MOISTURE-DEPENDENT PHYSICAL PROPERTIES OF MEDICAL TINY SEEDS: PART A: FLIXWEED (DESCURAINIA SOPHIA L.)
DOI:10.30825/5.EJPAU.197.2021.24.1

Amir Hossein Mirzabe¹, Ali Fadavi², Ali Mansouri^3
1 Department of Mechanical Engineering of Biosystems, College of Agriculture & Natural Resources, University of Tehran, Tehran, Iran
² Department of Food Technology, College of Aburaihan, University of Tehran, Tehran, Iran
³ Department of Mechanical Engineering of Biosystems, College of Aboureihan, University of Tehran, Tehran, Iran

ABSTRACT

Knowledge of agricultural seeds’ physical properties has significant importance for machinery and processing equipment design. Physical properties of flixweed (Descur ainia sophia L.) seeds were determined as a function of moisture content. Several properties were studied in the moisture range from 5.28 to 17.53% dry basis. Also, probability distribution of seeds’ principal dimensions were modeled by Gamma, Generalized Extreme Value, Lognormal, and Weibull functions. With increasing moisture content from 5.28 to 17.53%, properties including; length, width, thickness, geometric and arithmetic mean diameter, sphericity, specific surface area, volume, and projected area showed no specific trend. In contrast, the surface area increased from 6×10^-7 to 1×10^-6 m². The bulk and particle density decreased from 696.61 to 542.51 kg·m^-3, and 1217.50 to 1189.02 kg·m^-3, respectively. The porosity increased from 42.78 to 54.37%. The maximum external static angle of friction belonged to wood at all moisture content levels, followed by the iron and galvanized surfaces. At all moisture levels, the emptying angle of repose was more than the filling one.

Key words: Dimensional properties; Gravimetric properties; Frictional properties; Distribution modeling.

Nomenclature
AMD	Arithmetic mean diameter, m	V	Volume of the seeds, m3
ARE	Emptying angle of repose, Degree	W	Width of the seeds, m
ARF	Filling angle of repose, Degree	xavr	Mean of seeds dimension, m
CFG	Coefficient of friction on galvanized, Degree	xi	Midpoint of each class
CFI	Coefficient of friction on iron, Degree	Greek letters
CFW	Coefficient of friction on wood, Degree
GMD	Geometric mean diameter, m	α	Location parameter in Weibull
L	Length of the seeds, m	β	Scale parameter in Weibull
m	Mass of single seed, kg	Γ	Gamma function
Mc	Moisture content, % dry basis (d.b)	γ	Shape parameter in Weibull
Mf	Final moisture content of sample, % (d.b)	δ	location parameter in Gamma
Mi	Initial moisture content of sample, % (d.b)	ε	Shape parameter Gamma
MP	Mass of pycnometer, kg	ξ	Shape parameter in G. E. V
MPS	Mass of pycnometer and seeds, kg	Θ	Location parameter in lognormal
MPTS	Mass of pycnometer, toluene and seeds, kg	ΘE	Emptying angle of repose, degree
MT	Mass of pycnometer and toluene, kg	ΘF	Filling angle of repose, degree
MTD	Mass of displacement volume of toluene, kg	λ	Scale parameter in lognormal
Mw	Mass of water added, kg	µ	Location parameter in G. E. V
n	Number of occurrence	µs	Coefficient of static of friction
P	Porosity, %	ρb	Bulk density, kg·m-3
Pca	Projected area of the seeds, m2	ρt	Particle density, kg·m-3
S	Surface area of the seeds, m2	ρtoluene	Density of toluene, kg·m-3
STD	Standard deviation	σ	Scale parameter in Gamma
SS	Specific surface area, m-1	τ	Shape parameter in lognormal
Wi	Initial mass of the sample, g	φ	Sphericity, %
T	Thickness of the seeds, m	ω	Scale parameter in G. E. V
TSM	Thousand seeds mass, kg

1. INTRODUCTION

Flixweed (Descurainia sophia L.), an annual or winter annual herb, a cross- and self-pollinated species, is a member of the Brassicaceae family [13, 19]. It is believed to have originated in temperate and tropical Asia, South Europe, and North Africa [13]. Currently, flixweed has become naturalized (USDA, NRCS 2010), is widely distributed throughout the temperate zones of the world, and is one of the most abundant weeds in North America [6, 47], China [24, 48], and Iran. Flixweed is a prolific seed producer and a strong competitor, and it can substantially reduce crop yield [8].

