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I
REFERENCES
(1) BECKERS AND ROTH: 2. Elektrochem. 40, 835 (1934). (2) BERNAL:2. Krist. 78, 363 (1931). (3) GIAUQUE:J. Am. Chem. SOC.62,4816 (1930). AND CLAYTON: J. Am. Chem. SOC.66, 4875 (1933). (4) GIAUQUE J. Am. Chern. SOC.61, 2300 (1929). (5) GIAUQUEAND JOHNSTON: J. Am. Chem. SOC.60,1171 (1938). (6) HUFFMAN: J. Am. Chem. SOC.62, 1009 (1940). (7) HUFFMAN: (8) HUFFMAN:J. Am. Chem. SOC.63, 688 (1941). AND ELLIS: J. Am. Chem. SOC.67, 41 (1935). (9) HUFFMAN (10) JACOBS AND PARKS:J. Am. Chem. SOC.68, 1513 (1934). (11) JESSUP AND GREEN:J. Research Natl. Bur. Standards 13, 496 (1934). (12) ROSSINI: J. Research Natl. Bur. Standards 22, 407 (1939). (13) ROSSINIAND DEMING:J. Washington Acad. Sci. 29, 416 (1939). J. Research Natl. Bur. Standards 21, 491 (1938). (14) ROSSINIAND JESSUP: J. Am. Chem. SOC.67, 1734 (1935). (15) STIEHLERAND HUFFMAN: Bur. Standards J. Research 10, 552 (1933). (16) WASHBURN:
FLOTATION KINETICS.
I
I f E T H O D S FOR STEADY-STATE STUDY O F FLOT.4TIOiK PROBLEMS
R. SCHUHMANN, JR.
Department of Metallurgy, Massachusetts Institute of Technology, Cambridge, Massachusetts Received June 6 , 1048
Separation of minerals by the froth-flotation process involves two essential steps: ( 1 ) Chemical preparation of the mineral surfaces to make the particles of one mineral air-adherent while leaving the remaining mineral particles wateradherent. ( 2 ) Production of a froth from the water suspension of ore particles and separation of this froth from the suspension. The froth carries air-adherent particles and leaves the bulk of the water-adherent particles behind in suspension. Flotation kinetics may be regarded as the study of flotation problems in terms of the kinetics of the second or froth-production step of the process. The effectiveness of a flotation separation, for commercial purposes, is measured by the percentage recovery of valuable material in the conrentrate and by the grade or analysis of the concentrate. However, the recovery and grade data alone do not give a complete picture of flotation behavior, and as a result flotation technicians rely to a great extent on visual observations of flotation rates, froth properties, and other aspects of flotation behavior. In fact, as often as not, the most valuable information from a laboratory flotation test is derived from these qualitative observations rather than from the recovery and grade data for the test. This situation suggests the possibility that direct quantitative measurement of flotation rate, froth mineralization, and related kinetic variables
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R. SCHUHMAh’h’, JR.
should facilitate more positive and more accurate understanding of many flotation phenomena than can be obtained by conventional experimental procedures in which these variables are crudely estimated. This paper presents an experimental approach which has been developed for quantitative evaluation of mineral behavior during the froth-production step of the process. The experimental procedure is based on the study of the flotation system in the steady state, in contrast with the usual laboratory batch test for which the flotation system is in a rapidly changing unsteady state. To aid the interpretation of data, two new criteria of flotation behavior are proposed,the specific flotation rate and the coefficient of mineralization. The specific flotation rate, defined as the rate of flotation (weight per minute) of a pulp con-
FIQ.1. Laboratory flotation cell
stituent divided by the weight of that constituent in the pulp body of the flotation cell, is shown to be directly related to the kinetics of particle-bubble attachment. The coefficient of mineralization, defined as the concentration of a pulp constituent in the froth product (grams per liter of water) divided by the concentration of that constituent in the pulp body, is shown to be a significant measure of the kinetics of bubble levitation and froth draining. Applications of the kinetic approach are discussed briefly and illustrative data are given. EXPERIMENTAL
Flotation cell
The flotation cell used in this work (figure 1) is a subaeration-type cell of wellknown design (1). The cell is made of $-in. sheet celluloid and holds 1.6 liters of pulp under average operating conditions. The impeller is driven a t 1700R.P.M.
