Accepted Manuscript The analysis of the influence of xanthan gum and apple pectins on egg white protein foams using the large amplitude oscillatory shear method Paweł Ptaszek, Maciej Kabziński, Anna Ptaszek, Kacper Kaczmarczyk, Joanna Kruk, Agata Bieńczak PII:
S0268-005X(15)30116-8
DOI:
10.1016/j.foodhyd.2015.10.010
Reference:
FOOHYD 3164
To appear in:
Food Hydrocolloids
Received Date: 8 January 2015 Revised Date:
13 October 2015
Accepted Date: 14 October 2015
Please cite this article as: Ptaszek, P., Kabziński, M., Ptaszek, A., Kaczmarczyk, K., Kruk, J., Bieńczak, A., The analysis of the influence of xanthan gum and apple pectins on egg white protein foams using the large amplitude oscillatory shear method, Food Hydrocolloids (2015), doi: 10.1016/ j.foodhyd.2015.10.010. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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stress
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Chebyshev harmonics e3 e5 e7 strain amplitude
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ACCEPTED MANUSCRIPT The analysis of the influence of xanthan gum and apple pectins on egg white protein foams using
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the large amplitude oscillatory shear method
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Paweł Ptaszek1*, Maciej Kabziński1, Anna Ptaszek1, Kacper Kaczmarczyk1, Joanna Kruk1, Agata
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Bieńczak2
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Machinery for Food Industry, ul. Balicka 122, 30-149 Kraków, Poland.
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48126624761
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Agriculture University in Krakow, Faculty of Food Technology, Department of Engineering and
Industrial Institute of Agricultural Engineering, ul. Starolecka 31, 60-963 Poznań, Poland.
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corresponding author: Paweł Ptaszek, e-mail:
[email protected], phone: 48126624768, fax
Abstract: This research study analysed the rheological properties of fresh food foams based on egg
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white protein, and with the addition of apple pectins and xanthan gum. The rheological analysis was
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carried out using the large amplitude oscillatory shear (LAOS) technique. From the obtained results
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two types of Lissajous figures were constructed, describing the elastic and viscous properties. The
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obtained figures were subjected to geometrical decomposition, which resulted in the determination of
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the stress values characteristic of nonlinear purely elastic and purely viscous properties. The Fast
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Chebyshev Transform allowed for the calculation of the Chebyshev coefficients, and further detailed
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analysis of rheological behaviour of foams as a function of strain amplitude. The determination of the
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values of elastic and viscous Chebyshev coefficients allowed for the interpretation, with high
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resolution, of nonlinear rheological properties of the obtained foams.
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Keywords: foam, hydrocolloids, egg white protein, large amplitudes oscillatory shear (LAOS),
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geometrical decomposition
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1.
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Foams hold a prominent place among various food systems (Miyazaki et al. 2006; Balerin et al. 2007);
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they are multi-phase (dispersed) media, consisting of a liquid or continuous phase, in which a gas
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phase or air bubbles are dispersed. Their applications range from products such as ice creams, whipped
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cream or mousse, to baked goods (Perez et al. 2012). The main purposes for foaming food products
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Introduction
ACCEPTED MANUSCRIPT are: reduction of the product’s density, diminishing its caloric value, modification of its texture and
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rheological properties (Żmudziński et al. 2014; Liszka-Skoczylas et al. 2014), as well as improvement
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of its sensory features (Perez et al., 2012). The food foams prepared with egg white protein as a base
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constitute quite a wide-ranging group of foams. The egg white protein comprises high amounts of
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ovoalbumin, ovotransferrin and lysozyme (Al-Hakkak and Al-Hakkak 2010) and has excellent
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foaming capabilities (Van der Plancken et al. 2007; Foegeding and Davis 2011). Owing to these
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properties, the egg white protein is frequently used in the production of a variety of cakes and
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meringues (Van der Plancken et al. 2007).
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Due to their thermodynamic instability, foams tend to disintegrate over time (Solich et al. 1997;
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Sollich 1998; Makri and Doxastakis 2006; Stevenson et al. 2007; Indrawati et al. 2008). For this
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reason, various stabilizers are applied to the technological processes (Campbell and Mougeot 1999;
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Dickinson 2003; Miquelim et al. 2011). In the case of using hydrocolloids (xanthan gum or pectins)
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(Prins 1988; Miquelim et al. 2010), the foam stabilization is a result of increased viscosity of the
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continuous phase (Thakur at al. 2003; Mleko et al. 2007; Patino and Pilosof 2011; Ptaszek 2014).