Even though it causes a significant loss of crop yield, because of the high amount of seeds’ oil content (35 to 40%) and oil quality (the oil is rich in lino-lenic acid), flixweed has also been thought of as a potential oil crop. Its high productivity of seeds (from 2600 to 3000 kg·ha^-1) justifies its potential use as an oil crop [24, 26, 38, 46]. Moreover, flixweed seed has also been widely used in folk medicine [23]. In Middle Asia and the Middle East, the aerial part’s decoction is used as an antipyretic and for measles and smallpox for throat diseases [23]. The tincture is used as a diuretic and hemostatic for internal hemorrhages [5, 23]. Seeds of flixweed have also been used in China and Iran as a Chinese and Traditional Iranian Medicine to relieve cough, prevent asthma, reduce edema, promote urination, and cardiotonic effect. In some reports, the seeds can also be used to treat some cancers [23, 44].

As a medicinal material, flixweed seed is essential for its chemical composition. Thus far, several phytochemical studies have identified the presence of cardiac glycosides and glucosinolate degradation products such as isothiocyanates, nitriles, and epithiobutane derivates in flixweed seeds and dried aerial parts of the plant [10]. The physical and mechanical properties of flixweed are essential as much as its chemical composition. The proper design of agricultural process equipment depends essentially on the physical and mechanical properties of crops. Physical and mechanical properties of agricultural seeds are essential in designing the equipment for harvest, transport, storage, processing, cleaning, hulling, packing, and milling [1, 12, 42].

The size and shape of seeds are essential for designing separator and sorter machines and can be used to determine the limits of conveyors. Moreover, the characteristic dimensions allow a calculation of the surface area, projected area, and volume of seeds, essential aspects for the modeling of drying, modeling of ventilation, and calculating terminal velocity and aerodynamic properties. The bulk and particle densities (particle density is useful to design separation equipment) represent the measures of the weight of seeds per unit volume, while porosity affects the bulk density, which is also a necessary factor in the design of dryer, storage, and conveyer capacity [43]. The angle of external friction, angle of internal friction, and angle of repose play a chief role in designing the equipment for solid flow and storage, and knowledge of the frictional properties is needed in designing the effective machines for packaging [30].

Also, dimensions, mass, and other geometric properties can be determined for a single seed; however, these properties’ values differ for each seed to the others. Usually, knowledge of each seed’s properties is not of interest, but a description of the probability and cumulative frequency distribution of the dimensions of the whole sets of the seeds is needed [22].

Physical and mechanical properties of numerous agricultural seeds have been studied [3, 4, 20, 21, 27, 30, 35, 37, 40]; but, there is no published literature on the physical and mechanical properties of the flixweed seeds; therefore, the present study aims are the determination of physical and mechanical properties of seeds of flixweed using a solution based on image processing in order to determine the biggest size of each dimension of the flixweed seeds. Three principal dimensions (length, width, and thickness), geometric and arithmetic mean diameters, sphericity, volume, surface area, specific surface area, and projected area of the seeds were measured in four levels of moisture contents. The effects of the moisture content on bulk and particle densities, porosity, static coefficient of friction on various surfaces, emptying, and filling angle of repose of seeds were investigated. Furthermore, Gamma, Generalized Extreme Value (G.E.V), Lognormal, and Weibull modeled three principal dimensions of seeds.

2. MATERIAL AND METHOD

2.1. Sample preparation
Two kilograms of the dried seeds were bought from a local market in Shahreza, Isfahan, Iran, in 2012. The seeds were cleaned manually to remove all foreign materials.  The seeds were divided into four portions labeled A, B, C, and D. Initial moisture content of seeds was measured. For the experiments, the initial moisture content of the purchased seeds was considered as the first moisture level (sample A). To create three other more moisture levels (B, C, and D), the exact amount of distilled water was sucked into a syringe and added to a certain mass of seeds. While adding water, the seeds were stirred so that the added water came in contact with all the seeds. For each moisture level, mass of the distilled water was calculated based on the following Eq. [11, 16]:

(1)

The sample was packed in sealed polyethylene bags and kept in a refrigerator for 72 hours to let the moisture distribute uniformly throughout the samples. The final moisture content, after adding water, of each sample was measured using the standard hot air oven method at 105±1 oC for 24 h [2, 18, 36]. The average values of three replications were reported as moisture content for each sample. The samples with different moisture content were stored in a refrigerator until the test time.

2.2. Geometric properties
2.2.1. Equations and formulas
The three major perpendicular dimensions of seeds were measured by applying the image processing technique. The geometric mean diameter, GMD, and arithmetic mean diameter, AMD of the seed were calculated using the following Eqs. [16, 29]:

(2)

(3)

The sphericity (Φ) of flixweed seed was calculated using the following Eq. [30, 31]:

(4)

The surface area of seed (S) was found by analogy with a sphere of the same geometric mean diameter, using the following Eq. [14, 28]:

(5)

P is a constant equal to 1.6075. The volume of seed (V) was found using the following Eq. [9, 39]:

(6)

Specific surface area (S_s), in m^-1, of seed was calculated as:

(7)

The projected area of the seeds was calculated using the image processing method; the obtained pixels were converted to the projected area by the following Eq.:

(8)

2.2.2. Image processing set up
The image processing system consisted of a 45 cm × 45 cm × 45 cm box, a camera (Canon, IXY 600F, 12.1 megapixels, USB connection, Japan), and four white-colored fluorescent lamps  (32 W), and a laptop computer (VAIO, VPCEG34FX, Japan) equipped with MATLAB R2012a software package [30].

