Experimental Investigation of Particle Size Distribution ... · PDF fileExperimental...

14
JJKAU: Eng. Sci., Vol. 22 No. 2, pp: 187-200 (2011 A.D./1432 A.H.) DOI: 10.4197 / Eng. 22-2.10 187 Experimental Investigation of Particle Size Distribution in Commercial Tahina Nedim Turkmen Assistant Professor, Department of Thermal Engineering and Desalination, King Abdulaziz University, Jeddah, Saudi Arabia [email protected] Abstract. Tahina samples were obtained locally. Using a unique approach for particle size analysis, a microscope with electronic output was utilized, and the distributions of solid particles contained in tahina produced by various manufacturers were studied. Available software was employed to measure areas and perimeters of particles. Then average equivalent diameters and circularities were computed for samples of tahina from six manufacturers. It was determined that there exist substantial differences in particle size distributions, average equivalent diameters and circularities of tahina produced by the different manufacturers. Preliminary guidelines were proposed for the classification of tahina in the light of these findings. Keywords: Circularity, Equivalent diameter, Microscope, Particle size, Tahina 1. Introduction Tahin, tahina, taheena or sesame paste, as it is variously called, is a suspension that is produced by grinding peeled and roasted sesame seeds. It consists of about 45 to 50% sesame oil and the rest is fiber and other solid ingredients. Since the density of sesame oil is somewhat less than the density of solids, the oil in tahina tends to separate, and the solids settle down. Therefore, tahina requires stirring before use. Moreover, there are certain applications where coarsely ground tahina is not acceptable.

Transcript of Experimental Investigation of Particle Size Distribution ... · PDF fileExperimental...

Page 1: Experimental Investigation of Particle Size Distribution ... · PDF fileExperimental Investigation of Particle Size Distribution in Commercial Tahina ... [7] proposed a plan ... C

JJKAU: Eng. Sci., Vol. 22 No. 2, pp: 187-200 (2011 A.D./1432 A.H.)

DOI: 10.4197 / Eng. 22-2.10

187

Experimental Investigation of Particle Size Distribution in

Commercial Tahina

Nedim Turkmen

Assistant Professor, Department of Thermal Engineering and

Desalination, King Abdulaziz University, Jeddah, Saudi Arabia

[email protected]

Abstract. Tahina samples were obtained locally. Using a unique

approach for particle size analysis, a microscope with electronic

output was utilized, and the distributions of solid particles contained

in tahina produced by various manufacturers were studied. Available

software was employed to measure areas and perimeters of particles.

Then average equivalent diameters and circularities were computed

for samples of tahina from six manufacturers.

It was determined that there exist substantial differences in

particle size distributions, average equivalent diameters and

circularities of tahina produced by the different manufacturers.

Preliminary guidelines were proposed for the classification of

tahina in the light of these findings.

Keywords: Circularity, Equivalent diameter, Microscope, Particle size,

Tahina

1. Introduction

Tahin, tahina, taheena or sesame paste, as it is variously called, is a

suspension that is produced by grinding peeled and roasted sesame seeds.

It consists of about 45 to 50% sesame oil and the rest is fiber and other

solid ingredients. Since the density of sesame oil is somewhat less than

the density of solids, the oil in tahina tends to separate, and the solids

settle down. Therefore, tahina requires stirring before use. Moreover,

there are certain applications where coarsely ground tahina is not

acceptable.

Page 2: Experimental Investigation of Particle Size Distribution ... · PDF fileExperimental Investigation of Particle Size Distribution in Commercial Tahina ... [7] proposed a plan ... C

N. Turkmen 188

Particle size distribution in powders is usually found by sieving or

sedimentation. The material to be analyzed must be carefully blended,

and the sample withdrawn using techniques that avoid size segregation.

Particular attention must be laid to avoidance of loss of fines during

manipulation of the sample.

