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Flotation response prediction from interfacial properties
Colloids and Surfaces, 46 (1990) 255-269 Elsevier Science Publishers B.V., Amsterdam -
255 Printed in The Netherlands
Flotation Response Prediction from Interfacial Properties BRUCE E. NOVICH Ceramics Process Systems Corporation, 155 Fortune Boulevard, Milford, MA 01757 (U.S.A.) (Received 31 August 1989; accepted 2 October 1989)
ABSTRACT A quantitative relationship between contact angle and flotation response using a fundamental and measurable solution chemistry parameter, the critical micelle concentration, has been formulated. Bubble contact angles were measured for the quartz-alkylamine-water flotation system in which the effects of surfactant concentration, surfactant structure and solution pH on contact angle were determined. The alkylamines studied were n-hexylamine, di-n-hexylamine, n-dodecylamine, din-dodecylamine and 1,12diaminododecane. Peak contact angles were primarily a function of chain length, measured as 50” for the hexylamine system and 86” for the dodecylamine series. The diamine gave a contact angle of 60”. The contact angle was unaffected by solution pH over the range 8-10. The surfactant concentration, C,,, corresponding to the maximum contact angle, decreased with increasing number of hydrocarbon branches and increasing solution pH. Flotation recovery data and critical micelle concentrations were correlated to the contact angle data. The correlation analysis quantitatively indicated that 100% flotation recovery can be obtained at surfactant concentrations between 0.01 (C,) and the C, or between 0.01 (c.m.c.) and the c.m.c. for the flotation systems surveyed. This unique relationship between flotation response, micellixation and bubble contact angle suggests that solution chemistry near the particle surface and near the bubble surface governs the flotation process and the c.m.c., as a solution chemistry parameter, can be used to predict quantitatively flotation response.
INTRODUCTION
Flotation is the most widely used mineral separation process. Flotation can be broadly defined as an induced density separation brought about by interfaciai modification. In mineral engineering practice, flotation is the process of segregating one mineral type from another by selective gas bubble attachment onto one of the mineral surfaces, while submerged in a liquid medium. Selective separation is accomplished by modifying one of the mineralsurfaces with surface active agents, surfactants, to cause a favorable condition for gas bubble attachment. The particle-bubble aggregate, having a density that is less than the liquid medium, rises through the flotation cell and is collected at the top, leaving behind the other mineral types. 0166-6622/90/$03.50
0 1990 Elsevier Science Publishers B.V.
256
Bubble-particle contact and adhesion in aqueous suspension are the key factors controlling the froth flotation process. For flotation to occur, the gas bubble must contact and strongly adhere to the mineral surface. This attachment must be strong enough to survive the hydrodynamic shear forces present due to flotation cell mixing and aeration. The contact angle determination provides a direct measure of attachment strength between the bubble and mineral surface. Several studies have shown that a parallel relationship between contact angle and flotation recovery exists for a variety of flotations systems (e.g. alkylamine-quartz [l-4] or alkylsulphonate-alumina [ 51. While experimental and theoretical aspects of contact angle, as related to flotation systems, have been studied extensively, few investigators have adequately integrated experiment with theory. Further, practical aspects of these works have only been dealt with in empirical terms, which has inhibited the use of contact angle data as an online processing tool. The following study has provided a quantitative relationship between contact angle and flotation response using a fundamental and measurable solution chemistry parameter, the critical micelle concentration. Background To. understand better the gas-liquid-solid interface, several experimental studies have been carried out using the alkylamine-quartz flotation system as the model. Alkylamine adsorption at the bubble-solution (B/W) interface results from the non-polar hydrocarbon tail’s preference to be in a non-polar medium, air, and from the polar amine head’s preference to be in a polar environment, water. The alkylamine molecule acts as a bridge between the liquid-gas interface. Smith and Lai [2] stressed the importance of surfactant adsorption at the B/W interface by detecting time-dependent contact angle behavior at the air-alkylamine solution-quartz interface. Smith and Lai attributed this dynamic behavior to the reduction of the bubble/water and bubble/solid interfacial tensions, resulting from the adsorption of alkylamine on the bubble surface. This was later confirmed by Finch and Smith [ 61. Somasundaran [ 71, Digre and Sandvik [8] and Bleier et al. [9] calculated cationic amine adsorption densities at the B/W interface from surface tension measurements using the Gibbs adsorption equation: dot,, =2.303RZY’~NH4_,
dln(C,NH,._,)
(1)
where r is the adsorption density of cationic amine at the bubble surface and C is the concentration of cationic amine in bulk solution. Somasundaran [ 71 found that for a homologous series of n-alkylammonium acetates, the adsorption behavior at the B/W interface parallels the corresponding flotation and adsorption behavior at the S/W interface. Bleier et al. [9] calculated that the bubble surface is positively charged after cationic amine adsorption. Based on
257
this calculation, Bleier et al. postulated that one possible mechanism for bubble attachment is electrostatic attraction of the positive bubble surface to the negative quartz surface. EXPERIMENTAL
Quartz preparation High-purity quartz crystals were supplied by Western Electric Corporation, Merrimack Valley Works, North Andover, MA. These crystals were carefully grown from Brazilian quartz seed crystals to meet the exacting requirements for piezoelectric applications. The quartz samples used for contact-angle measurements were out from the crystals so that the test surfaces were parallel to either the (OOl), (OlO), (011) or (110) crystallographic planes. Each quartz surface, approximately 2 cm wide and 3 cm long, was wet ground with # 200, # 320 and # 500 silicon carbide and then with 3 and 0.5 p diamond paste. Scanning electron microscopy and surface profilometry revealed that the surface asperities were no higher than 1000 A. X-ray diffraction peaks were at least 25% more intense after the 0.5 pm grind than after the 3 pm diamond grind. Prior to each contact angle determination, the quartz surfaces were rinsed three times with 500 ml of deionized water and were then boiled in a 3 it4 nitric acid solution for 10 min. Immediately following the acid treatment, the quartz surfaces were washed five times with 500 ml of deionized water; crystals were soaked for at least 2 h in the final wash water. The surfaces were then dried at 23’ C under vacuum and were stored in a dry dessicator until further use. Properly cleaned crystals gave zero contact angle with a nitrogen bubble in water. Contact angle determination Bubble contact angle measurements were carried out on ground quartz surfaces using a Rame’ Hart contact angle goniometer. An optical glass cell was used to contain the mineral and surfactant solution system. Purified nitrogen bubbles were admitted to the cell through a Gilmont microburet with a flatfiled glass tip. All measurements were carried out in a plastic glove bag under positive nitrogen pressure to eliminate COz absorption, which leads to an unstable solution pH. Initial studies showed that the nitrogen environment was essential to obtaining stable and reproducible contact angle measurements. Solution pH was monitored and constant to 20.1 pH units throughout the treatment and measurement periods. The contact angle determination procedure was as follows: 150 ml of pH adjusted surfactant solution was placed into a dry optical glass cell, resting on top of a magnetic stirrer. The dry quartz plate was slowly submerged into the
258
surfactant solution, followed by a Teflon stirring bar. The magnetic stirrer was initiated at 40 rpm for 10 min, after which the stir bar was removed from the cell. The nitrogen microburet was inserted into the glass cell to a height of l2 mm above the mineral surface. A bubble was produced that touched the mineral surface by adjusting the microburet vernier by 0.05 ml. The buret was slowly withdrawn upwards from the mineral surface until the maximum contact angle was reached, while still maintaining bubble attachment. Decker [lo] characterizes this contact angle as the advancing angle. Reproducibility Analysis showed a measurement coefficient of variation of 5% (approximately 2 2 ’ ) for contact angles ranging from 22.0 to 86.7’ over a pH range from 6.0 to 10.0 at a constant dodecylamine concentration of 4-10m4 M. Contact angles measured on the (OOl), (llO), (010) and (011) crystallographic planes were the same within experimental error and were the same as those reported by Smith [ 111 and Lai [ 121 for polycrystalline quartz surfaces. Figure 1 compares contact angle data measured in this study to the results of Smith [ 3,111 for dodecylamine and di-n-hexylamine, showing excellent agreement.
