International Journal of Minerals, Metallurgy and Materials Volume 19, Number 4, Apr 2012, Page 284 DOI: 10.1007/s12613-012-0552-z

Corresponding author: Mehdi Rahimi E-mail: rahimi410@aut.ac.ir © University of Science and Technology Beijing and Springer-Verlag Berlin Heidelberg 2012

Influence of the roughness and shape of quartz particles on their flotation kinetics

Mehdi Rahimi1), Fahimeh Dehghani1), Bahram Rezai1), and Mohammad Reza Aslani2)

1) Department of Mining and Metallurgical Engineering, Amirkabir University of Technology, Hafez Avenue, Tehran, Iran. 2) Department of Mining Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran. (Received: 15 June 2011; revised: 20 July 2011; accepted: 28 July 2011)

Abstract: Surface roughness and shape play an important role on the behavior of particles in various processes such as flotation. In this re-search, the influence of different grinding methods on the surface roughness and shape characteristics of quartz particles as well as the effect of these parameters on the flotation of the particles was investigated. The surface roughness of the particles was determined by measuring their specific surface area via the gas adsorption method. The shape characteristics of the particles were measured and calculated by images obtained by scanning electron microscopy via an image analysis system. The flotation kinetics was determined using a laboratory flotation cell. The results showed that the particles of rod mill products have higher roughness and elongation ratio and lower roundness than the parti-cles of ball mill products. The flotation kinetics constant of the particles increased with their surface roughness increasing. Particles with higher elongation and lower roundness indicated higher floatability. In addition, the influence of the surface roughness on the flotation kinet-ics was greater than that of shape parameters.

Keywords: flotation; kinetics; quartz; shape parameters; surface roughness

1. Introduction

In the flotation process, cumulative recovery as a function of time can be considered as flotation rate. Many empirical models were proposed by different researchers for flotation kinetics [1-2]. Flotation kinetics can be expressed as a first-order rate equation as follows [3-6]:

*[1 exp( )]R R kt= − − (1)

where t is the cumulative flotation time, R is the cumulative recovery after time t, R* is the maximum theoretical flota-tion recovery, and k is the rate or kinetics constant.

The plot of *

*ln R RR

⎡ ⎤−−⎢ ⎥⎣ ⎦

vs. time is a straight line, and

the slope of this line is the first-order rate constant.

The particle shape characteristic will affect the next processes in mineral processing operations such as flotation. The distribution of particle shape has great importance in many industries such as civil engineering, chemical engi-

neering, pharmaceutical industry, and mining [7]. While do-ing microflotation tests for quartz, calcite and barite particles, Hiçyilmaz and Ulusoy et al. observed that by decreasing the elongation of particles and increasing the roundness of parti-cles, the wettability degree increased [7-8]. Kursun and Ulu-soy showed that talc particles with more elongation and flat-ness had a positive effect on the column flotation recovery, while talc particles with more roundness and relative width had a negative effect on the column flotation recovery [9].

The surface roughness characteristic of particles will af-fect the next processes in mineral processing operations such as flotation [10]. Ducker et al.[11] studied the flotation behavior of smooth ballotini and ground ballotini. They ob-served that there were many differences between flotation results of these materials. They expressed these differences as being due to a difference in their surface roughness. Feng and Aldrich [12] studied the influence of wet and dry grinding methods on the flotation behavior of complex sul-phide ores. After being crushed, sulphide ore was ground by the wet rod mill and dry rod mill. The surface roughness of these products was compared by scanning electron micro-

M. Rahimi et al., Influence of the roughness and shape of quartz particles on their flotation kinetics 285

scope (SEM) images. It was observed that dry ground prod-ucts had higher surface roughness than wet ground products. It was also observed that dry ground products had higher flotation recovery than wet ground products [12]. Kra-sowska and Malysa [13] prepared hydrophobic Teflon plates with different surface roughness and measured bubble at-tachment time to the Teflon plates. They observed that the bubble attachment time was lower for the plates with higher surface roughness, and the bubble was attached during the first collision.

In the reported works by others, the influence of surface roughness on the wettability of particles was investigated by measuring the contact angle and stability of intervening liq-uid films [13]. In some works, the influence of surface roughness on the wettability was investigated with a Halli-mond tube [7-8].

In this paper, the influence of surface roughness and par-ticle shape on flotation kinetics was investigated, which has not been studied by the other investigators. Also in this pa-per, the time parameter is considered during recovery.

2. Experimental

2.1. Materials

The representative sample was obtained from Ghazvin Province, Iran. Chemical and mineralogical analyses were done by X-ray fluorescence (XRF) spectrometry and X-ray diffraction (XRD) analysis methods, and the results showed that this sample was pure enough and its chemical composi-tion is listed in Table 1.

