Strain sweep test

To determine the linear (LVR) and nonlinear viscoelastic regions, a strain sweep test was performed. Strain was swept from 0.01 to 100 % at an oscillatory frequency of 10 rad/s. The measurement gap was set to 2 mm, and the axial force was allowed to relax below 10 N prior to measurement.

Frequency sweep test

In LVR, a frequency sweep test was conducted at 0.02 % strain between 0.1 and 10 rad/s. The measurement gap was set to 2 mm, and the axial force was allowed to relax below 10 N before measurement. The storage (G') and loss (G") moduli and complex viscosity (η*) were modelled using power law models as given in the following equations (8):

/1/

/2/

where K' and K" are consistency indices (Pa·s^n’ and Pa·s^n’’, respectively), n' and n" are oscillatory flow behaviour indices of storage and loss moduli, respectively and ω is angular frequency.

Creep recovery test

The creep recovery test was conducted under a constant stress (σ₀) of 200 Pa during the creep period and 0 Pa during the recovery period, with a gap height of 2 mm. The durations of the creep and recovery periods were 120 and 180 s, respectively. The strain data were then converted to creep compliance (J_c(t)) and recovery compliance (J_r(t)).

J_c(t) data were modelled with the 6-element Burgers model (comprising one Maxwell and two Kelvin-Voigt elements in series) as shown in the following equation (8):

/3/

where J_c,0 is the instantaneous compliance (Pa^-1), J_c,1 is the first element retarded compliance (Pa^-1), λ_c,1 is the first element retardation time (s), J_c,2 is the second element retarded compliance (Pa^-1), λ_c,2 is the second element retardation time (s) and μ_c,0 is the zero shear viscosity (Pa·s) of the free dashpot.

J_r(t) data were modelled with the 6-element Burgers model (one Maxwell and two Kelvin-Voigt elements in series) in the following equation (8):

/4/

where J_r,0 is the instantaneous recovery compliance (Pa^-1), J_r,1 is the first element retarded recovery compliance (Pa^-1), λ_r,1 is the first element recovery retardation time (s), J_r,2 is the second element retarded recovery compliance (Pa^-1), λ_r,2 is the second element recovery retardation time (s) and μ_r,0 is the zero shear viscosity (Pa·s) of the free dashpot.

Large amplitude oscillatory shear analysis

Large amplitude oscillatory shear (LAOS) properties of the dough samples were measured outside the LVR (9). The data collected were processed using MITlaos software (10). From these data, nonlinear measures (G’_L, η’_L, S and T) and Lissajous-Bowditch curves obtained.

Extensional rheological analysis

Biaxial extensional rheology measurements were conducted in the compression mode of the rheometer at a compression speed of 1.667·10^-5 m/s, with a sample diameter of 25 mm and a height of 10 mm. A constant volume approach was used, and the upper and lower plates were lubricated with paraffin oil. Biaxial extensional stress vs extensional strain rate data were obtained. Young’s modulus (YM) was calculated in the LVR using the slope of the stress-strain curve. Biaxial extensional viscosity vs extensional strain rate data were fitted to the power law model using the following equation (8):

/5/

where η_B is biaxial extensional viscosity (Pa·s), K_B is the power law constant (Pa·s^nB) and n_B is extensional thinning index. Maximum extensional strain rate (ε̇_b,max) was kept low (0.24 s^-1) to prevent lubricant loss.

Linear viscoelastic properties

Fig. 1 shows the linear viscoelastic rheograms. A strain sweep test was conducted to determine the linear viscoelastic region, and the strain sweep profiles of pasta doughs are shown in Fig. 1a.

