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Brazilian Journal of Chemical Engineering

On-line version ISSN 0104-6632

Braz. J. Chem. Eng. vol. 14 no. 3 São Paulo Sept. 1997 



G.A. da Silva

Escola Politécnica da USP - Departamento de Engenharia Química - Av. Prof. Luciano Gualberto - travessa 3,
380 05508-900 São Paulo SP - Brazil - Phone: (011) 818-5613 - Fax: (011) 211-3020 - E-mail:


(Received: April 14, 1997; Accepted: June 16, 1997)


Abstract: Bulk blending is a way to produce compound fertilizers in which the different nutrients are present in different particles. Due to the heterogeneous composition of bulk blends, particle segregation, when it occurs, is a serious problem to the fertilizer producer, as well as to the farmer.
Free fall is one of the main types of particle movement to promote segregation. The physical properties of the particles that potentially affect the tendency to segregate the most are size, density and shape. The main objective of this work is to study the influence of size and density of particles and distance of fall on segregation due to free fall. It was found that particle size is the most important physical characteristic to affect segregation; the greater the difference in particle size, the greater the segregation. Free fall is an important mechanical factor affecting segregation; the greater the distance of fall, the greater the segregation. No evidence of the influence of particle density on segregation was found.
Keywords: Bulk-blended, compound fertilizers, segregation by coning.



Particle segregation is the separation of particles having similar characteristics in the same region of a system of particulated solids. Generally, it occurs in all industrial processes in which solid particles are handled. Some examples are coal, ores, sand, cement, detergents, polimers, fertilizers, pharmaceutical compounds, cereals, etc.

In the particular case of the fertilizer industry, most of the final product is distributed as mixed granular fertilizers - fertilizers in granular form, containing at least two (usually three) of the primary nutrients (N, P, K). Mixed fertilizers may be either

  • compound fertilizers - obtained by chemical processing and comprising granules of a similar composition;
  • blended fertilizers - obtained by dry mixing of granular fertilizer materials and comprising granules of a heterogenous composition.

Segregation occurs in the handling of both types of mixed fertilizers, but it is a troublesome problem for blended fertilizers, due to their non-uniformity of composition. The lack of homogeneity may create problems for the blender in two ways: the product may fail to conform its guaranteed analysis and irregular field distribution causing spotty crop growth resulting in the dissatisfaction of the farmer.

The present paper is intended to contribute to an understanding of the segregation phenomenon in bulk-blended fertilizers.



For segregation to occur, two conditions are necessary:

  • relative movement between particles;
  • differences in one or more particle characteristics, which are sensitive to particle movement.

These characteristics are usually called segregation-inducing characteristics or properties.

The main segregation-inducing properties are particle size, particle density and particle shape (Hoffmeister et al., 1964; Johanson, 1978; Williams, 1976 and 1990). Angle of repose, particle resilience and friction coefficient have also been related to segregation (Williams, 1976 and Carson and Marinelli, 1994). Hoffmeister et al. (1964) and Williams (1990) point to particle size as the most important physical property to induce segregation.

The handling procedures that cause relative movement among particles and may induce segregation are

  • free fall or coning - as occurs when the particulate system is allowed to drop in to a conical sloping pile;
  • ballistic (Hoffmeister et al., 1964) or trajectory action (Williams, 1976) - as occurs when particles are projected horizontally, for example, as in the projection of fertilizer particles by fan-type spreaders;
  • vibration - as occurs when particles are subjected to vibrational energy (Hoffmeister et al., 1964; Williams, 1976 and 1990; Harris and Hildon, 1970 and Harwood, 1977).

It has been pointed out that coning is the most frequent and significant cause of segregation in fertilizer handling (Hoffemeister et al., 1964). It occurs in industrial operations as bag filling, feeding and discharging of bins, hoppers, etc.

The coning segregation modelling is hard due to the high number and complexity of the mechanical interactions to which the particles are exposed.

The movement of a particle submitted to coning comprises a maximum of three steps:

  • free fall in the air until the particle reaches the pile;
  • movement on the lateral surface of the pile; and
  • movement in the horizontal plan of the pile base.

