Physical and aerodynamic properties of date palm pollen grains

Physical and aerodynamic properties of date palm pollen grainsAbstract: The present study was designed to determine the effect of four moisture content levels (4, 5, 6, and 7 %) on the physical and aerodynamic properties of date palm pollen grain (DPP). The physical properties of DPP included pollen length ( L ), width ( w ), thickness ( T ), projected area ( A p ), geometric mean diameter ( d g ), mass (m), sphericity ( S ), and bulk density ( ρ p ). It was observed that the moisture content did not significantly influence the physical properties of the DPP. The aerodynamic properties of DPP included the terminal velocity ( V t ), drag coefficient ( D c ), drag force ( Df ), and Reynolds number ( Re ). The pollen Reynolds number ( Re ) is significant at different pollen grain moisture content, and regression models were developed in the form of polynomial and exponential relationships. Also, the 3 rd order polynomial relationship was found between Re and D c . The results showed that the average values of V t , D c , Df , and Re were about 0.6 m s -1 , (0.38 to 0.45), 1.09E-11 N, and (0.29 to 0.42), respectively. The results of this study will be helpful in the performance of date palm pollination machines


INTRODUCTION
Date palm is the source of a wide range of products and services, including many necessities of life.The primary product of the date palm is fruit, which is rich in protein, vitamins, and mineral salts.The total date palm production in Egypt is about 1.64 million tons annually (FAOSTAT, 2019).Date palm pollination has been identified as a major factor for successful date production since quality and fruit yield depend on the correct application of pollen grains.It has conclusively been shown that the benefits of the pollination process lie in obtaining large-sized, high-quality fruits, avoiding the presence of small fruits (Salomón-Torres et al., 2017).
In Egypt, farmers select male palm trees and exchange palm pollen between farms even over long distances from the country (Bekheet and El-Sharabasy, 2015) Notably, the production of pollen from male palms differs significantly according to changing geographic regions.Generally, any male palm variety's pollen can be used to pollinate any female variety.Either, to establish a perfect pollination and achieve the highest yield with good fruit quality, it was advantageous to mix pollen grains with different carriers, essential minerals and ascorbic acid.It also improves the effectiveness of pollination (Radwan et al., 2022).However, as most male palms are seedlings, there are significant variances in the pollen quality of these plants (Salomón-Torres et al., 2021).In addition, pollen's physical and aerodynamic properties are one of the most important properties that affect pollination.The characteristics of pollen can affect its transmission from date palm pollinating machines to female flowers.Alharbi and Mousa (2021) studied some physical properties of palm pollen in the Qassim region, Saudi Arabia; they reported that date palm pollen grains come in a wide variety of shapes, sizes, and surface marking characteristics.The palm pollen sizes range from 3.3 to 704 μm.The pollen shape found in this study was spherical.The aerodynamic properties are the most important in describing the movement of grains in the air.For designers and operators of agricultural machinery, knowledge of the aerodynamic properties of the grain (floating velocity, final velocity, aerodynamic coefficient of resistance) is important and essential (Polyák and Csizmazia, 2010).These properties are terminal velocity, drag force, drag coefficient, and Reynolds number (Khoshtaghaza and Mehdizadeh, 2006).Terminal velocity is the steady air velocity value at which an object or a material is suspended in the vertical air stream.In other words, the maximum or terminal speed attained in free fall before air resistance will keep it from falling faster (Mohsenin, 2020).The morphology of pollen grains may also affect the aerodynamic properties.The relationship between terminal velocity and moisture content of pistachio nut was studied by Unal et al. (2008), 14.2 % increasing percentage in the terminal velocity was found depending on the change in moisture content from 5.83 to 30.73 % (wb).Morever, Matouk et al. (2008) mentioned that coffee cherries ('Catual') drag coefficient decreased from 0.05 to 0.03 as moisture content increased from 10.7 to 53.9 % (d.b).According to Eşref, and Nazmi (2016), as the moisture content of yellow lentil seeds increased the terminal velocity increased linearly from 1.5 to 2.09 m s -1 due to the increasing seed mass per unit frontal that faces the air stream.Abubakar et al. (2019) fabricated a measuring device to determine the terminal velocity of paddy rice, sorghum, and bean grains.Terminal velocities results in that study were 6.95 ± 0.37, 4.71 ± 0.24, and 10.98 ± 0.27 m s -1 for paddy rice, sorghum, and beans, respectively.In addition, the device efficiency was found to be 70.06 %.Thus, the main objective of this article is to determine the physical and aerodynamic properties of date palm pollen grain because these properties significantly impact the performance of date palm pollination machines.