Fig. 1

The graphs show: a) strain sweep (with crossover strain numerical values marked in the inserted graph), b) frequency sweep and c) creep recovery profiles of the dough samples prepared with only water (plain, circles), whole egg (squares), and egg yolk (triangles)

Airey et al. (13) identified the nonlinear viscoelastic region of the strain sweep test data by considering the point where 5 % of the initial modulus decayed. The results of this study are consistent with previous research, showing that all samples exhibited nonlinear behaviour after a strain of 0.05 %. The strain values at which the dough samples entered the nonlinear viscoelastic region were recorded as 0.05 % for the plain sample, 0.08 % for the whole egg sample, and 0.20 % for the egg yolk sample. Similarly, Mastromatteo et al. (14) prepared bread dough using durum wheat and found that the linear viscoelastic region (LVR) was between 0.02 and 0.065 %, consistent with the plain samples. The highest moduli were observed in the egg yolk sample. Since the dough is characterised as a viscoelastic solid, the storage modulus (G') of each sample was greater than the loss modulus (G"). Within the LVR, the difference between G' and G" was more pronounced than in the nonlinear region, indicating that the elastic behaviour dominates until the structure starts to break down. As the strain amplitude increased, both moduli decreased, reflecting the disruption of the gluten-starch network. Similar behaviour was reported by Yazar et al. (1), who attributed this decrease to overstretching of the gluten network and the consequent loss of its structural integrity. Erturk et al. (15) further explained that, after the gluten network is overstretched, starch-starch interactions become more dominant, governing the viscoelastic response at large strain amplitudes. In this study, the observed reduction in G' and G" with increasing strain can therefore be explained by the transition from a gluten-dominated to a starch dominated structural response.

Within the measurement range, crossover strains were observed (see Fig. 1a). At higher crossover strain value, viscous behaviour dominates, and the dough behaves in a liquid-like manner. The crossover strain values are given in Table 1. The highest crossover strain was observed in the plain sample. The addition of whole egg or egg yolk prevents gluten network formation due to lipids in the egg yolk. In the study by Alamprese et al. (16), the break load of raw pasta dough decreased as the yolk amount increased, which they explained as the weakening of the protein network due to inhibition by egg yolk lipids. The reason for the decreasing crossover strain with increasing egg yolk content could be the same.

The frequency sweep profile of the samples is shown in Fig. 1b. In the LVR, storage modulus is greater than the loss modulus for all samples. The data obtained were fitted to the power law and the fitting results are given in Table 1.

For both G' and G", all oscillatory flow behaviour indices (n) are less than 1, indicating that all samples had shear thinning behaviour. Similarly, in the study by de la Peña et al. (17), the pasta dough prepared with various moisture contents (30–34 %) showed shear thinning behaviour. Both n' and n" were highest in samples made with whole eggs, indicating that increased oscillatory frequency results in a thicker dough than in the other samples. For n', the frequency dependency decreases in the following order: whole egg, plain, and yolk samples. In contrast, for n", the plain and yolk samples exhibit similar frequency dependencies. In this study, the final dough moisture mass fractions ranged approx. from 48 to 56 %, which are considerably higher than those obtained by de la Peña et al. (17). Such higher hydration degree could be used for model pasta dough. The addition of whole egg and egg yolk leads to enhanced protein network plasticisation and more pronounced viscoelastic responses. While de la Peña et al. (17) observed a decrease in apparent viscosity with increasing hydration, a similar trend can be observed in the present study, as higher water content facilitates molecular mobility. This reduces the dough resistance and results in shear thinning behaviour. The yolk sample exhibited the highest K', indicating the highest stress response to oscillatory shearing. The higher K' value of the sample containing egg yolk may be related to the fact that the egg yolk is more viscous and has a higher solid content than the samples containing whole eggs and water. Even though the presence of lipids interrupts the gluten network formation and weakens the dough structure, the higher consistency coefficient at LVR could be attributed to the limited water mobility due to more viscous nature of the egg yolk. Similar trend was observed in the K" values, which are related to the viscous properties of the sample. Since the dough is characterised as a viscoelastic solid and all samples have greater K' than K", the increasing K" values were observed as the viscosity of the liquid ingredient increased. From the perspective of dough processing, the frequency dependency of the samples is a crucial property for dough stability (8, 18). Higher frequency dependency results in more unstable dough, which could be a problem during mechanical processes. After kneading, rolling and cutting steps follow, and the instability such as disintegration or spring-back of the dough during these mechanical processes could interrupt proper handling of the overall process steps.