A white paper was placed on the bottom of the box to provide a white background. Two RGB color images were captured from up and front views of each seed. Several functions of the MATLAB software package improved the contrast between the seeds and the background. The steps of processing for each seed included 1) RGB color image was captured from up view of the seed and another one captured from the side view, 2) the RGB color space up and side images of seeds were converted into an eight-bit gray-scale level, 3) the threshold technique was performed to isolate each seed from its white background. Eight-bit gray-scale intensity represents different shades of gray from black to white (from 0 to 255), 4) the eight-bit gray-scale up and side images were digitized to a binary image by using binary transformation based on all the pixels with a brightness level equal to the average of the brightness levels of the three channels, 5) the threshold values of the flixweed seeds were determined experimentally, 6) the holes and noise of binary images are filling by morphological closing and opening. From the gray-scale images of flixweed seeds, pixel values less than 132 were converted to 0 (black). The values higher than 132 were converted to 255 (white), 7) the number of pixels representing the length, width, and thickness of the flixweed seeds was also measured on the captured images using MATLAB R2012a software package, 8) the pixels were converted to the millimeter by circulars and squares with identified dimensions that we had put on the white paper. Then a relation between pixel and length in millimeter was obtained (Fig. 1).

Fig. 1. Schematic of different steps of image processing and original RGB color image, gray-scale image, binary image, and outline image for an imaginary object

2.3. Gravimetric properties
The bulk material of seeds with different moisture content was obtained by a container with known volume (500 cm³). The seeds were poured into the container from the height of 150 mm [18]. The bulk density (ρ_b) is equal to the mass of bulk material divided by volume containing the mass.

The particle density (ρ_t) was determined using the liquid displacement method. The toluene (C₇H₈) was used in place of water because seeds absorb it to a lesser extent, the density of toluene is less than the water, and its surface tension is less than the water. It fills even shallow dips in seed, and its dissolution power is low [29]. The volume of the individual sample was determined by weighing the displacement volume of toluene [36]:

(9)

(10)

The porosity of bulk seed was calculated from bulk and particle densities using the Eq. (11) [41]:

(11)

2.4. Frictional properties
The coefficients of the seeds’ static friction were measured using the inclined plane method on iron, galvanized, and plywood surfaces. A topless and bottomless cylinder of 100 mm diameter and 50 mm height was filled with the samples. The cylinder was raised slightly so as not to touch the surfaces. The structural surface with the cylinder resting on it was inclined gradually with a screw device until the cylinder just started to slide down over the surface. The angle of tilt, α, was read by Auto Cad 2007 software. The coefficient of static friction, µs, was calculated from the following formula [35]. The scheme of the equipment used to measure coefficient of static friction is presented by Mirzabe e al. [33].

(12)

The filling and emptying angles of repose of the seeds were measured. The device used in this study consists of two boxes, with dimensions of 120 mm in length, 120 mm in height, and 60 mm in width [15]. The upper box was filled with the sample seeds. The upper box’s material could flow down through a removable port. The filling or static angle of repose is the surface’s angle with the horizon at which the seeds will stand when piled on the ground. The emptying angle of repose is the residual surface’s angle with the horizon in the upper box. The height of the seeds was measured, and the filling (Θ_F) and emptying (Θ_E) angle of reposes were calculated by the following relationships [42]. The scheme of the equipment used to measure filling and empting angles of repose is presented by Mirzabe e al. [30].

(13)

(14)

where: H and h are the height (mm), and A and a (mm) are the horizontal distances.

2.5. Modeling of dimensions
Length, width, and thickness of flixweed seeds distribution were modeled using four probability density functions. These functions were: Gamma, Generalized Extreme Value, lognormal, and Weibull distribution. The probability density function and cumulative frequency for Gamma distribution are described in the following Eq.s, respectively [7]:

(15)

(16)

(17)

(18)

If δ equals zero, the Gamma distribution would be two-parameter distribution; otherwise, it would be named three-parameter distribution. In the present work, for modeling the data, three-parameter Gamma distribution was used.

The probability density function and cumulative frequency for Generalized Extreme Value distribution are described in Eq. (19) and (20), respectively [32]:

(19)

(20)

The probability density function and cumulative frequency for lognormal distribution are described in the following Eq.s, respectively [22]:

(21)

(22)

Whenever θ was equal to zero, lognormal distribution was called two-parameter distribution. Otherwise, it was called three-parameter distribution. Whenever θ was equal to zero and λ was equal to one, the lognormal distribution was called standard lognormal distribution. In this study, the three-parameter lognormal distribution was used.

