trumic rad.pdf

8/18/2019 Trumic rad.pdf

http://slidepdf.com/reader/full/trumic-radpdf 1/8

New model of screening kinetics

Milan Trumic a,⇑ , Nedeljko Magdalinovic b

a University of Belgrade, Technical Faculty, VJ 12, Bor, Serbiab Megatrend University, Faculty of Management, Park suma kraljevica bb, Zajecar, Serbia

a r t i c l e i n f o

Article history:Received 24 April 2010Accepted 16 September 2010Available online 14 October 2010

Keywords:Mineral processingScreeningParticle size

a b s t r a c t

An understanding of screening requires a knowledge of screening kinetics. The new model of screeningkinetics presented in this paper is theoretically described and experimentally proven. Samples of differ-ent raw materials, different in their density, bulk density, particle size distribution and particle shape,were used.

The conducted experiments conrmed that the new model of screening kinetics successfully describesthe process of screening of various raw materials even when they are exposed to a range of factors thatmost inuence the screening process (dimensions of the screen, particle size distribution of raw materi-als, particle shape, and thickness of the bed on the screen).

The advantage of this model of screening kinetics lies in its simplicity as it is characterized by the factthat it has only one parameter, i.e., ( k) – the screening rate constant, which is experimentally measured.This constant can be measured on the basis of a single screening experiment. This fact is very signicantfor practical applications of the model to an industrial screen.

2010 Elsevier Ltd. All rights reserved.

1. Introduction

Previous studies have used two approaches to describe screen-ing kinetics: a stochastic approach, and a kinetic approach.

Within the stochastic approach ( Baldwin, 1963; Brereton andDymott, 1974; Brüderlein, 1972; Meinel and Schubert, 1972;Schlebusch, 1969 ), two models were studied – in terms of theoryand experiment:

(1) Free screening, where the particles do not have an impact onone another on the screening surface ( Kluge, 1951 ;Klockhaus, 1952 ) which was further developed andmodiedby more authors – ( Brüderlein, 1972; Meinel and Schubert,1972; Schranz and Bergholz, 1954; Schubert, 1968 ). The

main theoretical explanation was based on the assumptionthat the screening surface depends on the number of parti-cles that make contact with the screening surface in time(t ) and probability p = [1 (d/a)2] (Gaudin, 1939 ) that theparticle moves through an aperture, where d = particlediameter and a = aperture size.

(2) Tight screening with interaction between the particles waspresent during this operation. This model was analyzed indetail by Meinel and Schubert, (1971, 1972) by applyingand solving the differential equation of Fokker, Plank and

Kolmogorov for a very restricted condition where one of them states that the path of a particle ends in direct contactwith the screen surface, in other words the screeningprobability is p = 1. The theoretical interpretation of thisscreening model was studied and perfected by a number of authors. ( Baldwin, 1963; Brereton and Dymott, 1974;Brüderlein, 1972; Ferrara and Preti, 1975; Meinel andSchubert, 1971, 1972; Schlebusch, 1969; Standish and Meta,1985; Standish, 1985; Standish et al., 1986; Subasingheet al., 1989a,b, 1990 ).

Application of the tight screening model under real-time condi-tions requires changing and dening new limiting conditions,which further lead to extremely complex calculations.

Theother approach to the screeningprocess, adoptedby a num-ber of authors ( Andreev et al., 1966; Baldwin, 1963; Bodziony,1961; Nepomnjašc ˇ ij, 1962 ), is a kinetic one.

More than one model (Andreev et al., 1966; Lynch, 1977;Nepomnjašc ˇ ij, 1962 ) was suggested for the mathematical interpre-tation of screening kinetics. The one given in Eq. (1) is the simplestand the most appropriate for practical use.

dmdt ¼ km ð1 Þ

where dmdt is the rate particles of size ( a + 0) pass through thescreen

in time t , k the screening rate constant, m the mass of the particlesof size ( a + 0) on the screen at time t , and a is the aperture size.