Other common techniques are laser diffraction for sizing particles

from submicron to millimeter in size, Counter principle for sizing and

counting particles from micron to millimeter in size, and dynamic light

scattering for sizing submicron and nanometer particles. The equipment

needed for all of these techniques are all currently too expensive for

small industries to own and to operate.

The current practice in the tahina industry is to measure the particle

size in tahina by the use of a micrometer [1]

. While giving quick results, it

must be pointed out that the micrometer yields one number only to

represent the size of the largest particle entrapped between the jaws of

the micrometer. It cannot therefore indicate the actual particle size

distribution.

Most of the tahina produced in the Middle East is used for the

manufacture of various varieties of halawa, a middle-eastern delicacy.

Large quantities of tahina are also consumed by bakeries, restaurants and

households as salad dressings, sauces and for cooking. Current tahina

standards do not seem to call for any particle-size based classification of

tahina. In other words all tahina that is traded today is labeled simply

"tahina". There is no differentiation between tahina produced in different

batches or by using different grinding equipment or sequences, and

whether or not the tahina has been re-cycled during grinding. And yet

tahina experts refer to a given batch of tahina as "smooth", "medium" or

"coarse" or "unacceptably chunky".

During production of tahina, raw sesame seeds are screened and

cleaned, and then de-hulled (peeled). There is a phase of drying the

peeled seeds, after which they are roasted. The moisture content of the

seeds after roasting is normally reduced to about 0.5% [2]

. The next step

is to stone-grind the seeds, normally in several steps. The thick liquid that

emerges following the grinding operation is called tahina.

Page 3: Experimental Investigation of Particle Size Distribution ... · PDF fileExperimental Investigation of Particle Size Distribution in Commercial Tahina ... [7] proposed a plan ... C

Experimental Investigation of Particle …. 189

Although most tahina in the market is produced from peeled (de-

hulled) sesame seeds, there are reports however, that there is a kind of

tahina that is made from whole sesame seeds, and sold under the name

bozkir tahini in Turkey [3]

. Another study mentions a kind of tahina and

halawa to which mushroom has been added [4]

. Yet another study [5]

discusses the utilization of sunflower seeds in tahina and halawa

processing.

There has been a flurry of research activities on tahina recently.

Thus Akbulut[6]

studied the mineral contents of hulled sesame paste

(tahin), un-hulled sesame paste (bozkir tahin) and their blends. He found

that the bozkir tahini is richer in mineral content than tahini made from

peeled seeds.

Jamará and Isa [7]

proposed a plan for the production of tahina.

Kotzekidou [8]

undertook a study to investigate the microbial stability and

salmonella resistance of halva (halawa). Being a traditional low-moisture

confectionery, halva was studied with respect to microbial stability over

prolonged storage. It was kept under refrigeration or at room temperature

in air-sealed or vacuum packaging in moisture-proof material. In all

samples tested the microorganisms were in acceptable levels, while

sulfite-reducing clostridia, Salmonella spp., and molds were not detected.

An area that has seen a particular concentration of research efforts

is physico-chemical and rheological properties of tahini [9]

. Thus, Abu-

Jdayil et al. [10]

and Abu-Jdayil [11]

studied the rheological

characterization of milled sesame (tahineh). They noted that a major

concern facing the tehineh (tahina) industry is the production and

maintenance of the product while preserving the proper consistency,

stability, color, and texture properties. They found that tehina behaves as

a non-Newtonian pseudo-plastic fluid, and that the power-law model is

the most appropriate to fit the flow curves of tahina.

Altay and Ak [12]

investigated the effects of temperature, shear rate

and constituents on rheological properties of tahin (sesame paste).

Studying tahin at temperatures between 20 and 70 °C and shear rates in

the range 0.13-500 s-1

, they reported observing hysteresis loops in the

flow curves. They concluded that the behaviour of tahin was

pseudoplastic and describable by a power law model.