The results of the creep recovery test are shown in Fig. 1c. J_c(t) and J_r(t) data fitted to Burgers model (R²_adj>0.98) are given in Table 1. The six-element Burgers model was found to describe both the creep and recovery compliance data and it provides valuable insights into viscoelastic materials. Due to the second curvature of both the creep and recovery compliance data, an additional Kelvin-Voigt element in series with the four-element Burgers model was needed to describe the compliance behaviour. In the study by Van Bockstaele et al. (19), different wheat flour cultivars were used to prepare bread dough, and the creep recovery behaviour was investigated. Similar to our findings, they discovered that the best model for describing the creep behaviour was the six-element Burgers model, while the recovery behaviour was well modelled by the five-element Burgers model (the six-element Burgers model without the zero shear viscosity).

In the creep phase, the first and second element compliances of the plain sample were significantly greater than those of the other samples. Given the lower consistency index of the plain sample, this difference can be attributed to its greater ability to deform under shearing. Zhang et al. (20) studied the effect of freeze-thaw cycles on the rheological properties of pasta dough and showed that an increasing number of cycles reduced the rigidity of the dough, which was explained by the lowered G'. As rigidity increased, creep compliance decreased, which aligns with the findings of this study. The retardation times of the individual Kelvin-Voigt elements during creeping consisted of two distinct values, representing shorter and longer retardation times. λ_c1, which denotes the shorter retardation time, showed no statistically significant difference between the samples (p<0.05). For the longer retardation times in the creep phase, the highest value was observed in the whole egg sample. The increased protein content in the whole egg sample may contribute to the longer retardation time, likely due to the formation of a stronger network during kneading. The zero shear viscosity of the yolk sample was the highest and this value correlated with the consistency index obtained in the frequency sweep test.

During the recovery phase, the highest instantaneous compliance values were observed in the plain and whole egg samples. As with creep compliance, this phenomenon could be explained by the rigidity of the dough. For a shorter retardation time, the plain sample exhibited the lowest value, indicating that it recovered from the deformation applied during the creep phase more quickly. The longest retardation time was observed in the yolk sample, followed by the plain and then the whole egg samples. This could be attributed to the strength of the dough. After the rapid rearrangement of the macromolecules in the network associated with the short retardation time, the recovery from deformation took longer in the yolk sample, which was characterised by its stability. The zero shear viscosity during the recovery phase was the lowest in the plain sample.

Nonlinear viscoelastic properties

Lissajous-Bowditch curves for both the elastic and viscous components of the samples are shown in Fig. 2. All samples in the Lissajous-Bowditch curves had clockwise rotation, indicating intracycle strain stiffening behaviour (21). Using Lissajous-Bowditch curves, both qualitative and quantitative measures can be obtained. For quantitative comparison, the shape of the curves is informative. A circular structure indicates a viscous response, while a narrow ellipse indicates an elastic response of the stress to the strain input (22). In the LVR, the stress response to strain was linear, but outside the LVR, the Lissajous-Bowditch curves were distorted. In the gluten- and starch-rich formulations, undistorted Lissajous-Bowditch curves were observed due to the reorientation of starch without disruption of the gluten network (1). As a result, elasticity was provided by starch, and intracycle linearity was observed. In the quantitative analysis of Lissajous-Bowditch curves, the area enclosed by the elastic component curve serves as a measure of energy storage in the network against deformation. In this study, it was found that the yolk sample had a greater enclosed area as the strain increased, which means that higher shearing was required to deform this material. The trends in the increase of the enclosed areas for the plain and whole egg samples were similar. Energy dissipation during a cycle was discussed in the studies of Duvarci et al. (21) and Ozcan et al. (23), which explained the projection area of the stress-strain curves.