0892-6875/$ - see front matter 2010 Elsevier Ltd. All rights reserved.doi: 10.1016/j.mineng.2010.09.013

⇑ Corresponding author. Tel./fax: +381 30421749.E-mail address: [email protected] (M. Trumic).

Minerals Engineering 24 (2011) 42–49

Contents lists available at ScienceDirect

Minerals Engineering

j ou r na l hom epa ge : www.e l s ev i e r. co m / loc a t e /mine ng

http://dx.doi.org/10.1016/j.mineng.2010.09.013

mailto:[email protected]


http://www.sciencedirect.com/science/journal/08926875

http://www.elsevier.com/locate/mineng

http://www.elsevier.com/locate/mineng

http://www.sciencedirect.com/science/journal/08926875


mailto:[email protected]




The integral form of Eq. (1) would be:

mm0

¼ e kt or 1 mm 0

¼ 1 e kt or m0 mm 0

¼ 1 e kt ð2 Þ

that is:

E ¼ 1 e kt ð3 Þ

where the screen undersize recovery ( E ) is ratio: the mass of under-size particles passing through the screen ( m0–m) in time t and themass of undersize in the feed ( m0) in time ( t = t 0 = 0).

In order to test Eq. (3) , its logarithm can be used:

ln 1

1 E ¼ kt ð4 Þ

whichpresents theequation of a straight line in the coordinate sys-tem t ; ln 1

1 E .Experimentsconductedunderdifferent screeningconditionsand

usingvarious rawmaterialshave shownthat Eq. (4) doesnot alwaysdescribe the screening process. Therefore, Perov (Andreev et al.,1966) suggesteda more complex equation:

E ¼ 1 e k1 t n ð5 Þ

In order to test Eq. (5) , its logarithm can be used:

ln ln 1

1 E ¼ n ln t þ ln k1 ð6 Þ

which presents an equation of a straight line in the coordinate sys-tem ln t ; ln ln 1

1 E .Compared to the stochastic models, the kinetic ones are simple

and have one or, at the most, two parametres which are to be iden-tied by experiment. Figs. 1 and 2 are graphical illustrations of thekinetic models given by Eqs. (3) and (5) .

Observing the point arrangements on Figs. 1 and 2 , which de-scribe the screening kinetics of different raw materials by usingthe Eqs. (3) and (5) , the deviation in relation to the straight lineis clearly noticed.

Results of the screening kinetics being approximated by a linearrelationship, we get the correlation coefcient within the limitsfrom 0.7343 to 0.9406. Somewhat a lower correlation coefcient

suggests that the tested screeningkinetics model does not describethe screening kinetics in the best way.

Unfortunately, no serious work dealing with the study of thekinetics of sieving have been published in the last 10 years.

2. Theory of the new model of screening kinetics

The model tested in this study was basically the kinetic modelmodied by the introduction of the screening probability coef-cient ( k p).

The starting point of the newmodel of screening kinetics is thatthe speed of screening depends not only on the composition of aparticle ( a + 0) in the screen at a particular time, as assumed inmodel (1), but also on the change of probability of screeningthrough time:

dmdt ¼ kmk p ð7 Þ

where dmdt is the rate particles of size ( a + 0) pass through thescreen

in time t , k the screening rate constant, m the mass of a particle of size ( a + 0)on the screenat time t , a theaperturesize, and k p is thechange of the probability of screening coefcient.

The probability of screening depends on the relation betweenthe diameter of the particle ( d) and the aperture size ( a):

p ¼ 1 d

a 2

ð8 Þ

During screening, the sequence of particles going through thescreen is: ‘small’, (particles with the middle, diameter ( ds) smallerthan 0.75 a , where a is the aperture size, 0 < ds < 0.75 a), ‘small-to-large’ (particles with mean diameter ( dsl) larger than 0.75 a and

smaller than a , 0.75 a < dsl < a), and then ‘large’ (particles with themiddle diameter ( d1) larger than a and smaller than 1.5 a ,Fig. 1. Graphical illustration of the screening kinetics model described by Eq. (3) .

Fig. 2. Graphical illustration of the screening kinetics model described by Eq. (5) .