The probability density function and cumulative frequency for Weibull distribution are described in follow Eq.s, respectively [22]:

(23)

(24)

If α equals zero, the Weibull distribution would be two-parameter distribution; otherwise, that would be named three-parameter distribution. In the present work, for modeling the data, three-parameter Weibull distribution was used.

The adjustable parameters for each probability density function were calculated using the commercial spreadsheet package of Easy Fit 5.5. Kolmogorov-Smirnov methods were used for comparison of all probability density. The test is based on the vertical deviation between the observed cumulative density function and estimated cumulative density function based on the Eq. (25) [17]:

(25)

S(x) is the cumulative frequency distribution observed, and F(x) is the probability of the theoretical cumulative frequency distribution. In this Eq., small values of the test statistics Ks indicate a better fit. The Kolmogorov-Smirnov index for each probability density function was also calculated using the commercial spreadsheet package of Easy Fit 5.5.

2.6. Statistical analysis of geometric properties
Statistical indices, including maximum, minimum, average, and standard deviation (STD) for primary and complex petals’ geometric properties were calculated using Microsoft Office Excel 2010. Skewness and kurtosis are two statistical indices that were calculated so that the reader would better understand the probability density distribution data. The skewness and kurtosis were calculated using the Eq. (26) and (27) as reported by [25]:

(26)

(27)

Kurtosis is a measure of whether the data are peaked or flat relative to a normal distribution. Positive kurtosis indicates a relatively peaked distribution. Negative kurtosis indicates a relatively flat distribution . Two times of standard errors of skewness (SES) and kurtosis (SEK) for a normal distribution are equal to [45] :

(28)

(29)

where: n is the number of occurrences. In the present study, for all the parameters, n was equal to 50. So, to calculate the values of SES and SEK, n was replaced by 50 in Eq. (28) and Eq. (29) and values of SES and SEK were obtained between 0.3366 and 0.6619, respectively. If, for each parameter, the result of this division was between , it can suggest that population data are neither positively nor negatively skewed. If, for each parameter, the result of this division was between , it can suggest that population data are neither positively nor negatively kurtosis.

3. RESULTS AND DISCUSSION

3.1. Geometric properties
3.1.1. Statistical analysis
The primary geometric characteristics of flixweed seeds are presented in Table 1. The dimension of length, width and thickness for different moisture content ranged 2.1×10^-4–5×10^-4 m, 1.7×10^-4–3.5×10^-4 m, 1.3×10^-4–2.4×10^-4 m, respectively. The maximum values of length, width, thickness, geometric and arithmetic mean diameter were equal to 0.037, 0.028, 0.027, 0.027, and 0.028 mm when the moisture content was 9.39, 13.75, 17.53, 17.53, and 9.39% dry bases (d.b), respectively.

Table 1. Effect of moisture content on the primary geometric characteristic of flixweed seeds.

Parameter	Moisture content, % (d.b)	Number of repetition	(Mean ± STD) ×10-2	Skewness	Kurtosis
L (m)	5.28	50	0.027 ± 0.002	-0.045*	0.665*
	9.39		0.037 ± 0.006	0.429*	-1.042*
	13.75		0.031 ± 0.004	0.870*	0.887*
	17.53		0.028 ± 0.003	3.910**	23.538**
W (m)	5.28	50	0.022 ± 0.002	0.038*	-0.205*
	9.39		0.027 ± 0.001	-0.376*	-0.244*
	13.75		0.028 ± 0.002	0.378**	-0.280*
	17.53		0.027 ± 0.003	0.955**	0.057*
T (m)	5.28	50	0.016 ± 0.001	-0.002*	0.562*
	9.39		0.020 ± 0.001	-0.138*	-1.073*
	13.75		0.019 ± 0.001	0.194*	1.020*
	17.53		0.027 ± 0.002	-0.010*	0.022*
GMD (m)	5.28	50	0.021 ± 0.002	-0.146*	-0.061*
	9.39		0.027 ± 0.002	0.361*	-0.434*
	13.75		0.026 ± 0.002	0.850**	0.800*
	17.53		0.027 ± 0.002	0.758**	1.952**
AMD (m)	5.28	50	0.022 ± 0.002	-0.088*	0.063*
	9.39		0.028 ± 0.002	0.420*	-0.642*
	13.75		0.026 ± 0.002	0.871**	0.794*
	17.53		0.027 ± 0.002	1.182**	1.940**
* and **  indicated respectively a distribution with no significant and significant Skewness or Kurtosis, respectively.