FLOTBTIOX KINETICS.
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893
Air a t atmospheric pressure is drawn into the cell through a tube opening just below the center of the impeller. The violent agitation in the pulp zone below the grid disperses the air in the pulp and affords good opportunity for encounter of particles and bubbles. Above the grid the agitation is milder to allow formation of a froth layer. The froth product is scraped over the lip by a motordriven paddle (50 R.P.M.). When the cell is used for a conventional batch test, the pulp of finely ground ore and water is washed into the cell, and reagent treatment is completed using the cell as an agitator (air inlet closed). Then the frothing agent is added, the air valve is opened, and froth is removed for a period of minutes. Water is added as necessary to replace that discharged in the froth. When the test is completed, the pulp remaining in the cell (the tailings) and the froth product removed during the test (the concentrate) are dried, weighed, and analyzed to determine the balance of materials for the separation. The percentage recovery of valuable material in the concentrate and the grade of concentrate are usually abstracted from the materials balance for use in comparing different tests. With the batch procedure just described, quantitative measurements of the rate of flotation, the froth composition, or of other significant aspects of flotation behavior are very difficult because of the wide and rapid changes in the system during the test. For example, the rate of flotation of a mineral frequently decreases as much as tenfold during the first minute or so of the test, or as much as fiftyfold during the first 3 or 4 min. To avoid these and other difficulties, it has been necessary to develop a convenient laboratory technique for operating the cell shown in figure 1 on a continuous basis. Arrangement for continuous flotation Figure 2 shows the flotation cell with pulp-feeding apparatus for continuous operation. The cell is fed by a siphon, with a calibrated spigot, from a 17-liter glass storage tank. This tank has an agitator for maintaining a uniform suspension. The siphon moves vertically through guides and is supported by a celluloid float in the storage tank, so that the head a t the spigot remains constant and a constant feed rate is insured as the pulp level in the storage tank varies. A feed rate of 0.55 liter of pulp per minute has been satisfactory for most of this work, but higher or lower rates may be obtained by changing spigots. The spigot discharges into a Gooch-type funnel from which the pulp is carried through glass tubing to enter the bottom zone of the flotation cell just below the grid. An inverted Y-tube (8-mm. glass tubing) is connected by rubber tubing to a hole in the side of the cell, near the back and 1 in. above the grid. Control of pulp level and froth depth in the cell is accomplished by adjusting the position of the Y-tube. Millimeter scales, one engraved on the cell proper and the other mounted behind the Y-tube, facilitate this adjustment. Procedure The ore is wet ground to the desired fineness (Abbe jar mills, 1-gallon size, are convenient). One or more of the flotation reagents may be added to the pebble mill. The ground pulp is washed into the storage tank, diluted to 15, 16,