Page 4: Experimental Investigation of Particle Size Distribution ... · PDF fileExperimental Investigation of Particle Size Distribution in Commercial Tahina ... [7] proposed a plan ... C

N. Turkmen 190

The rheological characterization of tahin / pekmez (sesame paste /

cooked and concentrated grape juice) blends were investigated by Arslan

et al. [13]

. The authors used a concentric cylinder rotational viscometer to

study properties of tahin / pekmez blends at tahin concentrations of 20 to

32% and at temperatures ranging from 35 to 65 °C. They concluded that

the blends exhibited non-Newtonian, shear thinning behavior at all

temperatures and at all tahin concentrations. Apparent viscosity versus

shear rate data was successfully fitted to the power-law model.

In a similar study, Razavi et al. [14]

determined the time

independent rheological properties of low fat sesame paste/date syrup

blends. They used a Brookfield rotational viscometer at temperatures of

25, 35, 45, and 55 °C. They concluded that all sesame paste/date syrup

blends exhibit non-Newtonian, pseudo-plastic behavior at all

temperatures.

Akbulut and Çoklar [3]

and as well as El-Adawy and Mansour [15]

,

and Hamed and Sadek [16]

studied the physicochemical and rheological

properties of sesame pastes (tahin) processed from both hulled and

unhulled roasted sesame seeds and their blends at several levels and at

temperatures ranging from 15 to 65C and shear rates from 0.5 to 100 1/s.

They determined, like in earlier studies, that all blends of tahin exhibit

non-Newtonian, pseudoplastic behavior at all temperatures. Apparent

viscosity versus shear rate data was successfully fitted to the power law

model.

In a remarkable recent study, Çiftçi et al. [17]

studied the colloidal

stability and rheological properties of sesame paste (tahini). They

investigated particle size and temperature effects on the colloidal stability

and rheological characteristics of sesame paste, which is a kind of

protein–oil suspension. They determined multimodal particle size

distribution using a laser-scattering analyzer. It was detected that

colloidal stability of sesame paste was improved by decreasing the

median particle size below 5 μm. A decrease in the storage temperature

also caused the increase in colloidal stability.

In summary of the recent literature cited above, it is clear that

tahina is treated by researchers, as far as particle size distribution is

concerned, as if it is a substance of uniform properties. The only

exception is the study by Ciftci et al. [17]

, where reference is made to

particle sizes.

Page 5: Experimental Investigation of Particle Size Distribution ... · PDF fileExperimental Investigation of Particle Size Distribution in Commercial Tahina ... [7] proposed a plan ... C

Experimental Investigation of Particle …. 191

2. Materials and Methods

Handicapped by a tiny budget, it was clear that purchasing or even

loaning expensive research equipment was not feasible. It was decided to

go through a number of alternatives. One particular microscope, the

MD828T, with electronic readout was selected, and ordered along with

its accessories. Figure 1 shows the microscope and the computer

assembly.

Fig. 1. The test setup.

To this end exploratory studies were undertaken on locally

acquired tahina. Since tahina is oil-based, searches were started for

determining those agents that can be used to process samples of tahina on

slides of the microscope. Of various chemicals experimented with,

including water, alcohol and hexane. Hexane, which is used in industrial

oil extraction processes, yielded favorable results. It was noted that the

addition of hexane to tahina caused the oil in tahina to spread on the glass

slide. Then the layer dried up to yield a crisp picture of the particle

constituents (Fig. 2).

a) b) a)

Fig. 2: a) A thin layer of tahina under the microscope,

b) Adding various quantities of hexane to tahina.

Page 6: Experimental Investigation of Particle Size Distribution ... · PDF fileExperimental Investigation of Particle Size Distribution in Commercial Tahina ... [7] proposed a plan ... C

N. Turkmen 192

Figures 3-5 illustrate the process and results of treating tahina with

hexane.

In Fig. 5(b), the first number refers to the reference number of the

particle, the second number is the area of particle (in pixel2) and the third

number indicates the circumference in pixels.