If a particle of diameter D and density r is dropped from a height h in free fall, the kinetic energy it has when it reaches the pile is proportional to rD3h.

Johanson (1978) analysed the impact of the particles on the pile. He found that when the kinetic energy is sufficiently high, the impact can produce a crater on the top of the pile and the more resilient ones are caught in the crater. The particles with low kinetic energy and low resilience will bounce out to the pile.

Brown in Drahun and Bridgwater (1983) considers that the primary factor is the collisions between particles flowing onto the heap and those forming at the surface. As a consequence, small particle velocities will vary with in a wide spectrum, whereas the larger ones will vary with in a narrow interval.

Mathée (1967/1968) considers two kinds of motion on a slope: sliding and rolling. To evaluate the segregation he developed two models for each motion, using the conservation of energy. The parameter used to estimate segregation was l - the horizontal distance travelled by the particle after the slope. The equations obtained were

- for sliding only:

- for rolling only:


H = vertical distance between the point where the particle starts its motion slope down and the horizontal plane;
a = angle of the slope;
m = coefficient of friction
r = particle radius;
f = coefficient of rolling friction.

When there is only sliding, parameter l is independent of the size of the particle. Segregation would take place only for mixtures of components having different coefficients of friction. In the case of rolling only, it was found that segregation is also dependent on particle size.

Syskov and Lyan in Drahun and Bridgwater (1983) considered that the particles rolled down the inclined slope and that segregation was caused mainly by the roughness of the free surface.

The above studies indicate that particle size and density shall be the most important physical properties to induce coning segregation.

This paper describes an experimental study of the influence of particle size and density differences on the coning segregation of binary mixtures of fertilizers.



Two series of experiments were carried out in which the purpose was to evaluate the coning segregation of binary mixtures of particles of different sizes (serie I) and different densities (serie II).

The apparatus used was designed by Hoffmeister et al. (1964). The design was based on the segregation pattern observed in the quantitative measurement of segregation in conical piles. The observations show that compositions in a pile appeared to be constant along radial lines from the center of the bases of the pile. The apparatus is shown in Figure 1.


Figure 1: Apparatus for determination of the index of segregation.


The apparatus comprised a box 25 cm high, 35 cm long and 5 cm wide. The walls were transparent, colorless acrilic; the front wall was removable and the back wall was slotted to permit insertion of eight aluminum vanes at 10 degree intervals, attached to an acrilic plate.

The tests consisted of forming a section of a conical pile by pouring 450 g of a binary mixture (225 g of each component) into the box through a funnel located at a height h from the bottom of the box, forming a section of a conical pile. The vanes were then inserted in the slots by cutting the conical pile section in nine 10-degree angular segments. The apparatus was turned on its vaned plate, the removable wall was removed and the fraction of the mixture in each of the nine angular segments was removed. The two components (A and B) of each fraction were separated and weighed.

The materials used were three commercial granular fertilizers, each of which was separated into three granulometric fractions, giving a total of nine materials, as follows:

- DAP (diammonium phosphate) - particle density 1.43 g/cm3;
- MAP (monoammonium phosphate) - particle density 1.61 g/cm3; and
- KCl - particle density 1.94 g/cm3.

  • -6+8 - passed through a USS#6 sieve (3.353 mm) and retained in a USS #8 sieve (2.380 mm), with an apparent diameter of 2.87 mm;
  • -10+12 - passed through a USS#10 sieve (2.000 mm) and retained in a USS #12 sieve (1.679 mm), with an apparent diameter of 1.84 mm; and
  • -14+16 - passed through a USS#14 sieve (1.410 mm) and retained in a USS #16 sieve (1.191 mm), with an apparent diameter of 1.30 mm.

Using the nine materials (three different densities and three different particle sizes) two sets of binary mixtures were prepared:

  • set I - mixtures of materials with the same density and two different particle sizes;
  • set II - mixtures of materials with different densities and the same particle sizes.

Table 1 gives the composition of the eighteen binary mixtures used in the tests.

Each of the eighteen binary mixtures was tested for two fall heights: 30 cm and 50 cm. Each test condition was repeated five times.

In order to measure the segregation attained in each test, the author devised an index of segregation (IS) described elsewhere in the literature (Silva, 1995).