n 18 X lo-ftJ 80
.
6.4 X 10
+
4.0 X 10-4M
M
A
2.6 X 10-4M
-
_
n-dodecylamine Symbol -T
I
Ol
6
7
= CMC
I
I
I
I
I
8
9
10
11
12
Solution
1
pH
Fig. 1. Bubble contact angle on quartz as a function of dodecylamine solution concentration and PH.
Decker [lo] has shown that the bubble contact angle measurement is strongly a function of measurement technique and bubble size. Pushing the bubble slightly toward the surface after contact gives the receeding contact angle and pulling the bubble slightly away from the surface after contact gives the advancing contact angle. Decker has also shown that the difference between advancing and receeding contact angles can be as much as 50” for the quartzdodecylamine system. Wakamatsu and Fuerstenau [ 13 ] define the equilibrium contact angle as the average of the advancing and receeding measurement. The advancing contact angle measured in this study exhibited the best reproducibility. RESULTS
Bzdhk contact angle The advancing contact angle was measured as a function of solution pH, alkylamine concentration and alkylamine architecture. As shown in Fig. 1 for n-dodecylamine, the contact angle increases to a maximum value at a particular solution condition, and then decreases as the condition is exceeded. This general curve was observed when the independent condition was solution pH or alkylamine concentration. The increase in contact angle prior to the peak appears to be due to increasing alkylamine surface adsorption, as particle surface hydrophobicity increases with increasing surface coverage [ 141. The decreasing contact angle with increasing surfactant concentration may be due to limited solubility of the alkylamine in water and to bubble repulsion as surfactant adsorption at the air/liquid interface becomes important, as described by Bleier et al. [9]. Figures 2 and 3 show similar behavior for n-hexylamine, din-hexylamine, n-dodecylamine, di-n-dodecylamine and 1,12-diaminododecane at pH 8.0 and 10.0, respectively. The solution concentration corresponding to peak contact angle decreased with increased number of branches for the primary and secondary hexylamines and dodecylamines. Accordingly, the peak contact angle also decreased with increased number of branches. The decreasing peak contact angle with increased branching may be attributed to the reduced alkylamine adsorption onto the quartz surface stemming from reduced solubility of the branched compounds and from increased steric hinderance from the neutral carbon chains, which prevent access of the charged alkylamine head to the quartz surface. The 1,12diaminododecane had a broader window of peak angle, giving a peak contact angle of 50” over several orders of magnitude of solution concentration. The 12-carbon dodecylamine and the 24carbon didodecylamine gave similar peak contact angles of approximately 80 O, twice as great as the peak contact angles for the hexylamine series at roughly 40”. Peak contact angles and the corresponding alkylamine concentrations, C,, at pH 8.0 and 10.0 are listed in Table 1.
s mbol
m
n-hexylamine
V
di-n-hexylamine
A
1,12 diaminododecane
= CMC
T
l n-dodecylamine l d'l-n-dodecylamine
a -8
I
-7
I
-6
I
I
I
-5
-4
-3
loglo Alkylamine
I
-2
Concentration,
I
I
-1
0
M
Fig. 2. Bubble contact angle on quartz as a function of alkylamine solution concentration 8.0.
at pH
The contact angle results indicate that peak contact angle is primarily affected by the length of the carbon chain that extends into the solution from the quartz surface. The primary and secondary hexylamines gave approximately the same peak contact angles close to 50’) independent of their carbon number. The same trend was observed for the primary and secondary dodecylamines, which gave contact angles of approximately 80’. Branched com-
261
symbol
n
n-hexylamine
'I
di-n-hexylamine
;
1,12 diaminododecane n-dodecylamine
l
di-n-dodecylamine ?
= CMC
1
-
I
-7
-6
-5
-4
-3
_*
~~ ;1
d
0
loglo Alkylamine Concentration,M Fig. 3. Bubble contact angle on quartz as a function of alkylamine solution concentration at pH 10.0.
pounds gave similar peak contact angles at 1% of the concentration of the unbranched alkylamines, suggesting that equal flotation performance can be achieved at greatly reduced surfactant concentrations using the branched compounds. This is supported by flotation recovery data given by Novich and Ring [ 151. The window for peak contact angle can be broadened by increasing the
262 TABLE 1 Peak contact angle concentrations for quartz Alkylamine
n-Hexylamine Di-n-hexylamine n-Dodecylamine Didodecylamine Diaminododecane
Peak contact angle (degrees)
Peak contact angle concentration C, 04)
pH 8.0
pH 10.0
pH 8.0
pH 10.0
52 48 86 82 60
60 55 86 80 63
1.4.10-l 5.1.10-3 1.0*10-3 1.0.10-5 1.0.10-2
3.2.10-’ 4.0.10-4 1.0*10-4 1.4.10-5 5.0.10-4
surfactant ionicity, as demonstrated by the broad peak angle behavior of the lJ2diaminododecane with an accompanied decrease in bubble solid adhesion.
DISCUSSION
Bubble contact angle and flotation response Novich and Ring [ 151 measured flotation response for the aqueous alkylamine solution-quartz-nitrogen system using a modified Hallimond microflotation cell system as described by Fuerstenau et al. [ 161. Novich and Ring found that all of the flotation response curves, plotted as percentage flotation recovery as a function of alkylamine solution concentration at constant pH or as a function of solution pH at constant alkylamine solution concentration, had the same general shape, as shown in Fig. 4. Bleier et al. [ 91 defined a minimum critical flotation concentration, (c.f.c. ) min, as a characteristic concentration above which good flotation recovery is experienced. Novich and Ring defined the (c.f.c.), as a characteristic concentration above which poor flotation recovery is experienced. Optimal flotation system design calls for a collector concentration between (c.f.c.),, and (c.f.c.),,,. Table 2 shows the values for the critical flotation concentrations at pH 8.0 and 10.0 for the primary and secondary alkylamines and the diaminoalkane tested. Also listed in Table 2 is the ratio of peak contact angle concentration to critical flotation concentration. were constant within experimental The ratio of (c.f.c.),,/C, and (c.f.c.), error, as approximately 0.01 and 1, respectively. These results indicate that a proportional relationship exists between the solution chemistry corresponding to the peak contact angle and the solution chemistry corresponding to the peak flotation recovery.