Fig. 3: a) Tahina when diluted by 50% hexane,

b) Tahina when diluted by 75% hexane.

Fig. 4: a) Tahina when diluted by 83% hexane, b) Clear particles in tahina after being

washed out with hexane.

b) a)

a) b)

Page 7: Experimental Investigation of Particle Size Distribution ... · PDF fileExperimental Investigation of Particle Size Distribution in Commercial Tahina ... [7] proposed a plan ... C

Experimental Investigation of Particle …. 193

Fig. 5: a) Tahina particles after being washed out with hexane and printed as black and

white, b) Clarified picture of tahina particles after being measured.

During ensuing measurements and computations, the software that

came with the microscope was utilized. To convert the software

measurement, which is in pixel, to the micron a scaled lam that has 100

lines in 1 mm is used. Since software measures the area, the equivalent

diameter De is defined as:

ADe

4 (1)

The perimeter of the particle, P, also measured by the software. We

define a shape factor (circularity), Cf , were defined as:

e

fD

PC

(2)

Thus, for a perfectly circular particle, De = D, otherwise De < D.

The Cf of a perfectly round particle would be = 1.0. For any other shape

the Cf would be expected to be less.

Before starting wide-scale experimentation, a system was devised

for thoroughly mixing the tahina before taking samples, “washing” the

samples with hexane, and taking measurements after the drying of

hexane. The proper bookkeeping of the procedure and test results were

done and any observations were recorded. Thus tahina samples were

coded to indicate production date, manufacturer and sample number.

Testing of tahina was then initiated on batches purchased from the

local market. All in all, these were nine half-kg or one-kg tahina

b) a)

Page 8: Experimental Investigation of Particle Size Distribution ... · PDF fileExperimental Investigation of Particle Size Distribution in Commercial Tahina ... [7] proposed a plan ... C

N. Turkmen 194

containers from 6 different manufacturers. During testing, and after

rigorous mixing, about 10 samples were extracted from each tahina

container. This corresponded to about 100 particles of size 30 microns

and above per container. It became clear at this stage that dealing with

particles less than about 30 microns in diameter would prove to be too

laborious.

3. Results

It would be of fundamental importance to compare the results of

measurements with the current measurement system with those of a

universally recognized measuring system. To this end samples of tahina from

company H were sent for analysis to Sympatec (www.sympaTEC.com), a

laboratory specialized in particle size analysis. There the tahina was analyzed

using laser diffraction techniques. Simultaneously samples were analyzed at

KAU under the microscope, using the technique developed during the current

study. The results are displayed comparatively in Fig. 6. It may be noted in

Fig. 6 that the actual start of data at lower end from Sympatec occurs at about

5 microns. Data from KAU reading commences at 30 microns due to practical

reasons. It will be agreed that the results of the readings are by the two

techniques, as displayed in Fig. 6, are not exactly the same, but they are

reasonably close. This is especially true about the slopes of the curves.

0

10

20

30

40

50

60

70

80

90

100

0 1 10 100 1000

Par

ticl

e n

um

ber

(C

um

ula

tive,

%)

Diameter, micron

Microscope measurement (Sample H) Sympatec Measurements (Sample H)

Fig. 6. Comparison of results for essentially the same tahina by two different techniques.

Page 9: Experimental Investigation of Particle Size Distribution ... · PDF fileExperimental Investigation of Particle Size Distribution in Commercial Tahina ... [7] proposed a plan ... C

Experimental Investigation of Particle …. 195

Figure 7 shows particle size (De) distributions in tahina samples from

these six manufacturers. It was noticed that particle size distributions of tahina

produced at different times but from the same manufacturer did not seem to

vary substantially. This is evident in Fig. 8 for samples that were produced 6

weeks apart. For this reason particle size distribution of only one sample from

a given manufacturer is shown in Fig. 8 in order not to clutter the graph.

