MOCMP13PPVolumeP3PPROMANIANPTECHNICALPSCIENCESPAC ADEMYP:P2007PPPPPPPPPPPPPPP73P [617692]

MOCMP13P–PVolumeP3P–PROMANIANPTECHNICALPSCIENCESPAC ADEMYP:P2007PPPPPPPPPPPPPPP73P

STUDYPCONCERNINGPTHEPFORMSPOFPSOLIDPPARTICLESPP

MOȘNEUGUłUPEMILIANPFLORIN 1,PNEDEFFPVALENTIN 1,PBĂISANPIOAN 2,P
PANAINTEPMIRELA 1,PSAVINPCARMEN 1,PRISTEAPMIHAI 1P

1UniverityΦofΦBacauΦ
2”Gh.ΦAsachi”ΦTechnicalΦUniversityΦofΦIasiΦ
Φ

1.PINTRODUCTIONP

The vegetable products from agriculture and a part from products obtained after processes from food in dustry
(breaking up, granulate, briquette etc.) represents a heterogeneous mixture.
We will be considering that the mass of product is composed from particles mixture with different prop erties,
which made a heterogeneous mixture or a heterogeneo us system.
The heterogeneous mixtures by-path composed from tw o or more phases (parts) which have well determinat ed
different physical properties (sizes, form, mass, e tc.), which mean the appearance bounding surfaces i n indoors
mixtures.
The measuring of a mixture sizes and the processing date by mathematical statistics methods constitute the base
of determination of the dimensional characteristics .
By form, particles can be classificated in four ca tegories in depending on what relations exist betwe en three
sizes (l – length, b – width, c – thickness) (Table 1) [5]:
– particle of certain form: l > b > c: the seeds of c ereals (fig. 1.a)
– particle of form ellipsoid of rotation: l > b = c: the seeds of legume (fig. 1.b).
– particle of spherical form: l = b = c: pea the soy, rape etc.(fig. 1.c).
– particle of lenticular form: l = b > c: the lentil, corn etc.(fig. 1. d.)

Sizes of principal cereals. Table 1.
No. crt. The material analyses Length,
a (mm) Width,
b (mm) Thickness,
c (mm)
1. wheat 5 – 7.2 2.6 – 4 2.4 – 3.3
2. barley 8.4 – 14 3.1 – 3.9 2.3 – 3.2
3. rice 5 – 6.5 2.8 – 3.5 1.9 – 2.2
4. corn 8 – 12.3 7.5 – 11.8 3.7 – 6
5. the soy 7.1-9 5.4 – 7.3 4.5 – 5.9
6. rape 1.82 – 2.1 1.75 – 1.9 1.5 – 1.86
7. millet 2.7 – 4.4 2 – 2.4 1.5 – 1.9 Abstract: An important factor for different process (the dim ension or aerodynamic
separation) represents the form of solid particles. In this aim different correlations were
made between geometric elements of solid particle, these correlations being represented in
charts.
Depending on the type of used chart, solid particle will be clasificateed after their form.
P
KeyPwords : particle form, sphericity.

MOCMP13P–PVolumeP3P–PROMANIANPTECHNICALPSCIENCESPAC ADEMYP:P2007PPPPPPPPPPPPPPP74P

8. flax 3.8 – 4.8 2 – 2.4 0.7 – 1.2
9. poppy 1.4 – 1.9 1.1 – 1.4 0.5 – 0.8

.

Fig. 1.Particle principal dimensions.

After of breaking up corny seeds, the sizes of resu lted particles represent sort criteria of this. Kno wing the
intervals of variation average sizes as much to see ds, how much and to product result after breaking u p of this,
permit the choice corrects the sizes and forms orif ices classifying screens. No matter the process of provenance
of particles, these don't have same sizes and form, which leads to a heavier creation of a mathematica l model
concerning the process of assortment. Yet former fo und diverse research worker method which in use dif ferently
approximation [5].

2.PTHEORETICALPCONSIDERATIONP

In 1932 Wadell defined the sphericity as the report between the volume spheres of which diameter makes ones
living of particles and the volume spheres circumsc ribed the particles. The sphericity measured with h elp of the
following relation [2, 3]:

p
s
cV
VΦ = (1)

In this relation the volume particles Vp can be determined by measuring the aquatic volumes dislocate of
particle, and Vc can be calculated with spheres formula, taking the maximum size of particles as the diameter
circumscribed the spheres:

3
6CV a π= ⋅ (2)

For solid particle which forms is approximate ellip soidal, Vp is calculated with relation:

6pV a b c π= ⋅ ⋅ ⋅ (3)

Replacing the expressions (2) and (3) in relation ( 1) we have:

3
2Wb c
a⋅Φ = (4)
b
c
l
d) c l
c) b c b
l
b l
c
a)
c l
b) b

MOCMP13P–PVolumeP3P–PROMANIANPTECHNICALPSCIENCESPAC ADEMYP:P2007PPPPPPPPPPPPPPP75P

In 1958, Sneed and Folk argues as the volume partic les isn't so important as the maximum projection of
particles, in the case determination floating speed s of the solid particles, because of frictional for ces which react
on this. They defined maximum projection, the spher icity (ΦP) as is the report between maximum projection
areas of spheres with coequal one volume of particl es and maximum projection respective particles, cal culated
with relation:

2
3
SF c
a b Φ = ⋅ (5)

The values obtained with relation (5) was identical with one obtained from the determination of forms Corey (S.
F.) [1 ,6]:

. . cSF
a b =
⋅ (6)
Riley suggests the determination sphericity with th e next relation:

i
R
cd
dΦ = (7)
in which:
dc represents the diameter encircles particles,
d i – diameter circles take down the in particle.