Table 1. Chemical composition of the sample by the XRF technique wt%

SiO2 Al2O3 SO3 CaO Fe2O3 MgO K2O MnO

99.40 0.17 0.051 0.085 0.086 0.17 0.020 0.012 In this study, a collector with a trade name Armac C was

used for doing the flotation tests. Its manufacturer company is Akzo Nobel Surface Chemistry AB, and its chemical name is coco-alcyl-amine-acetate (C-N; R22-R34-R50). Its density is 880 kg/m3, and its solubility in water is good.

2.2. Grinding tests

The sample was ground by a jaw crusher, a cone crusher, and a roll crusher. The product size was from 841 to 2380 μm. Then the sample was ground by laboratory Denver ball and rod mills. The grinding by the ball mill was carried out using a laboratory mill of 184 mm in length and 200 mm in internal diameter. The ball milling time was 45 min, and the

sample weight was 1000 g. The grinding by the rod mill was carried out using a laboratory mill of 360 mm in length and 150 mm in internal diameter. The rod milling time was 55 min, and the sample weight was 1000 g.

2.3. Surface roughness measurement

Surface roughness is due to fluctuations around a surface solid [14]. In general, roughness is confined to changes in the surface representing movements of the surface larger than the interatomic distances. In Fig. 1, the real surface is XY, and AB represents the surface of a hypothetical solid of equal volume with a molecularly smooth surface. The sur-face roughness is defined by [15]

Area of the real surface XYSurface roughness=Area of the surface defined by AB

(2)

Fig. 1. A profile of solid surface [15].

Surface roughness is also calculated from the following equation [16]:

Surface roughness = A/A0 (3)

where A0 is the geometric surface area and is obtained from the assumption that mineral grains have regular geometric shapes, A is the specific surface area that is calculated by using the BET isotherm to gas adsorption data, and finally, this equation is obtained from Eq. (3) [16]:

BET

6DAρλ = (4)

where ABET is the BET specific surface area (m2/g), ρ is the grain density (g/cm3), D is the average grain diameter (µm), λ is the surface roughness (dimensionless). In this paper, BET specific surface area was measured by Micrometrics Gimini III 2375, USA.

2.4. Particle shape measurement

The characterization of shape parameters of the quartz particles was performed with an XL30-Philips SEM. Rep-resentative samples that were taken from 212-250, 125-150, and 75-106 µm size fractions of rod and ball mill products were used for SEM studies. The particles were covered with gold to provide the conductivity. Some images from differ-ent locals of the sample of each size fraction were taken by making proper magnification. Then the length (L), width (W), area (A) and perimeter (P) were measured using a

286 Int. J. Miner. Metall. Mater., Vol.19, No.4, Apr 2012

Clemex vision PE image analysis system for more than 100 particles in each representative sample. For the analysis, the particles at the corners of the frame and overlapped particles were disregarded. Thus, by using the measured length, width, area and perimeter, the elongation ratio (ER) and roundness (R) can be obtained from Eqs. (7) and (8) [8-9].

π4

LWA = (5)

1/ 2π 1.5( ) ( )2

P L W LW⎡ ⎤= + −⎣ ⎦ (6)

ER LW

= (7)

24πARP

= (8)

2.5. Flotation tests

Flotation tests were performed in a laboratory Denver machine (model D12), using a 1.5 L cell. The test conditions were 1000 r/min for rotor speed, 4 min for collector condi-tioning, 70 s for froth removal until the froth was barren of quartz. The sample weight for each test was 100 g, and the water volume was 1.2 L.

3. Results and discussion

For doing flotation kinetics tests, initial conditions in which the recovery is maximum were determined. Flotation

tests were done on the same samples with different collector dosages, and the maximum recovery was obtained in 1500 g collector dosage per ton of ore. Table 2 shows the results of these tests.

Table 2. Results of flotation tests for determining the op-timal collector dosage

Collector dosage / (g⋅t−1) 500 1000 1500 2000

Recovery / % 68.9150 94.9700 98.6025 97.2033 The appropriate pH value for quartz flotation kinetics

tests that maximize the recovery is 9 [17]. Therefore, flota-tion kinetics tests were done in the above conditions. All flotation kinetics tests were done in triplicate, and the re-producibility of the tests was good.

3.1. Results of particle shape measurement

From each size fraction, representative samples were prepared for SEM studies. The results are given in Table 3. Table 3 shows that when the particle size decreases, the par-ticle elongation ratio (ER) increases, and the particle round-ness (R) decreases because, in grinding, the larger particles are irregularly exposed to rounding. It can also be observed from Table 3 that for a particular size, rod mill products have higher elongation ratio (ER) and lower roundness (R) than ball mill products. These results were obtained using the Clemex vision PE image analysis system and Eqs. (7) and (8).

