MOISTURE-DEPENDENT PHYSICAL PROPERTIES OF MEDICAL TINY SEEDS: PART B: SUMMER SAVORY (SATUREJA HORTENSIS L.), BASIL (OCIMUM BASILICUM L.), CRESS (LEPIDIUM SATIVUM L.), AND AJOWAN (CARUM COPTICUM L.)
DOI:10.30825/5.EJPAU.198.2021.24.1

Amir Hossein Mirzabe¹, Ali Fadavi², Ali Mansouri³, Ahmad Raufi ^4
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
⁴ Department of Horticultural Science, School of Agriculture, Shiraz University, Shiraz, Iran

ABSTRACT

One of the most critical challenges of determining tiny seeds’ engineering properties is their dimensions. In the present study, a method based on digital image processing was employed to investigate the moisture content’s effect on geometric properties of summer savory, basil, cress, and ajowan seeds. Also, the gravimetrical and frictional properties of the seeds were measured. Gamma, Generalized Extreme Value, and Weibull distributions were used to model the probability frequency distribution of the seeds’ length, width, and thickness. This research indicated that the application of the image processing technique could be an excellent method to measure dimensional parameters of tiny seeds. Results showed that, with an increasing moisture content of seeds, the 1000-seed mass increased for basil, cress, and ajowan seeds; but, summer savory seeds showed that increasing-decreasing trend. For all four plant spices, increasing moisture content will result in the bulk density decrement. The particle density of summer savory, basil, and cress seeds decreased due to moisture content increment. However, the particle density of ajowan seeds increased with increasing moisture content. Results of measuring the angle of friction on iron, wood, and galvanized surfaces showed that, in most cases, the angle of friction increased by increasing moisture content. Also, except for the filling angle of repose of summer savory, increasing trends were observed for the emptying and filling angle of repose due to moisture content increment.

Key words: Image processing; Distribution modeling; Summer Savory; Basil; Cress; Ajowan.

Nomenclature
AMD	Arithmetic mean diameter, mm	TSM	1000-seed mass, g
EAR	Empting angle of repose, °	V	Volume of the seeds, mm3
f(x)	Probability density function	W	Width of the seeds, mm
F(x)	Cumulative density function	xavg	Mean of data
FAR	Filling angle of repose, °	xi	Midpoint of each class interval
GMD	Geometric mean diameter, mm	Greek letters
KS	Kolmogorov-Smirnov index
L	Length of the seeds, mm
Mi	Initial mass of sample, kg	α	Location parameter in Weibull distribution
MCf	Final moisture content, % (d.b.)	β	Scale parameter in Weibull distribution
MCi	Initial moisture content, % (d.b.)	Γ	Gamma function
Mw	Mass of water added, kg	γ	Shape parameter in Weibull distribution
n	Number of occurrence	δ	Location parameter in Gamma distribution
P	Porosity, %	ε	Shape parameter Gamma distribution
PA	Projected area, mm2	µ	Location parameter in G. E. V distribution
S	Surface area, mm2	ξ	Shape parameter in G. E. V distribution
SSA	Specific surface area, mm-1	ρb	Bulk density of seeds, kg·m-3
SEK	Standard errors of kurtosis	ρt	Particle density of seeds, kg·m-3
SES	Standard errors of skewness	σ	Scale parameter in Gamma distribution
STD	Standard deviation	φ	Sphericity of seeds, %
T	Thickness of the seeds, mm	ψ	Scale parameter in G. E. V distribution

1. INTRODUCTION

The proper design of process equipment agricultural products depends on the physical and mechanical properties of seeds, grains, nuts, kernels, fruits, vegetables, etc. Moisture content is a parameter that is essential in drying processes [47]. Besides, with the changing moisture content of seeds, grains, nuts, kernels, etc., their physical, mechanical, and chemical properties will change. So, physical and mechanical properties should be measured in different moisture content levels.

Although many studies have been conducted on crops and products' physical and mechanical properties [5, 6, 18, 25, 36, 38, 40, 43, 45, 46], they are not reported for some plant spices. Most tiny seeds have health benefits. Therefore, measuring their engineering properties are necessary. Little research has been done on measuring the physical properties of tiny seeds or grains [8, 11, 19, 30, 33, 41, 49, 51]. The dimensions of tiny seeds or grains are a limiting factor in measuring physical and mechanical properties. Dimensions of tiny seeds are too small. It is impossible to measure them by ordinary methods like a caliper, digital caliper, micrometer, and digital micrometer. Also, the seeds' small size makes it necessary to use accurate methods to measure the particle density. Besides, the small seed size makes it very difficult to measure mechanical properties such as rupture force, rupture energy, modulus of elasticity, hardness, and toughness.

The summer savory (Satureja hortensis L.) is an annual herbaceous plant from the Lamiaceae family [20]. Summer savory herb contains essential oils (0.5 to 2%), tans (4 to 9%), resins, flavonoids, carotenoids, and vitamin C [20]. People consumed its leaves and stem as vegetables and its seeds due to their undeniable health benefits.

Basil (Ocimum basilicum L.), known as garden or sweet basil, is commonly cultivated throughout Mediterranean regions [1, 2]. It is one of the most popular herbs native to Asia (India, Pakistan, Iran, Thailand, etc.). It can be observed growing wild in tropical and sub-tropical regions [27]. Basil seeds are used as diuretic, antipyretic, antispasmodic, and stomach medicine [1, 12]. Basil seed has reasonable amounts of gum with healthful properties. The Basil Seed Gum (BSG) extraction has been reported to be comprised of two significant fractions of glucomannan (43%) [24].

Cress or garden cress(Lepidium sativum L.) is an annual herb that belongs to the Cruciferae family and grows widely in the Middle East, Europe, and the USA [21, 35]. The parts of the plant which are used are the seeds, leaves, and roots. The edible whole seed is known to have health-promoting properties [14]. The cress seeds are bitter and have applications in treating various diseases such as leprosy, skin diseases, and diuretic [21]. Cress roots are bitter and acrid and have been used in treating secondary syphilis. Cress leaves are antibacterial and useful in treating scurvy [4, 21].

Ajowan (Carum copticum L.) is an herbaceous plant belonging to the Apiaceae family and grows in Mediterranean regions and Iraq, Iran, Afghanistan, India, and Egypt [16, 42]. It has been reported that ajowan seed oil has diuretic, carminative, analgesic, anti -shortness of breath, and anti-inflammatory compounds [50]. In traditional medicine, the water extract of ajowan seed is widely used to relieve flu symptoms in children [7, 22].

Because of the benefits of the summer savory, basil, cress, and ajowan seeds and lack of conducted study on their engineering properties, the aim of the current study was to a) measure length, width, and thickness, geometric and arithmetic mean diameters, b) calculate sphericity, volume, surface area, specific surface area, and projected area, c) measure 1000-seed mass, bulk density, particle density, and porosity, d) measure angle of external friction, emptying and filling angle of repose of seeds. Three principle dimensions of the seeds were modeled by Gamma, Generalized Extreme Value, and Weibull distributions.

2. MATERIAL AND METHOD

2.1. Sample preparation
Summer savory, basil, cress, and ajowan were purchased from a local market in Shahreza in 2013. Seeds were harvested in 2012 from local farms of Foodan located on Shahreza, Isfahan province, Iran (longitude of 31.59° N, the latitude of 51.50° E, average annual Precipitation 135 mm from 2000 to 2010, height above the sea level of 1845 m, the average annual temperature of 14.7°C from 1993 to 2010). The seeds were cleaned manually to remove 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 purchased seeds' initial moisture content was considered the first moisture level (sample A). The market storage moisture contents of summer savory, basil, cress, and ajowan seeds were 4.05, 5.20, 5.57, and 6.71% (d.b), respectively. 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. Mass of added water to samples calculated based on the Eq.1 [9, 13]:

(1)

Where: M_w is the mass of water added, kg; M_i is the initial mass of the sample, kg; MC_i is the initial moisture content of the sample, % (d.b); and MC_f is the final moisture content of the sample, % (d.b).

The authors intended to increase the moisture content by 5, 10, and 15% compared to the initial moisture content. However, pre-tests showed that for cress seeds at moisture content close to 20%, they stick to each other. Therefore, for cress seeds, the difference between moisture level A with levels B, C, and D was considered equal to 4, 8, and 12, respectively. It should be noted that although the authors considered the difference of 5 or 4% between consecutive moisture levels, the differences between consecutive moisture levels were not exactly equal to 4 or 5%. Differences between consecutive moisture levels were close to 4 or 5%. This can be attributed to errors in stirring the seeds to distribute moisture evenly throughout the sample.