For spherical particle Φs = 1, for particle spherical abrading Φs = 0, 95, and for particle from material breaking
up Φs = 0, 6 – 0, 8. In the case of a sphericity of a no n-spherical particle, Φs, he is apart from size particles, but
characterize the appearance of particle, this is ca used with relation [4]:

3
3 sa b c
a⋅ ⋅Φ = (8)

in which a,Φb and c represents the sizes solid particles.

On near the mathematical determination, sphericity was achieved, by dint of graphic representations, t he
identification particles in depending on form of th is. There for he achieved differently correlation b etween
dimensional element ale solid particles (fig. 4) [1 , 6, 7].
00.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

a) 00.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

b)
Equant

Oblate
(disk)
Bladed Elongated b
a
c
b Compact
Compact
platy Compact
bladed Compact
elongated
Platy Bladed Elongated
Very
platy Very
bladed Very
elongated c
a
a b
a c −
−

MOCMP13P–PVolumeP3P–PROMANIANPTECHNICALPSCIENCESPAC ADEMYP:P2007PPPPPPPPPPPPPPP76P

c) 1.00
0.00 0.00 1.00
0.00 0.30 0.50 0.70 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00
0.50
0.30 0.70
0.00 c : a b : a
(a – b) / (a – c) 1.00

d)
The identification Solid particles after form in de pending on the existing correlations between dimens ional
elements of this:
a) Zingg (1935); b) Bates and Jackson (1980); c) an d d) Sneed and Folk. Fig. 4.

3.PRESULTSPANDPDISCUSSIONSP

For the first matters presented in the table 1, in front they achieved the chart of identifies the sol id particles after
their form, depending on the correlation between di mensional element of this, using Zingg chart, Bates and
Jaskson chart and the ternary Sneed and Folk chart (fig. 5).
00,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1
soy bean maize wheat rice barley rape mellet flax poppy
a) c
a
a b
a c −
− SF Φ c
a
a b
a c −
− b
a

MOCMP13P–PVolumeP3P–PROMANIANPTECHNICALPSCIENCESPAC ADEMYP:P2007PPPPPPPPPPPPPPP77P

00,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1
soy bean maize wheat rice barley rape millet flax poppy
b)

1.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.70
0.50
0.30
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00
0.50
0.30 0.70
0.00
soy bean maize wheat barley rice
millet rape flax poppy c : a b : a
(a – b) / (a – c) 1.00
1.00
c)
The identification Solid particles after their form :
Zingg( 1935); b) Bates and Jackson( 1980); c) and d) Sneed and Folk. Fig. 5.

The first chart achieves the rating solid particles just after four categories: oblate, equate, blade and elongated.
The second chart achieves divide it a solid particl es after 10 compact category compact platy compact bladed
elongated, platy, bladed, elongated, very platy, ve ry bladed and very elongated. There through divide achieved a
class a precise maul solid particles.
Particle of the soy, as represented from chart from figure 5 a and c, are bladed, and for the chart fr om fig. 5. c are
compact. In the case of corn particles the integrat ion of this on to form was not made realized, becau se was
obtained a differed correspondent for each graphica l representation.
For particles of wheat, rice, barley, rape, Millet and flax in all three graphical representations of forms were
obtained the same correspondent, respectively: elon gate, bladed, elongate, compact, bladed and elongat ed
because is frontier, and the last is bladed. Like i n case of soy beans, particle of poppy was the blad ed form for
graphical representation form fig. 5. a and c, and for representation from figure 5 b are compact.

MOCMP13P–PVolumeP3P–PROMANIANPTECHNICALPSCIENCESPAC ADEMYP:P2007PPPPPPPPPPPPPPP78P

From graphic analysis consisted as the allocation s olid particles differ, this due to existing correla tions among
the sizes used particles in the graphic representat ion. (rape particle – spherical particle, particle of corny, rice,
barley – oblong particle).
P
P
4.PCONCLUSIONP

From analysis of graphics result:
– heterogeneous mixture are formed from particles wit h different properties;
– it is very important to know the particles form;
– solid particle can be grouped in four groups, takin g into account the form of the particles;
– the classification of solid particles by their for m from a chart to other is not respected;
– still, there were situation in which it was obtaine d the same classification for all graphical
representation.

BLIBLIOGRAFYP

[1]. Cheel R.J., IntroductionΦtoΦclasticsΦsedimentology,Φ Brock University, St. Catharines, Ontario, Canada, 2005;
[2]. Elisabeth T., Soga k. and Drummond T., ParticleΦshapeΦcharacterizationΦusingΦFourierΦAnaly sis,ΦCUED\D-
Soils\TR315, 2000;
[3]. Le Roux J.P., ComparationΦofΦsphericityΦindicesΦasΦrelatedΦtoΦthe ΦhydraulicΦequivalenceΦofΦsettingΦgrains,Φ
Journal of sedimentary Research, vol. 67, no. 3, 19 97, p. 527 – 530;
[4]. Monegutu E., ContributiiΦprivindΦsortareaΦaerodinamicaΦaΦproduse lorΦagricole,Φ Teza de Doctorat, Iasi,
2006;
[5] Nedeff V., Mosnegutu E. and Baisan I., SeparareaΦmecanicaΦaΦproduselorΦgranulometriceΦsiΦp ulverulenteΦdinΦ
industriaΦalimentara,Φ Ed. Tehnica-Info, Chisinau, 2001;
[6] Terence A., ParticleΦsizeΦmeasurement,Φ vol. I, Ed. Chapman & Hall, S.U.A., 1997;
[7] xxx, GrainΦ MorphologyΦ -Φ Roundness,Φ SurfaceΦ Features,Φ and Φ SphericityΦ ofΦ Grains,Φ
http://people.uncw.edu/dockal/gly312/grains/grains. htm .

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