Fig. 7. Particle size distributions in tahina samples from selected manufacturers.

0

10

20

30

40

50

60

70

80

90

100

10 100 1000

Par

ticl

e num

ber

(C

um

ula

tive,

%)

Diameter, micron

Sample H: (08/03/2009) Sample H: (17/09/2009)

Fig. 8. Particle size distribution in tahina that were produced 6 weeks apart by the same

manufacturer.

0

10

20

30

40

50

60

70

80

90

100

10 100 1000

Nu

mb

er o

f p

arti

cle

(cu

mu

lati

ve)

, [%

]

Diameter, micron

A B C D E H

Page 10: Experimental Investigation of Particle Size Distribution ... · PDF fileExperimental Investigation of Particle Size Distribution in Commercial Tahina ... [7] proposed a plan ... C

N. Turkmen 196

Table 1 depicts the distribution of average De and Cf between the

tahina of a number of manufacturers.

Table 1. Average equivalent diameters of tahina.

Company Average Equivalent

Diameter, De, (micron)

Shape factor

(circularity), Cf

A 86 0.52

B 104 0.40

C 126 0.52

D 110 0.47

E 80 0.35

F 109 0.67

G 162 0.48

H 141 0.41

It is to be pointed out in Table 1 that specimens C and F were

produced by the same company at different times, with an average De of

about 118 microns. The same is true for G and H, which were produced

by another company, and the average De for this company comes to about

152 microns.

Curiously enough, laser spectrometers are not able to detect

circularity. The microscope however readily determines circularity by

measuring the circumference of a particle. Average circularities of the

tahina samples studied are displayed in Table 1. It is observed from this

table that sample F has the largest value of circularity of about 0.65. The

circularities of the rest of the samples are less, ranging from about 0.35 to

0.5. There does not seem to be a clear-cut relationship between

circularity and equivalent particle size. In a similar manner, the average

circularity of tahina C and F produced by one company is observed to be

about 0.6 whereas for tahina G and H it is 0.45, indicating that in the

latter company tahina is passed through a ball mill that flattens the

particles.

4. Discussion and Conclusions

Referring to Fig. 7, all six tahina samples are seen to be uniform at

the 40 micron range, indicating that only about 5 % of the particles

would pass a sieve of this size. This uniformity disappears quickly

though when the samples are viewed at a sieve opening of 70 microns.

Thus tahina C and H seem to contain relatively large particles such that

only about 30 to 40 % of their particles pass the sieve of 70 micron size

Page 11: Experimental Investigation of Particle Size Distribution ... · PDF fileExperimental Investigation of Particle Size Distribution in Commercial Tahina ... [7] proposed a plan ... C

Experimental Investigation of Particle …. 197

whereas tahina A and B contain finer particles such that at the same sieve

opening 65 to 70 percent of their particles go through. A similar

distribution pattern is displayed at 100 micron sieve size. The disparity

between particle sizes does not disappear even at a sieve opening of 200

microns, where 95 % of almost all particles of tahina A, B, D and E pass

through although barely 80% of tahina C and H have gone through the

sieve. It looks like it took a sieve size of 400 microns for all particles of

all tahina to finally pass through.

The observations made on Fig. 7 are also reflected in the average

equivalent diameter distributions shown in Table 1. Here it is brought

into sharp focus that tahina A and E have an average size of around 80

microns, whereas particles in tahina G and H are nearly twice that size.

Average particle sizes in tahina B, C, D and F vary from 100 to about

120 microns.

An important point to note here has to do with what has been

defined as circularity above. This is a factor that is related to the shape of

the particle. Circularity is thought to depend on the grinding and

processing machinery utilized. Low values of circularity may also be

related to the aging of tahina and the onset of rancidity due to the

increase in surface area.

