Advances in Applied Agricultural Sciences 2 (2014); 6: 10-26
Viscoelasticity of the Bulk Quantities of Eight Saudi Date Cultivars
Abdullah Alhamdan 1, Hussain Sorour 1, Diaeldin Abdelkarim *1 and Mahmoud Younis 1
1 Chair of Dates Industry and Technology, King Saud University, Riyadh, Saudi Arabia.
Viscoelasticity of the bulk quantities of eight Saudi date cultivars namely, Barhi, Khudari, Khlass, Serri, Sukkari, Suffri, Sakkie, and Nubot Saif at Khalal, Rutab and Tamer stages of maturity, were experimentally determined in terms of stress relaxation parameters. Experimental results revealed the significant effect of stage of maturity. The values of initial stress (σ0) and equilibrium stress (σe) were higher at the Khalal stage compared to the Rutab stage for all eight date cultivars. The highest values were for Sakkie cultivar at both Khalal and Rutab stages and equal 9.85, 2.76 kPa and 9.72, 2.76 kPa, respectively. For Tamer stage the values of initial stress (σ0) and equilibrium stress (σe) were higher compared to Khalal for all tested cultivars except for Serri cultivar with values of 4.98 and 0.86 kPa, respectively. The maximum value of initial stress (σ0) at the Tamer stage was for Sukkri cultivar (17.57 kPa). Three mathematical models, namely, Generalized Maxwell, Nussinnovitch, and Peleg were tested for suitability of predicting experimental results. All three models fitted experimental data well; however the Generalized Maxwell model was the best, followed by Nussinnovitch model.
Keywords:Viscoelasticity, Stress relaxation, Date cultivars, Maxwell model, Maturity stage
The date fruits of the palm tree (Phoenix dactylifera L.) are the most important crop in the Middle-East. Ripening of date fruits is characterized by four stages namely; Kimri, Khalal, Rutab and Tamer stage depending on the colour, softness moisture and sugar content (Farahnaky and Afshari-Jouybari 2010). The Khalal stage of maturity follows the Hababauk and Kimri stages of maturity. During this stage the fruit color changes from green to yellow or red in some cultivars, weight gain is slow but sucrose content increases up to 62% on a dry basis, moisture content goes down to 55% on a wet basis, and tannins starts to precipitate and lose their astringency. The Rutab stage follows the Khalal stage of maturity. During this stage the moisture content for some cultivars decreases to about 20% wet basis, sucrose turns to inverted sugars, the fruit skin turns a brown color, and softening of tissues takes place.
The major components of agricultural materials and food, including dates are water and total solids (soluble and insoluble) of various in elements. When exposed to external applied forces they get deformed (strained) reflecting composite behavior of fluids (viscosity) and solids (elasticity). This viscoelastic behavior depends on the period of exposure to the applied forces. The relationships between the deformation (strain) and the applied force (stress) are time dependent. Moreover, when maintaining a constant level or value of deformation (strain) or distance, the force or stress values continue to decline with the passage of time in a non-linear manner this is known as stress relaxation, which can be described as the ability of a material to alleviate an imposed stress under conditions of constant strain. The time of relaxation show how fast the material dissipates stress after receiving a sudden deformation (Pappas et al. 1988; Li ma et al. 1998; Hassan et al. 2005).
Knowledge of viscoelastic behavior of foods and agricultural materials are important when considering harvesting, handling, transportation, processing, and storage.. Dates fruits at all stages are subject to fracture mechanical damage through a series of static and dynamic loads. Such loads cause significant loss by decreasing the quality and increasing the susceptibility to deterioration during storage (Baragale, et al. 1994). Data on viscoelastic properties are also required as an input for mathematical models, which describe and predict internal stress and cracking during different handling and processing procedures (Waananen and Okos 1992).
Stress relaxation of many vegetables and fruits and other food materials such as tomatoes, banana, canola, raisins, plantain and chickpea kernels have been investigated by various research workers (Kojima et al. 1991; Kojima et al. 1992; Cenkowski et al. 1992; Lewicki and Wolf 1995; Kajuna et al. 1998; Khazaei and Mann 2005).
