β/δP1 0

0.3 0.6 0.9 a

P1

0.3

a

NA

a

a

a

a

β/δP2 0.6

0

NA NA –

a a

–

0.3 NA – –

τP1 0 0.6

0

NA NA –

a

τP2 0 0.3

0.6

0 –

a

NA –

NA NA

a

a

a

a

a

Significant difference (HSD-Tukey test).

τP3 0 0.3 NA – –

0.6

0

P1 0.3

NA NA

–

NA

a

a

a

a

–

β/δ

0.6

0

0.3

0.6

NA NA

a

NA – –

NA NA –

a

0.3 0.6 0.9 a

– –

Significant difference (HSD-Tukey test).

P. Ptaszek / Food Research International 62 (2014) 299–307

305

A

ω

ω

ω

ω

γ ω

ω

ω

ω

ω

ω

ω

ω

ω

γ ω

ω

ω

ω

ω

ω

ω

ω

ω

ω

ω

ω

ω

ω

ω

γ ω

ω

ω

ω

ω

ω

ω

ω

γ ω

ω

ω

ω

ω

ω

ω

ω

ω

ω

ω

ω

Fig. 2. a, b. Fourier spectra in function of strain amplitudes for selected foams.

a synergistic effect of pectins and xanthan gum is clearly noticeable. The change in the nature of the figures in the function of strain amplitude (γ0) poses a particularly interesting issue. Solely, a point is noticeable within the linear range of the viscoelasticity which results from the low value of the deformation amplitude. However, as the value of γ0 increases, the shape of the figure becomes more ellipsoidal. The ellipse is extended in parallel to its longer semi-axis; this shape of the figure implicates viscoelastic behavior. Upon passing the yield stress τ0, the length of the shorter semi-axis of the ellipse suddenly begins to grow, resulting in the adoption of the shape described above. The further analysis of the Lissajous figure relates to the changes in its area. The area is considered as a hysteresis and is interpreted as the amount of energy dissipated by the system within one period. This notion is supported by the surface integral in Eq. (7). Fig. 3 displays changes of the energy dissipation coefficient φ in the function of γ0. The sigmoidal nature of the function is related to the fact that in the linear range of the viscoelasticity the amount of energy dissipated within one period is approximately constant in the function of γ0. Subsequently, the amount of the dissipated energy rapidly increases, which is associated with the passing of the yield stress, beyond which viscous forces dominate. The egg white protein-based foam shows a maximum within the non-linear range, and, subsequently, the course of φ becomes parallel to the γ0 axis. Supplementation with solely XG induces a steady behavior and the transition to a flatter characteristic φ(γ0) within the nonlinear range. Addition of pectins only caused a more rapid increase in the characteristic φ(γ0) after exceeding yield stress. Subsequently, depending on the pectin content, the characteristic initially adopts a moderate behavior and achieves a slight maximum during further development. The influence of the individual pectins on the nature of the foams is difficult to differentiate. It is only evident that foams with

P1 dissipate more energy in the first phase of the flow (as soon as τ0 has been passed). This suggests that systems containing P1 lose their elastic properties faster and the viscous behavior becomes predominant. However, the behaviors of foams with both P2 and P3 are almost identical. The foams with XG and P1 are characterized by rapid energy dissipation which is manifested by a shorter parallel course along the γ0 axis than the ones present in the XG P2 or P3 systems. The area of the primary parallel course of the dependence φ(γ0) for egg white protein- and XG-containing foams became visibly extended upon supplementation with an increasing amount of P2 and P3. The XG, P2 or P3 systems do not have an inflection point and are characterized by slow development of sigmoid function. This phenomenon is related to the larger elasticity of the systems compared with the foams with XG or Pi (i = 1,2,3) only. The foams containing XG, P2 and P3 are more prone to accumulate the mechanical energy in their structure than the foams with XG and P1. Similar behavior of the discussed foams can result from similar molecular characteristics of P2, P3, and XG (Table 2). Hydrocolloids used in production of analyzed foams are characterized by a similar average molecular weight (Mw). In the light of the theory of similarity of rheological phenomena it means the similar mechanism of dissipation and accumulation of mechanical energy by the analyzed foams (Ferry, 1980). Moreover, the foams dissipate very similar amounts of energy in the field of the mechanical forces, which is manifested by overlapping of the Q(γ0) courses. The majority of the courses tend towards the limiting value of φ ≈ 0.8 and at the proximity of this point they reach a maximum or plateau. The value φ ≈ 0.8 relates to the viscosity of the studied systems. As Eq. (7) demonstrates, φ = 1 corresponds to a perfectly plastic body. The investigated systems exhibit behavior which is typical for elasto-viscoplastic bodies. This indicates that despite the fact that large

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P. Ptaszek / Food Research International 62 (2014) 299–307

e , P3 ○, for Q: P1 +, P2 ●, P3 × , for: P1\, P2 --, P3 - - . Fig. 3. Dependence of energy dissipation coefficient (φ) and Q in function of strain amplitudes. For φ: P1 □, P2 Δ

amounts of energy are dissipated through the flow and the friction, the systems also reveal elastic properties (for the perfectly elastic body φ = 1), and thus they are capable of storing energy in their structure. Additionally, the value of the dissipation coefficient for perfectly viscous liquid is equal to φ = π/4 ≈ 0.785. This means that the analyzed values refer to the viscous flow. The values of φ decrease upon exceeding the maximum due to the presence of elastic forces. Fig. 3 also depicts the values of the deformation amplitudes (γ0) which correspond to the yield stresses reached by analyzed foams (τ0, Table 4). This image is consistent with the previously described interaction of pectins and XG; the amplitude at which τ0 is present shifts towards higher values. Conclusions Foams consisting of egg white protein, pectin of different methylation level and xanthan gum were investigated in terms of their rheological properties and their non-linear LAOS rheological properties. The type of pectin significantly influences both the yield stress and the relation of shear exponents within the range of large amplitudes. It was demonstrated by an extension of the observation horizon of the linear viscoelastic properties and by disappearance of the higher harmonics in the Fourier spectrum for large γ0. The presence of the higher harmonics of relatively great intensity in the Fourier spectrum can be treated as a criterion for the selection of

systems in terms of their nonlinear rheological behavior. Because of that the foam containing egg white protein only was classified among systems with the dominance of plastic properties, while foams with hydrocolloids, exhibiting disappearance of the higher harmonics (except 3ω), were classified among systems with the dominance of viscous features. The dependence Q(γ0) has a visible inflection point, which suggests that the systems have entered a non-linear area. As soon as the point is exceeded, the dependence gradually decreases, which indicates that the non-linear character of the analyzed rheological phenomena is increasing. The prevalence of the viscous contributions is visible when analyzing the Lissajous figures in the γ0 function. Their shape becomes ecliptic as the polysaccharide concentration grows. This can also be interpreted as disappearance of the higher harmonic (shape reduction). The alterations in the values of the area of the Lissajous figures caused by the increase in the polysaccharide concentration imply that the investigated foams dissipate more energy. This can also be interpreted as the disappearance of the higher harmonic (shape reduction). This corresponds to the increase in the value of the energy dissipation coefficient (φ), which approximates the value of 0.8. Such behavior is typical for systems in a flow area. The presented data suggest that both LAOS and FTR methods can be successfully applied in the analysis of the non-linear rheological properties of wet foams. Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.foodres.2014.03.002.

P. Ptaszek / Food Research International 62 (2014) 299–307

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