The samples were packed in sealed polyethylene bags and kept in a refrigerator for 72 hours to let the moisture distribute uniformly throughout the samples. The mean temperature and mean relative humidity of the ambient air were 35°C and 42%. The temperature of the refrigerator was five °C. The samples’ moisture contents were measured based on the standard hot air oven method [3, 17, 37]. The average values of the three replications were reported as the moisture content. Then, samples were stored in a refrigerator until the test time.

2.2. Geometric properties
2.2.1. Equations and formulas
The image processing technique measured the three major perpendicular dimensions. Geometric mean diameter, arithmetic mean diameter, sphericity, surface area, specific surface area, and volume of the seeds were calculated. The equations used to calculate these parameters are presented in Table 1. 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 Equation:

(9)

Table 1. The list of equations were used to calculate dimensional properties and porosity.

Parameter	Formula	Eq. No.	Reference
Sphericity, %		2	[31]
Geometric mean diameter, mm		3
Arithmetic mean diameter, mm		4
Surface area, mm2		5
Specific surface area, mm-1		6
Volume, mm3		7
Porosity, %		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 [31]. 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. Several functions of the MATLAB software package improved the contrast between the seeds and the background.

The steps of processing for each seed included a) the RGB color images were converted into the eight-bit gray-scale level, b) the threshold technique was performed to isolate each seed from its white background. Eight-bit gray-scale intensity represents different gray shades from black to white (0 to 255), c) the eight-bit gray-scale images were digitized to the 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, d) the threshold values of the seeds were determined experimentally, e) the holes and noise of binary images were removed by morphological closing and opening. From the gray-scale images, summer savory, basil, cress, and ajowan seeds, pixel values less than 112, 99, 104, and 185 were converted to 0 (black). The values higher than 112, 99, 104, and 168 respectively were converted to 255 (white) [31], f) the number of pixels representing the length, width, and thickness of the seeds was also measured on the captured images using MATLAB R2012a software package, g) 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 millimeters was obtained. Illustrations of measuring the geometric properties by the image processing technique are presented in other reports [29, 30].

2.2.3. Modeling of dimensions
Length, width, and thickness of summer savory, basil, cress, and ajowan seeds distribution were modeled using three probability density functions. These functions were: Gamma, Generalized Extreme Value, and Weibull distribution. The mathematical functions of probability density and cumulative frequency are presented in Table 2.

Table 2. The probability density function and cumulative frequency for Gamma, Generalized Extreme Value, log-normal and Weibull distribution.

Name	Probability density function	Cumulative frequency function
Gamma
G. E. V
Weibull

The adjustable parameters for each probability density function were calculated using the commercial spreadsheet package of Easy Fit 5.5. Kolmogorov-Smirnov goodness of fit test was used to evaluate fitted distributions [15]. The test is based on the vertical deviation between the observed cumulative density function and estimated cumulative density function based on Eq. (10):

(10)

F(x) is the observed cumulative frequency distribution, and f(x) is the probability of the theoretical cumulative frequency distribution. In this Equation, lower 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.

2.3. Gravimetric properties
2.3.1. 1000-seed mass
One hundred seeds were randomly selected from the bulk sample to measure the 1000-unit mass; the 100-unit mass was measured by a digital balance (Kern, Japan, the accuracy of ±0.001 g). Single seed mass was calculated by dividing the 100-seed mass by 100. 1000-seed mass was calculated by multiplying the 100-seed mass by 10.

2.3.2. Bulk density
The bulk material of seeds with different moisture content was obtained by a container with a known volume (0.5 Liter). The seeds were poured into the container from a height of 15 cm [17]. The bulk density is equal to the mass of bulk material divided by the volume of the container.

2.3.3. Particle density
The particle density is defined as the sample mass (Ms) divided by the sample volume (Vs). It was determined using the water displacement method. Toluene (C7H8) was used in place of water because seeds absorb it to a lesser extent. Also, the density of toluene is less than water [28]. The individual sample volume was determined by weighing the volume of displaced toluene [34].

2.3.4. Porosity
The seeds' porosity is defined as the ratio of the volume of pores to the total volume. Porosity or void fraction measures the void spaces or empty spaces in material between 0 to 100%. The bulk seeds’ porosity was calculated from bulk and particle density data and applying Eq. (8) mentioned in Table 1 [44].

2.4. Frictional properties
2.4.1 Angle of friction
The angle of external static friction is the ratio of the force required to start sliding the sample over a surface divided by the normal force. The seeds ’ static friction angles were measured using the inclined plane method on iron, wood, and galvanized surfaces. A topless and bottomless cylinder of 10 cm diameter and 5 cm height was filled with the seeds. 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. At this juncture, the tilt angle was read by Auto Cad 2007 software package [34].

2.4.2. Angle of repose
The device used in emptying and filling angle of repose measurement consists of two boxes, top, and bottom boxes, with dimensions of 12 cm in length, 12 cm in height, and 6 cm in width [10]. The upper box was filled with the samples. The material of the upper box 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 or dynamic angle of repose is the residual surface’s angle with the upper box’s horizon. The seeds’ height was measured, and the filling angle of repose and emptying angle of repose were calculated [47].

2.5. Statistical analysis of geometric properties
The maximum, minimum, average, and standard deviation (STD) for geometric properties were calculated using Microsoft Office Excel 2010. The number of repetitions for measuring or calculating each parameter is mentioned in Table 3. 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. (11) and (12) as reported by [26]:

(11)

(12)

where: n is the number of occurrences, xavg is the mean seed's size, xi is the midpoint of each class interval in metric. Two times of standard errors of skewness (SES) and kurtosis (SEK) for a normal distribution are equal to [48]:

(13)

(14)

Where: n is the number of occurrences.

Table 3. The list of number of repetitions were made to measure or calculate each parameter.

Parameter	Method to measure	Number of repetitions
L, mm	Image processing	50
W, mm	Image processing	50
T, mm	Image processing	50
PA, mm2	Image processing	50
ρb, kg·m-3	Mass of definite volume	5
ρt, kg·m-3	Water displacement method	3
TSM, g	Measuring the mass of 100 seeds and its multiplication by 10	5
AF, °	Incipient movement on the sloped plate and image processing	5
EAR and FAR, °	Image processing	5
Parameter	Equation NO.  to calculate	Number of repetitions
φ, %	2	50
GMD, mm	3	50
AMD, mm	4	50
S, mm2	5	50
SSA, mm-1	6	50
V, mm3	7	50
P, %	8	3

In the current study, for the four seeds (savory, basil, cress, and ajowan) and all the parameters, n was equal to 50. To calculate the values of SES and SEK, n was replaced by 50 in Eq. (13) and (14), and values of SES and SEK were obtained 0.3366 and 0.6619, respectively. If, for each parameter, the result of this division is between , it can suggest that population data are neither positively nor negatively skewed. If, for each parameter, the result of this division is between , it can suggest that population data are neither positively nor negatively kurtosis.

3. RESULTS AND DISCUSSION

3.1. Size and dimensions of seeds
3.1.1. Summer savory
Length, width, and thickness of the summer savory seeds were measured, and geometric and arithmetic mean diameters were calculated. Presented results in Table 4 showed that with increasing moisture content from 4.05% (d.b) to 10.69% (d.b), the average values of the length, width, thickness, geometric mean diameter, and arithmetic mean diameter increased from 0.291, 0.264, 0.236, 0.261, and 0.263 mm to 0.602, 0.528, 0.453, 0.524, and 0.528 mm, respectively. While, increasing moisture content from 10.69% (d.b) to 15.02% (d.b) and also increasing from 15.02% (d.b) to 18.65% (d.b) showed a decreasing trend in dimensions of summer savory seeds. Moreover, in all moisture levels, the arithmetic mean diameter values were more than geometric mean diameter values.

Table 4. Effect of the moisture content on the size and dimensions of summer savory seeds

Moisture content	Parameter	Max	Min	Average ± STD	Skewness	Kurtosis
4.05 % (d.b)	L, mm	0.360	0.242	0.291± 0.030	0.616*	-0.513*
	W, mm	0.356	0.180	0.264± 0.043	-0.018*	-0.456*
	T, mm	0.353	0.091	0.236± 0.066	-0.563*	-0.495*
	GMD, MM	0.356	0.164	0.261± 0.047	-0.179*	-0.380*
	AMD, MM	0.356	0.180	0.263± 0.043	-0.015*	-0.406*
10.69 % (d.b)	L, mm	0.799	0.405	0.602 ± 0.094	-0.308*	-0.378*
	W, mm	0.663	0.378	0.528 ± 0.072	-0.576*	-0.391*
	T, mm	0.560	0.328	0.453 ± 0.061	-0.410*	-0.617*
	GMD, MM	0.653	0.378	0.524 ± 0.071	-0.595*	-0.410*
	AMD, MM	0.663	0.378	0.528 ± 0.072	-0.576*	-0.391*
15.02 % (d.b)	L, mm	0.559	0.379	0.473 ± 0.049	-0.041*	-0.767*
	W, mm	0.482	0.362	0.424 ± 0.032	-0.124*	-0.597*
	T, mm	0.421	0.321	0.375 ± 0.024	-0.258*	-0.472*
	GMD, MM	0.479	0.360	0.422 ± 0.031	-0.146*	-0.590*
	AMD, MM	0.482	0.362	0.424 ± 0.032	-0.124*	-0.597*
18.65 % (d.b)	L, mm	0.581	0.387	0.466 ± 0.046	0.476*	-0.228*
	W, mm	0.503	0.368	0.420 ± 0.029	0.555*	0.320*
	T, mm	0.425	0.330	0.373 ± 0.021	-0.088*	-0.233*
	GMD, MM	0.499	0.367	0.418 ± 0.028	0.542*	0.337*
	AMD, MM	0.503	0.368	0.420 ± 0.029	0.555*	0.320*
* and ** mean significant and not significant skewness or kurtosis, respectively.