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The addition of these hydrocolloids causes the foams’ rheological properties to become quite complex;
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their flow starts to deviate strongly from the Newton’s law and nonlinear behaviours begin to occur.
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The reason for these non-linear behaviours, characteristic of most food liquids, is the dependence of
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viscosity on the conditions and the duration of the shear process. Moreover, food products may
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constitute viscoelastic systems, exhibiting the characteristics of multi-phase liquids or solids, eg.
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biopolymer solutions, dough or starch paste-based products. These systems become viscoelastic due to
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being composed mainly of biopolymers, whose molecular structures are capable of both storing, as
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well as dissipating of mechanical energy (Ferry 1980).
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Until now, the research of these kinds of systems has been usually conducted in the linear
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viscoelasticity range – in the time and frequency domains.
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More recently, methods expanding the capabilities of classical studies on frequency have gained the
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attention of scientists. The methods are: Large Amplitude Oscillatory Shear (LAOS) (Hyun et al.
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2006; Klein et al. 2007) and Fourier Transform Rheology (FTR) (Hyun and Wilhelm 2009; Hyun et al.
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2011), and they consist of subjecting the material to deformations that are sinusoidally variable within
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time and exhibit sufficiently high amplitude (γ0):
γ (ωt ) = γ 0 sin(ωt )
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(1)
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Under nonlinear conditions, the response of the material (stress) can be estimated with high accuracy
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using the following harmonic function:
τ (t; ω , γ 0 ) = γ 0 ⋅
[
]
∑ Gn (ω , γ 0 ) ⋅ sin(nωt ) + Gn (ω , γ 0 ) ⋅ cos(nωt ) (2)
n:odd
'
"
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In the case of small strains there is only one harmonic present, and therefore G’1 and G”1 become real
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(G’) and imaginary (G”) parts of the complex spring modulus (G*=G’+jG”), well known from the
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studies of linear viscoelasticity (Ferry 1980).
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The analysis of the obtained function requires not only the application of an extended harmonic
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analysis based on the Fourier transform, but also a study using the phase plane (analysis of the
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Lissajous figures) (Hyun et al. 2011). The analysis based on the Lissajous figures in a 3-D coordinate
66
system deserves particular attention (Ewoldt and Mckinley 2010b). This 3D figure is created within a
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coordinate system illustrating relations of deformation (γ) to shear rate ( γ& ) and stress (τ). The
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obtained closed curve represents both elastic and viscous properties of the examined system. Such
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figure can be split into two projections in 2-D coordinate systems (Fig. 1), namely: elastic stress
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(deformation) ( τ ' (γ ) ) and viscous stress (shear rate) τ ' ' (γ& ) (Cho et al. 2005). While the first figure
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describes the elastic properties of the system, the second figure represents the viscous properties. The
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described technique of separation into two 2-D Lissajous curves is based on the fact, that there is no
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possibility, in nonlinear area, to easily separate the obtained signal into two parts that would describe
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purely elastic or purely viscous behaviour.
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The studies using the LAOS technique and the analysis based on the Chebyshev coefficients provide a
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new, and increasingly popular, approach to the analysis of food systems. This group of methods has
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been previously applied in tests of rheological properties of pastes and dough (Ng and McKinley
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2010; Ng et al. 2011; Fuongfuchat et al. 2012), xanthan gum solution (Ewoldt et al. 2010) and O/W-
79
as well as W/O-type emulsions (Ewoldt et al. 2008). The LAOS methods were also used to analyse the
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rheological properties of cheeses (Melito et al. 2012) and food foams, beers (Wilhelm et al. 2012), and
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foams containing egg white proteins and non-starch hydrocolloids (Ptaszek 2014, 2015). These
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characteristics of substrates and food products. Another benefit of this approach is, that there is no
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need to use constitutive equations to isolate the purely viscous and purely elastic stresses in the non-
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linear range (Saramito 2007; Ewoldt et al. 2008; Saramito 2009). Apart from research value, it allows
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for new possibilities in designing and modelling of innovative food products, according to consumer
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requirements. Therefore it seems quite beneficial to utilise the LAOS methods in the analysis of the
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rheological properties of food products.