DATE PALM POLLEN GRAINS (DPP) PREPA-RATION
DPP collected from three resources of a local market in Siwa Oasis, Matrouh Governorate, Egypt, free of foreign matters, immature, and broken grains were selected for this study.The date palm pollen variety used in this research is not specified because commercial companies selling pollen have collected from more than one source and mixed them to improve the properties of the resulting crop.
Traditionally, pollen grains for some varieties are mixed and then used for pollination.Moisture content is one of the most important factors affecting the quality of the pollination process.The moisture content of the pollen grains was determined using the oven method at 103 ± 2 °C until reaching a constant mass (AOAC, 2000) and as described in many investigational studies.Results of minimum and maximum moisture content values of DPP were 3.6 and 8.2 % respectively.Considering the significance of moisture content in pollination process.Four levels of moisture content (4 %, 5%, 6 %, and 7 % db.) were used to determine the aerodynamic properties of the DPP.So far, each moisture content level was prepared using a pollen sample taken and placed in the oven at a temperature of 50 o C, then the sample mass was measured, and moisture content was calculated every 15 minutes' interval, in order to find out the time required to remove moisture to reach the different required moisture contents (4 %, 5 %, 6 %, and 7 % dry basis).After that, each sample was placed inside a desiccator in order to acclimatize it to the ambient environment (Coşkun et al., 2005).Conversely, the levels of chosen moisture content cover the range often seen in stored DPP and was checked before each experiment.

Date palm pollen grain mass (m)
The mass (m) of the date palm pollen grain was calculated by dividing the 1 g of pollen mass by the number of pollen per one gram.Using the hemocytometer method, it is possible to count the number of pollens in a specific volume of water (suspensions solution: water + pollen) (Mahmoud-Aly et al., 2018).A hemocytometer method consists of microscope (QUANTA FEG250, Japan) and a thick glass microscope slide (dimension 3×3 mm).The slide is divided into nine squares (dimension 1 × 1 mm), as shown in (Fig. 1).The volume covered by one square is calculated by multiplying the area of one square (1 mm x 1 mm = 1 mm 2 ) by the depth of the square (0.1 mm).Hence, the final volume of each square is 0.0001 ml.The 2.5 g of pollen grains were added to 500 ml of distilled water and mixed for 5 min using magnetic stiller, so the dilution factor is 200 ml of water 1 g -1 of pollen (500 ml of water 2.5 g -1 of pollen).The sample from suspension solution was loaded into slide by using a micropipette.Then the hemocytometer slide was placed under the microscope, so it could determine the pollens number.The average pollen per small square was calculated (448 pollen).The number of pollen grains per one gram was calculated from equation (1). (1) Where; N pg is the number of pollen grains per one gram, P ss is the average number of pollens per small square (448 pollen), Du is the dilution factor (equal to 200 ml g -1 ), and vss is the volume of suspension upper small square (equal to 0.0001 ml).

Date palm pollen grain dimensions and projected area
The DPP dimensions were measured at different moisture content levels (4, 5, 6, and 7 %) using scanning electron microscopy (SEM, JSM-5200, Jeol Japan).Twenty date palm pollen were randomly selected from each moisture content level to determine grain dimensions and projected area (Ap).Three major dimensions of the pollen grain, namely length (L, µm), width (w, µm), and thickness (T, µm) were measured according to the biggest and smallest surface of the pollen grain (Obi and Offorha, 2015).The pollen samples were placed on a copper holder and coated with a fine gold layer using a fine coat (JFC-1100 E, Ion sputtering device, JEOL, Japan) before the observation to avoid electrostatic charging during observation.Then, the sample was observed under a high vacuum with acceleration voltage (25 kV) and at 500, 2000, and 5000-fold magnifications.The projected area of the pollen was determined by using the Image J program.

