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Mechanism of action of grinding aids in comminution
229
Powder Technology, 71 (1992) 229-237
Mechanism
of action of grinding aids in comminution
Sureshan K. Moothedath
and S. C. Ahluwalia
National Council for Cement and Building Materials, New Delhi-110049 (India) (Received November 26, 1990; in revised form January 9, 1992)
Abstract In an attempt to delineate the mechanism of action of grinding aids in comminution the effect of these additives on the sub-processes of grinding, viz breakage and attrition, has been studied by isolating each one of them through specially designed experimentsin a laboratory ball mill. Also, the flow characteristics of limestone powder produced with and without grinding aids have been studied. While these additives cause positive effects on attrition and flow of the powder, the breakage rate function and breakage distribution function of (- 10 + 14) mesh material are not affected by them. The implications of these results on the mechanism of action of grinding aids in comminution has been discussed.
Introduction Grinding aids generally improve grinding efficiency, bring down the limit of grinding, prevent cold welding during metal grinding and reduce viscosity in wet grinding [l-3]. These additives, reportedly used by Bessemer for the first time in the production of metal powders, are presently being used in various industries where fine particles are produced by grinding, viz. cement, mineral, pigment, metal powder, etc. A survey of the published work in this area reveals that the use of grinding aids has preceded a proper understanding of the mode of action of these additives. Different researchers have different views about the mechanism. The mechanisms proposed by various researchers are discussed by Rose and Sullivan [l] and subsequently by many other authors [4-111. The results and explanations often become unrealistic and unconvincing in the absence of appropriate data. As grinding involves a few sub-processes, viz. breakage, attrition, classification and transport of the material in the mill, it is not possible to pinpoint the cause behind any effect, from the normal type of data on the fineness vs. time of grinding. A clear understanding of the mechanism of action of grinding aids calls for an indepth study on the effect of these additives on the individual components of the grinding and the contributory forces such as reduction in surface energy, changes in the attractive forces between particles, etc. The results of the experiments carried out in NCB on the effect of grinding aids on the individual components of grinding and its impli-
0032-5910192/$5.00
cations on the mechanism of action of grinding aids are presented in this paper.
Experimental
A schematic diagram of the new experimental set up designed and fabricated for this study is given in Fig. 1. This consists of a laboratory ball mill, 22 cm in diameter and 23 cm in length, resting on two rubberised rollers. The driving shaft is welded on one side of the mill and a flexible coupling connects it to the main shaft. This arrangement is made to reduce the loss of energy due to the slip between the mill and rubber rollers in conventional roller driven mills. The mill is driven by a three phase dynodrive motor through a belt drive for reducing the speed. The speed of the mill can be varied in the range of O-100 ‘pm. The input energy is measured using a 3-phase energy meter. The experiments were carried out on limestone, and laboratory grade triethanolamine (TEA); oleic acid and glycerol were used as the grinding aids. Density of the limestone was 2.73 g crne3 and the main constituents were CaO: 54.39%, LOI: 43.37%, SiO,: 0.85%, Fe,O,: 0.23%, A1203: 0.15% and MgO: 0.97%. The procedure of experimentation was suitably modified depending upon the specific sub-process under study. The procedure in each case is explained separately along with the results.
0 1992 - Elsevier Sequoia. All rights reserved
230
Fig. 1. Experimental set-up for a laboratory ball will. All dimensions are in mn~
Results The experiments in this study were designed so as to get information on the effect of grinding aids on the individual sub-processes in grinding by isolating each one of them. The operating variables are set in such a way that the size reduction takes place mainly by one mechanism, namely attrition or breakage. The results of the study on attrition, breakage, and transport characteristics are given in this section. In the light of these results the mechanism of action of grinding aids is briefly discussed in the following sections. Attrition Normally, in ball mills the size reduction takes place by way of breakage and attrition. A pictorial representation of breakage and attrition is given in ‘Fig. 2, which clearly shows the difference between these two mechanisms of size reduction. In this particular set of experiments which is aimed at the effect of grinding aids on attrition, necessary modifications were carried out in order to reduce the possibility of breakage of particles. l&15 mm ceramic balls were used in place of steel balls and the mill was run at 35 r-pm or less.
Fig. 2. Pictorial representation of breakage and attrition.
This corresponds to 38% of the critical speed of the mill. Under suchconditions size reduction due to impact is expected to be negligible. The attrition experiments were carried out on (- lO+ 14) mesh limestone and the grinding aids used were triethanolamine and oleic acid. When TEA was used the mill was run with 3 kg of material at 22 rpm for 2 h and as there was not much fines production, due to sliding, the speed was then increased to 35 r-pm. The whole set of experiments with TEA were carried out in the same manner with 3.5 kg of ceramic balls as grinding media. But when oleic acid was used, the
231
speed was kept at 35 r-pm from the very beginning and only 1.8 kg of ceramic balls were used as the grinding media. The procedure involved grinding a fixed quantity of the material for different durations of time and analysing the size distribution using test sieves. As the size reduction due to impact breakage is avoided in these experiments the change in the size distribution is expected to be very slow. Also, the type of distribution would be entirely different from that of the normal breakage. Figure 3 is a typical log-log plot of the cumulative undersize 11s.particle size for different durations of grinding. The additive concentrations used in this case are 0.0% and 0.03%. As the grinding time increases there is a gradual increase in the quantity of fines (- 63 pm material) without much of increase of material in the intermediate classes. The curves are nearly horizontal in the region between 63 pm and 200 pm, indicating that there is not much material in this region. The trend is similar both with and without grinding aid, but the amount of -63 pm material produced is more when the grinding aid is used. For a clearer understanding the differential distribution curves of 0.03% are plotted, where the frequency density is plotted against the particle size. These distributions are clearly bimodal with a very low frequency density in the intermediate classes. Breakage is characterised by formation of daughter fragments of l/2 to l/10 times that of the parent particles whereas attrition produces very fine particles directly without going through the intermediate stages. Hence,
0.02
0.05
0.1
SIZE,
0.2
0.5
1.0
2.0
mm
Fig. 3. Cumulative undersize distribution curves at different durations of grinding, (- .- Feed, without additives, --TEA 0.03%).