3.1.2. Basil
The results of measuring and calculating of dimensions of basil are presented in Table 5. The results showed that with increasing moisture content from 5.20% (d.b) to 9.97% (d.b), the average values of the length, width, thickness, geometric mean diameter, and arithmetic mean diameter increased from 0.576, 0.518, 0.463, 0.516, and 0.518 mm to 0.623, 0.565, 0.506, 0.562, and 0.565 mm, respectively. Also, increasing moisture content from 14.98% (d.b) to 19.98% (d.b) showed an increasing trend for all parameters. While increasing moisture content from 9.97% (d.b) to 14.98% (d.b) showed a decreasing trend for length, width, and diameters; thickness had an increasing trend in the moisture range from 5.20 to 19.98% (d.b). Moreover, in all moisture levels, the arithmetic mean diameter values were more than or equal to the geometric mean diameter values.

Table 5. Effect of the moisture content on the size and dimensions of basil seeds

Moisture content	Parameter	Max	Min	Average ± STD	Skewness	Kurtosis
5.20 % (d.b)	L, mm	0.692	0.485	0.576 ± 0.045	0.334*	0.004*
	W, mm	0.597	0.422	0.518 ± 0.042	-0.102*	-0.406*
	T, mm	0.513	0.397	0.463 ± 0.032	-0.276*	-1.110*
	GMD, MM	0.560	0.442	0.516 ± 0.028	-0.480*	-0.160*
	AMD, MM	0.567	0.445	0.518 ± 0.028	-0.422*	-0.154*
9.97 % (d.b)	L, mm	0.733	0.549	0.623 ± 0.031	0.299*	2.460**
	W, mm	0.682	0.483	0.565 ± 0.034	0.453*	2.419**
	T, mm	0.631	0.414	0.506 ± 0.047	0.697**	0.560*
	GMD, MM	0.681	0.480	0.562 ± 0.034	0.461*	2.278**
	AMD, MM	0.682	0.483	0.565 ± 0.034	0.453*	2.420**
14.98 % (d.b)	L, mm	0.712	0.495	0.569 ± 0.043	1.125**	2.401**
	W, mm	0.628	0.492	0.545 ± 0.030	0.595*	0.886*
	T, mm	0.592	0.468	0.522 ± 0.025	0.151*	0.396*
	GMD, MM	0.624	0.492	0.545 ± 0.029	0.548*	0.763*
	AMD, MM	0.628	0.492	0.545 ± 0.030	0.601*	0.818*
19.98 % (d.b)	L, mm	0.682	0.491	0.582 ± 0.040	0.293*	-0.146*
	W, mm	0.649	0.475	0.558 ± 0.033	0.201*	1.031*
	T, mm	0.633	0.308	0.531 ± 0.045	-2.219**	11.574**
	GMD, MM	0.649	0.444	0.556 ± 0.035	-0.348*	2.055**
	AMD, MM	0.649	0.459	0.557 ± 0.035	-0.161*	1.481**
* and ** mean significant and not significant skewness or kurtosis, respectively.

3.1.3. Cress
Results of moisture dependent on length, width, thickness, geometric, and arithmetic mean diameters of the cress seeds are shown in Table 6. Increasing moisture content from 5.57 to 17.19% (d.b) sowed an increasing trend for all the parameters. Results showed an increase in the average values of the length, width, thickness, geometric mean diameter, and arithmetic mean diameter increased from 0.606, 0.538, 0.478, 0.538, and 0.541 mm 0.643, 0.591, 0.539, 0.589, and 0.591 mm in the moisture range. Additionally, in all moisture levels, the arithmetic mean diameter values were more than the geometric mean diameter values.

Table 6. Effect of the moisture content on the size and dimensions of cress seeds

Moisture content	Parameter	Max	Min	Average ± STD	Skewness	Kurtosis
5.57 % (d.b)	L, mm	0.697	0.540	0.606 ± 0.024	-0.232*	0.553*
	W, mm	0.629	0.412	0.538 ± 0.056	0.652*	1.303**
	T, mm	0.520	0.416	0.478 ± 0.024	-0.645*	0.245*
	GMD, MM	0.587	0.462	0.538 ± 0.023	-0.627*	1.527**
	AMD, MM	0.590	0.465	0.541 ± 0.024	-0.536*	1.325**
9.38 % (d.b)	L, mm	0.733	0.549	0.623 ± 0.031	0.299*	2.460**
	W, mm	0.682	0.483	0.564 ± 0.033	0.401*	2.633**
	T, mm	0.635	0.414	0.507 ± 0.048	0.790**	0.790*
	GMD, MM	0.681	0.480	0.562 ± 0.035	0.463*	2.276**
	AMD, MM	0.682	0.483	0.565 ± 0.034	0.455*	2.418**
13.81 % (d.b)	L, mm	0.880	0.558	0.634 ± 0.054	2.471**	8.821**
	W, mm	0.744	0.511	0.582 ± 0.046	1.588**	3.346**
	T, mm	0.653	0.430	0.530 ± 0.052	0.580*	-0.491*
	GMD, MM	0.735	0.507	0.580 ± 0.046	1.497**	2.905**
	AMD, MM	0.744	0.511	0.582 ± 0.046	1.588**	3.346**
17.19 % (d.b)	L, mm	0.718	0.583	0.643 ± 0.031	0.447*	0.280*
	W, mm	0.678	0.528	0.591 ± 0.033	0.701**	0.278*
	T, mm	0.640	0.462	0.539 ± 0.049	0.425*	-0.671*
	GMD, MM	0.677	0.526	0.589 ± 0.034	0.679**	0.235*
	AMD, MM	0.678	0.528	0.591 ± 0.033	0.701**	0.278*
* and ** mean significant and not significant skewness or kurtosis, respectively.

3.1.4. Ajowan
The effect of changing moisture content on changing length, width, thickness, geometric, and arithmetic mean diameters of the ajowan seeds is shown in Table 7. Increasing moisture content from 6.71 to 20.98% (d.b) showed an increasing trend for all the parameters. Results showed an increase in the average values of the length, width, thickness, geometric mean diameter, and arithmetic mean diameter increased from 0.330, 0.287, 0.212, 0.271, and 0.276 mm 0.568, 0.471, 0.381, 0.466, and 0.473 mm in the moisture range. Moreover, in all moisture levels, the arithmetic mean diameter values were more than the geometric mean diameter values.

Table 7. Effect of the moisture content on the size and dimensions of ajowan seeds

Moisture content	Parameter	Max	Min	Average ± STD	Skewness	Kurtosis
6.71 % (d.b)	L, mm	0.477	0.271	0.330± 0.050	1.155*	0.723*
	W, mm	0.347	0.243	0.287± 0.021	0.193*	0.111*
	T, mm	0.246	0.189	0.212± 0.013	0.334*	0.206*
	GMD, MM	0.332	0.235	0.271± 0.021	0.590*	0.441*
	AMD, MM	0.348	0.238	0.276± 0.023	0.772**	0.750*
11.76 % (d.b)	L, mm	0.558	0.314	0.390 ± 0.047	1.470**	3.749**
	W, mm	0.424	0.282	0.348 ± 0.031	0.416*	0.436*
	T, mm	0.303	0.228	0.263 ± 0.014	0.224*	0.708*
	GMD, MM	0.413	0.283	0.329 ± 0.024	0.806**	2.328**
	AMD, MM	0.426	0.285	0.334 ± 0.026	0.933**	2.508**
16.68 % (d.b)	L, mm	0.676	0.346	0.461 ± 0.069	0.897**	1.118*
	W, mm	0.548	0.336	0.401 ± 0.044	1.400**	2.269**
	T, mm	0.354	0.271	0.318 ± 0.019	-0.037*	-0.346*
	GMD, MM	0.491	0.323	0.388 ± 0.035	0.729**	0.838*
	AMD, MM	0.515	0.326	0.393 ± 0.038	0.882**	1.254**
20.98 % (d.b)	L, mm	0.790	0.419	0.568 ± 0.094	0.694**	-0.380*
	W, mm	0.607	0.375	0.471 ± 0.049	0.542*	0.801*
	T, mm	0.518	0.299	0.381 ± 0.037	0.608*	2.915**
	GMD, MM	0.570	0.374	0.466 ± 0.045	0.054*	-0.021*
	AMD, MM	0.592	0.377	0.473 ± 0.048	0.126*	-0.106*
* and ** mean significant and not significant skewness or kurtosis, respectively.