The bulk density (ρ p )
The bulk density (ρ p ) defined as the mass per unit volume of a particle, was determined for date palm pollen grain at different moisture content levels according to Abdelhady et al. (2023).

The geometric mean diameter (d g )
The geometric mean diameter (d g , µm) was calculated from equation ( 2) according to Mohsenin (2020) (2) Where; L is the pollen grain length (µm), w is the pollen grain width (µm), and T is the pollen grain thickness (µm).

Sphericity (S)
The sphericity expresses the shape character of the pollen relative to that of a sphere of the same volume.Assuming that the diameter of the circumscribed sphere is equal to the longest intercept L of the ellipsoid and that the volume of the pollen grain is equal to the volume of a triaxle ellipsoid with intercepts L, w, and T. Also, the degree of sphericity (S) was calculated from equation (3), according to Mohsenin (2020). (3)

Terminal velocity (V t )
To evaluate the performance of pollination operations and options involving the presence of air flow, it is necessary to determine the terminal velocity of the date palm pollen grain.It will be used in studying the pollen grain in the airflow.When the pollen grain is immersed into an ascendant air flow, the pollen is subjected to the action of two kinds of forces: gravitational force and resisting drag force as shown in Fig. (2).
When these vector magnitudes are balanced (Fig. 2), the pollen grain begins a movement at a constant speed so-called terminal velocity that is depending on pollen mass (m), acceleration due to gravity (g), pollen grain density (ρ p ), air flow density (ρ a ), drag coefficient (D c ), and pollen grain projected area (A p ).
The experimental DPP terminal velocity (V t ) was measured at different moisture content levels using a device illustrated in Fig. (3).It consists of a centrifugal fan connected with an electric motor (Dayton-1/70 HP).The air velocity was controlled by a digital control switch/regulator inverter connected to the blower motor; it is allowed to change the speed of the motor (Obaia and Ibrahim, 2015).The next unit was a cylindrical tube, it is divided to three parts.The first part is a PVC pipe with a length of 200 mm and a diameter of 50 mm, connected at its upper end to a grid to homogenize airflow.The second part is a PVC pipe with a length of 700 mm and a diameter of 50 mm connected at its upper end to a perforated screen to carry pollen on it.This tube has two holes in the middle with a diameter of 5 mm to connect the sensors to measure the speed of the air stream.The third part of the tube is a transparent glass tube (acrylic) with a length of 900 mm and a diameter of 50 mm to watch the pollen grains being carried by the air stream.The terminal velocity of the studied DPP could be obtained by measuring the air velocity required to suspend the particles

The drag coefficient (D c )
The drag coefficient (D c ) of date palm pollen grains was calculated from equation (4) according to Mohsenin (2020). (4) Where D c is the drag coefficient (dimensionless), m is the date palm pollen grain mass (kg), g is the gravi-tational acceleration (9.81 m s -2 ), ρ p is the particle bulk density (kg m -3 ), ρ a is the air bulk density which equals to 1.206 kg m -3 at room temperature, A p is projected area of date palm pollen grain (m 2 ), and V t is the pollen grain terminal velocity (m s -1 ).

The drag force (Df)
When air flow occurs around the date palm pollen grain, the action of the forces involved can be illustrated by Fig. (4).
The pressure on the upper side of the pollen grain is less than the pressure P in the undisturbed air stream and that on the lower side is greater than the pressure P in the undisturbed air stream.The results in a decrease of pressure, -P, on the upper side indicated by arrows drawn To derive the drag force using the Kirchhoff and Gogh-Mann dimensional analysis method, the following steps are followed: 1. Determine the number of properties involved in the relation, n = 5 2. Write the dimensions of all the properties involved in the relationship are shown in table (1).
3. Choose three base quantities, in this case it is (ρ a , V t , Ap), which must satisfy the following condition: 4. Determine the number of criteria (k) K = n-3 = 5-3 = 2 5.The relation (5) can be writen as follows: (6) 6.On the basis of π theory, it can be writen: (7) 7. Estimating the values of μ, λ and τ for each criterion using dimensional analysis and solving equations algebraically and by substituting in the original exponential functional relationship, we get that: Where Df is the drag force (N), A p is the date palm pollen grain projected area (m 2 ), ρ a is the air density which is equal to 1.206 kg m -3 at room temperature (Gupta, 2013), and V t is the pollen grain terminal velocity (m s -1 ).