The viscoelastic nature for individual date fruits of popular eight Saudi date cultivars at their Khalal and Rutab stages of maturity were studied by estimating their relaxation parameters from experimental stress relaxation data (Hassan et al. 2005). The present study was taken up to describe the stress relaxation characteristic for bulk quantities of the same eight Saudi date cultivars at their Khalal, Rutab and Tamer stages of maturity, investigating the effect of maturity stage on the stress relaxation properties and to determine the best model for describing the obtained stress relaxation data.
Materials and Methods
Eight popular Saudi date cultivars at Khalal, Rutab and Tamer stages of maturity, namely, Barhi, Khudari, Khlass, Serrie, Sukkari, Suffri, Sakkie, and Nubot Saif were used in all the experiments.
The dates were obtained from the educational farm of King Saud University. Dates were sorted to discard the damaged fruits, and immediately kept for less than 24 h in a cold store at 5 ºC. The moisture content was determined for the flesh of dates using AOAC procedures (AOAC, 2005) where the samples were dried at 70 ºC for 48 h under a vacuum of 200 mm of mercury (Vacutherm model VT 6025, Heraeus Instrument, D-63450, Hanauer, Germany).
A texture analyzer (TA-HDi, Model HD3128, Stable Micro systems, Surrey, England) together with a 75 mm diameter disk plunger (# P 75) was used to conduct stress relaxation tests. The texture analyzer was interfaced with an IBM compatible PC. A software package called, Texture Expert Exceed, version 2.05 supplied by the same company was used. This package enabled the acquisition of data in Excel format. The software can determine the gradient of the curve between any two specified locations, the area under curves, and other options. All experiments were carried out at room temperature (23 ºC).
Stress relaxation test
In stress relaxation experiments of the bulk dates quantities, an aluminum cylinder of dimensions: 74.61 mm (dia.) x 145 mm (hight) was completely filled with fruits from each stage of maturity. Then stress had been imposed by compressing the samples of the bulk dates to a depth of 40 mm to reach a strain (deformation) level equals 27,59% (ε0 % = (40/145) x100 = 27.59%) and then the stress relaxation was measured while keeping the level of this strain (deformation) constant.
A generalized Maxwell model has frequently been used to interpret stress relaxation data of a linear viscoelastic material. The model contains (n) Maxwell elements and a spring in parallel; each element consisting of dashpot in series.
The generalized Maxwell model can be written as follows:
σ(t)=∑(i=1)^n▒Ci (e-( t⁄ti ))+ σe (1)
σ(t) stress at any time (t), kPa
Ci stress relaxation constants, kPa, = ε0Edi
t time, s
τi relaxation time, s and is defined by τi = (ηi/Ei)
σe equilibrium stress, kPa
ε0 initial strain, mm/mm
Ei modulus of elasticity of element no. i in the model, kPa
Edi decay modulus, kPa
ηi viscosity of element no. i in the model, kPa.s
Another two models that were successfully applied to biological materials are the Nussinovitch model and Peleg model (Peleg and Pollak 1982; Nussinovitch et al. 1989; Rao et al. 1995; Kajuna et al. 1998; Li Maet al. 1998). In the Nussinovitch model the relaxation time constants (τi) became steady at 10, 100, 1000, and it can be mathematically presented as follows:
The Peleg model in terms of stress can be expressed as follows (Peleg and Pollak 1982):
σ(t)= σ0 – σ0 (abt/1+bt) (3)
The constant (a) represents the level at which the stress begins to decay during relaxation. Consequently, at (a = 0), stress never relaxes (solid material like rubber), while at (a = 1) the stress relaxes to the value of (0) after the elapse of infinite time (liquids). The constant (b) represents stress relaxation rate (decay rate) while its inverse (1=b) represents the required time to reach the level of (a=2). For the case when (b ¼ 0), the stress never relaxes. For the viscoelastic materials and at small values of (b), relaxation slows down but it accelerates for the higher values of (b) (Peleg and Pollak 1982).