3.1.5 Comparison between seeds
A comparison between dimensions of summer savory, basil, cress, and ajowan seeds showed that in all moisture level average values of length, width, thickness, geometric and arithmetic mean diameter of cress seeds are more than the corresponding values of summer savory, basil, and ajowan seeds.

If the bulk of the data is at the left and the right tail is longer, the distribution is skewed right or positively skewed; if the peak is toward the right and the left tail is longer, the distribution is skewed left or negatively skewed (see to the Table 4, 5, 6, and 7). For the summer savory seeds, all the characteristics have no significant positively or negatively kurtosis. For the basil seeds, in 3 cases out of 20 cases, skewness was significant, and in 8 cases out of 20 cases, kurtosis was significant. The corresponding values for cress seeds were 8 and 11 cases for skewness and kurtosis, respectively. Moreover, the corresponding values for ajowan seeds were 9 and 6 cases, respectively.

3.2. Geometric properties
3.2.1. Summer savory
Sphericity, volume, surface area, and specific surface area of the summer savory seeds were calculated. The projected area was measured based on the image processing technique. Presented results in Table 8 showed that with increasing moisture content from 4.05 to 10.69% (d.b), the average values of the volume, surface area, specific surface area, and projected area increased from 0.010, 0.378, 0.334, and 0.965 mm to 0.079, 1.500, 1.023, and 1.900 mm, respectively. While, increasing moisture content from 10.69% (d.b) to 15.02% (d.b) and also increasing from 15.02% (d.b) to 18.65% (d.b) showed a decreasing trend in volume and surface area of the seeds. Moreover, in the moisture range, at first (increasing moisture content from 4.05 to 10.69% (d.b)), sphericity had a decreasing trend, while more increasing moisture content showed an increasing trend for sphericity.

Table 8. Effect of the moisture content on the geometrical parameters of summer savory seeds

Moisture content	Parameter	Max	Min	Average ± STD	Skewness	Kurtosis
4.05 % (d.b)	φ, %	99.956	61.149	89.466 ± 11.258	-1.182**	0.044*
	V, mm3	0.024	0.002	0.010 ± 0.005	0.618*	-0.023*
	S, mm2	0.673	0.167	0.378 ± 0.123	0.333*	-0.342*
	SSA, mm-1	0.594	0.148	0.334 ± 0.109	0.333*	-0.342*
	PA, mm2	1.321	0.734	0.965 ± 0.140	0.795**	0.368*
10.69 % (d.b)	φ, %	98.350	79.974	87.360 ± 4.526	0.597**	-0.247*
	V, mm3	0.146	0.028	0.079 ± 0.029	-0.059*	-0.456*
	S, mm2	2.316	0.759	1.500 ± 0.388	-0.310*	-0.488*
	SSA, mm-1	1.580	0.517	1.023 ± 0.265	-0.310*	-0.488*
	PA, mm2	2.326	1.534	1.900 ± 0.214	0.292*	-1.021*
15.02 % (d.b)	φ, %	97.857	82.993	89.466 ± 4.166	0.438*	-1.030*
	V, mm3	0.057	0.024	0.040 ± 0.009	0.148*	-0.651*
	S, mm2	1.229	0.694	0.956 ± 0.142	0.023*	-0.647*
	SSA, mm-1	0.903	0.510	0.703 ± 0.104	0.023*	-0.647*
	PA, mm2	2.659	1.503	1.965 ± 0.252	0.683**	0.376*
15.65 % (d.b)	φ, %	97.804	82.461	89.875 ± 3.872	0.013*	-1.061*
	V, mm3	0.065	0.026	0.039 ± 0.008	0.947**	1.275**
	S, mm2	1.338	0.717	0.937 ± 0.132	0.753**	0.727*
	SSA, mm-1	1.090	0.584	0.763 ± 0.108	0.753**	0.727*
	PA, mm2	2.439	1.473	1.959 ± 0.219	-0.260*	-0.741*
* and ** mean significant and not significant skewness or kurtosis, respectively.

3.2.2. Basil
The results of measuring and calculating the geometrical properties of basil are presented in Table 9. Results showed that with increasing moisture content from 5.20 to 9.97% (d.b), the average values of the sphericity, volume, surface area, and specific surface area increased. However, the average value of the projected area decreased. Also, increasing moisture content from 14.98 to 19.98% (d.b) showed an increasing trend for the sphericity and projected area. In comparison, increasing moisture content from 9.97% (d.b) to 14.98% (d.b) showed a decreasing trend for volume, surface area, and specific surface area. Moreover, increasing moisture content from 14.98 to 19.98% (d.b) showed an increasing trend for sphericity, volume, surface area, and projected area; but, the specific surface area had a decreasing trend.

Table 9. Effect of the moisture content on the geometrical parameters of basil seeds

Moisture content	Parameter	Max	Min	Average ± STD	Skewness	Kurtosis
5.20 % (d.b)	φ, %	98.392	79.672	89.927 ± 4.707	0.027*	-0.923*
	V, mm3	0.092	0.045	0.073 ± 0.011	-0.239*	-0.518*
	S, mm2	1.694	1.046	1.430 ± 0.153	-0.291*	-0.432*
	SSA, mm-1	0.640	0.395	0.540 ± 0.058	-0.291*	-0.432*
	PA, mm2	3.631	1.834	2.850 ± 0.388	-0.375*	0.133*
9.97 % (d.b)	φ, %	99.981	85.243	90.288 ± 3.633	0.998**	0.684*
	V, mm3	0.165	0.058	0.094 ± 0.018	1.191**	4.361**
	S, mm2	5.876	2.961	4.377 ± 0.638	0.728**	0.705*
	SSA, mm-1	1.993	1.004	1.485 ± 0.216	0.728**	0.705*
	PA, mm2	2.326	1.534	1.900 ± 0.214	0.292*	-1.021*
14.98 % (d.b)	φ, %	99.998	87.659	95.961 ± 3.018	-1.092**	0.948*
	V, mm3	0.128	0.062	0.085 ± 0.014	0.924**	1.515**
	S, mm2	2.089	1.284	1.581 ± 0.173	0.778**	1.225**
	SSA, mm-1	0.656	0.403	0.496 ± 0.054	0.778**	1.225**
	PA, mm2	3.965	2.532	3.351 ± 0.335	-0.433*	-0.313*
19.98 % (d.b)	φ, %	99.913	78.492	95.683 ± 3.789	-2.005**	7.310**
	V, mm3	0.143	0.046	0.091 ± 0.017	0.356*	2.088**
	S, mm2	2.236	1.109	1.649 ± 0.204	0.135*	1.595**
	SSA, mm-1	0.639	0.317	0.471 ± 0.058	0.135*	1.595**
	PA, mm2	4.709	0.042	3.553 ± 0.690	-2.478**	13.143**
* and ** mean significant and not significant skewness or kurtosis, respectively.

3.2.3. Cress
Results of statistical analysis of moisture dependent on cress seeds' complex dimensional properties are shown in Table 10. Increasing in the moisture content from 5.57 to 9.38% (d.b) caused increasing sphericity, volume, surface area, specific surface area, and projected area from 88.651, 0.082, 1.551, 0.576, and 3.582 to 90.288%, 0.094 mm³, 1.695 mm², 0.586 mm^-1, and 3.863 mm². Also, increasing moisture content from 9.38 to 13.81% (d.b) and 13.81 to 17.19% (d.b) caused increasing sphericity, volume, surface area, projected area, and specific surface area decreased.