the main manifestation of attrition is the appearance of a bimodal size distribution, which is clearly visible in Fig. 4. In order to confirm the dominance of the attrition mechanism, the ‘ Erosion Index’, which was recently proposed by PopplewelI and Peleg [12], has been calculated for all the distributions. Erosion Index, IE, is defined as the ratio between the fines accumulation and the size reduction of the coarse fraction, and is given by I
W(t) - WO)lvm) -&I E [I- JqO>l[x,(O)-Xc(t)1 =
(1)
where W(t) = weight fraction of fines at time t, XC(t) = mode of coarse fraction at time t, and X, = mode of fines. By virtue of the definition of this index, breakage will be dominant if IE < 1 and attrition will be dominant if &> 1. The indices were calculated for the distribution curves in Fig. 4, at 7 and 10 h of grinding with the distribution curve at 4 h as reference curve. The indices were found to be 1.72 and 1.95, which is a clear indication of the predominance of attrition in these experiments. Similar observations were made at other concentrations of grinding aid and also in the absence of grinding aid. The Erosion Index values in these cases were in the range of 1.3-2.5. The trend was also found to be the same in the case of oleic acid. In this case 2 kg of limestone was ground at 35 r-pm for 3, 6 and 9 h with 1.8 kg of 10-15 mm ceramic balls as the grinding media. The erosion indices for the distribution at 6 and 9 h of grinding are 2.97 and 3.1, which confirms that, in this case also, size reduction due to attrition is more predominant. The values of all the erosion indices are given in Table 1. Figure 5 is a plot of fines produced VS. grinding aid (TEA) concentration for different durations of grinding. It may be noted that the fines produced increase with the grinding aid concentration up to about 0.03% and then start decreasing. This shows that the grinding aid helps attrition if added in very small quantities, but a reversal takes place at larger concentrations. Figure 6 is a plot of fines produced VS. grinding time when oleic acid was used as the grinding aid. It can be seen that the presence of oleic acid improves the production of fines considerably. An increase of about 36% is noticed after 6 h of grinding, which subsequently reduces to about 20% after 9 h of grinding. Breakage This particular set of experiments were aimed at the effect of grinding aids on breakage characteristics of limestone. Any effect on breakage will clearly show up in the values of breakage rate function or breakage distribution function. The experiments for determi-
232
SIZE,
Fig. 4. Differential
TABLE grinding Grinding time (h)
7 10 A: B: c: D:
distribution
1. Erosion aids
curves at different
index values in the presence
Erosion
mm
durations
of grinding,
(TEA, 0.03%; 0, 4 h; Cl, 7 h; A, 10 h).
of different
index
A
B
C
D
2.00 1.37
1.72 1.95
2.31 2.54
3.10 2.97
without additives 0.03% TEA 0.05% TEA 0.08% oleic acid.
nation of these functions involve short duration grinding for 0.25, 0.5, 1, 2 and 4 min. Since attrition is comparatively a very slow process the effect of the same on such short duration experiments is expected to be negligible. The experiments for the determination of breakage functions were also carried out on (- lO+ 14) mesh limestone and the grinding aids used were TEA, glycerol, and oleic acid. The experimental procedure involved grinding of 3 kg of limestone for short durations, mentioned above, at a ball filling of 50% and obtaining the particle size distribution using standard test sieves. Equal weights of 1 in and 3/4 in steel balls were used as grinding media when TEA was used as grinding aid, and only 1 in balls were used when glycerol and oleic acid were used. Breakage rate function Breakage rate function, ki, quantifies the rate at which the particles are undergoing breakage. This is
01
0
I
I
I
0.05
0.1
0.15
I
0.2
GRINDING AID CONCENTRATION. %
Fig. 5. Effect of TEA concentration 0, 7 h; A, 10 h).
of
fines produced, (0, 4 h;
normally determined as the slope of the straight line obtained by plotting log[mi(t)] vs. time for materials that follow first order grinding where mi(t) is the mass fraction of material in the size class i [13]. Figure 7 is such a plot for the grinding of (- lO+ 14) mesh limestone with and without triethanolamine. It is clear from the plot that the presence of 0.1 wt.% of TEA has not affected the breakage rate function, as the slope remains 0.3 in both the cases. Similar observations were made at 0.2% and in the case of all the other grinding aids also tried. The plots between lOg[mi(t)]
233
z g-+
o.o!i-
Es r-, 5
tE_
0.02-
0.01
0
2
4
6
I 8
GRINGINGTltlE,min
Fig. 8. Determination of breakage rate function mesh limestone, (0, 0.08% glycerol; 0, 0.0%).
of -lo+14
0 3
0
6
TIME,
9
h
Fig. 6. Effect of oleic acid on the quantity (0, 0.08% oleic acid; Cl, 0.0%).
of fines produced,
0
2
4
6
8
GRINDING TIME. min
Fig. 9. Determination of breakage rate function mesh limestone, (0, 0.1% oleic acid; q, 0.0%).
of - lO+ 14
breakage from class j. The breakage distribution function, in this case, is represented by the following equation B,,j=~(xi-~/~j)“+(l-~)(~i-,/~j)a 0.02 0.01.
0
I
2
I
4
I 6
I 8
_
GRWDING TIME. min
Fig. 7. Determination of breakage rate function mesh limestone, (0, 0.1% TEA, Cl, 0.0%).
and t for oleic acid 8 and 9. the same plots.
of - lO+ 14
the determination of ki, when glycerol and were used as grinding aids, are given in Figs. The breakage rate function happens to be with and without grinding aids in all the
Breakage distribution function
Breakage distribution function b quantifies the fraction of the material that goes to be size class i after
(2)
where Bipj=Z.It_ibk ,j, Xi_ I and xj are sizes of the classes i- 1 and j, and 4, cy and /3 are constants. Normally, Bi,j’S are calculated from zero order production plots [13] or by a back calculation method [14, 151. In this investigation, a back-calculation method was adopted and the constants 4, (Yand p were determined using a computer programme in which an iterative optimisation procedure is made use of for the prediction of the grinding data. The programme consists of a module which calculates the product distribution using the batch mill equation with given parameters of breakage rate function {ki= k,(xi/X,)“} and breakage distribution function. These parameters are optimised by minimising the square of the difference between the calculated and experimental values, using Powell’s algorithm [16]. The optimum values of these parameters for different
234
conditions of grinding are given in Tables 2a and 2b. It can be seen that the values of the constants are more or less same when the grinding was done with and without grinding aids. Flow characteristics Three parameters were measured for assessing the changes in flow behaviour of limestone powder prepared using grinding aids. The ground limestone powder from the experiments on breakage characteristics were used for this purpose. The experimental set-up consisted of a hopper which can carry about 3 kg of limestone. This was provided with an arrangement to change the hole size at the bottom as required (3, 6, 9, 12, 15, 18, 25 mm) for finding out the minimum size of the hole for a smooth flow of the material. The three parameters measured were: (1) The minimum size of the hole required for a smooth flow of the material (critical hole size); (2) The time required for emptying 3 kg of material from the hopper using a particular hole size at the bottom (T,); (3) The angle of repose. When the material flows from the hopper it is allowed to form a cone on a horizontal surface. The angle of repose which is a characteristic of the material flowability is measured from this cone. It is known that the material flowability increases with decrease in the angle of repose. The experimental data on the flow characteristics obtained at different conditions are given in Tables 3 and 4. No change was noticed in the critical hole size in the presence of grinding aids. The hole size was 9 mm in all the cases studied. The material after 8 min of grinding was not flowing uniformly even at a hole size of 25 mm, except when oleic acid was used, where TABLE 2a. Values of breakage
distribution
parameters
Parameter
A
B
z a!