Figure 1: Stress relaxation of bulk dates at Khalal stage for eight date cultivars.
Figure 2: Stress relaxation of bulk dates at Rutab stage for seven date cultivars.
Figure 3: Stress relaxation of bulk dates at Rutab stage for Sakkie cultivar.
Figure 4: Stress relaxation of bulk dates at Tamer stage for eight date cultivars.
Preliminary statistical tests were conducted to determine optimum number of each model terms. The results revealed that three terms is the best for the Maxwell model, while the form of the Nussinovitch and Peleg models as represented by equation (2) and equation (3), respectively were adequate.
All needed analyses were performed using the IBM SPSS software package (IBM SPSS 2010), and data resented as means ± SE with a level of signiﬁcance of 5%. Duncan comparison test were carried out to establish statistical differences between the calculated means at each experimental condition tested. Experimental data and parameters of models were analyzed by means of one-factor analysis of variance (ANOVA). Non-linear regression analysis was used to predict the constants of Burgers model.
Table 1: Average values of moisture content (wet basis) of the date cultivars at three stages of maturity.
Table 2: The constants of (A) Generalized Maxwell, (B) Nussinovitch and (C) Peleg models for stress relaxation of bulk dates for eight date cultivars at Khalal stage of maturity.
(A) Generalized Maxwell model
(B) Nussinovitch model
(C) Peleg model
Results and Discussion
The mean values of moisture content (wet basis) of the eight date cultivars at three stages of maturity namely: Khalal, Rutab and Tamer are shown in Table 1. The moisture content values at Khalal stage for all cultivars are higher than that at Rutab stage with significant difference at 0.05 level, while the moisture content values at Rutab stage for all cultivars are higher than that at Tamer stage with significant difference at 0.05 level. The moisture content (wet basis) at the Khalal stage ranged from 55.6% (Serri) to 74.6% (Nubot Saif). From the values of moisture content at Khalal stage there are no significant differences between Barhi and Khudari, and between Suffri and Sukkari, and between Khlass, Sakkie and Suffri cultivars. Whereas there is significant difference between Sukkari and Serri, and between Barhi and Nubot Saif cultivars. At the Rutab stage the moisture content ranged from 19.1% (Sakkie) to 31.6% (Sukkari). There is no significant difference in moisture content between Barhi, Khlass, Sukkari, Suffri and Nubot Saif cultivars and between Khudari, Serri and Sakkie cultivars. The moisture content (wet basis) at the Tamer stage ranged from 7.18% (Barhi) to 12.56% (Sukkari). No significant differences were found between Khudari, Sukkari, Sakkie and Nubot Saif cuttivars at Tamer stage and also there are no significant differences between Barhi, Serri and Suffri. The variation in moisture content between cultivars and maturity stages beside other chemical changes has great effect on their physical and mechanical properties including viscoelastic behavior.
The experimental results on stress relaxation for the bulk dates quantities of the eight cultivars at the Khalal, Rutab, and Tamer stages of maturity are shown in (Figures 1 – 4). The data are typical of viscoelastic food materials such as apple, raisins, avocado, banana, plantain, potatoes, tomatoes and canola seeds (Cenkowski et al. 1992;, 1998; Kojima et al. 1991, 1992; Lewicki and Wolf 1995; Lima and Singh 1995; Sakurai and Nevins 1992; Saravacos and Kostaropoulos 1995).
The data on stress relaxation of bulk dates quantities at the Khalal stage is plotted and shown in Figure 1. It is seen that the initial applied stress values at time zero (σ0) varied widely depending on date cultivar. The highest values of the initial stress (σ0) and the stress at equilibrium (σe) are for Sakkie cultivar and equal 9.85 and 2.76 kPa, respectively. The initial applied stress (σ0) values and stress at equilibrium (σe) respectively for the other seven cultivars at Khalal stage equal 5.81 and 0.78 kPa for Barhi , 5.19 and 0.93 kPa for Serri, 2.77 and 0.49 kPa for Khudari, 3.58 and 0.66 kPa for Khlass, 2.76 and 0.77 kPa for Sukkari, 2.52 and 0.48 kPa for Suffri and 0.57 and 0.18 kPa for Nubot Saif. This indicates the firmness and cohesiveness of the structural tissue of Sakkie and Barhi followed by Serrie at Khalal stage. Nubot Saif, Suffri and Sukkari had the lowest firmness at the Khalal stage.
