Acta agriculturae Slovenica, 119/4, 1–11, Ljubljana 2023
doi:10.14720/aas.2023.119.4.13421 Original research article / izvirni znanstveni članek
Physical and aerodynamic properties of date palm pollen grains
Mohamed M. IBRAHIM
 1, 2
, Mohamed GHONIMY
  3, 1
, Eid ABD EL RAHMAN
 1
Received April 15, 2023; accepted October 02, 2023.
Delo je prispelo 15. aprila 2023, sprejeto 2. oktobra 2023
1 Department of Agricultural Engineering, Faculty of Agriculture, Cairo University, Giza, Egypt
2 Corresponding author, e–mail: mohamed.ibrahim@agr.cu.edu.eg
3 Department of Plant Production and Protection, College of Agriculture and Veterinary Medicine, Qassim University, Buraydah, Saudi Arabia
Physical and aerodynamic properties of date palm pollen 
grains
Abstract: 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
), geo-
metric 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 veloc-
ity (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 mod-
els 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 pollina-
tion machines.
Key words: aerodynamic, date palm, pollen grain, prop-
erties, terminal velocity
Fizikalne in aerodinamične lastnosti pelodnih zrn dateljeve 
palme
Izvleček: Namen raziskave je bil določiti učinek štirih 
vsebnosti vode (4, 5, 6, in 7 %) na fizikalne in aerodinamič-
ne lastnosti pelodnih zrn dateljeve palme (DPP). Fizikalne 
lastnosti so obsegale dolžino peloda (L), širino (w), debelino 
(T), projekcijsko površino (A
p
), poprečni geometrični premer 
(d
g
), maso (m), sferičnost (S), in gostoto (ρ
p
). Ugotovljeno je 
bilo, da vsebnost vode ni značilno vplivala na fizikalne lastno-
sti peloda. Aerodinamične lastnosti peloda so obsegale končno 
hitrost (V
t
), koeficient upora (D
c
), moč upora (Df) in Reynoldo-
vo število (Re). Reynoldovo število peloda (Re) je bilo značilno 
različno pri različnih vsebnostih vode, razvit je bil regresijski 
model na osnovi polinomnih in ekspotencialnih razmerij. Med 
Re in D
c  
je bilo ugotovljeno polinomno razmerje tretjega reda. 
Rezultati so pokazali, da so bile poprečne vrednosti parametrov 
V
t
, D
c
, Df, in Re okrog 0,6 m s
-1
, (0,38 do 0,45), 1,09E-11 N in 
(0,29 do 0,42). Rezultati raziskave bodo pripomogli k boljšemu 
delovanju opraševalnih naprav.
Ključne besede: aerodinamika, dateljeva palma, pelodna 
zrna, lastnosti, končna hitrost

Acta agriculturae Slovenica, 119/4 – 2023 2
M. M. IBRAHIM et al.
1 INTRODUCTION
Date palm is the source of a wide range of products 
and services, including many necessities of life. The pri-
mary 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 iden-
tified as a major factor for successful date production 
since quality and fruit yield depend on the correct ap-
plication of pollen grains. It has conclusively been shown 
that the benefits of the pollination process lie in obtain-
ing large-sized, high-quality fruits, avoiding the presence 
of small fruits (Salomón-Torres et al., 2017).
In Egypt, farmers select male palm trees and ex-
change palm pollen between farms even over long dis-
tances 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 estab-
lish a perfect pollination and achieve the highest yield 
with good fruit quality, it was advantageous to mix pol-
len grains with different carriers, essential minerals and 
ascorbic acid. It also improves the effectiveness of pollina-
tion (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 pol-
lination. The characteristics of pollen can affect its trans-
mission from date palm pollinating machines to female 
flowers. Alharbi and Mousa (2021) studied some physi-
cal 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 spheri-
cal. The aerodynamic properties are the most important 
in describing the movement of grains in the air. For de-
signers and operators of agricultural machinery, knowl-
edge of the aerodynamic properties of the grain (floating 
velocity, final velocity, aerodynamic coefficient of resist-
ance) 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 sus-
pended 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 per-
centage 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 cof-
fee 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 veloci-
ties 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 signifi-
cantly impact the performance of date palm pollination 
machines.
2 MATERIALS AND METHODS
2.1 DATE PALM POLLEN GRAINS (DPP) PREPA-
RATION
DPP collected from three resources of a local mar-
ket in Siwa Oasis, Matrouh Governorate, Egypt, free of 
foreign matters, immature, and broken grains were se-
lected for this study. The date palm pollen variety used in 
this research is not specified because commercial com-
panies 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 proper-
ties 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 