0.22 3.00 0.35
0.22 3.00 0.34
Grinding time (min)
0.5 1.0 2.0 4.0 8.0 A: B: C: D:
Angle of repose A
B
C
D
40 40-41 40-41 4142 -
3E-39 38-39 37-39 37-40 -
38-39 36-37 37 34-36 35-37
38 38-39 37-38 38-40 -
without additives 0.1% TEA 0.1% oleic acid 0.1% glycerol.
TABLE aids
4. Values of TF in the presence
Grinding time (min)
0.5
1.0 2.0 4.0 8.0 A: B: C: D:
(degrees)
of different
grinding
TF 6)
A
B
C
D
348 287 282 250 -
294 274 259 227 -
327 270 248 227 246
314 301 277 230 -
without additives 0.1% TEA 0.1% oleic acid 0.08% glycerol.
it was flowing smoothly through even the 9 mm hole. But there is a decrease in the angle of repose in the presence of grinding aids for all the grinding aids studied, as can be seen from Table 3. The change is of the order of l-5 degrees. There is a considerable improvement in the flowability of the material when grinding aids are used. This effect is clearly seen in the time required for the flow of 3 kg material (TF), given in Table 4. The reduction in TF is in the range of 17-54 s which amounts to 616% of the time of flow.
Discussion
A: without additive B: 0.1% TEA. TABLE 2b. Values of breakage
distribution
parameters
Parameter
A
B
C
a
0.20 4.10 0.35
0.20 4.20 0.36
0.21 4.20 0.35
A: without additives B: 0.1% oleic acid C: 0.1% glycerol.
TABLE 3. Values of angles of repose in the presence of different grinding aids
Attrition The grinding aids are adsorbed on the surface of the particles and this may cause many changes in the surface properties of the material. Rehbinder found that the surface hardness of the materials and their resistance to scratching with a fine point changes in the presence of grinding aids [17]. It was shown that there is a progressive decrease in the resistance to scratching with increasing quantities of additives adsorbed on the surface of the body, there being a close
235
correlation between the resistance to scratching and the adsorption isotherm. The minimum resistance to abrasion was observed under conditions of complete adsorption. Attrition is a surface phenomenon and the reduction in surface hardness would definitely help this process. This explains the increase in the quantity of fines with the increase in grinding aid concentration in Fig. 5. Also, this correlates well with the observations of Bouden and Tabor [18], where a reduction in wear resistance was observed in the presence of certain chemicals. Another surface property that is affected by the grinding aid is the coefficient of friction. Generally all the grinding aids have a lubricating property which causes a substantial reduction in the coefficient of friction on the particle surfaces, if added in sufficient quantities [19]. This is of utmost importance as this will have a direct impact on attrition. At high concentrations the decrease in coefficient of friction may outweigh the advantages gained by the reduction in attrition resistance as seen in the present investigation (Fig. 4). Breakage and flowability
In an ordinary ball mill the size reduction results from the fruitful interactions between the balls and the particles. Hence, the rate of grinding would be proportional to the frequency of interaction and the efficiency with which interactions result in breakage. Consequently, anything that improves the frequency of interaction and the efficiency is expected to improve the grinding. The frequency of interaction is influenced, among other things, by the speed of the mill, the number of balls, number of particles and the flowability of the material. The most relevent here in this investigation is the flowability. The flowability of the material determines how well the particles are carried to the grinding zone, thus increasing the probability of capture of the particles between the balls or between the wall and balls. The experiments on the flow characteristics have shown that the grinding aids improve the flowability considerably and this is certainly contributing to a better grinding. The efficiency with which the interactions result in breakage depends on the state of agglomeration or dispersion of the particles, force of collision, etc. It is known that the agglomerated particles reduce the probability of breakage due to the cushioning effect they provide during the collision. Qualitative examination of the powder in these experiments showed that the powder is at a highly dispersed state in the presence of grinding aids. This is reflected in the better flow characteristics which result from the dispersed state of the powder.
Breakage involves crack initiation and propagation under the action of stresses generated by external forces. The critical stress of crack propagation is given by Griffith’s equation [ll], where the stress is calculated based on the values of Young’s modulus, the surface energy and crack length. On adsorption of a gas or vapour the critical stress decreases as there is a reduction in surface energy [20]. Quantitatively, (Ilo-VI)’
$dhP 0
where u, and u1 are surface energy values in vacuum and in the presence of a gas respectively, R is gas constant, T is the temperature in K, M is the molecular weight of the adsorbate, S is the surface area, x is the adsorption in grams per gram of solid and P is the pressure. In practice, the reduction in critical stress is observed only at lower crack propagation velocities [21, 221. Usually in grinding operation the crack propagation velocities are quite high and at these velocities the molecules of the grinding aids may not be able to diffuse down to the crack tip [ll]. This may be the reason why there is no change in the breakage parameters in the present investigation. In the similar lines Schiebe et al. [23] have reported that there was no change in the value of Bond’s Work Index in presence of polyhydric alcohol. Interparticle forces
Though the authors have not done any work on interparticle forces in the present study, this is included in the discussion because of its importance and its relevance to this paper. When the particles become very fine during grinding they tend to agglomerate and form bigger particles under the influence of various forces. The dominant interaction force between particles in a powder is the Van der Waals force of attraction [24]. In addition to this, other attraction forces, such as capillary and electrostatic forces, may also operate in a gaseous environment, though they are much smaller than Van der Waals force. It is seen that Van der Waals force is considerable only when particles are very close (0.2-l nm) and when the distance exceeds a few microns it becomes negligible. Also, simple model calculations have shown that depending on the particle density, porosity and surface roughness, these cohesive forces will only be noticeable for particles a few ,microns in diameter or smaller. Any means to enlarge the separation distance will substantially reduce adhesive forces. Factors affecting the particle separation are roughening of the surface and the use of spacers. Spacers can be molecules adsorbed onto the interacting particles, and this explains
236
the reduction in agglomeration presence of grinding aids.