Table 3. Shape parameters of ball and rod mill products

Size / µm Mill type Area / µm² Perimeter / µm Length / µm Width / µm ER R Ball mill 100081.70 1164.601 447.462 284.785 1.571 0.927

212-250 Rod mill 99954.41 1165.911 449.004 282.916 1.590 0.924 Ball mill 28814.28 628.797 244.764 149.647 1.637 0.914

125-150 Rod mill 36878.87 713.332 278.784 168.418 1.655 0.911 Ball mill 10306.63 393.326 156.139 94.502 1.653 0.911

75-106 Rod mill 12743.04 420.887 165.557 97.982 1.690 0.903

3.2. Results of surface roughness measurement

The results of particle roughness are shown in Table 4. It can be observed that when the particle size decreases, the surface area for ball and rod mill products increases. Fur-thermore, for all size fractions, the surface area of rod mill

products is higher than that of ball mill products.

Table 4 shows that the surface roughness for both ball and rod mill products decreases when the particle size de-creases while the surface area increases. With size reduction, it is expected that the surface area and surface roughness of

Table 4. Results of specific surface area and surface roughness for products of each mill

Rod mill Ball mill

Fraction / µm Surface area / (m2⋅g−1) Surface roughness Fraction / µm Surface area / (m2⋅g−1) Surface roughness

212-250 0.3254 32.572 212-250 0.2857 28.598 125-150 0.3755 22.373 125-150 0.3231 19.253 75-106 0.4364 17.114 75-106 0.3958 15.5219

M. Rahimi et al., Influence of the roughness and shape of quartz particles on their flotation kinetics 287

particles increase. But according to Eq. (4), the surface roughness depends on both surface area and particle size. In this case, with a reduction in particle size, the surface area increases, but the influence of size reduction is higher than the increase of surface area. It can also be observed from Table 4 that for a particular size, rod mill products have higher surface roughness than ball mill products.

3.3. Results of flotation kinetics tests

For successful flotation, the collision and attachment of bubbles to particles must occur. For this reason, the inter-vening liquid film between bubbles and particles must rup-ture. The stability of this intervening liquid film depends on surface properties of the solid. For hydrophobic solids, this intervening liquid film has less stability, and the measured contact angle is higher [13].

To investigate the effect of surface roughness and particle shape on flotation kinetics, the flotation kinetics constant of ball and rod mill products were measured. Tables 5, 6, and 7 show these results. It can be seen from Tables 5, 6, and 7 that for a particular size, the rod mill products, which have higher surface roughness and higher elongation ratio than the ball mill products, have faster flotation kinetics.

Representative samples were taken every 10 s in the froth removal stage for each size fraction. SEM studies were per-formed and their shape parameters were obtained. The re-sults are shown in Tables 8, 9, and 10.

It can be seen from Tables 8, 9, and 10 that the particles with higher elongation ratio and lower roundness have faster flotation kinetics. Therefore, it can be concluded from

Table 5. Flotation recovery in different time for the 212-250 µm fraction of ball and rod mill products

Ball mill Rod mill Time /

s Recovery /

% Cumulative recovery / %

Time /

s Recovery /

% Cumulative recovery / %

10 60.4606 60.4606 10 61.3314 61.3314 20 28.5491 89.0097 20 31.0286 92.3600 30 7.8803 96.8900 30 4.8105 97.1705 40 1.9921 98.8821 40 1.7522 98.9227 50 0.3446 99.2267 50 0.5874 99.5101 60 0.2696 99.4963 60 0.2297 99.7398 70 0.2015 99.6978 70 0.1148 99.8546

*

*ln R R kx

R−

− = *

*ln R R kx

R−

− =

k = 6.341225 ± 0.02921 (min−1) k = 6.7503072 ± 0.0198 (min−1)2 0.97941r = 99253.02 =r

Table 6. Flotation recovery in different time for the 125-150 µm fraction of ball and rod mill products.

Ball mill Rod mill

Time / s

Recovery / %

Cumulative recovery / %

Time /

s Recovery /

% Cumulative

recovery / %)

10 50.5659 50.5659 10 60.2500 60.2500 20 33.1001 83.6660 20 28.7500 89.0000 30 9.1579 92.8239 30 6.6776 95.6776 40 4.2804 97.1043 40 2.0409 97.7185 50 1.6891 98.7934 50 1.1564 98.8749 60 0.5513 99.3447 60 0.4283 99.3032 70 0.4513 99.7960 70 0.2367 99.5399

*

*ln R R kx

R−

− = *

*ln R R kx

R−

− =

k = 5.61373 ± 0.01869 (min−1) k = 5.9315 ± 0.0109 (min−1) 2 0.9983128r = 2 0.994811r =

Table 7. Flotation recovery in different times for the 75-106 µm fraction of ball and rod mill products