Acta agriculturae Slovenica, 119/4 – 2023 3
Physical and aerodynamic properties of date palm pollen grains
minutes’ interval, in order to find out the time required 
to remove moisture to reach the different required mois-
ture 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 con-
tent cover the range often seen in stored DPP and was 
checked before each experiment.
2.2 PHYSICAL PROPERTIES OF DATE PALM POL-
LEN GRAIN
2.2.1 Date palm pollen grain mass (m)
The mass (m) of the date palm pollen grain was cal-
culated by dividing the 1 g of pollen mass by the num-
ber 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, Ja-
pan) 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 mag-
netic 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 calcu-
lated (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).
2.2.2 Date palm pollen grain dimensions and pro-
jected area
The DPP dimensions were measured at different 
moisture content levels (4, 5, 6, and 7 %) using scan-
ning electron microscopy (SEM, JSM-5200, Jeol Japan). 
Twenty date palm pollen were randomly selected from 
each moisture content level to determine grain dimen-
sions 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 cop-
per 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 un-
der 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.
Figure 1: Pollen number determination using hemocytometer methods: (a) hemocytometer slide, and (b) pollen under micro-
scope

Acta agriculturae Slovenica, 119/4 – 2023 4
M. M. IBRAHIM et al.
2.2.3 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 pol-
len grain at different moisture content levels according to 
Abdelhady et al. (2023).
2.2.4 The geometric mean diameter (d
g
)
The geometric mean diameter (d
g
, µm) was calcu-
lated 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 thick-
ness (µm).
2.2.5 Sphericity (S)
The sphericity expresses the shape character of the 
pollen relative to that of a sphere of the same volume. As-
suming 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)
2.3 AERODYNAMIC PROPERTIES OF DATE PALM 
POLLEN GRAIN
2.3.1 Terminal velocity (V
t
)
To evaluate the performance of pollination opera-
tions 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 re-
sisting 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 diam-
eter 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 pol-
len grains being carried by the air stream. The terminal 
velocity of the studied DPP could be obtained by meas-
uring the air velocity required to suspend the particles 
Figure 2: Pollen weight and drag force acting on the date palm 
pollen grain

Acta agriculturae Slovenica, 119/4 – 2023 5
Physical and aerodynamic properties of date palm pollen grains
in the vertical air stream. The air velocity was measured 
by using the hot wire air velocity meter connected with 
a velocity probe (TENMARS TM-4001-the air velocity: 
0.01 - 25 m s
-1
).
2.3.2 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
).
2.3.3 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 
Figure 3: Experimental set-up used for measuring the terminal velocity

Acta agriculturae Slovenica, 119/4 – 2023 6
M. M. IBRAHIM et al.
away from the surface, and an increase of pressure, +P, 
shown by arrows drawn toward the object. In addition, 
these forces normal to the surface of the pollen, and there 
are shear stresses, τ, acting tangential to the surface in the 
direction of airflow and resulting from frictional effects. 
The resultant force Fr, may be resolved into components 
of drag force (Df) and lift force (Fh). The equations for 
calculating Df and Fh have been derived by dimensional 
analysis assuming the smooth pollen grain having a pro-
jected area (Ap), moving through air flow density (ρ
a
), 
drag coefficient (D
c
), and air velocity (V
t
). Therefore, the 
Df will be as the following equation,
                           (5)
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 in-
volved 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 cri-
terion using dimensional analysis and solving equations 
algebraically and by substituting in the original exponen-
tial functional relationship, we get that:
                                         (8)
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
).
Figure 4: Air flow rate and force analysis acting the pollen grain
Table 1: Symbols and dimensions of the properties affecting 
the drag force of date palm pollen grain
Property Symbol
Dimension M
μ
 L
λ
 T
τ
μ λ τ
Drag force Df 1 1 -2
Air density ρ
a
1 -3 0
Air velocity V
t
0 1 -1
Projected area Ap 0 2 0
Drag coefficient D
c
0 0 0

Acta agriculturae Slovenica, 119/4 – 2023 7
Physical and aerodynamic properties of date palm pollen grains
2.3.4 Reynolds number (Re)
Reynolds number (Re) is an essential aerodynamic 
attribute that represents the ratio of inertial effects to vis-
cous 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 parti-
cle is moving in this case, air (Zare et al., 2013). In most 
recent methodology, the Reynolds number (Re) was cal-
culated from equation (9) (Grega et al., 2013):
                                           (9)
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).
The tested values of moisture content (MC) were 4, 
5, 6, and 7 % dry basis.
2.4 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.
3 RESULTS AND DISCUSSION
3.1 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 di-
ameter (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 mois-
ture 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 mois-
ture content increased from 4 to 5, 6, and 7 %, respec-
tively. 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).
3.2 AERODYNAMIC PROPERTIES OF DATE PALM 
POLLEN GRAIN
The average values of aerodynamic properties in-
cluded 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 mois-
ture content. However, the pollen Reynolds number Re 
are significant at different pollen grain moisture content.
Figure 5: Scanning electron microscopy of date palm pollen 
grain at different levels of moisture content