The stress relaxation curves at Rutab stage for seven date cultivars and for Sakkie cultivar are given in Figures 2 and 3. The results for Sakkie cultivar is shown in a separate figure because of high values compared to the other seven date cultivars. Experimental results for stress relaxation of bulk dates quantities at Rutab stage (Figures 2and 3) revealed that the highest values of the initial applied stress (σ0) as well as the stress at equilibrium (σe) are for Sakkie cultivar and equal 9.72 and 2.76 kPa, respectively. This also reflects the structural firmness and cohesiveness of Sakkie cultivar.
Table 3: The constants of (A) Generalized Maxwell, (B) Nussinovitch and (C) Peleg models for stress relaxation of bulk dates for eight date cultivars at Rutab stage of maturity.
(A) Generalized Maxwell model
(B) Nussinovitch model
(C) Peleg model
Table 4: The constants of (A) Generalized Maxwell, (B) Nussinovitch and (C) Peleg models for stress relaxation of bulk dates for eight date cultivars at Tamer stage of maturity.
(A) Generalized Maxwell model
(B) Nussinovitch model
(C) Peleg model
The initial applied stress (σ0) values and stress at equilibrium (σe) respectively for the other seven cultivars at Rutab stage equal 5.2 and 0.93 (k Pa) for Serri, 2.87 and 0.78 kPa for Sukkari, 1.53 and 0.31 kPa for Khlass, 1.52 and 0.12 kPa for Barhi, 1.50 and 0.12 kPa for Khudari, 1.44 and 0.35 kPa for Suffri and 0.57 and 0.13 kPa for Nubot Saif.
From (Figures 1, 2 and 3) it is clearly depicted that the initial applied stress (σ0) and stress at equilibrium (σe) values for all eight cultivars at Khalal stage were higher than their equivalents at Rutab stage. The reason for this is due to the major changes which take place in the structural tissues during the on-going maturation process and change from the Khalal to the Rutab stage of maturity. The most significant changes are in sugar type which converts from sucrose to fructose and glucose as a result of enzymatic action during the maturation process.
Figure 4 shows that at Tamer stage the values of the initial stress (σ0) and equilibrium stress (σe) were higher compared to Khalal and Rutab stages for all tested cultivars except for Serri cultivar with values of 4.98 and 0.86 kPa, respectively slightly less than its values of (5.19 and 0.93 kPa) at the Khalal stage. Sukkari cultivar attain the highest value of the initial stress (σ0) at Tamer stage (17.57 kPa) while its equilibrium stress (σe) value was equal to 2.46 kPa. The highest value of the equilibrium stress (σe) at Tamer stage is attained by Sakkie (2.84 kPa) while its initial stress (σ0) value was equal to 10.07 kPa. The values of initial stress (σ0) and equilibrium stress (σe) on descending order for the remaining five cultivars at the Tamer stage were equal to 10.95 and 1.29 kPa for Barhi, 5.38 and 0.88 kPa for Khlass , 4.83 and 0.76 kPa for Suffri, 3.12 and 0.58kPa for Khudari and 2.88 and 0.38 kPa for Nubot Saif.
Stress relaxation modeling
The results of the statistical non-linear regression analysis for testing the suitability of three mathematical models to express the experimental results of stress relaxation on bulk quantities of eight cultivars at Khalal, Rutab and Tamer are shown in Tables (2, 3 and 4) respectively.
From the values of the correlation coefficient of the results of non-linear analysis of the bulk quantities for the eight date cultivars at three stages of maturity, it is clear clearly that the Generalized Maxwell model was the best in expressing and predicting of the outcomes, followed by Nussinnovitch model then Peleg model. As can be seen that the Generalized Maxwell model fits very well with the experimental results for all eight date cultivars at the Khalal stage (0.989 ≤ R2≤ 0.998), Rutab stage (0.986 ≤ R2≤ 0.998)and Tamer stage (0.923 ≤ R2≤ 0.999) respectively.