With reference to Fig. 7 and Table 1, there seem to exist wide

differences and variations between the particle size distributions and

circularities of tahina in the market. The mean equivalent diameters of tahina

produced by certain manufacturers were found to be twice those of some

others. It seems to be also understood that the smoothness of tahina used for

certain processes needs to be different from that used for other processes. It

is therefore suggested that there be some indication of particle size for

informing the consumer as to what he is purchasing. The guideline given in

Table 2 may be considered an initial step in this direction.

Table 2. Suggested classification of Tahina according to average equivalent diameter.

Average equivalent particle size Classification

Less than 50 microns Extra smooth

Larger than 50 microns and less than 100 microns Smooth

Larger than 100 microns and less than 160 microns Coarse

Larger than 160 microns Extra course or chunky

Accordingly no manufacturer currently produces tahina that can be

classified as extra smooth. Only two companies, A and E produce tahina

Page 12: Experimental Investigation of Particle Size Distribution ... · PDF fileExperimental Investigation of Particle Size Distribution in Commercial Tahina ... [7] proposed a plan ... C

N. Turkmen 198

that would be classified as smooth. The tahina produced by most

companies, i.e., B, C, D and H, would be classified as coarse. The tahina

of one company, G, would be classified as extra course or chunky.

It follows from what has been presented above that it is possible to

conduct particle size analyses of tahina with indeed modest expenditures

in equipment. The current research effort required the purchasing of a

$400 microscope, a $1000 laptop computer and a few hundred dollars

worth of chemicals and dispensable items. This type of a budget would

not be imaginable with the laser equipment currently utilized for the

same purpose, which carry a tag of several hundred thousand dollars. It is

true that the manual labor requirement is a bit more with the microscope,

but not enough to upset the difference in investment.

Since the results from the two systems seem to be acceptably close,

it follows that particle size analyses can now be performed by tahina

manufacturers themselves, rather than investing in expensive laser

equipment or sending samples to specialized laboratories abroad for

analysis. It goes without saying that the classical method of measuring

the particle size in tahina by using a micrometer is unsatisfactory since it

only reveals the size of the largest particle between the jaws of the

micrometer.

Acknowledgement

The author would like to acknowledge the assistance of Drs M.

Akyurt and S. Aldousari and the financial support by KAU to this effort.

References

[1] Akyurt, M., Sesame, pp 93,TEMA - National Confectionary and Tahina Co., Jeddah,

(2007).

[2] Akyurt, M., The Sesame Line at TEMA, Technical Report, p. 83, National Confectionary

and Tahina Co., Jeddah (2007)

[3] Akbulut, M. and Çoklar, H., Physicochemical And Rheological Properties of Sesame

Pastes (Tahin) Processed From Hulled And Unhulled Roasted Sesame Seeds And Their

Blends At Various Levels. Journal of Food Process Engineering, 31: 488–502 (2008).

[4] Eissa, H.A. and Azza, Z., Quality and safety of halawa modified with mushroom, Journal

of the Science of Food and Agriculture, 86 (15): 2551 – 2559 (2006).

[5] Damir, A.A., Utilization of sunflower seeds in tahina and halawa processing, Food

Chemistry, 14(22): 83-92 (1984).

Page 13: Experimental Investigation of Particle Size Distribution ... · PDF fileExperimental Investigation of Particle Size Distribution in Commercial Tahina ... [7] proposed a plan ... C

Experimental Investigation of Particle …. 199

[6] Akbulut, M., Comparative studies of mineral contents of hulled sesame paste (tahin),

unhulled sesame paste (bozkir tahin) and their blends, Asian Journal of Chemistry, 20(3):

1801-1805 (2008).

[7] Jamará, M.I. and Isa, J.К., Microbiological Quality of Tehena and Development of a

Generic HACCP Plan for its Production, World Journal of Agricultural Sciences, 2(3): 290-

297, (2006).

[8] Kotzekidou, P., Microbial Stability and Fate of Salmonella Enteritidis in Halva, a Low-

Moisture Confection, Journal of Food Protection, 61(2): 181-185 (1998).