894
R. SCHUHMANN, JR.
or 17 liters, and the reagent treatment is completed. When reagent treatment is completed, the frothing agent is mixed in, and the siphon is started to feed the flotation cell. The air inlet and tailings discharge of the cell are clamped shut until the cell is full. When these are opened and froth starts to overflow, a stopwatch is started. Successive time samples of the froth and tailings products are collected in tared pans. Each product is weighed both wet and dry to obtain the amount of water by difference (no wash water is used!). The dried products are analyzed chemically, microscopically, or according to size, depending on what type of
FIG.2. Arrangement for continuous flotation
information is desired. From the completed data, the following are calculated for each pulp constituent and for each sampling period: (1) rate of flotation ( T ) , in grams per minute; (2) concentration in froth product (cy), in grams per liter of water; and (3) concentration in tailings product (cJ, in grams per liter of water. The steady state For the study of problems in flotation kinetics, the significant advantage of the continuous technique just described over a batch technique is the fact that
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the continuously operating system quickly reaches a steady state. In this steady state the variables to be measured do not vary with time and thus are easily measured and correlated. Figures 3a and 3b show how the steady state was reached in a continuous flotation test on a simple copper ore (bornite, CusFeSd, and quartz, SiO,). In figure 3a, the flotation rates of copper and of quartz’ are plotted against time from the start of flotation. Both the copper and the quartz floated mostrapidly
0
2
f
6 B / O I 2 1 f 1 6 Tim.minuteJ
FIG.3. Continuous flotation test on a copper ore
at the start of the test, but after only 5 min. of operation both rates of flotation had dropped severalfold from their starting values to their final equilibrium values. Figure 3b gives the concentrations of copper and quartz in the froth and tailings products as a function of time. The concentration data illustrate further the manner in which the steady state is reached about 5 min. from the start of flotation. I t is interesting to note that the time required to reach equilibrium is less than 1
Determined as “insol.”
896
R. SCHUHMAh'N,
JR.
the time necessary for the feed pulp (at 0.55 liter per minute) to twice displace the original contents of the cell (volume, 1.6 liters). However, this requirement varies somewhat with the test conditions. Considering data from other tests, this seems to be a maximum requirement. On the basis of these and other data for different materials, the experimental procedure has been simplified to include only three successive sampling periods: 5 to 7,7 to 9, and 9 to 11 min. Except for a small number of tests in which unsteady froth conditions were encountered, the data for these three periods have checked consistently, and averages may be taken to obtain a single set of figures for the equilibrium condition of the test. METHODS OF INTERPRETING DATA
Composition of pulp body The rate of circulation of pulp within the pulp body of the flotation cell used in this work is so large in comparison with the rate of feeding pulp or of removing products that it can be assumed that the pump composition is substantially constant throughout the pulp body. On this assumption, the tailings product of the continuously operating cell is equivalent to a continuously taken sample of the pulp body. Thus, in figure 3b for example, the curves showing concentrations of copper and quartz in the tailings are also taken to represent the concentrations in the pulp body. A test of this assumption by pipet sampling of various parts of the pulp body would be difficult to make without disturbing the operation of the system. An alternative test is to operate the cell with a shallow, lightly mineralized froth so that the amounts of solids and water in the froth layer are small in comparison with the total amounts in the pulp body. Then, after equilibrium is reached and sufficient tailings samples have been taken, the feed, air inlet, and tailings discharge are stopped simultaneously. The pulp in the cell is removed and its composition determined. Results of a test of this kind, using a feed pulp containing 62.5 g. of galena per liter of water, showed that the pulp body contained 18.5 g. of galena per liter of water as measured by the tailings sample and 19.4 g. of galena per kilogram of water as measured by taking out the contents of the cell. The slightly higher result obtained by the latter method is due to the inclusion of a small amount of froth in the sample. The specijc flotation rate Direct comparisons of flotation rates, expressed as weights per unit time, are of limited value as a means of comparing flotation behaviors. For example, in the data of figure 3a the rate of flotation of quartz was greater than that of copper in spite of the fact that a reasonably good separation was being made in the direction of floating the copper away from the quartz. Actually, the quartz flotation rate was greater than the copper flotation rate, simply because there was much more quartz than copper present in the pulp body during flotation. When the relative abundance of the two in the system is taken into account, it is obvious that the copper mineral was a much faster floater than the quartz
FLOTATION KINETICS.