and ball coating in
Comments on the mechanism of action of grinding aids Based on the results of the experimental investigation given and the subsequent discussion, the following points can be made on the mechanism of action of grinding aids. Rehbinder suggested that the adsorption of the additives on the surface of the particles made crack propagation easier by way of reduction in surface energy. Theoretically, a reduction in the surface energy and a consequent reduction in the critical stress of crack propagation is expected in the presence of grinding aids. But in the normal grinding practice the crack propagation velocities are very high and the grinding aids cannot diffuse down to the crack tips at such high velocities. Hence, an increase in the impact breakage rate is unlikely and this is found to be true as per the experimental results on the determination of breakage rate function. Bond was of the opinion that the prevention of ball coating is mainly responsible for all the positive effects. Certainly, the grinding aids reduce/delay the ball coating and agglomeration of the fine particles, but that does not seem to be the only mechanism causing all the positive effects. Contrary to Bond’s conclusions it is found that very small quantities of these additives can cause reduction or prevention of ball coating without any considerable improvement in the rate of grinding. Addition of slightly larger quantities of grinding aids caused a remarkable increase in the rate of grinding, indicating that prevention of ball coating is not the only mechanism that is responsible for all the effects. Surface hardness of the materials and their resistance to scratching with a fine point changes when grinding aids are adsorbed on the surfaces. Attrition being a surface phenomenon, the reduction in the surface hardness will definitely help this process. The experimental results on attrition characteristics reveal that grinding aids improve attrition if added in small quantities, but a reversal takes place at higher concentrations, probably because of lubrication. Flowability of the material plays a very important role in the transport of the material inside the mill. It is found that the flowability improves in the presence of grinding aids, thus increasing the possibility of the particles to reach the grinding zone, which in turn increases the probability of capture of the particles between the grinding media. Agglomeration of fine particles, which is caused mainly due to Van der Waals forces, is prevented or
reduced when a grinding aid is adsorbed on the particles’ surface. In the absence of agglomeration the grinding can proceed to a finer state as the limit of grinding is also shifted towards the finer region. The energy that is used for breaking agglomerates will now be used for breaking individual particles. The reduction in attractive forces causes better dispersion of the particles, which results in easier flow, reduction or prevention of ball and wall coating and a better classification efficiency.
Conclusions A method has been developed for isolating the attrition mechanism in ball milling. Small amounts of grinding aids are found to assist the attrition of limestone whereas excess quantities of the same result in a reversal. No change in the impact breakage rate of ( - 10 + 14) mesh limestone was noticed in the presence of grinding aids. A clear improvement in the flow characteristics was noticed in the presence of all the grinding aids tried. Rehbinder’s theory of easier crack propagation by way of reduction in surface energy due to the adsorption of grinding aids does not hold good in these experiments. In addition to Bond’s hypothesis of reduction in ball and mill wall coating and consequent improvement in the grinding performance, increase in the rate of attrition, improvement in the flowability and prevention or reduction of the fine particle aggregation in the presence of grinding aids cause the positive effects in grinding.
Acknowledgements The authors wish to thankfully acknowledge the help from Sh. A. S. R. Vijayakumar in the design of the experimental set-up and from Sh. R. L. Bhagwat in carrying out the experiments for this research work. This paper is based on the results of an R and D project of the National Council for Cement and Building Materials and is published with the permission of the Director of the Council.
List of symbols
bi.j Bi.j IE ki
breakage distribution function cumulative breakage distribution function erosion index breakage rate function of material in the size class i
237
30)
M
P R s t T TF
mass fraction of material in size class i at time t molecular weight of adsorbate pressure gas constant surface area of the powder time of grinding temperature in K time required for emptying 3 kg of material from the hopper weight fraction of fines at time t mode of coarse fraction at time t mode of fines
5 6 7 8 9 10 11 12 13 14 15
Greek letters (Y,p, #J constants in the equation for B surface energy v
16 17 18
References 1 H. E. Rose and R. M. E. Sullivan, A Treatise on the Internal Mechanics of Ball, Tube and Rod Mills, Constable, London, 1958, pp. 236-251. 2 D. W. Fuerstenau, K. S. Venkataraman and B. V. Velamakanni, Znt. J. Min. Process, 15 (1985) 251. 3 M. K. Sureshan, R. Vedaraman and M. Ramanujam, Partic. Sci. Technol., 1 (1983) 55. 4 F. J. Mardulier, Proc. ASTM, 61 (1961) 1078.
19 20 21 22 23 24
K. Shonert, Trans. Sot. Min. Eng. AZME, 252 (1972) 21. H. Rumph, Aufbereit. Tech., 14 (1973) 59. L. Opoczy, Epitoanyag, 27 (1975) 284. K. Schonert, Preprints of Fourth Tewsbuny Symp., Melbourne, 1979, pp. 3.1-3.30. H. E. Shall and P. Somasundaran, Powder Technol., 38 (1984) 257. H. Dombrowe, B. Hoffman and W. Schiebe, Zem.-Kalk-Gips, 35, 11 (1982) 571. H. Schubert, Aufbereit. Techn., 3 (1988) 115. L. M. Popplewell and M. Peleg, Powder Technol., 58 (1989) 145. J. A. Herbst and D. W. Fuerstenau, Znt. J Miner. Process., 7 (1980) 1. R. R. Khmpell and L. G. Austin, Znt. J. Min. Process., 4 (1977) 7. V. K. Gupta, D. Hodouin, M. A. Berube and M. D. Everell, Powder Technol., 28 (1981) 97. J. L. Kuester and J. H. Mize, Optimization Techniques with Fortran, McGraw-Hill, New York, 1973, p. 331. P. A. Rehbinder, Proc. 6th Phys. Congress, State, Moscow, 29, 1928. F. P. Bouden and D. Tabor, The Friction and Lubrication of Solids-Part Z, Clarendon, Oxford, 1964, pp. 295-298. E. Von Szantho and Z. Erzbergh, Metallhuthenw, 2 (1949) 353. S. J. Gregg, The Surface Chemistry of Solids, Chapman and Hall, London, p. 139. K. Schonert, A. Umhauer and W. Klemm, Proc. 2nd Znt. Conf Fracture, Brighton, 1969, paper 41, pp. 474-489. S. M. Weiderhom, J. Amer. Ceram. Sot., 50 (1967) 407. W. Schiebe, B. Hoffman and H. Dombrowe, Cem. Concr. Res., 4 (1974) 289. J. Visser, Powder Technol., 58 (1989) 1.