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In the case of previously described dispersed gas-liquid systems containing egg white protein and non-
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starch hydrocolloids (Ptaszek, 2014), we can expect various rheological behaviours. This is because
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the rheological properties of solutions containing proteins and hydrocolloids exhibit huge deviations
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from the Newton’s Law. With the introduction of the gaseous phase into the system (eg. air), the
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rheological response of these systems during flow becomes even more complex. The analysis of these
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foams, as well as their behaviour in the non-linear range, seems to be of key importance, due to the
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increasing interest in the usage of hydrocolloids as stabilisers for foams derived from animal proteins.
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The aim of this work was the application of decomposed Lissajous figures and the Chebyshev
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coefficients to carry out the complex analysis of the nonlinear rheological properties of fresh wet
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foams, prepared with egg white protein and added hydrocolloids i.e. xanthan gum (XG) and pectin (P).
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2. Materials and methods
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3.1
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In this study, the research materials comprised commercially available egg white protein (Ovopol,
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Poland) and food additives: xanthan gum (XG, Hortimex, Poland) and apple pectin, methylated at
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lowest level (P, Pektowin Jaslo, Poland). The protein content in egg white, calculated by the Kjeldahl
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method (ISO-1871:2009), was 83.9±0.1%.
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The molecular masses of polysaccharides were chromatographically determined according to the
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method of Lukasiewicz and Kowalski (2012). For the xanthan gum the following parameters were
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obtained: weighted molecular mass Mw=(19.6±0.9)·105 g·mol-1, number molecular mass
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Mn=(0.022±0.001)·105
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polydispersity
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and
for
pectin
respectively:
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Mw=(16.04±0.50)·105 g·mol-1, Mn=(86±0.01)·105 g·mol-1, polydispersity 18.0±2.9. The level of
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pectin’s methylation DE=50±2 was established according to Bochek et al. (2001).
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3.2
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The base for foams was prepared in the ratio of 9:1 (water: dry mass). The dry mass was composed of
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egg white protein and either one, or two, of the hydrocolloids. Table 1 shows the proportions of dry
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mass used in the production of the studied foams. The prepared foam bases were placed in an
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industrial planetary mixer (FCM Stalgast, Poland) and whipped at 300 rpm. The foams were prepared
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in a 20L container using a wire whip agitator with diameters varying from 100 to 200 mm. The initial
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volume of all mixtures subjected to foaming was 2 L. Based on preliminary tests, the whipping time
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was set to 120 s (Ptaszek 2014). This timescale was chosen based on the volume fraction of the gas
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phase (φ). The basic properties of the produced foams are presented in an earlier work (Ptaszek et al.
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2015). The pH value of all solutions (proteins and proteins-hydrocolloids) was 6.
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For the obtained foams, stability tests were performed according to the methodology proposed in the
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study by Żmudziński et al. (2014).
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3.3
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All rheological measurements were carried out using an RS6000 rheometer (Haake, Germany)
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equipped with a cone-plate geometry system (diameter of cone din = 35 mm, angle between cone and
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plate 2°) at the f=1 Hz frequency and for amplitudes in the γo range of 0.001 to 20. The rheological
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studies were preceded by multiple tests to eliminate the slip of the investigated material on the cone-
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plate walls. The preliminary studies included tests with the following measurement units: corrugated
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plate-plate type, flat plate-plate type, plate-plate with abrasive paper of high gradation (3000) attached,
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as well as plate-cone type geometry.
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The next step in the research was to select a measurement gap, as this particular parameter plays a key
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role in tests on dispersed systems. A set of measurement units and the size of the measurement gap
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were empirically determined in the course of the tests. 95% reproducibility of the results was accepted
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as a criterion. This led to the elimination of both the corrugated and flat plate-plate devices. The best
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results were obtained for the abrasive paper plate-plate and for the plate-cone devices. As the plate-
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measurement gap of 1 mm.
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All rheological measurements were carried out immediately after the preparation of the foams. The
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timescale of the experiment was selected to be shorter than the degradation time constants of the pure
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egg white protein foam, and set at 10 minutes. The appropriate rheological measurements were made
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in triplicate at 23°C. All time series obtained during the measurements were composed of 15 periods,
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of which the last 6 periods were analysed. There was no foam drainage observed after the completion
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of rheological measurements.