[9] Ozcan, M. and Akgul, A., Physical and chemical properties and fatty acid composition of

tahin (sesame paste), Gida, 19: 411-416 (1994).

[10] Abu-Jdayil, B., K. Al-Malah and Asoud, H., Rheological characterization of milled

sesame (tehineh), Food Hydrocolloids, 16 (1): 55-61, (2002).

[11] Abu-Jdayil, B., Modelling the time-dependent rheological behavior of semisolid foodstuffs,

Journal of Food Engineering, 57(1): 97-102 (2003).

[12] Altay, F.L. and Ak, M.M., Effects of temperature, shear rate and constituents on

rheological properties of tahin (sesame paste), Journal of the Science of Food and

Agriculture, 85 (1): 105 – 111 (2007).

[13] Arslan, E., Yener, M.E. and Esin, A., Rheological characterization of tahin/pekmez

(sesame paste / concentrated grape juice) blends, Journal of Food Engineering, 69(2): 167-

172 (2005).

[14] Razavi, S.M.A., Najafia, M.B.H. and Alaeea, Z., The time independent rheological

properties of low fat sesame paste/date syrup blends as a function of fat substitutes and

temperature, Food Hydrocolloids, 21(2): 198-202 (2007).

[15] El-Adawy, T.A. and Mansour, E.H., Nutritional and physicochemical evaluations of

tahina (sesame butter) prepared from heat-treated, Journal of the Science of Food and

Agriculture, 80(14): 2005 – 2011 (2000).

[16] Hamed, K.E.A. and Sadek, M.A. The nutritive value and consumption of sesame products

in Egypt, Alexandria Journal of Agricultural Research (Egypt), 37(3): 21-31 (1992).

[17] Çiftçi, D., Kahyaoglu, T., Kapucu, S. and Kaya S., Colloidal stability and rheological

properties of sesame paste, Journal of Food Engineering 87(3): 428-435 (2008).

Page 14: Experimental Investigation of Particle Size Distribution ... · PDF fileExperimental Investigation of Particle Size Distribution in Commercial Tahina ... [7] proposed a plan ... C

N. Turkmen 200

حجم الجسيمات فى أنواع الطحينة لتوزيع ةتجربة تحقيقي التجارية

نديم تركمان ، جامعة الممك عبد العزيز،هالمياتحمية الهندسة الحرارية وتقنية قسم

المممكة العربية السعودية – جدة

استتتتتندت الدراستتتتة عمتتتتى أ تتتتد عينتتتتة متتتتن منتتتتت الطحينتتتتة .المستتتتت م والتتك باتستتتعانة ،المحمتتى، كمتتا استتت دمت طريقتتة فتتاة لتحميتتل العينتتة

لكترونتتتتت، وتتتتتم فحتتتت عينتتتتات متتتتن المنتتتتت متتتتن قبتتتتل إبميكروستتتتكو ،لتتتى متتتتوفرإمصتتتانع م تمبتتتة بالمنطقتتتة، وباتستتتتعانة ببرنتتتام حاستتت

جتترح حستتا المستتتاحات والمحيطتتات المحتتددة لمعينتتتة محتتل البحتتت ، لألقطتار لعينتة منتت الطحينتتة يوبعتد التك تتم حستا المتوستتط المستاو .المتحصل عميها من هاه المصانع

دة فتتت حجتتم و ن هنتتاك ا تافتتات معتبتترة موجتتألقتتد تتتم استتتنتا ،توزيع العينة، والمتوسط المساوي لألقطار والدوائر ال اصتة بالطحينتة

.التت أنتجتها المصانع الم تمبة محل التجربة

جتترح تقتتديم مقترحتتات ،اتستتتنتاجات المست مصتتة وعمتتى ءتتو .طحينة المناسبةتتعمق بإرشادات مبدئية تتعمق بتحديد مواصبات ال