263
-
I
I
I
-5
-4
-3
I
O-
O-
O-
O-
O-
O-
o-
oD-
3-
-2
loglo Eukcylanxine Umcentration,M Fig. 4. Flotation recovery curve for dodecylamine and quartz at pH 8.0 (from Ref. [ 151).
Bubble contact angle and critical micelle concentration Micellization is a surfactant aggregation phenomenon which occurs at relatively high surfactant concentrations, close to the solubility limit. Typically, micelles are aggregates of 50-100 surfactant ions in which the hydrocarbon tails are weakiy bound together by van der Waals forces. The polar amine heads remain fully solvated, as they are directed outward into the polar solution, giving a spherical or ellipsoidal geometry [ 171. The surfactant concentration at which micellization occurs rapidly is the critical micelle concentration
264 TABLE 2 Critical flotation concentration Alkylamine
n-Hexylamine Di-n-hexylamine n-Dodecylamine Didodecylamine Diaminododecane
lOglo (c.f.c.) , i ,
log~o( c.f.c. ) m,~
loglo ( c.f.c. ) min/Cp
loglo (c.f.c.) m~/Cp
pH8.0
p H 10.0 p H 8 . 0
p H 10.0 p H 8 . 0
p H 10.0
pH8.0
p H 10.0
-3.3 -4.5 - 4.5 - 6.6 -4.1
-4.1 -4.7 - 5.5 - 6.5 -5.4
-2.4 -2.2 - 3.5 - 4.0 -3.0
-2.4 -1.7 - 1.7 - 1.8 -2.1
-0.1 0.4 0.8 0.8 0.7
0.1 1.1 0.5 0.8 0.3
-1.0 -1.7 - 1.9 - 4.0 -1.3
-2.2 -2.2 - 1.9 - 1.9 -2.1
(c.m.c.) which is accompanied by an abrupt change in solution properties such as viscosity, surface tension and specific conductivity. MiceUization is a solution process that reduces the alkylamine activity, having a significant effect on the interfacial properties at the solid/liquid/gas interface. Using coagulation experiments, Novich [ 18 ] has shown that micellization occurs at concentrations below the critical micelle concentration. Below the c.m.c., this aggregation becomes important at the solid/liquid interface and above the c.m.c., the surfactant aggregation becomes important at the liquid/gas interface. Gaudin and Fuerstenau [19] postulated that as surfactant ions adsorb onto solid surfaces from solution, the surfactant concentration in the double layer approaches the c.m.c., even though the bulk alkylamine solution concentration is several orders of magnitude lower than the c.m.c. Using Gouy-Chapman theory, Gaudin and Fuerstenau calculated that the ratio of surfactant concentration in the bulk to that in the double layer was 0.01 at monolayer surface coverage. They termed micelle formation in the double layer as hemi-micelle formation. Surface micelle formation with respect to surfactant structure and flotation response has been discussed by Somasundaran et al. [20]. Chander et al. [21] state that hemi-micelle formation is the direct analogue of bulk solution micelle formation, so that system conditions that affect micelle formation have a similar effect on hemi-micelle formation. The work of Chander et al. implies that system conditions such as temperature, pH and salt concentration, which effect micelle formation in solution, will simultaneously effect surface micelle formation and solid-liquid-gas interfacial properties. The study of Predali and Cases [22 ] of alkylamine adsorption onto biotite supports this hypothesis by showing how a homologous series of adsorption curves converge to one general curve when equilibrium surfactant concentration is normalized with critical miceUe concentration. Novich [18] showed the same curve convergence for several adsorption systems: alkylamine--quartz [18], aluminaalkylsulphonate [23] and the alkylamine-latex-G [24] systems. The generalized adsorption equation relating adsorption density, critical micelle concen-
265
I
I
I 10-4 Reduced
10-3 Equilibrium Alkylamine
Fig. 5. Zeta potential for the quartz-dodecylamine centration, X= C,/c.m.c. (from Ref. [ 201)
.
100
10-Z 10-l Concentration,X=C/CW
system plotted as a function of reduced con-
TABLE 3 Critical micelle concentrations, log,,(c.m.c.) Alkylamine
n-Hexylamine Di-n-hexylamine n-Dodecylamine Di-n-dodecylamine 1,12-Diaminododecane
c.m.c.
(c.f.c.),,/c.m.c.
(c.f.c.),/c.m.c.
C,/c.m.c.
pH8.0
pH 10.0 pH8.0
pH 10.0 pH8.0
pH 10.0 pH8.0
pH 10.0
-1.4 -2.1 -2.4 -4.3 -2.0
-2.2 -2.5 -3.7 -4.3 -3.4
-1.9 -2.3 -1.8 -2.2 -2.0
-0.1 0.3 0.2 0.3 0.4
0.5 -0.4 -0.3 -0.5 0.1
-1.9 -2.5 -2.5 -2.2 -2.1
0.4 0.4 0.4 0.3 0.4
0.5 -0.2 -0.3 -0.7 0.0
tration and equilibrium solution concentration is given and has been verified by Novich and Ring [ 151. Normalizing interfacial property results to c.m.c. has been shown to cancel effects of surfactant type, chain length, branching and solution chemistry for flotation recovery data and electrophoretic mobility [20] data, as shown in Fig. 5. Novich and Ring [ 151 determined critical micelle concentrations for the primary and secondary alkylamines and the diaminododecane as a function of solution pH. Their c.m.c. results are listed in Table 3, showing a decrease of
c.m.c. with increasing pH for the primary and secondary compounds. Table 3 also lists the peak contact angle and critical flotation concentrations when normalized to the c.m.c. at pH 8.0 and 10.0, showing the peak contact angle concentration and critical flotation concentration to be approximately equal to the c.m.c. The experimental results have shown that the peak contact angle concentration, the maximum critical flotation concentration and the critical micelle concentration are approximately equal. The experimental results also show that minimum critical flotation concentration, occurs at 1% of the C,, and c.m.c. This is consistent with Gaudin and Fuerstenau [ 191 and Aplan and Fuerstenau [ 251, who state that the condition required for the association of adsorbed alkylammonium ions at the quartz-solution interface at pH 7 is constant at an equilibrium solution concentration equal to 1% of the c.m.c., based upon electrokinetic data for the C8-, Cl,,-, C12-,C14-and GIG-alkylamines.These results were similar for all of the alkylamines that were tested. The contact angle and flotation data, as related to the c.m.c., can be used to develop a quantitative model for flotation. At surfactant concentrations less than the c.m.c. are greater than the (c.f.c.),in, the solid surface-solution interface can be depicted as a continuum of adsorbed surfactant molecules, with a majority of hydrocarbon tails pointing away from the particle surface [ 141, as shown in Fig. 5. Bleier et al. [ 91 showed that for the alkylamine system, the bubble surface is positively charged, as the hydrocarbon tails occupy the bubble gas space and the polar amine heads remain solvated in solution. Flotation can occur at this point, as the hydrocarbon tails bridge the particle surface and the bubble interior. As the surfactant concentration increases, more hydrocarbon tails are available for particle-bubble bridging, causing the contact angle to increase and flotation recovery to remain at 100%. As the solution surfactant concentration approaches the critical micelle concentration, very strong adhesion between the bubble and particle surface should result, as indicated by a maximum contact angle. Schubert [26] and Tamamushi and Tamaki [ 271 indicate that at the c.m.c. the adsorbed multilayer is saturated, from a leveling off of the adsorption curve. The c.m.c. condition represents a highly unfavorable condition for surfactant solvation and represents the most favorable condition for bubble attachment, as the hydrocarbon tails continue to bridge the particle-bubble interface and act to minimize the polar head repulsion at the bubble-solution interface [ 281. At concentrations greater than the c.m.c., alkylamine molecules micelle to the last layer adsorption, giving a bilayer structure [ 17,281, as the charged heads point into the bulk aqueous solution [ 191. As a saturated positively charged bubble surface comes into contact with the charged bilayer, repulsion results and the contact angle falls to zero.