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Simultaneously, we performed the measurements of the signal to noise ratio (S/N). The S/N ratio is
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defined as the ratio of the amplitude of the highest peak, divided by the standard deviation of the noise
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(Wilhelm et al. 2012). The preliminary rheological tests were carried out using the described cone-
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plate geometry. The calculation of the signal to noise ratio (S/N) was done as per procedures proposed
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by Wilhelm (Wilhelm et al. 1999; Wilhelm et al. 2012). As a first step,the rheological test was
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performed for a Newtonian liquid (glycerine), in order to determine the intensity of nonlinear effects
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generated by the rheometer. Based on the resulting Fourier spectrum, the ratio of S/N was estimated at
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9·104. The same procedure was performed on the studied foams and in this case the S/N ratio was
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estimated at 8.5·104.
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3.4
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The method of geometrical decomposition of the 2-D Lissajous figures, proposed by Cho et al., was
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applied to our study (Cho et al. 2005). According to the premise of this method, stresses (τ) can be
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subjected to the decomposition as expressed by the equation:
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τ ( x, y ) =
τ (x, y ) − τ (− x, y ) τ (x, y ) − τ (x,− y ) 2
+
2
= τ ' ( x ) + τ " ( y ) (3)
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x = γ , y = γ& / ω ; where the magnitude τ’(x;γ0,ω) stands for elastic stress, and the magnitude
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τ”(y;γ0,ω) corresponds to viscous stress. This indicates, that two curves should be obtained, as
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presented in Fig. 1. The curves split the Lissajous figure into two parts of equal area. The advantage of
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this approach is the decomposition of the experimentally obtained non-linear signal, into parts
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corresponding to the elastic and viscous properties respectively, without the need to apply any
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The curves may be subjected to further decomposition. For this purpose two methods are used: the
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first method applies regression analysis and the least squares method (Cho et al. 2005), whereas the
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second procedure is based on the Chebyshev polynomials of the first kind (Ewoldt et al. 2008),
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obtained according to the recurrence rule:
T0 ( x ) = 1
T1 ( x ) = x
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(4)
Then, τ’and τ” can be expressed by the following dependencies:
τ ' (x ) = γ 0 170
∑ n:odd
en (ω , γ 0 ) ⋅ Tn ( x )
∑
v n (ω , γ 0 ) ⋅ Tn ( y )
(5),
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Tn ( x ) = 2 x ⋅ Tn−1 ( x ) − Tn −2 ( x )
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n:odd
Where x = x / γ 0 = γ / γ 0 , y = y / γ 0 = γ& / γ&0 ; the scaling is a result of the conditions of the orthogonality
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of Chebyshev polynomials (Boyd 2001). The coefficients en and vn are called Chebyshev weighted
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coefficients and they correspond to elastic and viscous parts in the non-linear viscoelasticity,
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respectively. The distribution of values of the en and vn coefficients is depicted in Fig. 1. It should be
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mentioned, that Fourier coefficients (G’n,G”n) in the eq. 2 fully characterize the response of the
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material within time range; however, the physical interpretation of the higher harmonics may only be
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carried out based on the en and vn Chebyshev coefficients (Ewoldt et al. 2008; Hyun et al. 2011).
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Chebyshev coefficients may have both positive and negative values (Hyun et al. 2011). Usually, the
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interpretation of liquid’s properties may be carried out, by determining the values of e3 and v3:
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> 0 strain − stiffening > 0 shear − thickening e3 = = 0 linear elastic v3 = = 0 linear viscous (Newtonian ) < 0 strain − softening < 0 shear − thinning
(6)
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3. Results
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The first indication of the destabilisation of the egg white protein foam, in the form of drainage, was
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noted after 10 minutes from the moment the foam was prepared. After this time, the amount of
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effluent obtained accounted for 5% of total volume of the egg white protein foam. The addition of
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xanthan gum at 0.3g resulted in the foam that was stable within the specified experiment timeframe.
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to the base foam, as the drainage was noted after 40 minutes.
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All analysed foams exhibited ranges characteristic of linear viscoelasticity (fig. 2), which was
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manifested by a parallel course of the moduli to the γ0 axis, where G’ > G”. In the non-linear range,
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one can initially observe typical equalization of the G' and G” values, and then the G’ value becomes
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lower than that of G”. The Lissajous figures, discussed in the work by Ptaszek (2014) were subjected
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to geometrical decomposition and as a result, corresponding families of curves were obtained,
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representing non-linear purely elastic (τ’) (Fig. 3a) and purely viscous properties (τ”) (Fig. 3b).