Acta agriculturae Slovenica, 119/4 – 2023 8
M. M. IBRAHIM et al.
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 ma-
chines. The frequency distribution of the measured val-
ues 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 coef-
ficient (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 mois-
ture 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 in-
creased 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.
The relation between Reynolds number (Re) and 
drag coefficient (D
c
) is shown in Fig. (7). It’s clear that 
there is an inverse relationship between Re and D
c
. The 
data of Re and D
c
 was analyzed to give the best fit relation 
of the 3
rd
 order polynomial function:
                      (10)
The range of the Reynolds number (Re) into equa-
tion (10) were 0.42 ≥ Re ≥ 0.29 while, the values of the 
Table 2: Physical properties of date palm pollen grain at different moisture contents
MC,% 
dry basis
Pollen grain dimensions
S m, kg Ap, µm
 2
ρ
p
, kg m
-3
L, µm w, µm T, µm d
g
, µm
4 19.7 ± 8.6 a 8.6 ± 0.9 a 6.8 ± 2.6 a 10.4 ± 1.8 a 0.52 ± 0.1 a 1.1E-12 ± 6.2E-28 a 133.33 ± 58.0 a 692.9 ± 21.9 a
5 19.9 ± 4.1 a 8.8 ± 1.8 a 6.8 ± 1.7 a 10.4 ± 1.4 a 0.52 ± 0.1 a 1.1E-12 ± 6.2E-28 a 135.21 ± 41.9 a 697.6 ± 22.4 a
6 20.1 ± 4.2 a 8.8 ± 1.4 a 6.8 ± 1.4 a 10.5 ± 1.2 a 0.52 ± 0.1 a 1.1E-12 ± 6.2E-28 a 135.92 ±3 7.6 a 702.4 ±2 3.7 a
7 19.9 ± 4.3 a 8.9 ± 1.4 a 6.9 ± 1.4 a 10.4 ± 1.4 a 0.52 ± 0.1 a 1.1E-12 ± 6.2E-28 a 136.70 ± 38.1 a 711.2 ± 25.2 a
Significant n.s n.s n.s n.s n.s n.s n.s n.s
MC = Pollen 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
Table 3: Aerodynamic properties of date palm pollen grain at different moisture content
MC (% dry basis) V
t
, m s
-1
D
c
Df, N Re
4 0.59 ± 0.03 a 0.45 ± 0.16 a 1.09E-11 ± 7.1E-16 a 0.29 ± 0.014 b
5 0.60 ± 0.02 a 0.41 ± 0.13 a 1.09E-11 ± 3.1E-16 a 0.31 ± 0.015 b
6 0.60 ± 0.03 a 0.39 ± 0.12 a 1.09E-11 ± 5.1E-16 a 0.39 ± 0.011 a
7 0.60 ± 0.03 a 0.38 ± 0.10 a 1.09E-11 ± 7.2E-16 a 0.42 ± 0.039 a
Significant n. s n. s n. s *
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

Acta agriculturae Slovenica, 119/4 – 2023 9
Physical and aerodynamic properties of date palm pollen grains
constants a, b, c, and d were (-) 50.821, 60.238, (-) 23.846, 
and 3.527 respectively.
3.3 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 coef-
ficient (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 aerody-
namic 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 func-
tion of moisture content. A linear relationship was re-
ported 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 de-
rived by Matouk et al. (2008).
4 DISCUSSION
The present study evaluated and modeled the physi-
cal 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 mois-
ture content. The aerodynamic properties of DPP includ-
ed the terminal velocity (V
t
), drag coefficient (D
c
), drag 
force (Df), and Reynolds number (Re). The results indi-
cated 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 veloc-
ity 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 evi-
dence 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-
Figure 6: The frequency distribution of the pollen grain termi-
nal velocity
Figure 7: Drag coefficient (D
c
) versus Reynolds number (Re) 
at four levels of moisture content
Table 4: Regression models of aerodynamic properties of date 
palm pollen grain
Regression models R
2
V
t 
= - 0.0025 MC
2
 + 0.0155 MC + 0.5775 0.93
D
c
 = 0.0075 MC
2
 - 0.0605 MC + 0.5025 1.00
Df = Constant = 1.09E-11
Re = 0.249 e 
0.134 MC
0.95

Acta agriculturae Slovenica, 119/4 – 2023 10
M. M. IBRAHIM et al.
ers, which found an inverse relationship between the 
drag coefficient and the moisture content of seeds. The 
inverse connection could be explained by variations in 
the seeds’ surface characteristics, actual densities, mor-
phologies, and sizes as the moisture content increased. 
Also, it was mentioned by Nalbandi et al. (2010) that 
Makhobeli, triticale, and wheat seeds’ drag coefficient 
decreased by increasing seeds’ moisture content.; while 
Mohsenin (2020) reported that as the MC increased 
from 6.2 to 14.4 % (dry basis) for the cultivars NSFH-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 find-
ings are consistent with those of Pradhan 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 ap-
proximately similar to that reported by Schwendemann 
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 differ-
ent moisture content levels.
5 CONCLUSION
The physical and aerodynamic properties of date 
palm pollen grain (DPP) as a function of moisture con-
tent were evaluated. The physical properties of DPP 
included pollen grain dimensions (length L, width w, 
thickness T), projected area (A
p
), geometric mean diam-
eter (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 sphe-
ricity (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) in-
creased 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 prop-
erties 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 signifi-
cant 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.
6 ACKNOWLEDGMENTS
The authors acknowledge the financial support 
from Cairo University, Egypt for funding the project 
titled “Design and manufacture of date palm pollination 
machine operated by tractor” .
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