M. Trumic, N. Magdalinovic/ Minerals Engineering 24 (2011) 42–49 43



a < d1 < 1.5 a). In other words, the relation d/a is increased for theremaining particles ( a + 0), while the probability of screeningdecreases.

Themathematically dened changeof theprobability of screen-ing enables a more accurate model of the screening kinetics to bedened, which describes the screening process from beginning toend.

Searching for a mathematical denition which describes thechange of probability of screening, the starting point was theassumption that the coefcient of change of probability of screen-ing ( k p) can be dened in the following way:

k p ¼ mm 0

ð9 Þ

where m is the mass of particles of size ( a + 0) on the screen attime t , a the aperture size, m0 the initial mass of a particle ( a + 0).

This assumption is the result of the experiment shown in Fig. 3.Fig. 3 clearly shows that the shape of the change of the proba-

bility of screening depends on the proportions of ‘small’ particlesin the particle size range ( a +0). In other words, the speed of decreasing probability at the beginning grows as the proportionsof ‘small’ particles in the particle size range ( a + 0) increases.

Substitution of ( k p) from Eq. (9) into the differential Eq. (7),gives:

dmdt ¼ k

m2

m0ð10 Þ

By integrating Eq. (10) , the following equation is obtained:

Z m

m0

m 2 dm ¼ km0 Z

t

0dt ð11 Þ

That is:m 0

m ¼ 1 þ kt ð12 Þ

mm 0 ¼

1

1 þ kt ð13 Þ

The screen undersize recovery ( E ) may be given by the follow-ing formula:

E ¼ 1 mm0

ð14 Þ

Substitution of ( m/m 0) from Eq. (13) into Eq. (14) gives:

E ¼ 1 1

1 þ kt ð15 Þ

That is:

E 1 E ¼

kt ð16 Þ

Eq. (16) represents the new model of screening kinetics. It repre-sents the equation of a straight line in the coordinate systemt ; E

1 E , (Fig. 4).Based on Fig. 4, the following can be concluded:

k ¼ tg a ¼ ab ¼

E 21 E 2

E 11 E 1

t 2 t 1ð17 Þ

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0 50 100 150 200 250 300

Time, sec

k p

0% 20% 50% 70%

Participation of ‘light’ particles in lower class ofProportions of ‘small’ particles in the

particle size range (- a +0)

Fig. 3. Graphics of the coefcient of change of probability of screening magnesite-

large on a screen the opening of which was 6.68mm, with different proportions of ‘small’ particles in the particle size range ( a + 0).

Fig. 4. Graphics of the function (16) .

Fig. 5. Vibrating sieve shaker.

44 M. Trumic, N. Magdalinovic / Minerals Engineering 24 (2011) 42–49



The rst and most important characteristic of the new model of screening kinetics is its simplicity. It has only one parameter ( k),which is identied by experiment. This parameter ( k), which isthe screening rate constant, can be obtained based on the resultsof only one screening process. This fact is very important for prac-tical application of the model to the industrial screen, where con-ditions for conducting experiments are directly connected withnumerous difculties and limitations.

3. Experimental work

An ILM-LABOR sieve shaker was used to study sieving kineticsin the laboratory ( Fig. 5).

The sieving was carried out dry, using Tyler series sieves.Screening kinetics using the sieve shaker was studied on eight

raw material samples: metal balls, quartz sand, mica, small andlarge magnesite, coal, copper ore and gravel. The particle size dis-tribution, density and embankment density of screening are givenin Table 1 .

The samples were in a loose condition and lled the whole areaof the screen in one layer and in many characteristic layers.

Each experiment of the screening kinetics in the laboratoryusedone sample, which was removed from the sieve shaker after a spe-cic period in order to dene the screened mass and then returnedto the sieve shaker for further screening. The data concerning thecontent of the particle size range ( a + 0) were obtained in the fol-lowing way: screening was continued to the moment when nomore than 0.1% of mass per minute allowed though the screen.