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Figure 3a demonstrates the Lissajous figures in the (γ, τ) coordinate system. The figures illustrate the
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elastic part of the foam’s response to the applied deformation. Upon leaving the area of linear
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viscoelasticity, each of the foams begins to exhibit a distinct rheological behaviour. Supplementation
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with XG only, causes the Lissajous figures to become smoother; the shape of the figures becomes
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ellipsoidal. Moreover, the figures’ are as increasingly expand (the amount of the dissipated energy
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within one experimental cycle rises) as the concentration of XG increases. A substantial increase of
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the Lissajous figure area was noted for the highest level of XG concentration (0.9%). This can be
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explained by the increased viscosity of the system due to the presence of high amounts of the
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hydrocolloid.
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Supplementation only with pectin causes a visible change in the shape of the Lissajous figure within
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the non-linear range; the area, however, remains unchanged. This implies that the foams with pectin
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dissipate a similar amount of energy, in comparison to those containing only the egg white protein.
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Furthermore, a change in shape can be observed, from one characteristic of elastoviscoplastic systems
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(foam made of pure egg white protein) to another, corresponding to visco-elastic properties. The
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presence of both P and XG in the foam results in the expansion of the Lissajous figure’s area. This
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behaviour indicates, that the amount of dissipated mechanical energy increases mainly due to the level
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of the XG’s concentration.
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In the segments relating to the linear area, the curves (τ’) (Fig. 3a) become straight lines, due to the
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fact, that the applied stress causes an increase of the viscous dissipation of energy.
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ACCEPTED MANUSCRIPT As the amplitude rises, the shapes of the figures become more ellipsoidal. As a consequence, the
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decomposition line becomes a curve, presented in Fig. 3. For higher amplitudes, we can observe an
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occurrence of an inflexion point; followed by the appearance of an extremum (Ewoldt and McKinley
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2010). On the negative side of the deformation values we observe a maximum, whereas for the values
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on the positive side we observe a minimum. Figure 3b represents the Lissajous figures in the ( γ& , τ)
218
coordinate system. Similarly to the above, the figures initially adopt an ellipsoidal shape (Ewoldt et al.
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2010). As the deformation amplitude grows and the system moves towards the non-linear area, the
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nature of the figures undergoes various changes depending on the foams’ composition.
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The base foam, containing egg white protein only, produces secondary loops (SLs) and creates a very
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complicated shape. Supplementation with XG intensively suppresses this phenomenon; SLs of the
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foam containing 0.3% XG become very narrow, until they vanish entirely for increased XG
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concentrations, within the observed deformation amplitudes. A similar effect, although less intensive,
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is observed in the foams enriched with pectin. In this case, the supplementation with 0.3% P causes the
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shape of SLs to become smoother in comparison to the shape of the base foam. A further increase in
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the concentration of pectin (0.6% and 0.9%) within the system induces a gradual dissipation of the
228
SLs. The effect of combined XG and P on the shape of the obtained Lissajous figures is comparable.
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As demonstrated in previous studies (Ptaszek 2013, 2014, 2015), foams with the addition of XG
230
exhibit behaviours characteristic of soft glassy systems. These systems have a tendency towards
231
structural changes during the reversal of the flow, and display reversible stress overshoot (Ewoldt and
232
McKinley 2010). Moreover, foams based on the egg white protein behave as thixotropic systems
233
(Ptaszek 2013). Because of that, the occurrence of the observed Secondary Loops can be explained by
234
the disproportion of the timescale of thixotropic reorganisation of the fluid’s structure, and the scale of
235
harmonic fluctuations of the deformation (Ewoldt and McKinley 2010).
236
The presence of both XG and P in the foams caused SLs to completely disappear for all of the
237
analysed concentrations. In these cases, the Lissajous figures evolve from an ellipsoidal shape towards
238
a shape resembling a spindle. This behaviour implies a synergistic influence of XG and P on the
239
rheological properties of the studied foams. Contrary to supplementation with either XG or P, where
240
the disappearance of the inflection point requires high concentrations of the hydrocolloids, the
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ACCEPTED MANUSCRIPT combined supplementation with both results in an immediate disappearance of SLs. Further increase in
242
the hydrocolloids’ concentration (XG and P) only enhances this phenomenon.
243
The discussed figures were subjected to the geometrical decomposition; as a result, families of curves
244
were obtained, representing purely viscous stresses (τ”) in the analysed foams. The comparison of
245
values of (τ’) (Fig. 3a) and (τ’’) (Fig. 3b) indicates, that within the range of non-linear deformations
246
the viscous properties play the predominant role.