Fig. 2

Lissajous-Bowditch curves of elastic components of: a) plain, b) whole egg, c) yolk and viscous components of: d) plain, e) whole egg, and f) yolk samples

Strain stiffening ratio (S) and thickening ratio (T) are shown in Fig. 3a and Fig. 3b, respectively. The physical meaning of the S value is intracycle strain softening when less than 0 and intracycle strain stiffening when greater than 0 (10). The plain and whole egg samples showed strain stiffening behaviour after 1 % oscillatory strain, while the yolk sample exhibited this behaviour after 10 % strain. The T value indicates shear thinning when less than 0 and shear thickening when greater than 0. The plain sample had the lowest strain value at which dough passes to shear thinning behaviour. The next formulation was with whole egg, and the highest strain requirement was observed in the yolk sample. Simultaneous classification of stiffening and thickening behaviour based on S and T is shown in Fig. 3c. At small strain values, all samples exhibited shear thickening and strain softening. As the strain increased, all samples first entered the strain stiffening region and then exhibited shear thinning behaviour. Erturk et al. (15) explained this phenomenon as the gluten network disruption under higher shearing. It was speculated that the lipids in the yolk sample inhibited gluten network formation. This trend may be attributed to the rigidity of the yolk dough, which might cause it to exhibit shear thinning behaviour at higher deformation levels. This result provides important insight into the dough machinability, indicating that the samples containing egg yolk can resist deformation at a higher level compared to the other formulations.

Fig. 3

The ratios of: a) strain stiffening (S) and b) thickening (T) with respect to oscillatory strain amplitude; c) S vs T values

Extensional rheology

Biaxial extensional stress vs strain data for all samples are shown in Fig. 4a. It was found that the stress response to the biaxial compression was the highest in the yolk sample. The Young’s moduli (YM) of the samples were calculated as 6.32, 28.48 and 117.05 kPa for the plain, whole egg and yolk samples, respectively. The YM were calculated up to a strain of 0.01, where the material entered the nonlinear viscoelastic region. Yu and Ngadi (24) investigated the mechanical properties of noodle dough containing guar gum and varying moisture content. Their results showed that the decreasing moisture content increased the YM, which is in agreement with the findings of this study, and that the gum addition increased the YM by providing stronger interactions between water and macromolecules. The regions observed in the stress-strain curve were the linear elastic, plastic, and densification regions (25). The YM was calculated in the initial region, and as the material transitioned into the densification region, the stress difference between the samples increased. In this study, the highest densification was observed in the yolk sample. Higher strain values in dough machinability can lead to increased stress, which is directly proportional to the degree of dough rolling. This results in a higher energy requirement during rolling of the dough; in other words, the force applied to achieve the targeted strain is greater. On the other hand, the plain sample had the lowest densification, meaning that the strain induction during rolling did not cause excessive collapse in the polymeric network formed during kneading (4).

Fig. 4

The graphs show: a) biaxial extensional stress vs strain, b) biaxial extensional viscosity profile and c) torque change during rolling

The biaxial extensional viscosity profile is shown in Fig. 4b. The viscosity profiles of the samples were fitted to the power law, and the model parameters are given in Table 1. In terms of K_B, the plain and whole egg samples behaved similarly and were less consistent than the yolk sample. It was observed that the extensional thinning index decreased in the order of yolk, plain and whole egg samples. Liao et al. (26) studied the biaxial extensional viscosity profile of rolled noodle dough and explained the extensional thinning index as the orientation of the molecular chain of glutenin. The samples in this study also contained egg proteins, meaning that the orientation of the egg proteins also contributed to the thinning index. A lower thinning index indicates a greater ability to deform before structural breakdown. The whole egg sample had the lowest η_B (Table 1) value, meaning that its extensibility without structural damage was the most favourable for the rolling process.