Table 10. Effect of the moisture content on the geometrical parameters of cress seeds

Moisture content	Parameter	Max	Min	Average ± STD	Skewness	Kurtosis
5.57 % (d.b)	φ, %	95.144	81.914	88.651 ± 2.506	0.181*	0.897*
	V, mm3	0.106	0.052	0.082 ± 0.010	-0.253*	0.905*
	S, mm2	1.843	1.144	1.551 ± 0.135	-0.360*	0.996*
	SSA, mm-1	0.685	0.425	0.576 ± 0.050	-0.360*	0.996*
	PA, mm2	4.326	2.792	3.582 ± 0.338	-0.412*	0.078*
9.38 % (d.b)	φ, %	99.982	85.243	90.288 ± 3.634	0.999**	0.686*
	V, mm3	0.165	0.058	0.094 ± 0.018	1.190**	4.359**
	S, mm2	2.467	1.236	1.695 ± 0.206	0.812**	3.280**
	SSA, mm-1	0.852	0.427	0.586 ± 0.0713	0.8124**	3.2797**
	PA, mm2	4.570	2.981	3.863 ± 0.307	-0.476*	0.600*
13.81 % (d.b)	φ, %	98.653	83.540	91.554 ± 3.982	0.225*	-0.789*
	V, mm3	8.821	0.054	0.104 ± 0.028	2.055**	5.125**
	S, mm2	2.920	1.381	1.805 ± 0.303	1.860**	4.392**
	SSA, mm-1	0.946	0.447	0.584 ± 0.098	1.860**	4.392**
	PA, mm2	4.500	3.258	3.914 ± 0.310	-0.463*	-0.219*
17.19 % (d.b)	φ, %	99.426	85.798	91.677 ± 3.848	0.389*	-1.024*
	V, mm3	0.163	0.076	0.108 ± 0.019	0.966**	0.792*
	S, mm2	2.438	1.478	1.856 ± 0.211	0.838**	0.524*
	SSA, mm-1	0.711	0.431	0.541 ± 0.062	0.838**	0.524*
	PA, mm2	5.066	3.063	4.057 ± 0.376	-0.135*	0.979*
* and ** mean significant and not significant skewness or kurtosis, respectively.

3.2.4. Ajowan
The effect of changing moisture content on changing the ajowan seeds’ geometrical parameters is shown in Table 11. With increasing moisture content from 6.71 to 20.98% (d.b), volume, surface area, specific surface area, and projected area increased from 0.011, 0.406, 0.193, and 0.107 to 0.054 mm³, 1.192 mm², 0.375 mm^-1, and 0.252 mm², respectively. With increasing moisture content from 6.71 to 11.76% (d.b), sphericity increased but increasing moisture content from 11.76 to 20.98% (d.b) caused sphericity decrement.

Table 11. Effect of the moisture content on the geometrical parameters of ajowan seeds

Moisture content	Parameter	Max	Min	Average ± STD	Skewness	Kurtosis
6.71 % (d.b)	φ, %	91.870	69.435	84.440 ± 5.316	-1.074**	0.477*
	V, mm3	0.019	0.007	0.011 ± 0.003	1.055**	1.639**
	S, mm2	0.633	0.299	0.406 ± 0.069	0.993**	1.397**
	SSA, mm-1	0.302	0.142	0.193 ± 0.033	0.993**	1.397**
	PA, mm2	1.380	0.770	1.070 ± 0.140	0.490*	0.082*
11.76 % (d.b)	φ, %	93.695	69.370	84.635 ± 5.011	-0.916**	0.711*
	V, mm3	0.037	0.012	0.019 ± 0.004	1.585**	5.098**
	S, mm2	0.952	0.431	0.591 ± 0.095	1.292**	3.656**
	SSA, mm-1	0.424	0.192	0.264 ± 0.042	1.292**	3.656**
	PA, mm2	2.090	1.140	1.520 ± 0.211	0.378*	0.040*
16.68 % (d.b)	φ, %	99.921	69.824	84.469 ± 6.270	-0.403*	0.355*
	V, mm3	0.062	0.018	0.031 ± 0.009	1.327**	2.627**
	S, mm2	1.392	0.562	0.824 ± 0.163	1.213**	2.321**
	SSA, mm-1	0.502	0.203	0.298 ± 0.059	1.213**	2.321**
	PA, mm2	2.782	1.442	1.981 ± 0.301	0.713**	0.248*
20.98 % (d.b)	φ, %	92.149	67.404	83.907 ± 7.632	-0.970**	-0.247*
	V, mm3	0.097	0.027	0.054 ± 0.016	0.603*	0.452*
	S, mm2	1.834	0.750	1.192 ± 0.239	0.396*	0.179*
	SSA, mm-1	0.576	0.236	0.375 ± 0.075	0.396*	0.179*
	PA, mm2	3.822	1.740	2.52 ± 0.431	0.672**	0.684*
* and ** mean significant and not significant skewness or kurtosis, respectively.

3.2.5. Comparison between seeds
A comparison between dimensions of summer savory, basil, cress, and ajowan seeds showed that average values of sphericity of basil and ajowan seeds were respectively more and less in all moisture levels than the corresponding values of the other seeds. In all moisture level values of volume and projected area of cress seeds were more than the others. In most moisture levels, values of the surface area of cress and summer savory seeds were more and less than the others, respectively. Furthermore, values of the ajowan seeds' specific surface area, in all moisture levels, were less than the other seeds.

For the summer savory seeds, in 6 cases out of 20 cases, skewness was significant. In 1 case out of 20 cases, kurtosis was significant; in 10 cases out of 20 cases, skewness in 9 cases out of 20 cases, kurtosis was significant. The corresponding values for cress seeds were 10 and 6 cases for skewness and kurtosis, respectively. Moreover, the corresponding values for ajowan seeds were 14 and 9 cases, respectively.

3.3. Modeling dimensions
Length, width, and thickness of the seeds distributions were modeled using the Gamma, Generalized Extreme Value (G. E. V), and Weibull probability density functions distribution; the results for summer savory, basil, cress, and ajowan seeds are shown in Table 12, 13, 14, and 15, respectively. Results of summer savory seeds showed that to model the length of the seeds, in 2 cases out of 4 cases G. E. V distribution had the best performance and in 2 other cases had the worst performance (Table 12). Also, to model the seeds' width, in 2 cases out of 4 cases, G. E. V distribution had the best performance while, in 3 cases out of 4 cases, Gamma distribution had the worst performance (Table 12). Moreover, to model the seeds' thickness, in 3 cases out of 4 cases, the G. E. V distribution had the best performance. In contrast, in 4 cases out of 4 cases, Gamma and Gamma distribution had the worst performances (Table 12).

Table 12. Calculated parameter values of the Gamma, Generalized Extreme Value (G. E. V), and Weibull probability density function for length, width, and thickness of the summer savory seeds

Moisture content	Parameter	Distribution name	Shape parameter	Scale parameter	Location parameter	Kolmogorov-Smirnov index	Rank
4.05 % (d.b)	L, mm	Gamma	3.549	0.016	0.234	0.0895	1
		G. E. V	-0.009	0.024	0.277	0.0943	2
		Weibull	1.804	0.058	0.240	0.1033	3
	W, mm	Gamma	139.010	0.006	-0.560	0.1288	3
		G. E. V	-0.570	0.074	0.222	0.0661	1
		Weibull	15.916	0.876	-0.611	0.0779	2
	T, mm	Gamma	79.407	0.005	-0.125	0.0873	3
		G. E. V	-0.288	0.044	0.248	0.0827	2
		Weibull	3.191	0.138	0.140	0.0782	1
10.69 % (d.b)	L, mm	Gamma	147.350	0.008	-0.547	0.0833	3
		G. E. V	-0.418	0.101	0.575	0.0719	2
		Weibull	4.945	0.432	0.206	0.0674	1
	W, mm	Gamma	192.720	0.005	-0.484	0.1348	3
		G. E. V	-0.569	0.080	0.512	0.0827	2
		Weibull	11.910	0.725	-0.166	0.0821	1
	T, mm	Gamma	147.210	0.005	-0.287	0.1300	3
		G. E. V	-0.486	0.066	-0.287	0.1038	1
		Weibull	6.758	0.363	0.115	0.1163	2
15.02 % (d.b)	L, mm	Gamma	99.069	0.005	-0.018	0.0738	3
		G. E. V	-0.298	0.051	0.456	0.0711	1
		Weibull	3.067	0.151	0.338	0.0716	2
	W, mm	Gamma	114.000	0.003	0.086	0.0832	3
		G. E. V	-0.321	0.033	0.413	0.0629	1
		Weibull	3.692	0.114	0.321	0.0754	2
	T, mm	Gamma	166.380	0.002	0.070	0.0804	3
		G. E. V	-0.404	0.025	0.367	0.0518	1
		Weibull	4.656	0.103	0.281	0.0545	2
18.65 % (d.b)	L, mm	Gamma	6.919	0.018	0.343	0.0591	1
		G. E. V	-0.109	0.042	0.446	0.0670	3
		Weibull	2.014	0.100	0.377	0.0646	2
	W, mm	Gamma	9.294	0.010	0.330	0.0664	1
		G. E. V	-0.115	0.026	0.407	0.0665	2
		Weibull	2.134	0.067	0.360	0.0737	3
	T, mm	Gamma	150.390	0.002	0.119	0.0776	3
		G. E. V	-0.362	0.022	0.366	0.0586	1
		Weibull	3.528	0.072	0.308	0.0618	2

Results of basil seeds showed that to model the seeds’ length, in 3 cases out of 4 cases, G. E. V distribution had the best performance, but in 3 cases out of 4 cases, Weibull distribution had the worst performance (Table 13). Also, to model the basil seeds' width, Gamma distribution had the best performance in 4 cases out of 4 cases. However, in 4 cases out of 4 cases, the Weibull distribution had the worst performance (Table 13). Moreover, to model the basil seeds' thickness, in 3 cases out of 4 cases, the G. E. V distribution had the best performance. However, in 2 cases out of 4 cases, Gamma and Weibull distribution had the worst performances (Table 13).