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897
under the same conditions. The specific flotation rate, defined below, affords a simple and logical means of allowing for the effect of relative abundance. The specific flotation rate of a pulp constituent is defined the rate of flotation of that constituent per unit weight of that constituent present in the pulp body. That is,
QEL ct
v
in which Q is the specific flotation rate of a given pulp constituent, r is its rate of flotation (weight per minute), and c f is its concentration in the pulp body (weight per liter of water), and V is the amount of water in the pulp body2 (liters). The dimensions of the specific flotatioll rate3thus are 2"-1 (min.-l). Referring to the data of figures 3a and 3b, for the steady state: For copper, r = 6 g. per minute, c t = 1.05 g. per liter of water, and V = 1.6 liters; hence
6
Q = __- = 3.57 min.-' 1.05 X 1.6
For "insol.," r = 7.2 g. per minute, c f = 190 g. per liter of water, and V = 1.6 liters ; henre
Q
=
7.2 = 0.024 min.-' 190 X 1.6 ~
The magnitudes of the specific flotation rates of copper and quartz are indicative of the large differences in flotation behavior commonly obtained between floating mineral and gangue. Relation of spec$c jZotation rate to kinetics of particle-bubble attachment According to the direct-encounter hypothesis of Gaudin (2), attachment of particles to air bubbles occurs &s the result of direct collisions of particles with bubbles. In analyzing this mechanism, both a probability of collision ( P c )and a probability of adhesion (P.) should be considered, and the mathematical treatment is similar in a general way to the well-known treatments of the kinetics of first-order homogerieous reactions and of the kinetics of coagulation. The probability of collision with an air bubble, for a given particle and given time interval, obviously will depend on the degree and kind of aeration of the pulp, the degree and kind of agitation of the pulp, and the hydrodynamic behavior of the particle. The probability of adhesion will depend on the relative magnitudes of the air-adherence of the particle surface and of the hydraulic and inertia forces tending to separate the particle from the bubble. For a given species of particles in a flotation pulp, Approximately equal t o the total volume of the pulp body, not including the air. It is interesting t o note that the speczficflotatzon rate has the same dimensional significance as the specific reacticm rate for a first-order chemical reaction. Also, as will be seen in the next section, the two specific rates are similarly related to the kinetics of the respective processes to which they apply.
898
ll. SCHUHMANN, JR.
Rate of flotation = Collision frequency X Probability of adhesion x Weight per particle X Froth stability factor
(2) The froth stability factor takes into account the fact that even a particle adhering tightly to a bubble may not float if thp bubble coalesces with other bubbles in the froth, or with the free air surface, and drops mineral back into the pulp body. Since Collision frequency = Probability of collision X Xumber of particles in pulp and Weight of particles in pulp = Number of particles in pulp X Weight per particle equation 2 may be written as Rate of flotation = Probability of collision X Probabilitv of adhesion x Froth stability factor X Weight of particles in pulp
(3)
From equation 3 and from the definition of specific flotation rate,
Q
=
P,
x
Pa
x
F
(4)
in which Q is the specific flotation rate, P , is the probability of collision, P. is the probability of adhesion, and F is the froth stability factor. The relation in equation 4 affords a starting point for the experimental study and application of the direct-encounter hypothesis of flotation mechanism. For example, it is readily possible to arrange series of experiments in which two of the terms in the right-hand member of the equation are substantially constant, and then the specific flotation rate can be used as a measure of variations in the remaining factor.
Coefiient of mineralization Particle-bubble attachment alone does not give a scparation, it is also necessary to segregate and remove the air-mineral aggregates from the pulp containing unattached particles. The separation of air-mineral aggregates from pulp, made by allowing the bubbles to rise and form a froth layer and by allowing the froth layer to drain briefly before skimming, is far from perfect in the usual flotation operation. Some pulp is always retained in the bubble walls of the froth. For the quantitative study of this aspect of flotation mechanism, it is convenient to use a new criterion of flotation behavior,-the coefficient of mineralization. The coefficient of mineralization for a given pulp constituent is simply the ratio between the concentration of that constituent in the froth product and its concentration in the pulp body (concentrations expressed as grams per liter of water). For the floating mineral, the coefficient of mineralization measures the effectiveness of the flotation operation in dewatering the mineral. That is, if the coefficient of mineralization is M units, this means simply that the floating
FLOTATION KINETICS.