The screening kinetics were studied under semi-industrial con-ditions using a continuous semi-industrial vibration-screen of thebrand ‘‘DENVER” ( Fig. 6), the dimensions of which were B

L = 300 600 mm. The vibration-screen has circular and ellip-soid vibrational movements.

The screening surface used in the experiments was square withopenings of 5 mm, 8 mm and 10mm. The inclination of the screen

was 12 . The screening was carried out dry.For the purposes of examining the screening kinetics, the

screening area was devided into ve sections: 100, 200, 300, 400,and600 mm.For eachexperimentundersemi-industrial conditions,onesamplewasallowedthroughthe rstsection(0–100 mm),while

the others were covered. After measurement, the sample wasallowed through thersttwo sections(0–200 mm),while theothers

were covered. The same procedure was performed until all vesections (0–600mm) hadbeen uncovered.The screening kinetics on the semi-industrial vibration-screen

was studied on samples of six raw materials: calcite, andesite,limestone, coal, copper ore and gravel.

Table 1

Characteristics of the samples for the laboratory experiments.

Particle size range (mm) Gravel Coal Copper ore Large magnesite Small magnesite Quartz sand Metal balls Mica

W (%) D (%) W (%) D (%) W (%) D (%) W (%) D (%) W (%) D (%) W (%) D (%) W (%) D (%) W (%) D (%)

13.33 + 9.52 13.6 100.0 38.7 100.0 30.2 100.0 18.7 100.0 – – – – – – – –9.52 + 6.68 13.3 86.4 20.9 61.3 27.2 69.8 37.7 81.3 – – – – – – – –6.68 + 4.699 10.4 73.1 15.1 40.4 10.7 42.6 18.6 43.6 – – – – – – – –4.699 + 3.327 8.4 62.7 7.4 25.3 9.3 31.9 9.9 25.0 – – – – – – – –3.327 + 2.362 8.9 54.2 5.7 17.9 5.5 22.6 6.2 15.1 15.8 100.0 – – – – – –2.362 + 1.651 14.1 45.3 12.2 12.2 17.1 17.1 8.9 8.9 22.3 84.2 – – – – – –1.651 + 1.168 15.6 61.9 – – – – – –1.168 + 0.833 31.2 31.2 11.9 46.2 2.3 100.0 13.3 100.0 – –0.833 + 0.589 9.4 34.4 9.5 97.7 22.8 86.7 – –0.589 + 0.417 25.0 25.0 24.8 88.2 22.0 63.9 9.0 100.00.417 + 0.295 24.2 63.4 21.7 41.9 20.2 91.00.295 + 0.208 19.5 39.2 14.5 20.2 24.2 70.80.208 + 0.149 19.7 19.7 5.7 5.7 19.0 46.60.149 + 0.106 13.0 27.60.106 + 0 14.6 14.6

100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0

Density (kg/m 3) 2672 1494 2710 2922 2922 2630 4986 2655

Bulk density (kg/m 3) 1754 792 1531 1500 1347 1450 3234 998

Note : W – particular weight percent.

D – cumulative weight percent undersize.

Fig. 6. Continuous semi-industrial vibration-screen of the brand ‘‘DENVER” Fig. 7Particle shape of the raw material samplesemployed in the laboratory experiments.




The particle size distribution, density and embankment densityof the screening are given in Table 2 .

The experiments were conducted on raw materials the particlesof which differed in shape and size. The shapes of the different par-ticles employed in the laboratory and semi-industrial experimentsare given in Figs. 7 and 8 , respectively.

4. Results

The testing of the new model of screening kinetics was con-ducted on dry samples of different raw materials, with particlesof different shapes and sizes, different thicknesses of the bed onthe screen, different aperture sizes and different proportions of ‘small’ and ‘small-to-large’ particles. This means that all the mostimportant factors were varied in the screening process.