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The image obtained after the decomposition (the τ’ and τ” curves), is a combined result based on all
248
parts involved in the observed phenomenon. In order to precisely describe the main factors influencing
249
the discussed rheological events, a further analysis of the τ’ and τ” curves was carried out, using the
250
fast Chebyshev transform method. The results of the analysis are presented in Figures 3a and 3b.
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Figure 4a shows the relation of the reduced e3/e1, e5/e1 and e7/e1 Chebyshev coefficients in the function
252
of deformation amplitude. The examined foams show great variability in the third coefficient.
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The value of the e3/e1 is initially equal to zero, which is equivalent to the linear range; subsequently,
254
the values become positive. The non-linear segment, i.e. the third Chebyshev harmonic, is the decisive
255
factor for the majority of foams to be classified as systems stiffened by deformation. The foam
256
consisting of egg white protein only produces a maximum for the e3/e1 values, as well as e5/e1. This
257
phenomenon also appears in the foams containing XG or pectin. In the foams enriched with XG only,
258
the maximum systematically moves towards the higher values of the deformation amplitude; at the
259
same time the maximum becomes hardly visible for the XG concentration of 0.9%.
260
Similarly, for the foams supplemented with P only, the maximum migrates towards a higher value of
261
the deformation amplitude. Moreover, the foams enriched with 0.6% P and 0.9% P exhibit a small
262
minimum in the initial part of the non-linear area. Due to this fact, the foams demonstrate a strain-
263
softening type of behaviour within a narrow range of γ0. The foams with both XG and P become
264
stiffened by deformation (e3>0) within the entire non-linear area. With the exception of the foams with
265
0.3% XG and 0.3% P, the typical maximum was not observed. This indicates, that the tested
266
hydrocolloids act synergistically, enhancing the non-linear sections of the material’s response to the
267
applied deformation.
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ACCEPTED MANUSCRIPT The analysis also revealed the presence of higher Chebyshev coefficients (i>3) ei as well as vi. These
269
coefficients are not attributed with the same physical interpretation as e3 and v3; their presence stems
270
from the complexity of the material’s response to the applied deformation, and is a consequence of the
271
curvature of the geometrical decomposition line (τ’ and τ”). The analysis of the higher Chebyshev
272
coefficients: e5/e1, e7/e1 (Fig. 4a) in the foams with egg white protein only revealed that, initially, the
273
parameters adopt negative values, immediately after the system enters the non-linear area.
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Subsequently, the values rapidly grow and become positive, with a visible maximum; then the values
275
drop asymptotically towards zero. This dependency was not observed for the foams supplemented
276
with XG. In this case, only small negative values can be observed in the initial phase of the non-linear
277
area; then, the values of e5/e1, e7/e1 increase.
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The foams supplemented with pectin initially mirror the behaviour of the foam with white egg protein
279
only (0.3% P); however further increase in P concentration in the foam causes the previously observed
280
extreme for e5/e1 to become blurred and the course to become flat. The e7/e1 dependency is determined
281
by the concentration of pectin in the foam. For 0.6% P, the values of the e7/e1 fluctuate around zero,
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whereas in the case of 0.9% P concentration, the values initially decrease until they reach the
283
minimum, and then they begin to steadily rise.
284
Supplementation with both XG and P causes the reduction of values of the e5/e1, e7/e1 coefficients. The
285
values of e5/e1 adopt small negative values within a wide range of amplitudes; this process is followed
286
by a gradual increase. The e7/e1 coefficients show small negative values within the entire non-linear
287
range.
288
Figure 4b shows the v3/v1, v5/v1,v7/v1 dependencies in the function of the deformation amplitude. The
289
parameters represent pure viscous behaviour of the analysed foams.
290
The foam with egg white protein only demonstrates typical shear-thickening behaviour (v3>0) in the
291
beginning of the non-linear area; thereafter the v3/v1 values decline and the system becomes shear-
292
thinned. These dependencies are also observed in foams containing only XG, as well as only P. This
293
indicates, that non-linear viscous properties of the discussed foams are similar. In the beginning, the
294
systems are shear-thickening, which suggests that their behaviour is opposite to the typical general
295
tendency for shear thinning, induced by the main coefficient (v1). Upon crossing a certain critical value
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ACCEPTED MANUSCRIPT of amplitudes, the system becomes filled with such high level of mechanical energy, that it is no
297
longer capable of opposing the influence of the main coefficient; consequently, the v3/v1 values
298
become negative and the foam becomes shear-thinning.