267
I
Q~
0
~Q
¥ =-
2o
io
I,
15
~
0
M
I
~^
~d v
=I ~ 8 ,.Q
°~ d~../~
~ 0
=,
~ °~
io
L~
2
I';
.o V
c;
i'F-
268 SUMMARY AND CONCLUSIONS
Bubble contact angles were measured for the quartz-alkylamine-water flotation system in which bubble contact angle and flotation response were measured as a function of surfactant concentration, surfactant structure and solution pH. Maximum bubble contact angles were approximately 50” for hexylamines and 80’ for dodecylamines. The equilibrium surfactant concentration corresponding to the maximum contact angle, C,, decreased with increased carbon number, increased number of hydrocarbon branches and increased pH. The critical micelle concentration, c.m.c., which describes the surfactant behavior in solution, was correlated to the bubble contact angle data and showed a parallel relationship between C,, and the c.m.c. Normalizing the flotation recovery data to C, and the c.m.c. indicated that full flotation recovery can be predicted at approximate surfactant concentrations between 0.01 C,, c.m.c. and 1.0 C,, c.m.c. A model was proposed to relate contact angle, flotation recovery and c.m.c. Hydrocarbon bridging between the particle surface and bubble appear to be the principal bubble adhesion mechanism corresponding to 100% flotation recovery and increasing contact angle. Flotation cessation at surfactant concentrations above the c.m.c. results from bubbleparticle repulsion. Interfacial properties can be used to predict quantitatively flotation response as a function of flotation system conditions. Surfactant micellization at the solid surface-solution interface is responsible for the onset of flotation and surfactant micellization at the bubble-solution interface is responsible for the termination of flotation. ACKNOWLEDGEMENTS
The author would like to acknowledge the valuable input and assistance from Dr Terry A. Ring and the valuable program support from the W.R. Grace Co. and the SOHIO Center for Excellence at M.I.T.
REFERENCES 1 2 3 4 5 6 7 8 9
D.W. Fuerstenau, Trans. AIME, 208 (1957) 1365. R.W. Smith and R.W. Lai, Trans. AIME, 235 (1966) 413. R.W. Smith, Trans. AIME, 254 (1973) 353. D.W. Fuerstenau, T.W. HeaIy and P. Somasundaran, Trans. AIME, 229 (1964) 321. I. Iwasaki, S.R.B. Cooke and Y.S. Kim, Trans. AIME, 223 (1962) 113. J.A. Finch and G.W. Smith, Trans. IMM (London), 77 (1968) C213. P. Somasundaran, Trans. AIME, 241 (1968) 105. M. Digre and K.L. Sandvik, Trans. IMM (London), 77 (1968) C61. A. Bleier, E. Goddard and R. K&arm, in M.C. Fuerstenau (Ed.), Flotation, A.M. Gaudin Memorial Volume, Vol. 1, AIME, (1976) 117.
10 11 12 13 14
15 16 17 18 19 20 21 22 23 24 25 26 27 28
T. Decker, Ph.D. Thesis, MIT, Cambridge, MA, 1964. R.W. Smith, Trans. AIME, 226 (1963) 427. R.W. Lai, Ph.D. Thesis, University of California, Berkeley, CA, 1970. T. Wakamatsu and D.W. Fuerstenau, Trans. AIME, 254 (1973) 123. B.M. Moudgil, H. Soto and P. Somasundaran, in P. Somasundaran and B. Moudgil (Eds), Reagents in Mineral Technology, Surfactant Sci. Ser., Vol. 27, Marcel Dekker, New York, 1988, p. 79. B.E. Novich and T.A. Ring, Langmuir, 1 (1985) 701. D.W. Fuerstenau, P.H. Metzger and G.D. Seele, Eng. Mining, 158 (1957) 93. C. Tanford, The Hydrophobic Effect: Formation of Micelles and Biological Membranes, Wiley Interscience, New York, 1973. B.E. Novich, Sc.D. Thesis, MIT, Cambridge, MA, 1984. A.M. Gaudin and D.W. Fuerstenau, Trans. AIME, 202 (1955) 958. P. Somasundaran, T.W. Healy and D.W. Fuerstenau, J. Phys. Chem., 68 (1964) 3562. S. Chander, D.W. Fuerstenau and D. Stigter, in R.H. Ottewill (Ed.), Adsorption From Solution, Academic Press, New York, 1983, p. 197. J.J. Predah and J.M. Cases, in M.J. Jonesa (Ed.), Proc. 10th Int. Mineral Processing Congress, London, IMM, London, 1974, p. 473. P. Somasundaran and D.W. Fuerstenau, J. Phys. Chem., 70 (1966) 90. P. Connor and R.H. Ottewill, J. Colloid Interface Sci., 37 (1971) 642. F.F. Aplan and D.W. Fuerstenau, in D.W. Fuerstenau (Ed.), Froth Flotation, 50th Anniversary Volume, AIME, New York, 1962, pp. 170-214. H. Schubert, Freiberger Forschungshefte, 355 (1965) 51. B. Tamamushi and K. Tamaki, in J.H. Schulman (Ed.), Reagents in Mineral Technology, Surfactant Sci. Ser., Vol. 27, Marcel Dekker, New York, 1988, p. 79. J.H. Fendler and E.J. Fendler, Catalysis in Micellular and Macromolecular Systems, Academic Press, New York, 1975.