The results of the screening kinetics on the laboratory discon-tinual screens are graphically shown in the coordinate systemt ; E

1 E in Figs. 9–11 .The results of the screening kinetics on the semi-industrial

vibration-screen of continual effect are graphically shown in thecoordinate system L;

E

1 E in Fig. 12 .

The straight-line sequence of experimental points in all graphs,for all samples under various screening conditions, with very highcorrelation coefcients R = 0.980–0.999, shows that the newmodelof screening kinetics describes the screening process very well,both on the laboratory and semi-industrial vibration-screens.

The assumption based on the experiments that the screeningspeed is in direct proportion to the mass of the particles ( a + 0)that is on the screen at a given point in time and the coefcientof change of screening probability, was proven to be absolutelycorrect.

Based on the experiment results, the screening rate constant ( k)was determined using the least squares method. Table 3 showsnumerical values of the screening rate constant for experimentson the laboratory vibration-screen and Table 4 for those on thesemi-industrial screen.

The only parameter that affects the screening speed in this newmodel is the screening rate constant ( k). Therefore, the dependencyof the constant on the most important factors derived from theparticle size distribution, particle shape as well as the conditionswhere screening takes place will be described in more detail.

The rst conclusion to be drawn is that the screening rate con-stant varies for different raw materials although the aperture size

Table 2

Characteristics of the samples for the semi-industrial experiments.

Particle size range (mm) Gravel Coal Copper ore Limestone Andesite Calcite

W (%) D (%) W (%) D (%) W (%) D (%) W (%) D (%) W (%) D (%) W (%) D (%)

17.00 + 13.33 – – 16.8 100.0 20.0 100.0 14.4 100.0 15.3 100.0 9.9 100.013.33 + 9.52 13.6 100.0 22.2 83.2 14.3 80.0 22.5 85.6 34.6 84.7 12.1 90.19.52 + 6.68 13.3 86.4 13.8 61.0 12.1 65.7 15.8 63.1 16.9 50.1 18.8 78.06.68 + 4.699 10.4 73.1 8.1 47.2 9.4 53.6 11.8 47.3 8.9 33.2 36.8 59.24.699 + 3.327 8.4 62.7 6.5 39.1 7.6 44.2 9.1 35.5 6.0 24.3 19.1 22.43.327 + 2.362 54.2 54.2 32.7 32.7 36.6 36.6 26.4 26.4 18.3 18.3 3.3 3.32.362 + 1.1681.168 + 0

100.0 100.0 100.0 100.0 100.0 100.0

Density, (kg/m 3) 2672 1494 2710 2600 3015 2644

Bulk density (kg/m 3) 1750 790 1530 1530 1570 1490

Note : W – particular weight percent.D – cumulative weight percent undersize.

Fig. 7. Particle shape of the raw material samples employed in the laboratory experiments.




and other conditions may be the same. Three factors are importanthere: particle shape, proportions of ‘small’ and ‘small-to-large’ par-ticles in the particle size range ( a +0) (particle size distribution of raw materials) and density of raw materials, which affects the dy-namic movement of the particles along the screen. As far as parti-cle shape is concerned, the experiments clearly showed that therate constant is lower when the particles are not round (as wasthe case with coal, mica, magnesite and copper ore), and that itis signicantly higher when they are round (gravel, metal balls).This can be illustrated by the following example: if we take gravel

and copper ore (mass of 600 g) which have approximately thesame density, on a screen with an aperture size of 4.699 mm, thescreening rate constant ( k) will be 3.268 for gravel (round parti-cles) and 0.389 for copper ore (spiky shape).

Fig. 8. Particle shape of the raw material samples employed in the semi-industrial experiments.

Fig. 9. Screening kinetics of quartz sand (the mass was 100g).

Fig. 10. Screening kinetics of quartz sand (the mesh size was 0.295mm).

Fig. 11. Screening kinetics of gravel, coal, magnesite-large, copper ore (the masswas 600g, mesh size was 3.327 mm).

Fig. 12. Screening kinetics of limestone, coal, copper ore, andesite, calcite (meshsize 8mm).