Powder Technology, 71 (1992) 229-237
Mechanism
of action of grinding aids in comminution
Sureshan K. Moothedath
and S. C. Ahluwalia
National Council for Cement and Building Materials, New Delhi-110049 (India) (Received November 26, 1990; in revised form January 9, 1992)
Abstract In an attempt to delineate the mechanism of action of grinding aids in comminution the effect of these additives on the sub-processes of grinding, viz breakage and attrition, has been studied by isolating each one of them through specially designed experimentsin a laboratory ball mill. Also, the flow characteristics of limestone powder produced with and without grinding aids have been studied. While these additives cause positive effects on attrition and flow of the powder, the breakage rate function and breakage distribution function of (- 10 + 14) mesh material are not affected by them. The implications of these results on the mechanism of action of grinding aids in comminution has been discussed.
Introduction Grinding aids generally improve grinding efficiency, bring down the limit of grinding, prevent cold welding during metal grinding and reduce viscosity in wet grinding [l-3]. These additives, reportedly used by Bessemer for the first time in the production of metal powders, are presently being used in various industries where fine particles are produced by grinding, viz. cement, mineral, pigment, metal powder, etc. A survey of the published work in this area reveals that the use of grinding aids has preceded a proper understanding of the mode of action of these additives. Different researchers have different views about the mechanism. The mechanisms proposed by various researchers are discussed by Rose and Sullivan [l] and subsequently by many other authors [4-111. The results and explanations often become unrealistic and unconvincing in the absence of appropriate data. As grinding involves a few sub-processes, viz. breakage, attrition, classification and transport of the material in the mill, it is not possible to pinpoint the cause behind any effect, from the normal type of data on the fineness vs. time of grinding. A clear understanding of the mechanism of action of grinding aids calls for an indepth study on the effect of these additives on the individual components of the grinding and the contributory forces such as reduction in surface energy, changes in the attractive forces between particles, etc. The results of the experiments carried out in NCB on the effect of grinding aids on the individual components of grinding and its impli-
0032-5910192/$5.00
cations on the mechanism of action of grinding aids are presented in this paper.
Experimental
A schematic diagram of the new experimental set up designed and fabricated for this study is given in Fig. 1. This consists of a laboratory ball mill, 22 cm in diameter and 23 cm in length, resting on two rubberised rollers. The driving shaft is welded on one side of the mill and a flexible coupling connects it to the main shaft. This arrangement is made to reduce the loss of energy due to the slip between the mill and rubber rollers in conventional roller driven mills. The mill is driven by a three phase dynodrive motor through a belt drive for reducing the speed. The speed of the mill can be varied in the range of O-100 ‘pm. The input energy is measured using a 3-phase energy meter. The experiments were carried out on limestone, and laboratory grade triethanolamine (TEA); oleic acid and glycerol were used as the grinding aids. Density of the limestone was 2.73 g crne3 and the main constituents were CaO: 54.39%, LOI: 43.37%, SiO,: 0.85%, Fe,O,: 0.23%, A1203: 0.15% and MgO: 0.97%. The procedure of experimentation was suitably modified depending upon the specific sub-process under study. The procedure in each case is explained separately along with the results.
0 1992 - Elsevier Sequoia. All rights reserved
230
Fig. 1. Experimental set-up for a laboratory ball will. All dimensions are in mn~
Results The experiments in this study were designed so as to get information on the effect of grinding aids on the individual sub-processes in grinding by isolating each one of them. The operating variables are set in such a way that the size reduction takes place mainly by one mechanism, namely attrition or breakage. The results of the study on attrition, breakage, and transport characteristics are given in this section. In the light of these results the mechanism of action of grinding aids is briefly discussed in the following sections. Attrition Normally, in ball mills the size reduction takes place by way of breakage and attrition. A pictorial representation of breakage and attrition is given in ‘Fig. 2, which clearly shows the difference between these two mechanisms of size reduction. In this particular set of experiments which is aimed at the effect of grinding aids on attrition, necessary modifications were carried out in order to reduce the possibility of breakage of particles. l&15 mm ceramic balls were used in place of steel balls and the mill was run at 35 r-pm or less.
Fig. 2. Pictorial representation of breakage and attrition.
This corresponds to 38% of the critical speed of the mill. Under suchconditions size reduction due to impact is expected to be negligible. The attrition experiments were carried out on (- lO+ 14) mesh limestone and the grinding aids used were triethanolamine and oleic acid. When TEA was used the mill was run with 3 kg of material at 22 rpm for 2 h and as there was not much fines production, due to sliding, the speed was then increased to 35 r-pm. The whole set of experiments with TEA were carried out in the same manner with 3.5 kg of ceramic balls as grinding media. But when oleic acid was used, the
231
speed was kept at 35 r-pm from the very beginning and only 1.8 kg of ceramic balls were used as the grinding media. The procedure involved grinding a fixed quantity of the material for different durations of time and analysing the size distribution using test sieves. As the size reduction due to impact breakage is avoided in these experiments the change in the size distribution is expected to be very slow. Also, the type of distribution would be entirely different from that of the normal breakage. Figure 3 is a typical log-log plot of the cumulative undersize 11s.particle size for different durations of grinding. The additive concentrations used in this case are 0.0% and 0.03%. As the grinding time increases there is a gradual increase in the quantity of fines (- 63 pm material) without much of increase of material in the intermediate classes. The curves are nearly horizontal in the region between 63 pm and 200 pm, indicating that there is not much material in this region. The trend is similar both with and without grinding aid, but the amount of -63 pm material produced is more when the grinding aid is used. For a clearer understanding the differential distribution curves of 0.03% are plotted, where the frequency density is plotted against the particle size. These distributions are clearly bimodal with a very low frequency density in the intermediate classes. Breakage is characterised by formation of daughter fragments of l/2 to l/10 times that of the parent particles whereas attrition produces very fine particles directly without going through the intermediate stages. Hence,
0.02
0.05
0.1
SIZE,
0.2
0.5
1.0
2.0
mm
Fig. 3. Cumulative undersize distribution curves at different durations of grinding, (- .- Feed, without additives, --TEA 0.03%).