Reynolds number (Re)
Reynolds number (Re) is an essential aerodynamic attribute that represents the ratio of inertial effects to viscous effects on the particle, in similar words, it is the ratio between the product of the particle's velocity and length scale to viscosity of the medium/fluid in which the particle is moving in this case, air (Zare et al., 2013).In most recent methodology, the Reynolds number (Re) was calculated from equation ( 9) (Grega et al., 2013): where ρ a is the air density, which is equal to 1.206 kg m -3 at room temperature, V t is the pollen grain terminal velocity (m s -1 ), d g is the geometric mean diameter of the seed (m), and μ is air viscosity (1.816 × 10 -5 N s m -2 at room temperature).

STATISTICAL PROCEDURE
Measured data with all variables were statistically analyzed by a software program (CoStat ver. 6.400, 2008), applying a complete randomized design via analysis of variance.The means of the treatments were obtained, and Student-Newman-Keuls differences were tested at a 5 % level of probability.

PHYSICAL PROPERTIES OF DATE PALM POL-LEN GRAIN
The average values of the date palm pollen grain length (L), width (w), thickness (T), geometric mean diameter (d g ), projected area (A p ), mass (m), sphericity (S) and bulk density (ρ p ) at four levels of moisture content 4, 5, 6, and 7 % are listed in Table (2) and Fig. ( 5).It is clear that the pollen grain dimensions L, w, T, d g , S, m, and ρs were insignificant at different pollen grain moisture content.The pollen grain length (L) increased by 1.0 and 2.03 % when the moisture content increased from 4 to 5, and 6 %, respectively while the L decreased by 1.5 % when the moisture content increased from 6 to 7 %.Also, the L increased by 1.0 % when the MC increased from 5 % to 6 %.The same trend was found for w, and T. The geometric mean diameter (d g ) remained nearly con-stant (10.4 µm), with the MC increased from 4 to 7 %.The pollen mass (m), and sphericity (S) remained nearly constant at 1.1E-12 kg, and 0.52, respectively, with the MC increased from 4 to 7 %.The pollen grain projected area (Ap) increased by 1.4, 1.9, and 2.5 % when the moisture content increased from 4 to 5, 6, and 7 %, respectively.Also, the Ap increased by 0.5 and 1.1 % when the pollen grain moisture content increased from 5 % to 6 and 7 %, respectively.The bulk density (ρ p ) increased by 0.7, 1.4, and 2.6 % when the moisture content increased from 4 to 5, 6, and 7 %, respectively.Also, the ρ p increased by 0.7 and 1.9 % when the pollen grain moisture content increased from 5 % to 6 and 7 %, respectively.The lack of increase in the dimensions and projected area of date pollen grain with the increase of moisture content is due to the hardness of the pollen cover and its lack of water absorption (Pope, 2010;Bunderson and Levetin, 2015).