The proposed index of segregation is calculated from the mass fractions of components A (fAi) and B (fBi) and mixture (fTi) accumulated between angular segments 1 until i:


mAi = mass of component A in the angular segment i;
mBi = mass of component B in the angular segment i;
MAi = SmAi and MBi = SmBi

The definition of the index of segregation is illustrated in Figure 2, where are plotted the mass fractions fA and fB versus fT. Based in Figure 2a the index of segregation (IS) is defined as the ratio between the shadowed area and the quadrangle KLMN area.

The following equation is used to calculate the index of segregation:


Figure 2b illustrates the case of no segregation (fa = fB) and IS = 0. Figure 2c ilustrates the case of total segregation, when IS = 0.5.


Figure 2: Mass fractions of components A and B versus mass fraction of mixture.


Table 1: Composition of the binary mixtures used in the tests to evaluate coning segregation

Mixture no. Component A Component B DA/DB rA/rB
DA(mm) rA(g/cm3) DB(mm) rB(g/cm3)
I.1 2.87 1.94 1.30 1.94 2.21 1.00
I.2 2.87 1.94 1.84 1.94 1.56 1.00
I.3 1.84 1.94 1.30 1.94 1.42 1.00
I.4 2.87 1.61 1.30 1.61 2.21 1.00
I.5 2.87 1.61 1.84 1.61 1.56 1.00
I.6 1.84 1.61 1.30 1.61 1.42 1.00
I.7 2.87 1.43 1.30 1.43 2.21 1.00
I.8 2.87 1.43 1.84 1.43 1.56 1.00
I.9 1.84 1.43 1.30 1.43 1.42 1.00
II.1 2.87 1.94 2.87 1.43 1.00 1.36
II.2 2.87 1.94 2.87 1.61 1.00 1.20
II.3 2.87 1.61 2.87 1.43 1.00 1.13
II.4 1.84 1.94 1.84 1.43 1.00 1.36
II.5 1.84 1.94 1.84 1.61 1.00 1.20
II.6 1.84 1.61 1.84 1.43 1.00 1.13
II.7 1.30 1.94 1.30 1.43 1.00 1.36
II.8 1.30 1.94 1.30 1.61 1.00 1.20
II.9 1.30 1.61 1.30 1.43 1.00 1.13


Table 2: Results of coning segregation tests with a binary mixture of KCl with particle diameters of 2.87 cm (A) and 1.30 cm (B); h = 50 cm

Ang. seg. Mass of components in the binary mixture (g)
Run 1 Run 2 Run 3 Run 4 Run 5
1 125.73 30.96 125.64 31.06 125.60 31.09 125.50 31.20 125.46 31.24
2 79.87 20.51 79.76 20.54 79.84 20.58 79.80 20.61 79.78 20.60
3 51.46 37.86 51.58 37.75 51.45 38.05 51.63 37.80 51.58 37.95
4 45.64 34.54 45.65 34.51 45.89 34.31 45.27 34.45 45.66 34.54
5 32.40 38.51 32.43 38.47 32.45 38.47 32.02 38.49 32.28 38.65
6 22.20 56.69 22.19 56.67 21.90 56.99 22.16 56.74 22.20 56.71
7 18.39 61.94 18.36 61.99 18.47 62.44 18.41 61.95 18.40 62.00
8 18.36 73.65 18.77 73.25 18.84 73.06 18.79 72.94 18.77 73.26
9 50.65 88.93 50.62 89.01 50.50 88.13 50.47 89.18 50.41 89.22



Silva (1995) presents the results of the 180 experiments. Table 2 shows, as an example, the results of the test for a distance of fall of 50 cm, with a binary mixture of the following components:

- component A: KCl (r = 1.94 g/cm3) with a particle diameter of 2.87 cm and

- component B: Kcl (r = 1.94 g/cm3) with a particle diameter of 1.30 cm.

Tables 3 and 4 present the calculated indices of segregation, respectively, for the two sets (I and II) of experiments.