Complex geometric characteristic of flixweed seeds in terms of sphericity, surface area, specific surface area, volume, and projected area are presented in Table 2. The average values of sphericity increased with moisture content and were recorded 79.33, 74.56, 82.81, and 98.88% when the moisture content was 5.28, 9.39, 13.75, 17.53% (d.b), respectively, i.e. an increase of 226 percentage points of  moisture content, only raised the sphericity 25 percentage points. The corresponding values for the surface area were 6×10^-7, 6×10^-7, 8×10^-7, and 1×10^-6 m². Specific surface area’s corresponding values were 2.1×10^-4, 3.2×10^-4, 2.7×10^-4, and 2.8×10^-4 m^-1. Volume’s corresponding values were 5×10^-12, 1×10^-11, 9×10^-12, and 1.1×10^-11 m³. Also, 9×10^-7, 9×10^-7, 1×10^-6, and 1×10^-6 m² were the corresponding values of projected area.

Table 2. Effect of moisture content on the complex geometric characteristic of flixweed seeds.

Parameter	Moisture content, % (d.b)	Number of repetition	Mean ± STD	Skewness	Kurtosis
(%)	5.28	50	79.33 ± 3.57	-0.018*	-0.040*
	9.39		74.56 ± 8.06	-0.028*	-1.230*
	13.75		82.81 ± 5.72	-0.214*	1.043*
	17.53		98.88 ± 6.99	-1.128**	5.035**
S (m2)	5.28	50	(6 ± 1) ×10-7	0.146*	0.153*
	9.39		(6 ± 1) ×10-7	0.518*	-0.520*
	13.75		(8 ± 1) ×10-7	1.075**	1.305*
	17.53		(10 ± 1) ×10-7	1.440**	4.887**
SS (m-1)	5.28	50	(2.1 ± 3) ×10-4	0.146*	0.153*
	9.39		(3.2 ± 5) ×10-4	0.518*	-0.520*
	13.75		(2.7 ± 4) ×10-4	1.075**	1.305*
	17.53		(2.8 ± 4) ×10-4	1.440**	4.887**
V (m3)	5.28	50	(5 ± 1) ×10-10	0.284*	0.077*
	9.39		(10  ± 2) ×10-10	0.633*	-0.259*
	13.75		(9  ± 2) ×10-10	1.264**	1.946**
	17.53		(11  ± 2) ×10-10	1.360**	4.049**
Pa (m2)	5.28	50	(9 ± 1) ×10-7	0.136*	0.171*
	9.39		(9 ± 1) ×10-7	0.170*	0.174*
	13.75		(10 ± 1) ×10-7	0.788**	0.646*
	17.53		(10 ± 2) ×10-7	3.734**	21.007**
* and **  indicated distribution with significant and no significant Skewness or Kurtosis, respectively.

Furthermore, skewness and kurtosis of the primary and complex geometric properties are noted in Tables 1 and 2, respectively. As mentioned before, SES and SEK values were obtained 0.3366 and 0.6619, respectively. Therefore, when the absolute magnitude of skewness and kurtosis are more than 0.6732 and 1.3238, respectively, skewness and kurtosis are significant; otherwise, they are not significant.

At the moisture content levels of 5.28 and 9.39% (d.b), skewness and kurtosis of all geometric properties were not significant. Also, in the moisture level of 13.75% (d.b), skewness and kurtosis of length, thickness, and sphericity were not significant, while for the other geometric properties, except volume, skewness was significant and kurtosis was not. Besides, in the moisture content levels of 5.28 and 9.39% (d.b), skewness and kurtosis were significant for the flixweed seed volume. Moreover, when the moisture content was 17.53% (d.b), for all properties except thickness, both skewness and kurtosis were significant, while for thickness, both skewness and kurtosis were not significant.

3.1.2. Distribution modeling
The probability density distribution data of length, width, and thickness of the flixweed seeds were modeled by Gamma, G. E. V, Lognormal, and Weibull functions (Figs. 2-4). Then the performance of the functions was compared with each other using the Kolmogorov-Simonov index. In the range of evaluated moisture, shape parameter, scale parameter, location parameter, Kolmogorov-Simonov index, and rank of each function was noted in Tables 3-5.

A.  B.  C.  D.

Fig. 2. Probability density distribution of length of flixweed seeds for the four moisture content levels (A) 5.28% (d.b), (B) 9.39% (d.b), (C) 13.75% (d.b), and (D) 17.53% (d.b).

A.  B.  C.  D.

Fig. 3. Probability density distribution of width of flixweed seeds for the four moisture content levels (A) 5.28% (d.b), (B) 9.39% (d.b), (C) 13.75% (d.b), and (D) 17.53% (d.b).

A.  B.  C.  D.

Fig. 4. Probability density distribution of thickness of flixweed seeds for the four moisture content levels (A) 5.28% (d.b), (B) 9.39% (d.b), (C) 13.75% (d.b), and (D) 17.53% (d.b).