299
Supplementation with both XG and P causes a significant change in the values of v3/v1 coefficients.
300
Within the studied range of deformation amplitudes, only the shear-thickening behaviour (v3/v1>0) was
301
observed. This phenomenon is a result of the hydrocolloids’ joint impact on the non-linear properties
302
of the foams.
303
The remaining analysed v5/v1 and v7/v1 coefficients exhibit certain variability, depending on the foam’s
304
composition. For the foams with egg white protein only, the values of v5/v1 form a maximum, before
305
they become negative and form a plateau. This behaviour is observed in all examined foams; however,
306
as the concentrations of XG and P rise, the area decreases within the observed range of amplitudes.
307
For the pure egg white protein-based foam, the v7/v1 dependency shows three extrema. At the
308
beginning of the non-linear area, the values rise and reach a maximum; subsequently, they drop and
309
form a minimum on the side of the negative values, to finally reach another maximum on the positive
310
side. The foams enriched with pectin behave similarly; however, the increase in the pectin’s
311
concentration causes a reduction in intensity of this behaviour. The foams containing solely XG, at the
312
concentration of 0.3%, demonstrate only a small maximum and minimum at the outset, subsequently
313
both extrema rise visibly. For foams with both XG and P, the function of v7/v1 in the deformation
314
amplitudes exhibits low values, which increase in the range of high amplitudes.
315
4. Conclusions
316
The test methods utilising LAOS technique and the plane phase, enable a precise analysis of very
317
complex non-linear rheological characteristics. Additionally, the use of geometrical decomposition of
318
the Lissajous figures and the fast Chebyshev transform allows for the separation of non-linear elastic
319
and viscous properties, in a manner similar to that applied in the analysis of the linear viscoelastic
320
properties. The application of these types of methods in the analysis of non-linear properties of foams
321
enabled us to establish the nature of the foams’ behaviour within the range of high deformation
322
amplitudes.
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ACCEPTED MANUSCRIPT The analysis of Lissajous figures in the (γ, τ) coordinate system revealed, that supplementation with
324
only XG results in an evolution of the figures’ shapes from rectangular to increasingly ellipsoidal, and
325
a visible increase in the figures’ areas. This implies, that the systems become increasingly viscous and,
326
consequently, dissipate a higher amount of energy in each cycle. The decomposition of the Lissajous
327
figures in the (γ, τ) coordinate system, as well as in ( γ& , τ), demonstrated that the tendency to flow,
328
observed in these systems, is triggered by force that is sinusoidally variable in time.
329
This is confirmed by lower values of elastic stresses (τ’) in comparison to viscous (τ”). Further
330
analysis with the use of the fast Chebyshev transform showed, in the non-linear part of the elastic
331
response, the presence of the e3 coefficient with positive values; this correlates to the system inducing
332
structure-stiffening properties during the flow. Additionally, the analysis of the v3 coefficient in the
333
function of the deformation amplitude revealed, that higher non-linear coefficients of the examined
334
systems are responsible for shear-thickening.
335
The above is confirmed by values of the v3 coefficient, which are positive within a wide range of
336
analysed amplitudes. This is manifested by a convergence of both viscous and elastic behaviours (e3
337
and v3 coefficients), whose values reflect the formation of new structures during shearing.
338
Clear synergistic effects have been observed in the properties of the foams supplemented with both
339
XG and P. As a result, we produced new foams with very specific rheological properties; they can be
340
subjected to pressure and forming, without the risk of destruction to their structure (i.e. the air bubbles
341
dispersed in the continuous phase).
342
6.
343
This work is supported by the Polish Ministry of Science and Higher Education in 2014.
344
The studies on physical properties of foams were supported by the financial program of the Polish
345
Ministry of Science and Higher Education for Young Scientists in 2014.
346
7.
347
Al-Hakkak, J., Al-Hakkak, F. (2010). Functional egg white–pectin conjugates prepared by controlled
348
Maillard reaction. Journal of Food Engineering, 100, 152-159.