the main manifestation of attrition is the appearance of a bimodal size distribution, which is clearly visible in Fig. 4. In order to confirm the dominance of the attrition mechanism, the ‘ Erosion Index’, which was recently proposed by PopplewelI and Peleg [12], has been calculated for all the distributions. Erosion Index, IE, is defined as the ratio between the fines accumulation and the size reduction of the coarse fraction, and is given by I
W(t) - WO)lvm) -&I E [I- JqO>l[x,(O)-Xc(t)1 =
(1)
where W(t) = weight fraction of fines at time t, XC(t) = mode of coarse fraction at time t, and X, = mode of fines. By virtue of the definition of this index, breakage will be dominant if IE < 1 and attrition will be dominant if &> 1. The indices were calculated for the distribution curves in Fig. 4, at 7 and 10 h of grinding with the distribution curve at 4 h as reference curve. The indices were found to be 1.72 and 1.95, which is a clear indication of the predominance of attrition in these experiments. Similar observations were made at other concentrations of grinding aid and also in the absence of grinding aid. The Erosion Index values in these cases were in the range of 1.3-2.5. The trend was also found to be the same in the case of oleic acid. In this case 2 kg of limestone was ground at 35 r-pm for 3, 6 and 9 h with 1.8 kg of 10-15 mm ceramic balls as the grinding media. The erosion indices for the distribution at 6 and 9 h of grinding are 2.97 and 3.1, which confirms that, in this case also, size reduction due to attrition is more predominant. The values of all the erosion indices are given in Table 1. Figure 5 is a plot of fines produced VS. grinding aid (TEA) concentration for different durations of grinding. It may be noted that the fines produced increase with the grinding aid concentration up to about 0.03% and then start decreasing. This shows that the grinding aid helps attrition if added in very small quantities, but a reversal takes place at larger concentrations. Figure 6 is a plot of fines produced VS. grinding time when oleic acid was used as the grinding aid. It can be seen that the presence of oleic acid improves the production of fines considerably. An increase of about 36% is noticed after 6 h of grinding, which subsequently reduces to about 20% after 9 h of grinding. Breakage This particular set of experiments were aimed at the effect of grinding aids on breakage characteristics of limestone. Any effect on breakage will clearly show up in the values of breakage rate function or breakage distribution function. The experiments for determi-
232
SIZE,
Fig. 4. Differential
TABLE grinding Grinding time (h)
7 10 A: B: c: D:
distribution
1. Erosion aids
curves at different
index values in the presence
Erosion
mm
durations
of grinding,
(TEA, 0.03%; 0, 4 h; Cl, 7 h; A, 10 h).
of different
index
A
B
C
D
2.00 1.37
1.72 1.95
2.31 2.54
3.10 2.97
without additives 0.03% TEA 0.05% TEA 0.08% oleic acid.
nation of these functions involve short duration grinding for 0.25, 0.5, 1, 2 and 4 min. Since attrition is comparatively a very slow process the effect of the same on such short duration experiments is expected to be negligible. The experiments for the determination of breakage functions were also carried out on (- lO+ 14) mesh limestone and the grinding aids used were TEA, glycerol, and oleic acid. The experimental procedure involved grinding of 3 kg of limestone for short durations, mentioned above, at a ball filling of 50% and obtaining the particle size distribution using standard test sieves. Equal weights of 1 in and 3/4 in steel balls were used as grinding media when TEA was used as grinding aid, and only 1 in balls were used when glycerol and oleic acid were used. Breakage rate function Breakage rate function, ki, quantifies the rate at which the particles are undergoing breakage. This is
01
0
I
I
I
0.05
0.1
0.15
I
0.2
GRINDING AID CONCENTRATION. %
Fig. 5. Effect of TEA concentration 0, 7 h; A, 10 h).
of
fines produced, (0, 4 h;
normally determined as the slope of the straight line obtained by plotting log[mi(t)] vs. time for materials that follow first order grinding where mi(t) is the mass fraction of material in the size class i [13]. Figure 7 is such a plot for the grinding of (- lO+ 14) mesh limestone with and without triethanolamine. It is clear from the plot that the presence of 0.1 wt.% of TEA has not affected the breakage rate function, as the slope remains 0.3 in both the cases. Similar observations were made at 0.2% and in the case of all the other grinding aids also tried. The plots between lOg[mi(t)]
233
z g-+
o.o!i-
Es r-, 5
tE_
0.02-
0.01
0
2
4
6
I 8
GRINGINGTltlE,min
Fig. 8. Determination of breakage rate function mesh limestone, (0, 0.08% glycerol; 0, 0.0%).
of -lo+14
0 3
0
6
TIME,
9
h
Fig. 6. Effect of oleic acid on the quantity (0, 0.08% oleic acid; Cl, 0.0%).
of fines produced,
0
2
4
6
8
GRINDING TIME. min
Fig. 9. Determination of breakage rate function mesh limestone, (0, 0.1% oleic acid; q, 0.0%).
of - lO+ 14
breakage from class j. The breakage distribution function, in this case, is represented by the following equation B,,j=~(xi-~/~j)“+(l-~)(~i-,/~j)a 0.02 0.01.
0
I
2
I
4
I 6
I 8
_
GRWDING TIME. min
Fig. 7. Determination of breakage rate function mesh limestone, (0, 0.1% TEA, Cl, 0.0%).
and t for oleic acid 8 and 9. the same plots.
of - lO+ 14
the determination of ki, when glycerol and were used as grinding aids, are given in Figs. The breakage rate function happens to be with and without grinding aids in all the
Breakage distribution function
Breakage distribution function b quantifies the fraction of the material that goes to be size class i after
(2)
where Bipj=Z.It_ibk ,j, Xi_ I and xj are sizes of the classes i- 1 and j, and 4, cy and /3 are constants. Normally, Bi,j’S are calculated from zero order production plots [13] or by a back calculation method [14, 151. In this investigation, a back-calculation method was adopted and the constants 4, (Yand p were determined using a computer programme in which an iterative optimisation procedure is made use of for the prediction of the grinding data. The programme consists of a module which calculates the product distribution using the batch mill equation with given parameters of breakage rate function {ki= k,(xi/X,)“} and breakage distribution function. These parameters are optimised by minimising the square of the difference between the calculated and experimental values, using Powell’s algorithm [16]. The optimum values of these parameters for different
234
conditions of grinding are given in Tables 2a and 2b. It can be seen that the values of the constants are more or less same when the grinding was done with and without grinding aids. Flow characteristics Three parameters were measured for assessing the changes in flow behaviour of limestone powder prepared using grinding aids. The ground limestone powder from the experiments on breakage characteristics were used for this purpose. The experimental set-up consisted of a hopper which can carry about 3 kg of limestone. This was provided with an arrangement to change the hole size at the bottom as required (3, 6, 9, 12, 15, 18, 25 mm) for finding out the minimum size of the hole for a smooth flow of the material. The three parameters measured were: (1) The minimum size of the hole required for a smooth flow of the material (critical hole size); (2) The time required for emptying 3 kg of material from the hopper using a particular hole size at the bottom (T,); (3) The angle of repose. When the material flows from the hopper it is allowed to form a cone on a horizontal surface. The angle of repose which is a characteristic of the material flowability is measured from this cone. It is known that the material flowability increases with decrease in the angle of repose. The experimental data on the flow characteristics obtained at different conditions are given in Tables 3 and 4. No change was noticed in the critical hole size in the presence of grinding aids. The hole size was 9 mm in all the cases studied. The material after 8 min of grinding was not flowing uniformly even at a hole size of 25 mm, except when oleic acid was used, where TABLE 2a. Values of breakage
distribution
parameters
Parameter
A
B
z a!