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899
particles carry with them into the froth product only 1/M times as much water as they are associated with in the pulp body. For effective flotation, M should be several times greater than unity. Values ranging all the way from 2 to over 200 have been observed in the laboratory work to date. Data of figure 3b, for example, give a value of 40( =
42 g. per liter of water 1.05 g. per liter of water
for the coefficient of mineralization of the copper. The coefficient of mineralization also is useful in evaluating the flotation behavior of non-floatable pulp constituents,-that is, of constituents which are recovered in the froth product only by mechanical inclusion in the interbubble liquid. If, for example, the gangue mineral were very fine clay, it would be expected that the clay concentration in the interbubble pulp of the froth product and the ciay concentration in the pulp body would be the same; that is, the coefficient of mineralization would be unity. Coarser particles will tend to settle from the water in the bubble walls of the froth layer, resulting in values less than unity for the coefficient of mineralization. Referring again to the data in figure 3b, for example, the coefficient of mineralization of the quartz was found to be 50 g. per liter of water 190 g. per liter of water indicating relatively effective settling of quartz from the interbubble pulp of the froth layer. Viewed in a different way, the coefficient of mineralization of a pulp constituent may be regarded as the floatability of the constituent relative to water. If a mineral is floated by selective attachment to air bubbles, it will be recovered in the froth product more readily than water and M will be greater than 1. If the mineral does not become attached to air bubbles, it will not be floated as well as water because of settling, and M will be less than 1. APPLICATIONS
The solution of flotation problems frequently depends on the integration of information obtained by several distinctly different methods of investigation. For example, present knowledge of the chemistry of collector action on minerals is based on such different lines of experimentation as contact-angle measurement, chemical analysis of reaction products in solution and on the mineral surface, and simple batch flotation tests. Each particular method of experimentation furnishes certain information which the other methods are not capable of furnishing. Likewise, it is believed that the study of flotation problems in terms of the kinetic behavior of minerals during the act of flotation, as outlined in this paper, will in many cases supply worthwhile information not satisfactorily obtainable by other available experimental methods. The experimental methods described in this paper are being applied to a
'
900
R . SCHUHMANN, JR.
variety of problems in the Richards Mineral Dressing Laboratories a t the Massachusetts Institute of Technology. Particularly interesting data have been obtained in a study of the relation of particle size and flotation behavior. This work is covered in a separate paper (3). In the remaining part of this paper, other of the most promising fields of application are outlined briefly, with illustrative data. The design and operation of flotation machines have been based largely on the accumulation of practical data, with only qualitative consideration of the details of mineral behavior within the machines. The kinetic study of the design variables offers a method of attack for placing cell design on a more scientific basis. One simple aspect of this study is illustrated by the data in
&a 50
30 20
M
5 3 2
I0
a3 Fmth drpth. centimeters
FIG.4 FIG.5 FIQ.4. Effect of froth depth on behavior of a galena pulp FIG.5. Effect of amount of frother on behavior of a galena pulp
figure 4,showing the effect of varying froth depth on the flotation of a galena pulp. As would be expected, changes in froth depth over a considerable range have no appreciable effect on the process of particle-bubble attachment as measured by the specific flotation rate. The breaks a t the right ends of these curves represent the experimental result that froth layers appreciably deeper than 2.8 cm. could not be maintained with the frother amount and other conditions in this series of tests, because the bubbles would break and drop their mineral loads back into the pulp body. The important effect of varying the froth depth is shown by the coefficient of mineralization, which increased over tenfold as the depth of the froth layer was increased from 0.65 to 2.8 cm. The effect of time of residence of bubbles in the froth layer on the extent of draining