255 Printed in The Netherlands
Flotation Response Prediction from Interfacial Properties BRUCE E. NOVICH Ceramics Process Systems Corporation, 155 Fortune Boulevard, Milford, MA 01757 (U.S.A.) (Received 31 August 1989; accepted 2 October 1989)
ABSTRACT A quantitative relationship between contact angle and flotation response using a fundamental and measurable solution chemistry parameter, the critical micelle concentration, has been formulated. Bubble contact angles were measured for the quartz-alkylamine-water flotation system in which the effects of surfactant concentration, surfactant structure and solution pH on contact angle were determined. The alkylamines studied were n-hexylamine, di-n-hexylamine, n-dodecylamine, din-dodecylamine and 1,12diaminododecane. Peak contact angles were primarily a function of chain length, measured as 50” for the hexylamine system and 86” for the dodecylamine series. The diamine gave a contact angle of 60”. The contact angle was unaffected by solution pH over the range 8-10. The surfactant concentration, C,,, corresponding to the maximum contact angle, decreased with increasing number of hydrocarbon branches and increasing solution pH. Flotation recovery data and critical micelle concentrations were correlated to the contact angle data. The correlation analysis quantitatively indicated that 100% flotation recovery can be obtained at surfactant concentrations between 0.01 (C,) and the C, or between 0.01 (c.m.c.) and the c.m.c. for the flotation systems surveyed. This unique relationship between flotation response, micellixation and bubble contact angle suggests that solution chemistry near the particle surface and near the bubble surface governs the flotation process and the c.m.c., as a solution chemistry parameter, can be used to predict quantitatively flotation response.
INTRODUCTION
Flotation is the most widely used mineral separation process. Flotation can be broadly defined as an induced density separation brought about by interfaciai modification. In mineral engineering practice, flotation is the process of segregating one mineral type from another by selective gas bubble attachment onto one of the mineral surfaces, while submerged in a liquid medium. Selective separation is accomplished by modifying one of the mineralsurfaces with surface active agents, surfactants, to cause a favorable condition for gas bubble attachment. The particle-bubble aggregate, having a density that is less than the liquid medium, rises through the flotation cell and is collected at the top, leaving behind the other mineral types. 0166-6622/90/$03.50
0 1990 Elsevier Science Publishers B.V.
256
Bubble-particle contact and adhesion in aqueous suspension are the key factors controlling the froth flotation process. For flotation to occur, the gas bubble must contact and strongly adhere to the mineral surface. This attachment must be strong enough to survive the hydrodynamic shear forces present due to flotation cell mixing and aeration. The contact angle determination provides a direct measure of attachment strength between the bubble and mineral surface. Several studies have shown that a parallel relationship between contact angle and flotation recovery exists for a variety of flotations systems (e.g. alkylamine-quartz [l-4] or alkylsulphonate-alumina [ 51. While experimental and theoretical aspects of contact angle, as related to flotation systems, have been studied extensively, few investigators have adequately integrated experiment with theory. Further, practical aspects of these works have only been dealt with in empirical terms, which has inhibited the use of contact angle data as an online processing tool. The following study has provided a quantitative relationship between contact angle and flotation response using a fundamental and measurable solution chemistry parameter, the critical micelle concentration. Background To. understand better the gas-liquid-solid interface, several experimental studies have been carried out using the alkylamine-quartz flotation system as the model. Alkylamine adsorption at the bubble-solution (B/W) interface results from the non-polar hydrocarbon tail’s preference to be in a non-polar medium, air, and from the polar amine head’s preference to be in a polar environment, water. The alkylamine molecule acts as a bridge between the liquid-gas interface. Smith and Lai [2] stressed the importance of surfactant adsorption at the B/W interface by detecting time-dependent contact angle behavior at the air-alkylamine solution-quartz interface. Smith and Lai attributed this dynamic behavior to the reduction of the bubble/water and bubble/solid interfacial tensions, resulting from the adsorption of alkylamine on the bubble surface. This was later confirmed by Finch and Smith [ 61. Somasundaran [ 71, Digre and Sandvik [8] and Bleier et al. [9] calculated cationic amine adsorption densities at the B/W interface from surface tension measurements using the Gibbs adsorption equation: dot,, =2.303RZY’~NH4_,
dln(C,NH,._,)
(1)
where r is the adsorption density of cationic amine at the bubble surface and C is the concentration of cationic amine in bulk solution. Somasundaran [ 71 found that for a homologous series of n-alkylammonium acetates, the adsorption behavior at the B/W interface parallels the corresponding flotation and adsorption behavior at the S/W interface. Bleier et al. [9] calculated that the bubble surface is positively charged after cationic amine adsorption. Based on
257
this calculation, Bleier et al. postulated that one possible mechanism for bubble attachment is electrostatic attraction of the positive bubble surface to the negative quartz surface. EXPERIMENTAL
Quartz preparation High-purity quartz crystals were supplied by Western Electric Corporation, Merrimack Valley Works, North Andover, MA. These crystals were carefully grown from Brazilian quartz seed crystals to meet the exacting requirements for piezoelectric applications. The quartz samples used for contact-angle measurements were out from the crystals so that the test surfaces were parallel to either the (OOl), (OlO), (011) or (110) crystallographic planes. Each quartz surface, approximately 2 cm wide and 3 cm long, was wet ground with # 200, # 320 and # 500 silicon carbide and then with 3 and 0.5 p diamond paste. Scanning electron microscopy and surface profilometry revealed that the surface asperities were no higher than 1000 A. X-ray diffraction peaks were at least 25% more intense after the 0.5 pm grind than after the 3 pm diamond grind. Prior to each contact angle determination, the quartz surfaces were rinsed three times with 500 ml of deionized water and were then boiled in a 3 it4 nitric acid solution for 10 min. Immediately following the acid treatment, the quartz surfaces were washed five times with 500 ml of deionized water; crystals were soaked for at least 2 h in the final wash water. The surfaces were then dried at 23’ C under vacuum and were stored in a dry dessicator until further use. Properly cleaned crystals gave zero contact angle with a nitrogen bubble in water. Contact angle determination Bubble contact angle measurements were carried out on ground quartz surfaces using a Rame’ Hart contact angle goniometer. An optical glass cell was used to contain the mineral and surfactant solution system. Purified nitrogen bubbles were admitted to the cell through a Gilmont microburet with a flatfiled glass tip. All measurements were carried out in a plastic glove bag under positive nitrogen pressure to eliminate COz absorption, which leads to an unstable solution pH. Initial studies showed that the nitrogen environment was essential to obtaining stable and reproducible contact angle measurements. Solution pH was monitored and constant to 20.1 pH units throughout the treatment and measurement periods. The contact angle determination procedure was as follows: 150 ml of pH adjusted surfactant solution was placed into a dry optical glass cell, resting on top of a magnetic stirrer. The dry quartz plate was slowly submerged into the
258
surfactant solution, followed by a Teflon stirring bar. The magnetic stirrer was initiated at 40 rpm for 10 min, after which the stir bar was removed from the cell. The nitrogen microburet was inserted into the glass cell to a height of l2 mm above the mineral surface. A bubble was produced that touched the mineral surface by adjusting the microburet vernier by 0.05 ml. The buret was slowly withdrawn upwards from the mineral surface until the maximum contact angle was reached, while still maintaining bubble attachment. Decker [lo] characterizes this contact angle as the advancing angle. Reproducibility Analysis showed a measurement coefficient of variation of 5% (approximately 2 2 ’ ) for contact angles ranging from 22.0 to 86.7’ over a pH range from 6.0 to 10.0 at a constant dodecylamine concentration of 4-10m4 M. Contact angles measured on the (OOl), (llO), (010) and (011) crystallographic planes were the same within experimental error and were the same as those reported by Smith [ 111 and Lai [ 121 for polycrystalline quartz surfaces. Figure 1 compares contact angle data measured in this study to the results of Smith [ 3,111 for dodecylamine and di-n-hexylamine, showing excellent agreement.