Table 13. Calculated parameter values of the Gamma, Generalized Extreme Value (G. E. V), and Weibull probability density function for length, width, and thickness of the basil seeds

Moisture content	Parameter	Distribution name	Shape parameter	Scale parameter	Location parameter	Kolmogorov-Smirnov index	Rank
5.20 % (d.b)	L, mm	Gamma	19.471	0.010	0.377	0.0731	2
		G. E. V	-0.211	0.044	0.558	0.0634	1
		Weibull	2.485	0.117	0.471	0.0856	3
	W, mm	Gamma	155.600	0.003	-0.003	0.0818	1
		G. E. V	-0.302	0.042	0.503	0.0937	2
		Weibull	3.832	0.155	0.378	0.0987	3
	T, mm	Gamma	130.050	0.003	0.089	0.1285	3
		G. E. V	-0.428	0.035	0.454	0.0982	1
		Weibull	6.265	0.181	0.295	0.1175	2
9.97 % (d.b)	L, mm	Gamma	150.120	0.002	0.245	0.1112	3
		G. E. V	-0.364	0.031	0.614	0.0922	1
		Weibull	3.188	0.104	0.529	0.1097	2
	W, mm	Gamma	95.767	0.003	0.238	0.1233	2
		G. E. V	-0.284	0.032	0.553	0.1125	1
		Weibull	3.062	0.109	0.467	0.1361	3
	T, mm	Gamma	9.938	0.015	0.359	0.0961	2
		G. E. V	-0.078	0.040	0.486	0.0907	1
		Weibull	2.288	0.115	0.404	0.1113	3
14.98 % (d.b)	L, mm	Gamma	5.888	0.017	0.466	0.0914	2
		G. E. V	-0.049	0.035	0.550	0.0894	1
		Weibull	1.900	0.089	0.490	0.1022	3
	W, mm	Gamma	15.070	0.007	0.432	0.0733	1
		G. E. V	-0.154	0.027	0.533	0.0761	2
		Weibull	2.249	0.071	0.482	0.0814	3
	T, mm	Gamma	111.780	0.002	0.263	0.0670	1
		G. E. V	-0.276	0.024	0.513	0.0675	2
		Weibull	3.074	0.077	0.453	0.0746	3
19.98 % (d.b)	L, mm	Gamma	33.939	0.007	0.350	0.0672	2
		G. E. V	-0.160	0.037	0.565	0.0608	1
		Weibull	2.929	0.120	0.474	0.0730	3
	W, mm	Gamma	143.510	0.003	0.169	0.0870	1
		G. E. V	-0.314	0.032	0.548	0.0934	2
		Weibull	3.395	0.113	0.455	0.0973	3
	T, mm	Gamma	408.070	0.002	-0.432	0.1820	3
		G. E. V	-0.544	0.042	0.522	0.1450	1
		Weibull	15.773	0.603	-0.055	0.1508	2

Results of cress seeds showed that to model the seeds' length, in 3 cases out of 4 cases, G. E. V distribution had the best performance, but in 3 cases out of 4 cases, Weibull distribution had the worst performance (Table 14). Also, to model the cress seeds' width, in 2 cases out of 4 cases, G. E. V distribution had the best performance, but in 3 cases out of 4 cases, Weibull distribution had the worst performance (Table 14). Moreover, to model the thickness of the cress seeds, in 3 cases out of 4 cases, the G. E. V distribution had the best performance. However, in 2 cases out of 4 cases, Gamma and Weibull distribution had the worst performances (Table 14).

Table 14. Calculated parameter values of the Gamma, Generalized Extreme Value (G. E. V), and Weibull probability density function for length, width, and thickness of the cress seeds

Moisture content	Parameter	Distribution name	Shape parameter	Scale parameter	Location parameter	Kolmogorov-Smirnov index	Rank
5.57 % (d.b)	L, mm	Gamma	64.199	0.004	0.377	0.0762	1
		G. E. V	-0.199	0.028	0.600	0.0805	2
		Weibull	3.090	0.095	0.526	0.0882	3
	W, mm	Gamma	179.190	0.003	-0.077	0.0732	3
		G. E. V	-0.351	0.047	0.518	0.0560	2
		Weibull	5.115	0.217	0.333	0.0504	1
	T, mm	Gamma	194.330	0.002	0.139	0.1521	3
		G. E. V	-0.515	0.026	0.472	0.0948	2
		Weibull	11.512	0.236	0.253	0.0852	1
9.38 % (d.b)	L, mm	Gamma	150.120	0.002	0.245	0.1112	3
		G. E. V	-0.364	0.031	0.614	0.0922	1
		Weibull	3.188	0.104	0.529	0.1097	2
	W, mm	Gamma	95.767	0.003	0.238	0.1233	2
		G. E. V	-0.284	0.032	0.553	0.1125	1
		Weibull	3.062	0.109	0.467	0.1361	3
	T, mm	Gamma	9.925	0.015	0.359	0.0961	2
		G. E. V	-0.077	0.040	0.486	0.0907	1
		Weibull	2.287	0.115	0.404	0.1114	3
13.81 % (d.b)	L, mm	Gamma	3.384	0.025	0.545	0.1251	2
		G. E. V	0.141	0.032	0.610	0.1050	1
		Weibull	1.563	0.088	0.555	0.1480	3
	W, mm	Gamma	3.447	0.023	0.501	0.0906	2
		G. E. V	0.119	0.031	0.560	0.0661	1
		Weibull	1.667	0.082	0.509	0.1074	3
	T, mm	Gamma	6.513	0.020	0.397	0.1342	2
		G. E. V	-0.004	0.042	0.505	0.1247	1
		Weibull	2.227	0.122	0.421	0.1345	3
17.19 % (d.b)	L, mm	Gamma	21.661	0.006	0.502	0.0978	2
		G. E. V	-0.132	0.027	0.630	0.0914	1
		Weibull	2.481	0.080	0.572	0.1055	3
	W, mm	Gamma	7.286	0.012	0.503	0.0734	1
		G. E. V	-0.031	0.027	0.576	0.0763	2
		Weibull	2.198	0.077	0.523	0.0860	3
	T, mm	Gamma	4.269	0.024	0.435	0.0599	3
		G. E. V	-0.101	0.044	0.518	0.0569	1
		Weibull	1.801	0.095	0.454	0.0582	2

Results of ajowan seeds showed that to model the seeds’ length, in 2 cases out of 4 cases, G. E. V and Gamma distributions had the best performances. In 3 cases out of 4 cases, the Weibull distribution had the worst performance (Table 15). To model the width of the ajowan seeds, Gamma distribution had the best performance in 3 cases out of 4 cases. In contrast, in 2 cases out of 4 cases, the Weibull distribution had the worst performance (Table 15). Moreover, to model the thickness of the ajowan seeds, in 2 cases out of 4 cases, G. E. V and Gamma distributions had the best performances. In comparison, in 4 cases out of 4 cases, the Weibull distribution had the worst performance (Table 15).