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Acknowledgments
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ACCEPTED MANUSCRIPT Table 1. XG 0.6%
0.9%
0%
9.1%
8.8%
8.5%
8.2%
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%
RI PT
0.3%
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SC
P
0%
AC C
EP
TE
D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
RI PT SC M AN U TE
D 100 10 1 0.1
EP
1000 100 10 1 0.1
G' G''
AC C
G', G'', Pa
ACCEPTED MANUSCRIPT
100 10 1 0.1 100 10 1 0.1 0.001 0.01 0.1
1
10
0.01 0.1
1
10
f, Hz
0.01 0.1
1
10
0.01 0.1
1
10
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
Xanthan gum
0% τ τ'
100
50
50
0
0
-50
-50
-100
-100
-150
-150 -8
-6
-4
-2
0
2
4
6
-2
0
2
100
50
50
0
0
-50
-50
-100
-100
-150 4
6
8
-150 -8
-6
-4
-2
0
2
4
6
8 150
100
100
50
50
50
0
0
0
-50
-50
-50
-100
-100
-100
-150
-150
EP
150
100
0
-100 -150 -8
-6
-4
-2
150 100
AC C
Pectin τ, Pa τ', Pa
-4
100
150
50
0
2
4
6
8
0
-8
-6
-4
-2
0
2
4
6
8
-6
-4
-2
0
2
4
6
8
150
150
150
100
100
100
50
50
50
0
0
0
-50
-50
-50
-50
-100
-100
-100
-150 -8
-6
-4
-2
0
2
4
6
8
-150 -8
-6
-4
-2
0
2
4
6
8
-6
-4
-2
0
2
4
6
8
150
150
150
100
100
100
100
50
50
50
50
0
0
0
0
-50
-50
-50
-50
-100
-100
-100
-100
-150
-150
-150
-6
-4
-2
0
2
4
6
8
-8
-6
-4
-2
0
2
4
6
8
-4
-2
0
2
4
6
8
-8
-6
-4
-2
0
2
4
6
8
-8
-6
-4
-2
0
2
4
6
8
-8
-6
-4
-2
0
2
4
6
8
-150 -8
γ
-6
-150 -8
150
-8
-8
-150 -8
-100 -150
0.9%
-6
150
100
-50
0.6%
-8
0.9%
0.6%
150
150
50
0.3%
8
D
100
0%
0.3% 150
TE
150
-6
-4
-2
0
2
4
6
8
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
Xanthan gum
0%
τ, Pa τ", Pa
Pectin
20 -20 -40 -60
-80 -50 -40 -30 -20 -10 0 10 20 30 40 50 80 60
40
40
0 -20 -40 -60
20
-20
40 20 0
0.6%
100 80 60 40 20 0 -20 -40 -60 -80 -100 -50 -40 -30 -20 -10 0 10 20 30 40 50
0.9% 150 100 50 0 -50 -100 -150 -50 -40 -30 -20 -10 0 10 20 30 40 50
150
150
100
100
50
50
0
0
0
-50
-50
-100
-100
-150 -50 -40 -30 -20 -10 0 10 20 30 40 50
-150 -50 -40 -30 -20 -10 0 10 20 30 40 50
-40
-80 -50 -40 -30 -20 -10 0 10 20 30 40 50 80
D
0
60
60
-20 -40 -60 -80 -50 -40 -30 -20 -10 0 10 20 30 40 50 80 60
0.9%
40
80
20
0.6%
60
TE
τ τ"
80
EP
0.3%
100 80 60 40 20 0 -20 -40 -60 -80 -100 -50 -40 -30 -20 -10 0 10 20 30 40 50
AC C
0%
0.3%
-60
-80 -50 -40 -30 -20 -10 0 10 20 30 40 50 100 80 60 40 20 0 -20 -40 -60 -80 -100 -50 -40 -30 -20 -10 0 10 20 30 40 50
150
150
100
100
50
50
0
0
-50
-50
-100
-100
-150 -50 -40 -30 -20 -10 0 10 20 30 40 50
-150 -50 -40 -30 -20 -10 0 10 20 30 40 50
150
150
100
100
50
50
0
0
40 20 0 -20
-80 -50 -40 -30 -20 -10 0 10 20 30 40 50
150 100
-50
-50
-100
-100
-150 -50 -40 -30 -20 -10 0 10 20 30 40 50
-150 -50 -40 -30 -20 -10 0 10 20 30 40 50
-40 -60
200
50 0 -50 -100
. γ, s-1
-150 -200 -50 -40 -30 -20 -10 0 10 20 30 40 50
ACCEPTED MANUSCRIPT Highlights: LAOS measurements were done for wet foams
•
Geometrical decomposition of Lissajous figures was done
•
Synergistic effects have been observed in the foams with xatnthan gum and pectin
AC C
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•