n 18 X lo-ftJ 80
.
6.4 X 10
+
4.0 X 10-4M
M
A
2.6 X 10-4M
-
_
n-dodecylamine Symbol -T
I
Ol
6
7
= CMC
I
I
I
I
I
8
9
10
11
12
Solution
1
pH
Fig. 1. Bubble contact angle on quartz as a function of dodecylamine solution concentration and PH.
Decker [lo] has shown that the bubble contact angle measurement is strongly a function of measurement technique and bubble size. Pushing the bubble slightly toward the surface after contact gives the receeding contact angle and pulling the bubble slightly away from the surface after contact gives the advancing contact angle. Decker has also shown that the difference between advancing and receeding contact angles can be as much as 50” for the quartzdodecylamine system. Wakamatsu and Fuerstenau [ 13 ] define the equilibrium contact angle as the average of the advancing and receeding measurement. The advancing contact angle measured in this study exhibited the best reproducibility. RESULTS
Bzdhk contact angle The advancing contact angle was measured as a function of solution pH, alkylamine concentration and alkylamine architecture. As shown in Fig. 1 for n-dodecylamine, the contact angle increases to a maximum value at a particular solution condition, and then decreases as the condition is exceeded. This general curve was observed when the independent condition was solution pH or alkylamine concentration. The increase in contact angle prior to the peak appears to be due to increasing alkylamine surface adsorption, as particle surface hydrophobicity increases with increasing surface coverage [ 141. The decreasing contact angle with increasing surfactant concentration may be due to limited solubility of the alkylamine in water and to bubble repulsion as surfactant adsorption at the air/liquid interface becomes important, as described by Bleier et al. [9]. Figures 2 and 3 show similar behavior for n-hexylamine, din-hexylamine, n-dodecylamine, di-n-dodecylamine and 1,12-diaminododecane at pH 8.0 and 10.0, respectively. The solution concentration corresponding to peak contact angle decreased with increased number of branches for the primary and secondary hexylamines and dodecylamines. Accordingly, the peak contact angle also decreased with increased number of branches. The decreasing peak contact angle with increased branching may be attributed to the reduced alkylamine adsorption onto the quartz surface stemming from reduced solubility of the branched compounds and from increased steric hinderance from the neutral carbon chains, which prevent access of the charged alkylamine head to the quartz surface. The 1,12diaminododecane had a broader window of peak angle, giving a peak contact angle of 50” over several orders of magnitude of solution concentration. The 12-carbon dodecylamine and the 24carbon didodecylamine gave similar peak contact angles of approximately 80 O, twice as great as the peak contact angles for the hexylamine series at roughly 40”. Peak contact angles and the corresponding alkylamine concentrations, C,, at pH 8.0 and 10.0 are listed in Table 1.
s mbol
m
n-hexylamine
V
di-n-hexylamine
A
1,12 diaminododecane
= CMC
T
l n-dodecylamine l d'l-n-dodecylamine
a -8
I
-7
I
-6
I
I
I
-5
-4
-3
loglo Alkylamine
I
-2
Concentration,
I
I
-1
0
M
Fig. 2. Bubble contact angle on quartz as a function of alkylamine solution concentration 8.0.
at pH
The contact angle results indicate that peak contact angle is primarily affected by the length of the carbon chain that extends into the solution from the quartz surface. The primary and secondary hexylamines gave approximately the same peak contact angles close to 50’) independent of their carbon number. The same trend was observed for the primary and secondary dodecylamines, which gave contact angles of approximately 80’. Branched com-
261
symbol
n
n-hexylamine
'I
di-n-hexylamine
;
1,12 diaminododecane n-dodecylamine
l
di-n-dodecylamine ?
= CMC
1
-
I
-7
-6
-5
-4
-3
_*
~~ ;1
d
0
loglo Alkylamine Concentration,M Fig. 3. Bubble contact angle on quartz as a function of alkylamine solution concentration at pH 10.0.
pounds gave similar peak contact angles at 1% of the concentration of the unbranched alkylamines, suggesting that equal flotation performance can be achieved at greatly reduced surfactant concentrations using the branched compounds. This is supported by flotation recovery data given by Novich and Ring [ 151. The window for peak contact angle can be broadened by increasing the
262 TABLE 1 Peak contact angle concentrations for quartz Alkylamine
n-Hexylamine Di-n-hexylamine n-Dodecylamine Didodecylamine Diaminododecane
Peak contact angle (degrees)
Peak contact angle concentration C, 04)
pH 8.0
pH 10.0
pH 8.0
pH 10.0
52 48 86 82 60
60 55 86 80 63
1.4.10-l 5.1.10-3 1.0*10-3 1.0.10-5 1.0.10-2
3.2.10-’ 4.0.10-4 1.0*10-4 1.4.10-5 5.0.10-4
surfactant ionicity, as demonstrated by the broad peak angle behavior of the lJ2diaminododecane with an accompanied decrease in bubble solid adhesion.
DISCUSSION
Bubble contact angle and flotation response Novich and Ring [ 151 measured flotation response for the aqueous alkylamine solution-quartz-nitrogen system using a modified Hallimond microflotation cell system as described by Fuerstenau et al. [ 161. Novich and Ring found that all of the flotation response curves, plotted as percentage flotation recovery as a function of alkylamine solution concentration at constant pH or as a function of solution pH at constant alkylamine solution concentration, had the same general shape, as shown in Fig. 4. Bleier et al. [ 91 defined a minimum critical flotation concentration, (c.f.c. ) min, as a characteristic concentration above which good flotation recovery is experienced. Novich and Ring defined the (c.f.c.), as a characteristic concentration above which poor flotation recovery is experienced. Optimal flotation system design calls for a collector concentration between (c.f.c.),, and (c.f.c.),,,. Table 2 shows the values for the critical flotation concentrations at pH 8.0 and 10.0 for the primary and secondary alkylamines and the diaminoalkane tested. Also listed in Table 2 is the ratio of peak contact angle concentration to critical flotation concentration. were constant within experimental The ratio of (c.f.c.),,/C, and (c.f.c.), error, as approximately 0.01 and 1, respectively. These results indicate that a proportional relationship exists between the solution chemistry corresponding to the peak contact angle and the solution chemistry corresponding to the peak flotation recovery.