Based on ranking, when the moisture levels were 5.28, 9.39, 13.75, and 17.53% (d.b), the G. E. V, Weibull, G. E. V, and G. E. V functions had the best, and the Gamma, G. E. V, Weibull, and Weibull functions had the worst performances to model the distribution of flixweed seeds’ length, respectively (Table 3). Also, to model the width distribution G. E. V, Weibull, G. E. V, and Gamma functions had the best and Gamma, Gamma, Lognormal, and G. E. V functions had the worst performance in the moisture levels of 5.28, 9.39, 13.75, and 17.53% (d.b), respectively. Besides, the corresponding functions for modeling of thickness distribution were Lognormal, G. E. V, G. E. V, and G. E. V (the best performance) and Weibull, Weibull, Weibull, and Gamma functions (the worst performance).

Table 3. Calculated parameter values of the different probability density functions used to model the length of flixweed seeds in different moisture content levels.

Moisture content	Distribution name	Shape parameter	Scale parameter	Location parameter	Kolmogorov- Simonov index	Rank
5.28% (d.b)	Gamma	149.750	1.9 ×10-4	-0.001	0.0919	4
	G. E. V	-0.341	0.002	0.026	0.0785	1
	Lognormal	0.037	-2.796	0.034	0.0882	3
	Weibull	3.781	0.009	0.019	0.0828	2
9.39% (d.b)	Gamma	1.810	0.005	0.027	0.0869	2
	G. E. V	-0.064	0.005	0.034	0.1029	4
	Lognormal	0.504	4.479	0.024	0.0934	3
	Weibull	1.446	0.010	0.027	0.0868	1
13.75% (d.b)	Gamma	7.972	0.001	0.021	0.1064	3
	G. E. V	-0.008	0.003	0.029	0.0872	1
	Lognormal	0.260	-4.341	0.018	0.1008	2
	Weibull	2.182	0.008	0.024	0.1224	4
17.53% (d.b)	Gamma	9.408	9.2 ×10-4	0.019	0.1709	3
	G. E. V	0.006	0.002	0.027	0.1412	1
	Lognormal	0.0249	-4.547	0.017	0.1677	2
	Weibull	2.002	0.007	0.021	0.2255	4

Generally, G. E. V functions had the best performance (in 8 cases its rank was one and the sum of its ranks was 21), followed by Lognormal (sum of its ranks was 30), Weibull (sum of its ranks was 34), and Gamma had the worst performance (in 4 cases its rank was four and sum of its ranks was 35).

Length, width, and thickness distributions of the flixweed seeds are illustrated in Figs. 2-4, to draw an easy comparison between Gamma, G. E. V, Lognormal, and Weibull functions and to understand the effects of the positive and negative values of skewness and kurtosis on the distribution of the data in four moisture content levels.

See Fig. 2 (D), Fig. 4 (A), and Fig. 3 (B) and compare these Figures with each other; in the first one, skewness has a significant and positive value (3.910, which is mentioned in Table 1) while in the second and third ones, it has shallow and not significant value (-0.002) and not significant and negative value (-0.376).

Kurtosis is determined to see if the data have reached their highest point and have a peak or flat. The data sets with high kurtosis tend to have separate peaks near the mean (see Fig. 2 and (D) Table 1). Data sets with low kurtosis tended to have a flat top near the mean rather than a sharp peak (see Fig. 4 (D) and Table 1). Data sets with negative kurtosis did not have a separate peak near the mean, and the height of the peak is less than the height of the normal distribution (see Fig. 4 (B) and Table 1).

Based on the data mentioned in Tables 1, 3, 4, and 5, we can make a relationship between values of the skewness and kurtosis and functions’ performance. Results of the modeling showed that whenever values of both skewness and kurtosis are positive and significant or both are positive and not significant G. E. V had the best and the worst performance. While whenever values of both skewness and kurtosis are positive and significant or both are positive and not significant, Weibull had the worst performance. Also, whenever skewness and kurtosis are negative and not significant, G. E. V had the best performance, too (for example, length of the seeds when the moisture content is 17.53% dry basis). Besides, whenever one of skewness or kurtosis is negative and not significant, and another one is positive and not significant, the G. E. V have the best performance (for example, the width of seeds when the moisture content is 5.28% dry basis).

Table 4. Calculated parameter values of the different probability density functions used to model the width of flixweed seeds in different moisture content levels.