FLOTATION KINETICS,
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90 1
is of course well known, but in the author’s knowledge no quantitative mcasurements have been made heretofore. Much remains to be learned regarding the action of frothing agents in the flotation system. The steady-state technique of flotation seems particularly appropriate for the study of frothers because the behavior of the frother, like that of the ore, must reach a steady state. In fact, to those interested in the principles of foaming, apart from flotation, measurements of the specific flotation rate and the coefficient of mineralization of the frothing agent itself might be of analytical value. Figure 5 gives results from a series of tests with a galena
Potaurun ethy ronthoie pandr pn
(exald
FIG.6. Effect of amount of collector on behavior of a galena
pulp in which the rate of feeding terpineol to the flotation cell was varied over a wide range. Variations in the amount of terpineol had surprisingly little effect on the froth draining under the conditions of this series of tests, as is shown by the fact that the coefficient of mineralization was nearly constant. On the other hand, the specific flotation rate was very sensitive to small variations in frothing agent in the range below 6.5 mg. per minute, showing in clear quantitative fashion the function of the frothing agent in stabilizing the froth. These tests show a well-defined optimum rate of feeding terpineol a t 6.5 mg. per minute. The specific flotation rate and the coefficient of mineralization are both very sensitive t o variations in the surface properties of the floating mineral. This is
902
A. M. QAUDIN, R. SCHUHMANN, JR., AND A.
w.
SCHLECBTEN
shown by the data in figure 6, for the flotation of a galena pulp with varying additions of potassium ethyl Ranthate. For comparison, a series of conventional batch tests (of 6 min. duration each) were made paralleling the steadystate tests. The percentage recoveries in the batch tests are plotted in the upper part of figure 6, on the same scale as the rate and mineralization data for the steady-state tests. It is apparent from these plots that the usual method of gauging reagent effects by comparing percentage recoveries in batch tests does not show the magnitudes of the surprisingly large variations in flotation behavior which can result from reagent variations. I t should be noted also that the kinetic criteria show variations in flotation behavior between difEerent amounts of xanthate (above 0.6 pound per ton) all of which give substantially complete recovery of the galena in batch tests. The author wishes to express his gratitude to Professor A. M. Gaudin for much constructive criticism and advice. REFERENCES (1) DIETRICH, W.F.,ENGEL,A . L., AND GUGGENHEIM, M.: “Ore Dressing Tests and their Significance,” U. S. Bur. Mines, Rept. Investigations No. 3328, p. 26 (1928). A. M.: Flotation, pp. 86-119. McGraw-Hill Book Company, Inc., New York (2) GAUDIN, (1932). (3) GAUDIN, A. M., SCHUHMANN, R., JR., AND SCHLECHTEN, A. W.: J. Phys. Chem. 46, 902 (1942).
FLOTATIOK KINETICS. I1
THEEFFECTOF SIZE ON
THE
BEHAVIOR OF GALEKA PARTICLES~
A. M. GAUDIN, R. SCHUHMANN, JR., AND A. W. SCHLECHTEN’ Department of Metallurgy, Massachusetts Institute of Technology, Cambridge, Massachusetts Received June 6 , 1942
It is well known that particle size imposes limitations upon flotation, but despite the economic significance of this relationship, it has not been investigated by many workers. Obviously, the maximum size of particles that can be floated is limited by the lifting power of the surface forces ( 5 ) . I t has been shown, also, that in the flotation of sulfide particles the ease of flotation decreases with decreasing particle size (6, 7, 8, 9). Thus, particles of a size near the maximum that can be floated should have the optimum floatability. 1 The material in this paper is from a thesis submitted by A . W. Schlechten to the Faculty of the Graduate School of the Massachusetts Institute of Technology in partial fulfillment of the requirements for the degree of Doctor of Science, May, 1940. Present address: Department of Mining Engineering, Oregon State College, Corvallis, Oregon.