Table 15. Calculated parameter values of the Gamma, Generalized Extreme Value (G. E. V), and Weibull probability density function for length, width, and thickness of the ajowan seeds

Moisture content	Parameter	Distribution name	Shape parameter	Scale parameter	Location parameter	Kolmogorov-Smirnov index	Rank
6.71 % (d.b)	L, mm	Gamma	1.332	0.045	0.270	0.0768	1
		G. E. V	0.165	0.032	0.305	0.0851	3
		Weibull	1.185	0.063	0.270	0.0845	2
	W, mm	Gamma	76.499	0.002	0.104	0.0481	1
		G. E. V	-0.262	0.021	0.279	0.0529	3
		Weibull	2.867	0.062	0.232	0.0485	2
	T, mm	Gamma	30.870	0.002	0.143	0.0682	1
		G. E. V	-0.188	0.012	0.207	0.0731	2
		Weibull	2.489	0.033	0.183	0.0806	3
11.76 % (d.b)	L, mm	Gamma	4.907	0.020	0.291	0.0792	2
		G. E. V	0.017	0.035	0.369	0.0720	1
		Weibull	1.814	0.091	0.309	0.0928	3
	W, mm	Gamma	26.342	0.006	0.191	0.1158	3
		G. E. V	-0.201	0.029	0.336	0.1113	1
		Weibull	2.683	0.087	0.271	0.1120	2
	T, mm	Gamma	119.330	0.001	0.113	0.0606	2
		G. E. V	-0.219	0.013	0.257	0.0585	1
		Weibull	3.437	0.047	0.220	0.0717	3
16.68 % (d.b)	L, mm	Gamma	5.637	0.029	0.300	0.0718	2
		G. E. V	-0.021	0.056	0.430	0.0688	1
		Weibull	1.912	0.142	0.335	0.0832	3
	W, mm	Gamma	2.954	0.024	0.329	0.0882	1
		G. E. V	0.136	0.029	0.379	0.0865	2
		Weibull	1.611	0.074	0.334	0.0963	3
	T, mm	Gamma	125.700	0.001	0.103	0.0645	2
		G. E. V	-0.245	0.019	0.311	0.0550	1
		Weibull	3.825	0.072	0.253	0.0715	3
20.98 % (d.b)	L, mm	Gamma	3.224	0.053	0.396	0.0765	1
		G. E. V	0.011	0.076	0.524	0.0777	2
		Weibull	1.725	0.175	0.412	0.0908	3
	W, mm	Gamma	20.237	0.011	0.254	0.0645	1
		G. E. V	-0.157	0.044	0.451	0.0664	2
		Weibull	2.641	0.127	0.358	0.0765	3
	T, mm	Gamma	50.372	0.005	0.122	0.1042	1
		G. E. V	-0.316	0.036	0.369	0.1091	2
		Weibull	2.721	0.107	0.285	0.1121	3

To determine the best distribution, we used the results in Table 12, 13, 14, and 15. Based on the Kolmogorov-Smirnov index, we ranked the distributions for each parameter of each seed. Then we comprised the rank of the distributions. In sum, to model the length of seeds, Generalized Extreme Value distribution had the best performance because in 10 cases out of 16, its ranks were 1 (see Table 12, 13, 14, and 15). Also, to model the length of seeds, the Weibull distribution had the worst performance because in 10 cases out of 16, its ranks were 3. In total, to model the width of seeds, Generalized Extreme Value distribution had the best performance because in 6 cases out of 16, its ranks were 1 (although ranks of Gamma distribution in 8 cases were one its rank in 5 cases was three; therefore the G. E. V had the best performance). Also, to model the seeds' width, the Weibull distribution had the worst performance because in 10 cases out of 16, its ranks were 3. Furthermore, in sum, to model the seeds' thickness, G. E. V distribution ranks in 11 cases out of 16 were one, so it had the best performance. Also, to model the thickness of the seeds, ranks of Weibull distribution in 8 cases out of 16 were three, so it had the worst performance (although ranks of Gamma distribution in 8 cases were three but its ranks in 3 cases were 1, while ranks of Weibull in 2 cases were 1).

The modeling showed that whenever skewness and kurtosis had negative values, Generalized Extreme Value and Weibull distribution had a good performance. In contrast, Gamma distribution had a poor performance to model the data. Also, whenever skewness had a positive value and kurtosis a negative value, G.E.V and Weibull distributions showed good performance, while Gamma distributions had a poor performance to model data.

Khazaei et al. [23] modeled mass and size distributions of two varieties of sunflower seeds and kernels by Log-normal, normal and Weibull distributions. They cited that when skewness had a positive value, Log-normal distribution was the best and normal distribution was the worst for data prediction. Mirzabe et al. [32] modeled distance between adjacent sunflower seeds on sunflower heads of three varieties using the Log-normal, normal and Weibull distributions. They cited that whenever skewness and kurtosis had negative value, Weibull distribution was the best fit one.

Skewness and kurtosis are two statistical indices calculated so that the reader would better understand the probability density distributions. The first thing that usually must be noticed about a distribution’s shape is whether it has one peak or more than one. If it has just one peak, like most data sets, the next thing noticed is whether it is symmetric or skewed to one side. If the bulk of the data is at the left and the right tail is longer, the distribution is skewed right or positively skewed; if the peak is toward the right and the left tail is longer, the distribution is skewed left or negatively skewed [33].

Kurtosis is a measure of whether the data set are peaked or flat relative to a normal distribution; that is, data sets with high kurtosis tend to have a distinct peak near the mean, decline rather rapidly, and have heavy tails [33]. Data sets with low kurtosis tend to have a flat top near the mean rather than a sharp peak.

3.4. Gravimetric properties
3.4.1. 1000-seed mass
The moisture content's effect on the variation of 1000-seed mass of the summer savory, basil, cress, and ajowan seeds are shown in Fig. 1. Results showed that with increasing moisture content from 5.20 to 19.98% (d.b), 5.57 to 17.19% (d.b), and 6.71 to 20.98% (d.b), values of the 1000-seed mass of the basil, cress, and ajowan seeds increased from 1.668 to 1.972 g, 1.888 to 2.172 g, and 0.875 to 1.272 g, respectively. Increasing moisture content from 4.05 to 10.60% (d.b) increased the 1000-seed mass of the summer savory from 0.622 to 0.772 g more increasing moisture content caused a decreasing trend for the 1000-seed mass of summer savory from 0.772 to 0.622 g. A comparison between seeds showed that the 1000-seed mass of the cress seeds is more than the other seeds in all moisture levels while the summer savory values are lower than the others.

Fig. 1. Effect of the moisture content on 1000-seed mass (TSM) of four tiny seeds

3.4.2. Bulk density
The moisture content's effect on the variation of bulk density of the summer savory, basil, cress, and ajowan seeds is shown in Fig. 2. Results showed that with increasing moisture content from 4.05 to 18.65% (d.b), 5.20 to 19.98% (d.b), 5.57 to 17.19% (d.b), and 6.71 to 20.98% (d.b), values of bulk density of the summer savory, basil, cress, and ajowan seeds decreased from 549.051 to 506.521 kg·m^-3, 637.347 to 563.443 kg·m^-3, 701.384 to 633.454 kg·m^-3, and 417.019 to 399.662 kg·m^-3, respectively. A comparison between seeds showed that in all moisture levels, the values of bulk density of the cress seeds are more than the other seeds while the ajowan values are lower than the others.

Fig. 2. Effect of the moisture content on the bulk density of four tiny seeds

Increasing moisture content increases the size of the seeds. Larger seeds cannot fill the gaps between them as well as smaller seeds. Therefore, although increasing the moisture content increases the seeds' mass, it causes a smaller number of seeds to be in a certain volume. Therefore, increasing the moisture content reduces the bulk density of the sample.

3.4.3. Particle density
The moisture content’s effect on the variation of the particle density of the summer savory, basil, cress, and ajowan seeds is shown in Fig. 3. Results showed that with increasing moisture content from 4.05 to 18.65% (d.b), 5.20 to 19.98% (d.b), and 5.57 to 17.19% (d.b), values of the particle density of the summer savory, basil, and cress seeds decreased from 1068.676 to 981.871 kg·m^-3, 1200.431 to 1126.941 kg·m^-3, and 1281.664 to 1265.081 kg·m^-3, respectively. Increasing moisture content from 6.71 to 20.98% (d.b) increased the ajowan seeds' particle density from 1074.133 to 1099.848 kg·m^-3. A comparison between seeds showed that the cress seeds' values of particle density are more than the other seeds in all moisture levels, while the summer savory values are lower than the others.

Fig. 3. Effect of the moisture content on the particle density of four tiny seeds

In plant tissues, there are pores inside or between cells that can be occupied by water or air. Two scenarios may occur with increasing plant tissue moisture content. In the first scenario, the volume of pores in the seeds tissue is remarkable. With increasing moisture content, the air in the pores is removed, and the water is replaced. In this case, the amount of change in seed volume is either zero or very small. Therefore, since water density is much higher than air, the increase in particle density occurs due to the increase in moisture content. In the second scenario, the pore volume of the seed tissue does not account for a significant fraction of the grain volume. In this case, increasing the moisture content leads to an increase in seed size and volume. If the density of seed dry matter is higher than the density of water, the increase in volume due to the increase in moisture content will decrease particle density.