Ball Mill Rod Mill

Time / s

Recovery / %

Cumulative recovery / %

Time /

s Recovery /

% Cumulative recovery / %

10 53.3678 53.3678 10 52.0000 52.0000 20 29.2014 82.5692 20 34.0000 86.0000 30 8.9212 91.4904 30 6.4720 92.4720 40 3.9416 95.4320 40 4.0511 96.5231 50 2.6323 98.0643 50 1.4789 98.0020 60 0.7092 98.7735 60 1.0083 99.0103 70 0.5654 99.3389 70 0.4027 99.4130

*

*ln R R kx

R−

− = *

*ln R R kx

R−

− =

k = 5.2179 ± 0.0198 (min−1) k = 5.39547 ± 0.01756 (min−1)2 0.99629r = 2 0.990476r =

Table 8. Shape parameters for the 212-250 µm fraction after flotation test

Ball mill Rod mill

Time / s

Elongation ratio

Roundness Time /

s Elongation

ratio Roundness

10 1.595595 0.922566 10 1.595975 0.92249120 1.56298 0.928924 20 1.584838 0.92467330 1.526328 0.935946 30 1.565938 0.92835240 1.521309 0.936895 40 1.534541 0.93438550 1.511688 0.938708 50 1.528407 0.93555160 1.491441 0.942484 60 1.521866 0.93679170 1.48249 0.944136 70 1.507229 0.939542

288 Int. J. Miner. Metall. Mater., Vol.19, No.4, Apr 2012

Table 9. Shape parameters for the 125-150 µm fraction after flotation test

Ball mill Rod mill

Time / s

Elongation ratio

Roundness Time /

s Elongation

ratio Roundness

10 1.645169 0.910935 10 1.663943 0.908973

20 1.623847 0.916986 20 1.647288 0.912313

30 1.612447 0.919245 30 1.634369 0.914893

40 1.607341 0.920253 40 1.588812 0.923896

50 1.597729 0.922146 50 1.575561 0.926483

60 1.572557 0.927067 60 1.550011 0.931425

70 1.532370 0.934798 70 1.530419 0.935169

Table 10. Shape parameters for the 75-106 µm fraction after flotation test

Ball mill Rod mill

Time / s

Elongation ratio

Roundness Time /

s Elongation

ratio Roundness

10 1.656907 0.910386 10 1.698583 0.901978

20 1.649696 0.911831 20 1.680706 0.905595

30 1.648898 0.911991 30 1.678303 0.90608

40 1.646388 0.912493 40 1.677896 0.906162

50 1.643434 0.913084 50 1.651776 0.911414

60 1.642510 0.913269 60 1.634382 0.91489

70 1.629151 0.915932 70 1.612505 0.919233

Tables 5-10 that the particles with higher surface roughness and higher elongation ratio have faster flotation kinetics. These results are in agreement with those reported by Hiçy-ilmaz et al. [7], Feng and Aldrich [12], and Krasowska et al. [13]. It can be seen from Table 3 that when the particle size decreases, the elongation ratio (ER) for ball and rod mill products increases. Therefore, with size reduction, it is ex-pected that the flotation kinetics constant of particles in-creases, but Tables 5, 6, and 7 show that when the particle size decreases, the flotation kinetics constant of particles decreases. Also, it can be seen from Table 4 that when parti-cle size decreases, the surface roughness for ball and rod mill products decreases. Therefore, it can be concluded that the effect of surface roughness on flotation kinetics is greater than the effect of particle shape parameters. There-fore, when the quartz particle size decreases, the flotation kinetics constant for ball and rod mill products decreases because the effect of surface roughness is greater than that of particle shape parameters.

4. Conclusions

Surface roughness and particle shape are physical proper-ties that can be effective in mining industries. Surface roughness for different fractions of ball and rod mill prod-ucts was determined by measuring the BET specific surface area. The shape parameters for different fractions of ball and rod mill products were studied by scanning electron mi-croscopy. Shape characteristics of particles were measured and calculated by images obtained by scanning electron mi-croscopy via an image analysis system. Experimental results for quartz particles showed that the surface roughness de-creases with a reduction of particle size. For a particular size, the rod mill products have higher surface roughness than the ball mill products. When particle size decreases, the particle elongation ratio increases and the particle roundness de-creases. For a particular size, the rod mill products have higher elongation ratio and lower roundness than the ball mill products. Results of flotation kinetics tests for the rod and ball mill products show that for a particular size, the rod mill products that have higher surface roughness and higher elongation ratio than the ball mill products have faster flota-tion kinetics. The particles with higher elongation ratio and lower roundness have faster flotation kinetics. When the quartz particle size decreases, the flotation kinetics constant for ball and rod mill products decreases because the effect of surface roughness is greater than that of particle shape pa-rameters.

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