0.22 3.00 0.35
0.22 3.00 0.34
Grinding time (min)
0.5 1.0 2.0 4.0 8.0 A: B: C: D:
Angle of repose A
B
C
D
40 40-41 40-41 4142 -
3E-39 38-39 37-39 37-40 -
38-39 36-37 37 34-36 35-37
38 38-39 37-38 38-40 -
without additives 0.1% TEA 0.1% oleic acid 0.1% glycerol.
TABLE aids
4. Values of TF in the presence
Grinding time (min)
0.5
1.0 2.0 4.0 8.0 A: B: C: D:
(degrees)
of different
grinding
TF 6)
A
B
C
D
348 287 282 250 -
294 274 259 227 -
327 270 248 227 246
314 301 277 230 -
without additives 0.1% TEA 0.1% oleic acid 0.08% glycerol.
it was flowing smoothly through even the 9 mm hole. But there is a decrease in the angle of repose in the presence of grinding aids for all the grinding aids studied, as can be seen from Table 3. The change is of the order of l-5 degrees. There is a considerable improvement in the flowability of the material when grinding aids are used. This effect is clearly seen in the time required for the flow of 3 kg material (TF), given in Table 4. The reduction in TF is in the range of 17-54 s which amounts to 616% of the time of flow.
Discussion
A: without additive B: 0.1% TEA. TABLE 2b. Values of breakage
distribution
parameters
Parameter
A
B
C
a
0.20 4.10 0.35
0.20 4.20 0.36
0.21 4.20 0.35
A: without additives B: 0.1% oleic acid C: 0.1% glycerol.
TABLE 3. Values of angles of repose in the presence of different grinding aids
Attrition The grinding aids are adsorbed on the surface of the particles and this may cause many changes in the surface properties of the material. Rehbinder found that the surface hardness of the materials and their resistance to scratching with a fine point changes in the presence of grinding aids [17]. It was shown that there is a progressive decrease in the resistance to scratching with increasing quantities of additives adsorbed on the surface of the body, there being a close
235
correlation between the resistance to scratching and the adsorption isotherm. The minimum resistance to abrasion was observed under conditions of complete adsorption. Attrition is a surface phenomenon and the reduction in surface hardness would definitely help this process. This explains the increase in the quantity of fines with the increase in grinding aid concentration in Fig. 5. Also, this correlates well with the observations of Bouden and Tabor [18], where a reduction in wear resistance was observed in the presence of certain chemicals. Another surface property that is affected by the grinding aid is the coefficient of friction. Generally all the grinding aids have a lubricating property which causes a substantial reduction in the coefficient of friction on the particle surfaces, if added in sufficient quantities [19]. This is of utmost importance as this will have a direct impact on attrition. At high concentrations the decrease in coefficient of friction may outweigh the advantages gained by the reduction in attrition resistance as seen in the present investigation (Fig. 4). Breakage and flowability
In an ordinary ball mill the size reduction results from the fruitful interactions between the balls and the particles. Hence, the rate of grinding would be proportional to the frequency of interaction and the efficiency with which interactions result in breakage. Consequently, anything that improves the frequency of interaction and the efficiency is expected to improve the grinding. The frequency of interaction is influenced, among other things, by the speed of the mill, the number of balls, number of particles and the flowability of the material. The most relevent here in this investigation is the flowability. The flowability of the material determines how well the particles are carried to the grinding zone, thus increasing the probability of capture of the particles between the balls or between the wall and balls. The experiments on the flow characteristics have shown that the grinding aids improve the flowability considerably and this is certainly contributing to a better grinding. The efficiency with which the interactions result in breakage depends on the state of agglomeration or dispersion of the particles, force of collision, etc. It is known that the agglomerated particles reduce the probability of breakage due to the cushioning effect they provide during the collision. Qualitative examination of the powder in these experiments showed that the powder is at a highly dispersed state in the presence of grinding aids. This is reflected in the better flow characteristics which result from the dispersed state of the powder.
Breakage involves crack initiation and propagation under the action of stresses generated by external forces. The critical stress of crack propagation is given by Griffith’s equation [ll], where the stress is calculated based on the values of Young’s modulus, the surface energy and crack length. On adsorption of a gas or vapour the critical stress decreases as there is a reduction in surface energy [20]. Quantitatively, (Ilo-VI)’
$dhP 0
where u, and u1 are surface energy values in vacuum and in the presence of a gas respectively, R is gas constant, T is the temperature in K, M is the molecular weight of the adsorbate, S is the surface area, x is the adsorption in grams per gram of solid and P is the pressure. In practice, the reduction in critical stress is observed only at lower crack propagation velocities [21, 221. Usually in grinding operation the crack propagation velocities are quite high and at these velocities the molecules of the grinding aids may not be able to diffuse down to the crack tip [ll]. This may be the reason why there is no change in the breakage parameters in the present investigation. In the similar lines Schiebe et al. [23] have reported that there was no change in the value of Bond’s Work Index in presence of polyhydric alcohol. Interparticle forces
Though the authors have not done any work on interparticle forces in the present study, this is included in the discussion because of its importance and its relevance to this paper. When the particles become very fine during grinding they tend to agglomerate and form bigger particles under the influence of various forces. The dominant interaction force between particles in a powder is the Van der Waals force of attraction [24]. In addition to this, other attraction forces, such as capillary and electrostatic forces, may also operate in a gaseous environment, though they are much smaller than Van der Waals force. It is seen that Van der Waals force is considerable only when particles are very close (0.2-l nm) and when the distance exceeds a few microns it becomes negligible. Also, simple model calculations have shown that depending on the particle density, porosity and surface roughness, these cohesive forces will only be noticeable for particles a few ,microns in diameter or smaller. Any means to enlarge the separation distance will substantially reduce adhesive forces. Factors affecting the particle separation are roughening of the surface and the use of spacers. Spacers can be molecules adsorbed onto the interacting particles, and this explains
236
the reduction in agglomeration presence of grinding aids.