Moisture content	Distribution name	Shape parameter	Scale parameter	Location parameter	Kolmogorov- Simonov index	Rank
5.28% (d.b)	Gamma	112.350	2.2 10-4	0.003	0.0876	4
	G. E. V	-0.310	0.002	0.021	0.0667	1
	Lognormal	0.050	-3.083	-0.024	0.0842	3
	Weibull	3.121	0.007	0.015	0.0787	2
9.39% (d.b)	Gamma	211.060	8.1 10-5	0.010	0.1059	4
	G. E. V	-0.450	0.001	0.027	0.0664	2
	Lognormal	0.031	-3.275	-0.011	0.0930	3
	Weibull	5.691	0.006	0.021	0.0659	1
13.75% (d.b)	Gamma	19.039	5.04 10-4	0.018	0.0819	3
	G. E. V	-0.112	0.002	0.027	0.0713	1
	Lognormal	0.155	-4.273	0.014	0.0831	4
	Weibull	2.672	0.006	0.022	0.0767	2
17.53% (d.b)	Gamma	1.506	0.002	0.023	0.0913	1
	G. E. V	0.113	0.002	0.026	0.1182	4
	Lognormal	0.627	-5.580	0.022	0.0959	2
	Weibull	1.275	0.004	0.023	0.1018	3

Table 5. Calculated parameter values of the different probability density functions used to model the thickness of flixweed seeds in different moisture content levels.

Moisture content	Distribution name	Shape parameter	Scale parameter	Location parameter	Kolmogorov- Simonov index	Rank
5.28% (d.b)	Gamma	151.270	1.05 10-4	4.07 10-4	0.0584	2
	G. E. V	-0.0281	0.001	0.016	0.0675	3
	Lognormal	0.040	-3.436	-0.016	0.0582	1
	Weibull	3.857	0.005	0.12	0.0693	4
9.39% (d.b)	Gamma	124.300	1.05 10-4	0.006	0.1121	2
	G. E. V	-0.357	0.001	0.019	0.0973	1
	Lognormal	0.040	-3.548	-0.009	0.1137	3
	Weibull	3.318	0.004	0.016	0.1146	4
13.75% (d.b)	Gamma	121.880	1.3 10-4	0.003	0.0929	3
	G. E. V	-0.304	0.001	0.019	0.0833	1
	Lognormal	0.045	-3.458	-0.012	0.0874	2
	Weibull	3.117	0.005	0.015	0.0989	4
17.53% (d.b)	Gamma	150.610	1.56 10-4	0.004	0.0758	4
	G. E. V	-0.315	0.002	0.027	0.0654	1
	Lognormal	0.039	-3.027	-0.021	0.0672	2
	Weibull	3.453	0.006	0.023	0.0682	3

Mirzabe et al. [31] modeled the diameter and thickness of the different sunflower head varieties. They cited that whenever skewness and kurtosis had positive values, G. E. V and Lognormal functions had an excellent performance. Also, whenever skewness and kurtosis had negative values, G. E. V and Weibull had an excellent performance. Moreover, whenever skewness had a positive value and kurtosis had a negative value, Weibull and G.E.V had an excellent performance.

Khazaei et al. [22] modeled mass and size distributions of two varieties of sunflower seeds and kernels by Lognormal, Normal, and Weibull functions. They showed that when skewness had a positive value, Lognormal was the best, and Normal was the worst model for predicting data.

Mirzabe et al. [32] modeled distance between adjacent seeds of three varieties of sunflower seeds by Lognormal, normal, and Weibull functions. They showed that whenever skewness and kurtosis had negative value, Weibull distribution was the best fit.

Although the shape of the seeds’ dimensions distributions and the performance of mathematical functions in fitting the distributions are not affected by seeds size, it may seem illogical to compare seeds of cucumber and sunflower that are much larger than flixweed. However, there are reports with similar results for modeling seed dimensions similar to the dimensions of flixweed seeds. For example, Mirzabe et al. [34] modeled three main dimensions of celery seeds. They results showed that whenever both skewness and kurtosis had positive values, G. E. V. had good performance, while Weibull distribution had poor performance.

3.2. Gravimetric results
3.2.1. Bulk density
The bulk density of the flixweed seeds at different moisture levels is shown in Fig. 5. Results showed that the bulk density of the seed decreases with the increase in the seed moisture content. Bulk density decreased from 696.61 to 542.51 kg.m-3 when the moisture content increased from 5.28 to 17.53% (d.b). This result may be explained by the fact that the flixweed seeds absorb moisture, their size and volume increases; consequently, their shapes and bulk volumes change. This behavior causes to decrease in the number of flixweed seeds occupying a specific volume. The positive and negative relationships between the bulk density and the moisture content have also been observed by other researchers [30].

Fig. 5. Variation of bulk density of flixweed seeds with moisture content.

3.2.2. Particle density
The particle density of the flixweed seeds at different moisture levels is shown in Fig. 6. Results indicated that the seeds’ particle density decreases linearly from 1217.503 to 1189.016 Kg m-3 when the moisture content increases from 5.28 to 17.53% (d.b). These values showed that the flixweed seeds were heavier than water; thus, it was natural that the combined water and seed had a lower density.

Fig. 6. Variation of the particle density of flixweed seeds with moisture content.

This characteristic can be used to separate the flixweed seeds from other lighter foreign materials.