The second conclusion to be drawn is that the greater is the pro-portions of ‘small’ particles in the raw material, the higher will bethe screening rate constant. This can be illustrated by the exampleof the screening of large magnesite on a screen the opening of

which was 6.68 mm with a changeable content of ‘small’ particlesin the particle size ( a + 0) ranges from 0% to 70%. The graphicalillustration of these results is shown in Fig. 13, while Table 5 con-tains the values the constant ( k) for different proportions of ‘small’particles. The change of the content of ‘small’ particles in the par-ticle size ( a + 0) from 0% to 50% causes a relatively small increasein the constant ( k). The constant ( k) increased more when the con-tent of ‘small’ particles was increased from 50% to 70%.

When dealing with raw materials of lower density with theother conditions being constant (the same aperture size, the samethickness of the bed on the screenand the sameparticle shape), theconstant ( k) is lower. This conclusion can clearly be illustrated if the constant for coal and that for copper ore on the laboratoryscreen the opening of which was 6.68mm are compared ( Table3). The particles of coal and copper ore had more or less the sameshape ( Fig. 7). For approximately the same thickness of the bed

(coal 300 g, copper ore 600 g), the screening rate constant for coalwas 0.373 and for copper ore 0.672. The larger constant for copperore is the result of the greater density of copper ore in comparisonto that of coal. The greater density results in more dynamic move-ment of the particles, which enables the particles ( a + 0) to movefaster through the larger particles and nally to slip through thescreen.

Generally, the constant decreases when the thicknessof the bedis greater. This is because particles ( a + 0) takemore time to cometo the screen if the bed on the screen is thicker. Certain results of the conducted experiements show some exceptions to this rule.For example, in the case of large magnesite, copper ore and gravel,when aperture size were a = 9.52, 6.68, and 4.699 mm, the coef-cient was here lower than when a thicker bed was screened. This

can be explained by the fact that a smaller thickness means moredynamic movement of the particles and that further means lower

Table 3

Numerical values of the screening rate constant ( k ) from the experiments on the laboratory vibration-screen.

Mesh size (mm) Gravel Coal Copper ore Magnesite-largeMass, g Mass, g Mass, g Mass, g

600 900 1200 300 450 600 400 600 800 600 900 1200

9.52 0.3278 0.2397 0.3656 0.3053 0.3749 0.4929 0.32576.68 0.3730 0.3075 0.0730 0.6338 0.6717 0.4295 0.1830 0.1292 0.09124.699 3.2679 3.8010 1.6642 0.2519 0.1210 0.0690 0.3906 0.3894 0.3485 0.3057 0.1840 0.09233.327 1.1058 1.3484 0.8533 0.2348 0.0982 0.0661 0.6612 0.6598 0.5237 0.1357 0.1108 0.07932.362 1.0091 0.8301 0.81301.651 0.8127 0.5616 0.5729

Magnesite small Quartz sand Metal balls MicaMass, g Mass, g Mass, g Mass, g

300 500 800 100 300 500 400 600 800 50 100 200

2.362 0.2686 0.2819 0.20361.651 0.1699 0.1582 0.16831.168 0.1340 0.1554 0.16150.833 0.1315 0.0935 2.7400 1.7872 1.52390.589 0.4881 0.2338 0.1876 0.8997 0.5406 0.83650.5 0.3455 0.2067 0.1805 0.5024 0.4046 0.40990.417 0.1525 0.0810 0.0764 0.3569 0.3261 0.26350.295 0.1093 0.0800 0.0689 0.1625 0.1330 0.0916 0.0583 0.0569 0.05460.208 0.0806 0.0541 0.0366 0.0526 0.0409 0.03980.149 0.0419 0.0401 0.0381

Table 4

Numerical values of the screening rate constant ( k ) from the experiments on the semi-industrial vibration-screen.

Mesh size (mm) Gravel Coal Copper ore Andesite Limestone Calcite

10 0.06378 0.2361 0.2639 0.1380 0.1055 0.09005 0.0920 0.3191 0.5579 0.2337

Fig. 13. Graphical presentation of the screening kinetics of large magnesite on ascreen the opening of which was 6.68 mm, for different amounts of ‘small’ particlesin the particle size range ( a + 0).