Table 3: Indices of segregation for binary mixtures of the same material but with different particle sizes

Test conditions Run no.
material R = DA/DB h (cm) 1 2 3 4 5
KCl 2.21 50 0.4601 0.4590 0.4582 0.4587 0.4588
MAP 0.4612 0.4613 0.4625 0.4596 0.4588
DAP 0.4567 0.4576 0.4594 0.4588 0.4591
KCl 1.56 50 0.4082 0.4090 0.4077 0.4075 0.4069
MAP 0.4069 0.3670 0.4064 0.4075 0.4108
DAP 0.4078 0.4074 0.4086 0.4071 0.4078
KCl 1.42 50 0.3583 0.3599 0.3593 0.3579 0.3572
MAP 0.3587 0.3573 0.3559 0.3585 0.3580
DAP 0.3587 0.3576 0.3598 0.3577 0.3582
KCl 2.21 30 0.3269 0.3275 0.3248 0.3275 0.3239
MAP 0.3242 0.3258 0.3243 0.3256 0.3251
DAP 0.3252 0.3254 0.3265 0.3269 0.3272
KCl 1.56 30 0.2828 0.2916 0.2910 0.2909 0.2901
MAP 0.2887 0.2893 0.2905 0.2908 0.2906
DAP 0.2889 0.2837 0.2876 0.2890 0.2904
KCl 1.42 30 0.2504 0.2498 0.2517 0.2521 0.2524
MAP 0.2525 0.2524 0.2543 0.2522 0.2517
DAP 0.2513 0.2523 0.2532 0.2513 0.2524


Table 4: Indices of segregation for binary mixtures of different materials with the same particle sizes

Test conditions Run no.
Part. size (mm) r = rA/rB h (cm) 1 2 3 4 5
2.87 1.36 50 0.0099 0.0091 0.0100 0.0100 0.0100
1.85 0.0076 0.0075 0.0092 0.0076 0.0081
1.30 0.0078 0.0075 0.0072 0.0075 0.0077
2.87 1.20 50 0.0094 0.0094 0.0094 0.0093 0.0094
1.85 0.0071 0.0072 0.0073 0.0072 0.0072
1.30 0.0075 0.0074 0.0076 0.0076 0.0073
2.87 1.13 50 0.0098 0.0099 0.0101 0.0100 0.0100
1.85 0.0081 0.0080 0.0080 0.0080 0.0080
1.30 0.0071 0.0069 0.0070 0.0072 0.0072
2.87 1.36 30 0.0095 0.0096 0.0095 0.0095 0.0095
1.85 0.0071 0.0069 0.0071 0.0070 0.0070
1.30 0.0057 0.0062 0.0060 0.0061 0.0062
2.87 1.20 30 0.0094 0.0085 0.0095 0.0095 0.0096
1.85 0.0065 0.0065 0.0065 0.0065 0.0064
1.30 0.0075 0.0077 0.0077 0.0075 0.0075
2.87 1.13 30 0.0094 0.0092 0.0091 0.0088 0.0091
1.85 0.0062 0.0062 0.0062 0.0062 0.0062
1.30 0.0057 0.0057 0.0057 0.0059 0.0053



Effect of Particle Size

To evaluate the effect of variation of the particle size diameter ratio on coning segregation an analysis of variance of the results showed in table 2 was done. Table 5 summarizes this analysis.

The comparison of the ratios of variance (F) with values in table D (BOX et al., 1978) indicates that the sources of variation, h (F = 14,335) and D (F = 2,604) and the interaction between them (F = 66.07) are highly significant; interaction hxRxr (F = 1.31) is not significant. For all the other sources of variation - r (F = 0.53); hxr (F = 0.42) and Dxr (F = 0.53) - with F < 1, it was found that the inverses of F are not significant either.

These findings lead to the following observations:

- differences in particle size in a mixture is an important factor in inducing coning segregation;
- the fall height is a mechanical factor that has a large influence on the coning segregation induced by particle size differences; and
- in this set of tests it was not possible to detect an influence of particle density on the coning segregation induced by differences in the particle size.

These results are shown in Figure 3, where the index of segregation is plotted against the particle diameters ratio; each line represents one distance of fall. It can be noted that the amount of segregation increases as the diameter ratio and distance of fall increase.

The coincidence of the curves for the three different densities for both distances of fall is clearly shown in Figure 3d. This observation is evidence of the small influence of density on the coning segregation induced by differences in particle size.