3.2.3. Porosity
The porosity of flixweed seeds was calculated by the average values of bulk density and particle density of each batch (Fig. 7). It was observed that when moisture content increased from 5.28 to 17.53% (d.b), the porosity increased from 42.78% to 54.37%. The results showed that an increase in the moisture content decreased the bulk and particle density. Also, a comparison between bulk and particle density showed that the percentage increase in particle density was more than the bulk; therefore, based on Eq. 11, porosity increased.

Fig. 7. Variation of porosity of flixweed seeds with moisture content.

3.3. Frictional properties
3.3.1. Angle of static friction
It must be mentioned that the static angle of friction is an important parameter to design the storage bins, hoppers, pneumatic conveying system, screw conveyors, forage harvesters, threshers, etc. The angle of static friction of flixweed seed on three surfaces (iron, galvanized, and wood sheet) against moisture content is shown in Fig. 8. It was observed that the static angle of friction of seeds increased with an increase in moisture content from 5.28 to 13.75% (d.b) for all contact surfaces, while it decreased with an increase in moisture content from 13.75 to 17.53% (d.b) for all contact surfaces. The angle of friction increased from 24.36 to 29.64°, 20.59 to 24.92°, and 17.01 to 24.05° for iron, wood, and galvanized, respectively, as the moisture content increased from 5.28% to 13.75% (d.b); then it decreased from 29.64 to 25.84°, 24.92 to 24.64°, and 24.05 to 20.84° for iron, wood and galvanized, respectively, as the moisture content increased from 13.75 to 17.53% (d.b).

Fig. 8. Variation of the coefficient of friction of flixweed seeds with moisture content.

For all moisture contents, the maximum angle of friction was offered by wood, followed by the iron, and galvanized surfaces. The least static angle of friction of flixweed seeds may be due to the smoother and more polished surface of the galvanized sheet than the other materials used. Angle of friction and moisture content correlate to each other based on the following Eqs.:

(30)

(31)

(32)

3.3.2. Angle of repose
The effects of the moisture content on filling and emptying angles of repose of flixweed seeds are shown in Fig. 9. The values of filling angle of repose were found to increase from 28.86 to 36.62° in the moisture range of 5.28 to 17.53% (d.b) while, the corresponding values for the emptying one were found to decrease from 34.36 to 33.41°, in the moisture range of 5.28 to 9.39% (d.b), then increase from 33.41 to 39.47°, in the moisture range of 9.39 to 17.53% (d.b). Also, at all moisture levels, the repose’s emptying angle’s value was more than the filling one; there are some papers with the same results [30, 34].

Fig. 9. Variation of filling and emptying angle of repose of flixweed seeds with moisture content.

4. CONCLUSION

Dimensional properties of seeds are essential for designing of sorters, separators, aerodynamic cleaners, storage structures, material handling equipment, hydrodynamic and aerodynamic separation, transportation systems, dryers and aeration equipment, belt conveyors, and oil extractor machines. Improvements in post-harvest equipment design depend on better knowledge of seeds’ properties.In summary, the purpose of the present studywas to investigate flixweed seeds’ physical properties, enlarging the knowledge about this species, and providing useful data for its post-harvest handling and further industrial processing.

The following conclusions were drawn from this investigation about the physical properties of flixweed seed at different moisture levels. The results of geometric properties showed that there is no linear relationship between moisture content and geometrical parameters. Modeling results showed that whenever values of skewness and kurtosis are both positive and significant, both are positive and not significant, both skewness and kurtosis are negative and not significant, or one of skewness or kurtosis has a negative and not significant and another one has a positive and not significant value, the G. E. V had the best performance.

The particle density values showed that the flixweed seeds are heavier than water and will not float in so, particle density can be used to separate the flixweed seeds from other lighter foreign materials. The external static angles of friction on three different contacting materials have been found, and the results showed that the mean value of static angle friction was the least in the case of galvanizes sheet while it is the highest for wood.

5. Acknowledgement

The authors would like to thank the University of Tehran and Dr. Mohammad Hassan Torabi for providing technical support for this work.

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Received: 28.10.2020
Reviewed: 29.11.2020
Accepted: 10.01.2021

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Amir Hossein Mirzabe
Department of Mechanical Engineering of Biosystems, College of Agriculture & Natural Resources, University of Tehran, Tehran, Iran
Telephone: 098 3153239185
Cell phone: 0989399442161
a_h_mirzabe@yahoo.com
email: a_h_mirzabe@alumni.ut.ac.ir

Ali Fadavi
Department of Food Technology, College of Aburaihan, University of Tehran, Tehran, Iran
Phone: 098 21 360 406 14
Mob: 0989128440566
email: afadavi@ut.ac.ir

Ali Mansouri
Department of Mechanical Engineering of Biosystems, College of Aboureihan, University of Tehran, Tehran, Iran
Telephone: 098 3153239185
Cell phone: 0989171837151
email: ali.mansouri@ut.ac.ir

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