Table 5

Screening rate constant ( k ) of magnesite-large.

Content of ‘small’particles (%)

Screeningrate constant(k)

Correlation coefcient(R)

0 0.085 0.99720 0.089 0.99850 0.102 0.99670 0.345 0.996




screening speed. This was observed during conducting theexperiments.

For the same raw material when the proportions of ‘small’ par-ticles was the same, the constant ( k) decreasedas the aperture sizebecame smaller. This is understandable and expected if one takesinto account that a smaller opening means a lower coefcient of the open area. Theoretically, the screening probability is propor-tion to the coefcient of the open area. The results of certain exper-iments (copper ore, large magnesite) showed exceptions to thisrule. For example, for copper ore of mass m = 600g, and an aper-ture size a = 9.52 mm, k was 0.366, while k was 0.672 on a screenwith opening a = 6.68mm . This may occur when the negative ef-fect of the lowered coefcient of the open area is lower than thepositive effect of the greater proportions of ‘small’ particles inthe particle size range ( a +0). In the case when the openingwas a = 9.52 mm, the proportions of ‘small’ particles was 61%,and for the opening a = 6.68 mm, it was 75%, i.e., much more,which in accordance with the results given in Table 3 .

The above drawn conclusions based on the results of experi-ments conductedusing the laboratory vibration-screen arealso va-lid for the results of the experiments in the semi-industrialvibration-screen.

5. Conclusion

The research conducted in this paper gives the theoretical basisof a new model of screening kinetics, which was also experimen-tally proven on laboratory and semi-industrial vibration-screens,and its differential equation is as follows:

dmdt ¼ kmk p

Its integral form is:

E ¼ k t 1 þ k t

where dmdt is the rate particles of size ( a + 0) pass through thescreenin time t , k the screening rate constant, (1/s), k p the change of prob-ability of screening coefcient, t the screening time (s), E is thescreen undersize recovery (unit parts)

All the conducted experiments showed a signicant straight-line sequence of experimental points of a high correlation coef-cient ( R = 0.98–0.999), which indicates that the new model of screening kinetics describes well the process of screening differenttypes of raw materials under a range of the most inuential factors(dimensions of the screen, particle size distribution of the rawmaterial, particle shape and thickness of the bed on the screen).

One of the advantages of the new model lies in its simplicitywhich can be seen in the fact that it has only one parameter ( k)which is obtained by experiment. The screening rate constant ( k)

can be obtained from the results of only one screening experiment.This fact is extremely signicant for practical application of themodel to an industrial screen, where the conditions for conductingexperiments are connected with numerous difculties andlimitations.

The practical value of the model, applied to the industrialscreen, may be seen in the possibility of optimization and autom-atization of the screening process in the sense that the capacity of ascreen for a given screenundersize recovery ( E ) canbe determined,and vice versa . In that way, it is possible to manage the screeningprocess under given conditions with the given inuential charac-teristics of the raw materials.

The only parameter, that in this model predetermines thescreeningspeed is the screening rate constant ( k). The results show

that this constant depends on: the dimensions of the aperture size,the particle size distribution of the raw material, or, more accu-

rately, on the proportions of ‘small’ and ‘small-to-large’ particlesin the particle size range ( a + 0), the thickness of the bed on thescreen, the particle shape and the density of the raw material).

For the sameraw material, the rule is that for approximately thesame proportions of ‘small’ particles in the particle size range( a + 0), the screening rate constant ( k) as the aperture size be-comes smaller. This is expected, bearing in mind that the smallerthe opening is, the lower is the open area coefcient, and thatthe probability of screening is in proportion to the open areacoefcient.

Thegreater theproportions of ‘small’ particles in the lower classof largeness, the higher the screening rate constant ( k). Changingthe content of ‘small’ particles in the lower class of largeness from0% to 50% causes a relatively insignicant increase in the screeningrate constant ( k). A relatively greater increase in the constant oc-curs when the content of ‘small’ particles is over 50%.