263
-
I
I
I
-5
-4
-3
I
O-
O-
O-
O-
O-
O-
o-
oD-
3-
-2
loglo Eukcylanxine Umcentration,M Fig. 4. Flotation recovery curve for dodecylamine and quartz at pH 8.0 (from Ref. [ 151).
Bubble contact angle and critical micelle concentration Micellization is a surfactant aggregation phenomenon which occurs at relatively high surfactant concentrations, close to the solubility limit. Typically, micelles are aggregates of 50-100 surfactant ions in which the hydrocarbon tails are weakiy bound together by van der Waals forces. The polar amine heads remain fully solvated, as they are directed outward into the polar solution, giving a spherical or ellipsoidal geometry [ 171. The surfactant concentration at which micellization occurs rapidly is the critical micelle concentration
264 TABLE 2 Critical flotation concentration Alkylamine
n-Hexylamine Di-n-hexylamine n-Dodecylamine Didodecylamine Diaminododecane
lOglo (c.f.c.) , i ,
log~o( c.f.c. ) m,~
loglo ( c.f.c. ) min/Cp
loglo (c.f.c.) m~/Cp
pH8.0
p H 10.0 p H 8 . 0
p H 10.0 p H 8 . 0
p H 10.0
pH8.0
p H 10.0
-3.3 -4.5 - 4.5 - 6.6 -4.1
-4.1 -4.7 - 5.5 - 6.5 -5.4
-2.4 -2.2 - 3.5 - 4.0 -3.0
-2.4 -1.7 - 1.7 - 1.8 -2.1
-0.1 0.4 0.8 0.8 0.7
0.1 1.1 0.5 0.8 0.3
-1.0 -1.7 - 1.9 - 4.0 -1.3
-2.2 -2.2 - 1.9 - 1.9 -2.1
(c.m.c.) which is accompanied by an abrupt change in solution properties such as viscosity, surface tension and specific conductivity. MiceUization is a solution process that reduces the alkylamine activity, having a significant effect on the interfacial properties at the solid/liquid/gas interface. Using coagulation experiments, Novich [ 18 ] has shown that micellization occurs at concentrations below the critical micelle concentration. Below the c.m.c., this aggregation becomes important at the solid/liquid interface and above the c.m.c., the surfactant aggregation becomes important at the liquid/gas interface. Gaudin and Fuerstenau [19] postulated that as surfactant ions adsorb onto solid surfaces from solution, the surfactant concentration in the double layer approaches the c.m.c., even though the bulk alkylamine solution concentration is several orders of magnitude lower than the c.m.c. Using Gouy-Chapman theory, Gaudin and Fuerstenau calculated that the ratio of surfactant concentration in the bulk to that in the double layer was 0.01 at monolayer surface coverage. They termed micelle formation in the double layer as hemi-micelle formation. Surface micelle formation with respect to surfactant structure and flotation response has been discussed by Somasundaran et al. [20]. Chander et al. [21] state that hemi-micelle formation is the direct analogue of bulk solution micelle formation, so that system conditions that affect micelle formation have a similar effect on hemi-micelle formation. The work of Chander et al. implies that system conditions such as temperature, pH and salt concentration, which effect micelle formation in solution, will simultaneously effect surface micelle formation and solid-liquid-gas interfacial properties. The study of Predali and Cases [22 ] of alkylamine adsorption onto biotite supports this hypothesis by showing how a homologous series of adsorption curves converge to one general curve when equilibrium surfactant concentration is normalized with critical miceUe concentration. Novich [18] showed the same curve convergence for several adsorption systems: alkylamine--quartz [18], aluminaalkylsulphonate [23] and the alkylamine-latex-G [24] systems. The generalized adsorption equation relating adsorption density, critical micelle concen-
265
I
I
I 10-4 Reduced
10-3 Equilibrium Alkylamine
Fig. 5. Zeta potential for the quartz-dodecylamine centration, X= C,/c.m.c. (from Ref. [ 201)
.
100
10-Z 10-l Concentration,X=C/CW
system plotted as a function of reduced con-
TABLE 3 Critical micelle concentrations, log,,(c.m.c.) Alkylamine
n-Hexylamine Di-n-hexylamine n-Dodecylamine Di-n-dodecylamine 1,12-Diaminododecane
c.m.c.
(c.f.c.),,/c.m.c.
(c.f.c.),/c.m.c.
C,/c.m.c.
pH8.0
pH 10.0 pH8.0
pH 10.0 pH8.0
pH 10.0 pH8.0
pH 10.0
-1.4 -2.1 -2.4 -4.3 -2.0
-2.2 -2.5 -3.7 -4.3 -3.4
-1.9 -2.3 -1.8 -2.2 -2.0
-0.1 0.3 0.2 0.3 0.4
0.5 -0.4 -0.3 -0.5 0.1
-1.9 -2.5 -2.5 -2.2 -2.1
0.4 0.4 0.4 0.3 0.4
0.5 -0.2 -0.3 -0.7 0.0
tration and equilibrium solution concentration is given and has been verified by Novich and Ring [ 151. Normalizing interfacial property results to c.m.c. has been shown to cancel effects of surfactant type, chain length, branching and solution chemistry for flotation recovery data and electrophoretic mobility [20] data, as shown in Fig. 5. Novich and Ring [ 151 determined critical micelle concentrations for the primary and secondary alkylamines and the diaminododecane as a function of solution pH. Their c.m.c. results are listed in Table 3, showing a decrease of
c.m.c. with increasing pH for the primary and secondary compounds. Table 3 also lists the peak contact angle and critical flotation concentrations when normalized to the c.m.c. at pH 8.0 and 10.0, showing the peak contact angle concentration and critical flotation concentration to be approximately equal to the c.m.c. The experimental results have shown that the peak contact angle concentration, the maximum critical flotation concentration and the critical micelle concentration are approximately equal. The experimental results also show that minimum critical flotation concentration, occurs at 1% of the C,, and c.m.c. This is consistent with Gaudin and Fuerstenau [ 191 and Aplan and Fuerstenau [ 251, who state that the condition required for the association of adsorbed alkylammonium ions at the quartz-solution interface at pH 7 is constant at an equilibrium solution concentration equal to 1% of the c.m.c., based upon electrokinetic data for the C8-, Cl,,-, C12-,C14-and GIG-alkylamines.These results were similar for all of the alkylamines that were tested. The contact angle and flotation data, as related to the c.m.c., can be used to develop a quantitative model for flotation. At surfactant concentrations less than the c.m.c. are greater than the (c.f.c.),in, the solid surface-solution interface can be depicted as a continuum of adsorbed surfactant molecules, with a majority of hydrocarbon tails pointing away from the particle surface [ 141, as shown in Fig. 5. Bleier et al. [ 91 showed that for the alkylamine system, the bubble surface is positively charged, as the hydrocarbon tails occupy the bubble gas space and the polar amine heads remain solvated in solution. Flotation can occur at this point, as the hydrocarbon tails bridge the particle surface and the bubble interior. As the surfactant concentration increases, more hydrocarbon tails are available for particle-bubble bridging, causing the contact angle to increase and flotation recovery to remain at 100%. As the solution surfactant concentration approaches the critical micelle concentration, very strong adhesion between the bubble and particle surface should result, as indicated by a maximum contact angle. Schubert [26] and Tamamushi and Tamaki [ 271 indicate that at the c.m.c. the adsorbed multilayer is saturated, from a leveling off of the adsorption curve. The c.m.c. condition represents a highly unfavorable condition for surfactant solvation and represents the most favorable condition for bubble attachment, as the hydrocarbon tails continue to bridge the particle-bubble interface and act to minimize the polar head repulsion at the bubble-solution interface [ 281. At concentrations greater than the c.m.c., alkylamine molecules micelle to the last layer adsorption, giving a bilayer structure [ 17,281, as the charged heads point into the bulk aqueous solution [ 191. As a saturated positively charged bubble surface comes into contact with the charged bilayer, repulsion results and the contact angle falls to zero.