Effect of Particle Density

The evidence concerning the effect of particle density on coning segregation may lead to the following question:

"Doesn’t the difference in particle density really affect coning segregation or does the influence of difference in particle size hide it?"

The analysis of variance of the results of the set II tests may answer the question. Table 6 shows this analysis.

The comparison of the ratios of variance (F) (or of its inverses when F<1) corresponding to all sources of variation with values in table D (BOX et al., 1978) indicates that none are significant. In this condition two hypotheses arise:

a) no significant segregation was found in the tests with mixtures of particles of different densities, or

b) segregation was found, but all indices of segregation were statistically the same.

Considering that none of the sources of variation were significant, the mean and standard deviation of all indices obtained from the tests were calculated for this set of tests, which results:

mean = 0.008657

standard deviation = 0.007333

Considering that the index of segregation is, by definition, always positive and that the distribution is monocaudal, it results that the probability of the mean being other than zero is 25%. So, either the differences in particle density do not induce coning segregation or they induce a segregation so small that the index of segregation is of the same magnitude as the experimental error.

Figure 4 presents the results of this set of tests as a graph where the index of segregation is plotted against the densities ratio; each line corresponds to a fixed distance of fall.


Table 5: Analysis of variance of the test results for different particle size ratios

Source of variation Freedom degrees Sum of squares (x103) Average squares (x103) F
Distance of fall (h) 1 316.26 316.26 14,335
Particle size (D) 2 114.89 57.45 2,604
Density (r) 2 0.02 0.01 0.53
Interaction h x D 2 2.92 1.46 66.07
Interaction h x r 2 0.02 0.01 0.42
Interaction D x r 4 0.05 0.01 0.53
Interaction h x D x r 4 0.12 0.03 1.31
Residue 72 1.59 0.02 1.00
Total 89 435.86    



Figure 3: Index of segregation versus particle diameters ratio.


Table 6: Analysis of variance of the test results for density ratios

Source of variation Freedom degrees Sum of squares (x104) Average squares (x103) F
Distance of fall (h) 1 6.46 6.46 1.109
Particle size (D) 2 8.23 4.12 0.707
Density (r) 2 8.60 4.30 0.736
Interaction h x D 2 9.51 4.76 0.817
Interaction h x r 2 8.06 4.03 0.692
Interaction D x r 4 27.71 6.93 1,190
Interaction h x D x r 4 26.53 6.63 1,140
Residue 72 419.01 5.82 1,000
Total 89 514.11    


It is not possible to identify any tendency for a variation in the index of segregation with the ratio of densities for one of the three diameters. This probably means that the deviations found for any given condition are due to experimental errors. Comparison of indices of segregation calculated for both sets of tests leads to the observation that the figures for set II are smaller than those for set I. This fact, associated with the absence of a tendency towards variation, may lead to the first hypothesis, that no significant segregation is induced by differences in particle density.


Figure 4: Index of segregation versus densities ratio.


It can also be noted from Figure 4 that the indices of segregation for a diameter of 2.87 cm are higher than those for diameters of 1.84 cm and 1.30 cm which, by the way, are statistically the same. Further experiments would be needed to find a critical value of particle diameter, above which segregation induced by difference in particle density would increase.



  • The main factor to induce coning segregation is the difference in the particle sizes in the mixture; in other words, particle size is the main physical property to induce coning segregation.
  • There is a tendency to increase segregation by increasing the particle size ratio.
  • The distance of fall has a large influence on coning segregation induced by differences in particle size: the higher the value of h, the higher the index of segregation.
  • There is a synergy between difference in particles size and distance of fall, as far as coning segregation is concerned.
  • Particle density does not affect coning segregation induced by difference in particle size.
  • Differences in particle density do not induce coning segregation.



D Particle diameter

f Mass fraction

F Ratio of variance

h Distance of free fall

IS Index of segregation

m Mass in angular segment i

M Mass in the pile section

r Particle radius


i Angular segment

A Component A of the mixture

B Component B of the mixture

T Total mixture

Greek Letters

a Angle of the slope of a conical pile

m Coefficient of friction

r Particle density



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