When dealing with raw materials of greater particle densitywhen the other screening conditions are the same, the screeningrate constant ( k) is higher. Thegreater particledensity causes moredynamic movement of the particles, which enables particles( a + 0) to move faster between the larger particles and slipthrough the screen.

The screening rate constant ( k) decreases as the mass of the ini-tial sample, i.e., the thickness of the bed on the screen, increases.This occures because the particles ( a + 0) take more time to movethrough larger particles and slip through the screen when thethickness on the screen is greater.

References

Andreev, S.E., Zverevic, V.V., Perov, V.A. 1966. Droblenie, izmel’c ˇ enie i grochoc ˇ eniepoleznych iskopaemych, Izdatel’stvo ‘’Nedra’’, Moskau.

Baldwin, P.L.,1963. Thecontinuous separation of solid particles by at deckscreens.Transactions of the Institution of Chemical Engineers and the ChemicalEngineer 41, 255–263.

Bodziony, J., 1961. Mathematische erfassung des siebvorganges. Bergakademie 2,90–101.

Brereton, T., Dymott, K.R. 1974. Some factors which inuence screen performance.Proceedings of 10th International Mineral Processing Congress, London, pp.181–194.

Brüderlein, J., 1972. Bewegungsvorgänge auf siebmaschinen. Aufbereitungs Technik7, 401–407.

Ferrara, G., Preti, U.A. 1975. A contribution to screening kinetics. EleventhInternational Mineral Processing Congress, Cagliari, pp. 183–217.

Gaudin, A.M., 1939. Principles of Mineral Dressing. Mc-Graw-Hill, New York.Klockhaus, W., 1952. Fördergeschwindigkeit von Schwingrinnen und

Schwingsieben. Erdöl und Kohle 5, 493–495.Kluge, W., 1951. Neuzeitliche Siebmaschinen für die Aufbereitungs Technik. Erdöl

und Kohle 11, 705–711.Lynch, A.J., 1977. Mineral Crushing and Grinding Circuits, Their Simulation,

Optimization, Design and Control. Elsevier, New York.Meinel, A., Schubert, H., 1971. Principles of ne screening. Aufbereitungs Technik 3,

128–133.Meinel, A., Schubert, H., 1972. Über einige Zusammenhänge zwichen der

Einzelkorndynamik und der stochastichen Siebertheorie bei der Klassierungauf Stösselschwingsiebmaschinen. Aufbereitungs Technik 7, 408–416.

Nepomnjašc ˇ ij, E.A., 1962. Nektorye resul’taty teoretic ˇ eskogo analiza processagrochocˇ enija. Obogašc ˇ enie rud 5, 29–35.

Schlebusch, L., 1969. Dünnschichtsiebung und Systematik der direkterregten Siebe.Aufbereitungs Technik 7, 341–348.

Schranz, H., Bergholz, W., 1954. Die bewegungsvorgänge bei wurfsieben.Bergbauwissenschaften 8, 223–234.

Schubert, H. 1968. Aufbereitung fester mineralischer Rohstoffe, Band I, VEBDeutscher Verlag für Grundstofndustrie, Leipzig.

Standish, N., Meta, I.A., 1985. Some kinetic aspects of continuous screening. PowderTechnology 41, 165–171.

Standish, N., 1985. The kinetic of batch sieving. Powder Technology 41, 57–67.Standish, N., Bharadwaj, A.K., Hariri-Akbari, G., 1986. A study of the effect of

operating variables on the efciency of a vibrating screen. Powder Technology48, 161–172.

Subasinghe, G.K.N.S., Schaap, W., Kelly, E.G., 1989a. Modelling the screeningprocess-an empirical approach. Minerals Engineering 2 (2), 235–244.

Subasinghe, G.K.N.S., Schaap, W., Kelly, E.G., 1989b. Modelling the screeningprocess: a probabilistic approach. Powder Technology 59, 37–44.

Subasinghe, G.K.N.S., Schaap, W., Kelly, E.G., 1990. Modelling screening as a

conjugate rate process. International Journal of Mineral Processing 28 (3–4),289–300.


trumic rad.pdf

Documents