AERODYNAMIC PROPERTIES OF DATE PALM POLLEN GRAIN
The average values of aerodynamic properties included terminal velocity (V t ), drag coefficient (D C ), drag force (Df), and Reynolds number (Re) of the date palm pollen grain (DPP) at different moisture content (4, 5, 6, and 7 %) are listed in Table (3).It's clear that the V t , D C , and Df were insignificant at different pollen grain moisture content.However, the pollen Reynolds number Re are significant at different pollen grain moisture content.For terminal velocity (V t ), the average values of V t were about 0.59 and 0.6 m s -1 .The terminal velocity (V t ) of pollen grains was thoroughly examined as it plays an important role in the performance of pollination machines.The frequency distribution of the measured values of V t are shown in Figure ( 6).It is clear that the 25, 35, 30, and 30 % of the V t measured values ranged from 0.59 to 0.6 m s -1 for 4, 5, 6, and 7 % (dry basis) of moisture content, respectively.Also, from Table (3), the average values of drag coefficient (D c ) were 0.45 ± 0.16, 0.41 ± 0.13, 0.39 ± 0.12, and 0.38 ± 0.10 for 4, 5, 6, and 7 % (dry basis) of moisture content respectively.The results confirmed an inverse relationship between D c and pollen moisture content, as the moisture content of pollen grains increased from 4 to 7 %.(dry basis) the drag coefficient decreased from 0.54 to 0.38.The pollen grain D c decreased by 8.0, 13.3, and 15.5 % when the moisture content increased from 4 to 5, 6 and 7 % (dry basis) respectively.While, the D c decreased by 4.9, and 7.3 % when the moisture content increased from 5 to 6 and 7 % (dry basis) respectively.In addition, the D c decreased by 2.6 % when the moisture content increased from 6 to 7 % (dry basis).For drag force (Df), the Df remained nearly constant, 1.09E-11 N, with the MC increased from 4 to 7 % (dry basis).This means that the DPP mass is not affected by the increase in moisture content (From Table 3), and therefore, it does not need an increase in the drag force.
The Reynolds number (Re) of date palm pollen grain increased by increasing moisture content.A direct relationship was observed for the Re as it increased from 0.29 to 0.42 as the moisture content increased from 4 to 7 % (dry basis) and Re increased by 6.9, 34.5, and 44.8 % when the moisture content increased from 4 to 5, 6, and 7 % (dry basis), respectively.While the Re increased by 25.8, and 35.5 % when the moisture content increased from 5 to 6 and 7 % (dry basis) respectively.In addition, the Re increased by 7.7 % when the moisture content increased from 6 to 7 % (dry basis).The maximum value of drag coefficient was found at moisture content level 4% (dry basis), while the highest value of V t and Re were performed at 7 % (dry basis) moisture content level.

REGRESSION MODELS
Data from the research of the date palm pollen grain's (DPP) aerodynamic characteristics at various MC levels were fitted and the best fit was chosen.The models created for the DPP's terminal velocity (V t ), drag coefficient (D c ), and Reynolds number (Re) as functions of MC are shown in Table 4.The R 2 varied between 0.93 and 1.00.The suitable models for predicting the aerodynamic characteristics of DPP as a function of moisture content were found to be polynomial regression models.As a function of moisture content, Pradhan et al. (2010) initiated a polynomial model for the terminal velocity of mung bean seeds, whereas linear models were created for the drag coefficient and Reynolds number.Additionally, Nalbandi et al. (2010) initiated a polynomial model for predicting Makhobeli seed terminal velocity as a function of moisture content.A linear relationship was reported by Khodabakhshian et al. (2012) between the V t of Tef grain and its MC, while for the terminal velocity of coffee cherries and beans as a function of their moisture content and true density, a non-linear equation was derived by Matouk et al. (2008).

DISCUSSION
The present study evaluated and modeled the physical and aerodynamic properties of date palm pollen grain (DPP) as a function of moisture content.In summary, the physical properties of DPP included pollen length (L), width (w), thickness (T), projected area (A p ), geometric mean diameter (dg), mass (m), sphericity (S), and bulk density (ρ p ).It was observed that the physical properties of the DPP were not significantly influenced by the moisture content.The aerodynamic properties of DPP included the terminal velocity (V t ), drag coefficient (D c ), drag force (Df), and Reynolds number (Re).The results indicated that the terminal velocity increased slightly from 0.59 to 0.6 m s -1 with an increase in moisture content from 4 to 7 % (dry basis).As it was noted by Nalbandi et al. (2010) the slight increase in the terminal velocity of the DPP with an increase in the moisture content may be attributed to the formation of the pollen grain cover is a solid layer that does not absorb water, so there is no increase in the pollen grain mass thus the critical speed of pollen is not affected.Furthermore, Sharma et al. (2012) reported an increase in the terminal velocity of mung bean from 4.86 to 5.29 m s -1 as the moisture content increased from 7.28 to 17.77 % (db).Strong evidence was found according to Galedar et al. ( 2010) study, the terminal velocity (m s -1 ) of sunflower, soybean, and canola seeds increased by 10.67 %, 2.16 %, and 4.31 %, as the moisture content of the seeds increased from 7.35 to 23.7, 9.52 to 24.64, and 7.11 to 25.72 % (wb), respectively, these results agree with the present study findings.Also results showed that the D c od DPP decreased from 0.45 to 0.38 with the increase in moisture content from 4 to 7 % (dry basis).The results of this investigation concur with the bulk of other studies conducted by various research-