267
I
Q~
0
~Q
¥ =-
2o
io
I,
15
~
0
M
I
~^
~d v
=I ~ 8 ,.Q
°~ d~../~
~ 0
=,
~ °~
io
L~
2
I';
.o V
c;
i'F-
268 SUMMARY AND CONCLUSIONS
Bubble contact angles were measured for the quartz-alkylamine-water flotation system in which bubble contact angle and flotation response were measured as a function of surfactant concentration, surfactant structure and solution pH. Maximum bubble contact angles were approximately 50” for hexylamines and 80’ for dodecylamines. The equilibrium surfactant concentration corresponding to the maximum contact angle, C,, decreased with increased carbon number, increased number of hydrocarbon branches and increased pH. The critical micelle concentration, c.m.c., which describes the surfactant behavior in solution, was correlated to the bubble contact angle data and showed a parallel relationship between C,, and the c.m.c. Normalizing the flotation recovery data to C, and the c.m.c. indicated that full flotation recovery can be predicted at approximate surfactant concentrations between 0.01 C,, c.m.c. and 1.0 C,, c.m.c. A model was proposed to relate contact angle, flotation recovery and c.m.c. Hydrocarbon bridging between the particle surface and bubble appear to be the principal bubble adhesion mechanism corresponding to 100% flotation recovery and increasing contact angle. Flotation cessation at surfactant concentrations above the c.m.c. results from bubbleparticle repulsion. Interfacial properties can be used to predict quantitatively flotation response as a function of flotation system conditions. Surfactant micellization at the solid surface-solution interface is responsible for the onset of flotation and surfactant micellization at the bubble-solution interface is responsible for the termination of flotation. ACKNOWLEDGEMENTS
The author would like to acknowledge the valuable input and assistance from Dr Terry A. Ring and the valuable program support from the W.R. Grace Co. and the SOHIO Center for Excellence at M.I.T.
REFERENCES 1 2 3 4 5 6 7 8 9
D.W. Fuerstenau, Trans. AIME, 208 (1957) 1365. R.W. Smith and R.W. Lai, Trans. AIME, 235 (1966) 413. R.W. Smith, Trans. AIME, 254 (1973) 353. D.W. Fuerstenau, T.W. HeaIy and P. Somasundaran, Trans. AIME, 229 (1964) 321. I. Iwasaki, S.R.B. Cooke and Y.S. Kim, Trans. AIME, 223 (1962) 113. J.A. Finch and G.W. Smith, Trans. IMM (London), 77 (1968) C213. P. Somasundaran, Trans. AIME, 241 (1968) 105. M. Digre and K.L. Sandvik, Trans. IMM (London), 77 (1968) C61. A. Bleier, E. Goddard and R. K&arm, in M.C. Fuerstenau (Ed.), Flotation, A.M. Gaudin Memorial Volume, Vol. 1, AIME, (1976) 117.
10 11 12 13 14
15 16 17 18 19 20 21 22 23 24 25 26 27 28
T. Decker, Ph.D. Thesis, MIT, Cambridge, MA, 1964. R.W. Smith, Trans. AIME, 226 (1963) 427. R.W. Lai, Ph.D. Thesis, University of California, Berkeley, CA, 1970. T. Wakamatsu and D.W. Fuerstenau, Trans. AIME, 254 (1973) 123. B.M. Moudgil, H. Soto and P. Somasundaran, in P. Somasundaran and B. Moudgil (Eds), Reagents in Mineral Technology, Surfactant Sci. Ser., Vol. 27, Marcel Dekker, New York, 1988, p. 79. B.E. Novich and T.A. Ring, Langmuir, 1 (1985) 701. D.W. Fuerstenau, P.H. Metzger and G.D. Seele, Eng. Mining, 158 (1957) 93. C. Tanford, The Hydrophobic Effect: Formation of Micelles and Biological Membranes, Wiley Interscience, New York, 1973. B.E. Novich, Sc.D. Thesis, MIT, Cambridge, MA, 1984. A.M. Gaudin and D.W. Fuerstenau, Trans. AIME, 202 (1955) 958. P. Somasundaran, T.W. Healy and D.W. Fuerstenau, J. Phys. Chem., 68 (1964) 3562. S. Chander, D.W. Fuerstenau and D. Stigter, in R.H. Ottewill (Ed.), Adsorption From Solution, Academic Press, New York, 1983, p. 197. J.J. Predah and J.M. Cases, in M.J. Jonesa (Ed.), Proc. 10th Int. Mineral Processing Congress, London, IMM, London, 1974, p. 473. P. Somasundaran and D.W. Fuerstenau, J. Phys. Chem., 70 (1966) 90. P. Connor and R.H. Ottewill, J. Colloid Interface Sci., 37 (1971) 642. F.F. Aplan and D.W. Fuerstenau, in D.W. Fuerstenau (Ed.), Froth Flotation, 50th Anniversary Volume, AIME, New York, 1962, pp. 170-214. H. Schubert, Freiberger Forschungshefte, 355 (1965) 51. B. Tamamushi and K. Tamaki, in J.H. Schulman (Ed.), Reagents in Mineral Technology, Surfactant Sci. Ser., Vol. 27, Marcel Dekker, New York, 1988, p. 79. J.H. Fendler and E.J. Fendler, Catalysis in Micellular and Macromolecular Systems, Academic Press, New York, 1975.