The values of stress relaxation constant (C1) in the Generalized Maxwell model were the highest at the Tamer stage of the bulk quantities for all date cultivars except Serri, and varied in the limits of 5.99 kPa for Barhi to 0.242 kPa for Nubot Saif. The second stage was Khalal for all cultivars except Barhi where (C1) values varied in the range of 1.76 kPa for Sakkie to 0.2 kPa for Nubot Saif. While the values are relatively low for all cultivars except Barhi at the Rutab stage and ranged within the limits of 1.73 kPa for Sakkie to 0.12 kPa for Nubot Saif.
The relaxation time for the first Maxwell element (τ1) was the longest for all cultivars in the Tamer stage, where it varied for six cultivars in the limits of (159.96 s) for Sukkari to (87.87 s) for Serri. The lowest relaxation times at Tamer stage were for Khudari (8.6 W) and Barhi (0.31 W). At Khalal stage the stress relaxation times for six cultivars varied from 115.43 kPa for Sukkari to 64.47 s for Barhi, while the values were low for Khudari (9.91 s) and Nubot Saif (0.69 s). The stress relaxation times at the Rutab stage were the least and varied within the range of (115.8 s) for Sukkari to (0.5 s) for Khlass cultivar.
Nussinnovitch model expressed well the experimental results for the bulk quantities of eight date cultivars at Khalal (0.918 ≤ R2 ≤ 0.983), Rutab (0.899 ≤ R2 ≤ 0.997) and Tamer stage (0.886 ≤ R2 ≤ 0.985). But the constants A1 to A4 did not follow a regular pattern, whether on the basis of date cultivars or stages of maturity.
The Peleg model for which the correlation coefficients are the least compared to the other two models for Khalal (0.918 ≤ R2 ≤ 0.983), Rutab (0.899 ≤ R2 ≤ 0.997) and Tamer stage (0.886 ≤ R2 ≤ 0.985). Its constant a followed a clear pattern where its values were high for all the eight date cultivars at the Tamer stage and varied within the limit of 0.87 for Barhi to 0.705 for Sakkie. The Khalal stage ranked second with constant (a) values varied within the limits of 0.856 for Barhi to 0.703 for Sukkari, while its values varied at the Rutab stage in the range of 0.809 for Serri to 0.42 for Nubot Saif. The constant (b) which represents the rate of stress relaxation has followed the same pattern of the constant (a), where its values were relatively high for all eight date cultivars at the Tamer stage and varied from 0.841 s -1 for Khlass to 0.203 (s -1) for Sakkie. Then followed by Khalal stage and the values varied within the limits of 0631 (s -1) for Khlass to 0188 s -1 for Sakkie. And at the Rutab stage the constant (b) values ranged in the limits of 0638 s -1Serri to 0.012 s -1 for Nubot Saif cultivar.
The data on stress relaxation of bulk dates quantities of eightSaudi date cultivars revealed that the stress relaxation behavior is highly affected by the stage of maturity. The initial applied stress (σ0) and stress at equilibrium (σe) values at Tamer stage were the highest for all tested cultivars except for Serri cultivar, followed by Khalal stage then Rutab stage. The values varied widely depending on date cultivar. Sakkie cultivar showed firmness and cohesiveness of the structural tissue at both Rutab and Khalal stages followed by Barhi then Serrie cultivars at Khalal stage and Serrie then Sukkari cultivars at Rutab stage. The Sukkari cultivar attains the highest value of the initial stress (σ0) at Tamer stage. It was found that the Generalized Maxwell model was the best in predicting experimental data, However the Nussinovitch and Peleg models were valid as well for quantifying relaxation behaviour of the bulk dates quantities of the eight Saudi date cultivars tested in this study.
The authors gratefully thank the Deanship of Scientific Research and the Research Chairs Program, King Saud University for their financial support to the Chair of Dates Industry and Technology for completing this research work.
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