CONCLUSION
The physical and aerodynamic properties of date palm pollen grain (DPP) as a function of moisture content were evaluated.The physical properties of DPP included pollen grain dimensions (length L, width w, thickness T), projected area (A p ), geometric mean diameter (dg), mass (m), sphericity (S), and bulk density (ρ p ).The results indicated that, the pollen grain dimensions' L, w, T, and dg were insignificant at different pollen grain moisture content.Also, the pollen mass (m), and sphericity (S) remained nearly constant 1.1E-12 kg and 0.52, respectively, with the moisture content increased from 4 to 7 %.While, the pollen grain projected area (Ap) increased by 1.4, 1.9, and 2.5 % when the moisture content increased from 4 to 5, 6, and 7 % respectively.The pollen grain bulk density increased from 692.9 to 711.2 when the moisture content increased from 4 % to 7 %.The aerodynamic properties of DPP included the terminal velocity (V t ), drag coefficient (D c ), drag force (Df), and Reynolds number (Re).The results of aerodynamic properties indicated that the pollen grain V t , Df, and Df were insignificant at different pollen grain moisture content.However, the pollen grain Reynolds number is significant at different pollen grain moisture content.There is an inverse relationship between the Re and D c .The op-timal models for predicting the aerodynamic properties of DPP as a function of moisture content were found to be polynomial regression models.Finally, the results of this study will be helpful in the performance of date palm pollination machines.

Figure 2 :
Figure 2: Pollen weight and drag force acting on the date palm pollen grain

Figure 3 :
Figure 3: Experimental set-up used for measuring the terminal velocity

Figure 4 :
Figure 4: Air flow rate and force analysis acting the pollen grain

Figure 5 :
Figure 5: Scanning electron microscopy of date palm pollen grain at different levels of moisture content moisture content, L = pollen length, w = pollen width, T = pollen thickness, d g = pollen geometric mean diameter, S = pollen sphericity, m = pollen mass, Ap = pollen projected area, ρ p = pollen bulk density n.s.Not significant at the 0.05 and 0.01 probability levels

Figure 6 :Figure 7 :
Figure 6: The frequency distribution of the pollen grain terminal velocity

Table 2 :
Physical properties of date palm pollen grain at different moisture contents

Table 3 :
Aerodynamic properties of date palm pollen grain at different moisture content MC = Moisture content, V t = Terminal velocity, D c = drag coefficient, Df = drag force, Re = Reynolds number * Significant at the 0.05 probability level.n.s.Not significant at the 0.05 and 0.01 probability level constants a, b, c, and d were (-) 50.821, 60.238, (-) 23.846, and 3.527 respectively.

Table 4 :
Schwendemann et al. (2007)ynamic properties of date palm pollen grain (dry basis) for the cultivarsNSFH-36,  PSFH-118, GKSFH-2002, and SH-3322, respectively, the drag coefficient of four different cultivars of unshelled sunflower seeds decreased from 0.23 to 0.18, 0.31 to 0.20, 0.27 to 0.16, and 0.36 to 0.12.The current study's findings are consistent with those ofPradhan et al. (2010)for mung bean seed; the drag coefficient decreased as moisture content increased.The trend observed in the Reynolds number of DPP investigated in this study as the moisture content increased from 0.29 to 0.42 was approximately similar to that reported bySchwendemann et al. (2007)for saccate pollen grains.It was reported that the Reynolds number of saccate pollen grains increased from 2.3E-2 to 6.5E-2 with increased moisture content.The Df of DPP remained constant (1.09E-11 N) at different moisture content levels.