3.4.4. Porosity
The moisture content’s effect on the variation of porosity of the summer savory, basil, cress, and ajowan seeds is shown in Fig. 4. Results showed that with increasing moisture content from 5.20 to 19.98% (d.b), 5.57 to 17.19% (d.b), and 6.71 to 20.98% (d.b), values of porosity of the basil, cress, and ajowan seeds increased from 46.91 to 50%, 45.27 to 49.93%, 61.18 to 63.66%, respectively. Increasing moisture content from 4.05 to 15.02% (d.b) increased the summer savory's porosity from 48.62 to 50.87%. However, more increasing moisture content caused a decreasing trend for summer savory porosity from 50.87 to 48.41. A comparison between seeds showed that in all moisture levels, the cress seeds' porosity values are more than the other seeds. Moreover, when the moisture content is less than 13% (d.b), the value of the porosity of cress seeds is less than the other seeds; when the moisture content is between 13 to 18% (d.b), the value of the porosity of basil seeds is less than the other seeds; when the moisture content is more than 18% (d.b), the value of the porosity of summer savory seeds is less than the other seeds.

Fig. 4. Effect of the moisture content on the porosity of four tiny seeds

3.5. Frictional properties
3.5.1. Angle of friction
The static angle of friction, which affects the processing machine's design, was determined on three different contacting materials (iron, wood, and galvanized plate).  These are common materials used for transportation, storage, and handling operations of grains, seeds, construction of storage, and drying bins.  The static angle of friction of summer savory, basil, cress, and ajowan seeds is shown in Fig. 5. It is observed that the static angle of friction of the four seeds increased with the increase in the moisture content for all contact surfaces.

Fig. 5. Effect of the moisture content on the angle of friction (EAR) of four tiny seeds on different surfaces, (A) summer savory, (B) basil, (C) cress, (D) ajowan.

The angle of static friction of the summer savory seeds increased from 22.38° to 24.39°, 25.46° to 26.23°, and 20.36° to 21.26° for iron, wood, and galvanized plate, respectively, as the moisture content increases from 4.05 to 18.65% (d.b). Also, the angle of static friction of the basil seeds increased from 22.24° to 24.54°, 23.75° to 26.46°, and 20.67° to 24.43° for iron, wood, and galvanized plate, respectively, as the moisture content increases from 5.20 to 19.98% (d.b). Moreover, the corresponding values for cress seeds were 20.59° to 25.34°, 24.36° to 27.24°, and 17.01° to 23.94° for iron, wood, and galvanized plate, respectively, as the moisture content increases from 5.57 to 17.19% (d.b). Furthermore, the corresponding values for ajowan seeds were 22.06° to 29.06°, 28.06° to 30.66°, and 19.87° to 25.07° for iron, wood, and galvanized plate, respectively, as the moisture content increases from 6.71 to 20.98% (d.b).

A comparison between seeds showed that on an iron surface when the moisture content is less than 10% (d.b), the angle of friction of summer savory seeds is more than the other seeds; but when the moisture content is more than 10% (d.b), angle of friction of ajowan seeds is more than the other seeds. On the wood surface, the angle of ajowan seeds' friction is more than the other seeds in all moisture levels. On the galvanized surface, when the moisture content is less than 20% (d.b), the angle of friction of basil seeds is more than the other seeds; but when the moisture content is more than 20% (d.b), the angle of friction of ajowan seeds is more than the other seeds.

A metal surface is more polished than a wooden surface, so less friction coefficient on metal surfaces is expected. The increase of friction coefficient at higher moisture content may be due to the water present in the seed, offering an adhesive force on the surface of contact [31, 39].

3.5.2. Angle of repose
The repose angle is a useful parameter for calculating the belt conveyor width and designing the storage shape [47]. The repose angle is an indicator of the product flowability [31]. The moisture content's effects on emptying and filling angles of repose of the summer savory, basil, cress, and ajowan seeds are shown in Figs. 6 and 7, respectively.

Fig. 6. Effect of the moisture content on emptying angle of repose (EAR) of four tiny seeds

Fig. 7. Effect of the moisture content on filling angle of repose (EAR) of four tiny seeds

The values of filling and emptying angle of repose of summer savory seeds were found to change from 36.46° to 36.84° and increase 37.60° to 39.30° in the moisture range of 4.05 to 18.65% (d.b). The values of filling and emptying angle of repose of the basil seeds were found to increase from 33.44° to 37.10° and 36.38° to 41.04°, respectively, in the moisture range of 5.20 to 19.98% (d.b).  Moreover, the corresponding values for cress seeds were found to increase from 28.86° to 36.62° and 34.36° to 39.47°, respectively, in the moisture range of 5.57 to 17.19% (d.b).  Furthermore, the corresponding values for cress seeds were found to increase from 39.70° to 42.26° and 40.86° to 44.33°, respectively, in the moisture range of 6.71 to 20.98% (d.b). A comparison between seeds showed that the filling and emptying angle of repose of ajowan seeds were more than the other seeds in all moisture levels.

For summer savory, basil, cress, and ajowan seed, the emptying method’s repose angles were greater than filling one.  The filling angle of repose can be considered as a dynamic angle of repose. Because the seeds that are forming the bulk mass are falling under the influence of gravity acceleration. Also, dynamic collisions occur between the seeds during the fall. However, the discharge or emptying angle of repose can be considered a static angle of repose because, due to internal friction, the seeds have a low velocity before leaving the discharge valve. Therefore, it can be expected that the filling angle of repose is less than the emptying one due to its dynamics.

4. CONCLUSION

One of the most critical complexities or challenges to measuring tiny seeds’ engineering properties is their dimensions. Dimensions of tiny seeds are too small. It is impossible to measure them by ordinary methods like a caliper, digital caliper, micrometer, and digital micrometer. A practical method to measure the dimensions of tiny seeds is the image processing technique. In the current study, to measure engineering properties, four tiny seeds (summer savory, basil, cress, and ajowan) have some medical effects of treating different illnesses, or food industry processes were selected.

In the present study, the effect of the moisture content on length, width, thickness, geometric and arithmetic mean diameter, sphericity, volume, surface area, specific surface area, projected area, 1000-seed mass, bulk density, particle density, porosity, angle of external friction, and emptying and filling angle of repose were investigated. The length, width, and thickness of the seeds were modeled by Gamma, Generalized Extreme Value, and Weibull distributions. Modeling results showed that, in sum, to model the length, width, and thickness of the seeds, Generalized Extreme Value distribution had the best performance.

Results showed that, with increasing moisture content from 4.05 to 18.65 for summer savory,  5.20 to 19.98 for basil, 5.57 to 17.19 for cress, and 6.71 to 20.98% (d.b) for ajowan seeds, values of the length, width, and thickness of the seeds changed from 0.291 to0.466, 0.264 to 0.420, and 0.236 to 0.373 for summer savory, 0.576 to 0.582, 0.518 to 0.558 , and 0.463 to 0.531 for basil, from 0.606 to 0.643, 0.538 to 0.591,  and 0.478 to 0.539 for cress, and from 0.330 to 0.568, 0.287 to 0.471, and 0.212 to 0.381 mm for ajowan seeds, respectively.

Based on the results, in the moisture ranges, values of bulk density of the basil, cress, and ajowan seeds decreased from 549.051 to 506.521 kg·m^-3, 637.347 to 563.443 kg·m^-3, 701.384 to 633.454 kg·m^-3, and 417.019 to 399.662 kg·m^-3, respectively. Also, values of the particle density of the basil, cress, and ajowan seeds decreased from 1068.676 to 981.871 kg·m^-3, 1200.431 to 1126.941 kg·m^-3, and 1281.664 to 1265.081 kg·m^-3, respectively. Results showed that, in the moisture ranges, the basil's porosity values, cress, and ajowan seeds increased from 46.91 to 50%, 45.27 to 49.93%, 61.18 to 63.66%, respectively.

On different surfaces, in the moisture ranges, values of external angle of friction of summer savory, basil, cress, and ajowan seeds changed from 20.36 to 26.23°, 20.67 to 26.46°, 17.01 to 26.46°, and 19.87 to 30.66°, respectively. Based on the results, in all moisture levels, filling and emptying angles of repose of ajowan seeds were more than the other seeds, and emptying angles of repose were higher than that of the filling ones. .

5. Acknowledgement

The authors would like to thank the University of Tehran for providing technical support for this work. The authors would also like to thank Prof. Mohammad Hossein Kianmehr for their technical help and support while doing this research. The authors would also like to thank Dr. Mohammad Hassan Torabi for his support in editing the paper’s language.

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Received: 18.10.2020
Reviewed: 22.11.2020
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

Ahmad Raufi
Department of Horticultural Science, School of Agriculture, Shiraz University, Shiraz, Iran
Phone: 098 3153239185
Mob: 098 9139035547
email: ahmad.raofi@alumni.ut.ac.ir

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Responses to this article, comments are invited and should be submitted within three months of the publication of the article. If accepted for publication, they will be published in the chapter headed 'Discussions' and hyperlinked to the article.

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