and ball coating in
Comments on the mechanism of action of grinding aids Based on the results of the experimental investigation given and the subsequent discussion, the following points can be made on the mechanism of action of grinding aids. Rehbinder suggested that the adsorption of the additives on the surface of the particles made crack propagation easier by way of reduction in surface energy. Theoretically, a reduction in the surface energy and a consequent reduction in the critical stress of crack propagation is expected in the presence of grinding aids. But in the normal grinding practice the crack propagation velocities are very high and the grinding aids cannot diffuse down to the crack tips at such high velocities. Hence, an increase in the impact breakage rate is unlikely and this is found to be true as per the experimental results on the determination of breakage rate function. Bond was of the opinion that the prevention of ball coating is mainly responsible for all the positive effects. Certainly, the grinding aids reduce/delay the ball coating and agglomeration of the fine particles, but that does not seem to be the only mechanism causing all the positive effects. Contrary to Bond’s conclusions it is found that very small quantities of these additives can cause reduction or prevention of ball coating without any considerable improvement in the rate of grinding. Addition of slightly larger quantities of grinding aids caused a remarkable increase in the rate of grinding, indicating that prevention of ball coating is not the only mechanism that is responsible for all the effects. Surface hardness of the materials and their resistance to scratching with a fine point changes when grinding aids are adsorbed on the surfaces. Attrition being a surface phenomenon, the reduction in the surface hardness will definitely help this process. The experimental results on attrition characteristics reveal that grinding aids improve attrition if added in small quantities, but a reversal takes place at higher concentrations, probably because of lubrication. Flowability of the material plays a very important role in the transport of the material inside the mill. It is found that the flowability improves in the presence of grinding aids, thus increasing the possibility of the particles to reach the grinding zone, which in turn increases the probability of capture of the particles between the grinding media. Agglomeration of fine particles, which is caused mainly due to Van der Waals forces, is prevented or
reduced when a grinding aid is adsorbed on the particles’ surface. In the absence of agglomeration the grinding can proceed to a finer state as the limit of grinding is also shifted towards the finer region. The energy that is used for breaking agglomerates will now be used for breaking individual particles. The reduction in attractive forces causes better dispersion of the particles, which results in easier flow, reduction or prevention of ball and wall coating and a better classification efficiency.
Conclusions A method has been developed for isolating the attrition mechanism in ball milling. Small amounts of grinding aids are found to assist the attrition of limestone whereas excess quantities of the same result in a reversal. No change in the impact breakage rate of ( - 10 + 14) mesh limestone was noticed in the presence of grinding aids. A clear improvement in the flow characteristics was noticed in the presence of all the grinding aids tried. Rehbinder’s theory of easier crack propagation by way of reduction in surface energy due to the adsorption of grinding aids does not hold good in these experiments. In addition to Bond’s hypothesis of reduction in ball and mill wall coating and consequent improvement in the grinding performance, increase in the rate of attrition, improvement in the flowability and prevention or reduction of the fine particle aggregation in the presence of grinding aids cause the positive effects in grinding.
Acknowledgements The authors wish to thankfully acknowledge the help from Sh. A. S. R. Vijayakumar in the design of the experimental set-up and from Sh. R. L. Bhagwat in carrying out the experiments for this research work. This paper is based on the results of an R and D project of the National Council for Cement and Building Materials and is published with the permission of the Director of the Council.
List of symbols
bi.j Bi.j IE ki
breakage distribution function cumulative breakage distribution function erosion index breakage rate function of material in the size class i
237
30)
M
P R s t T TF
mass fraction of material in size class i at time t molecular weight of adsorbate pressure gas constant surface area of the powder time of grinding temperature in K time required for emptying 3 kg of material from the hopper weight fraction of fines at time t mode of coarse fraction at time t mode of fines
5 6 7 8 9 10 11 12 13 14 15
Greek letters (Y,p, #J constants in the equation for B surface energy v
16 17 18
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K. Shonert, Trans. Sot. Min. Eng. AZME, 252 (1972) 21. H. Rumph, Aufbereit. Tech., 14 (1973) 59. L. Opoczy, Epitoanyag, 27 (1975) 284. K. Schonert, Preprints of Fourth Tewsbuny Symp., Melbourne, 1979, pp. 3.1-3.30. H. E. Shall and P. Somasundaran, Powder Technol., 38 (1984) 257. H. Dombrowe, B. Hoffman and W. Schiebe, Zem.-Kalk-Gips, 35, 11 (1982) 571. H. Schubert, Aufbereit. Techn., 3 (1988) 115. L. M. Popplewell and M. Peleg, Powder Technol., 58 (1989) 145. J. A. Herbst and D. W. Fuerstenau, Znt. J Miner. Process., 7 (1980) 1. R. R. Khmpell and L. G. Austin, Znt. J. Min. Process., 4 (1977) 7. V. K. Gupta, D. Hodouin, M. A. Berube and M. D. Everell, Powder Technol., 28 (1981) 97. J. L. Kuester and J. H. Mize, Optimization Techniques with Fortran, McGraw-Hill, New York, 1973, p. 331. P. A. Rehbinder, Proc. 6th Phys. Congress, State, Moscow, 29, 1928. F. P. Bouden and D. Tabor, The Friction and Lubrication of Solids-Part Z, Clarendon, Oxford, 1964, pp. 295-298. E. Von Szantho and Z. Erzbergh, Metallhuthenw, 2 (1949) 353. S. J. Gregg, The Surface Chemistry of Solids, Chapman and Hall, London, p. 139. K. Schonert, A. Umhauer and W. Klemm, Proc. 2nd Znt. Conf Fracture, Brighton, 1969, paper 41, pp. 474-489. S. M. Weiderhom, J. Amer. Ceram. Sot., 50 (1967) 407. W. Schiebe, B. Hoffman and H. Dombrowe, Cem. Concr. Res., 4 (1974) 289. J. Visser, Powder Technol., 58 (1989) 1.