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Double-layer effects in the flotation of fine particles
DOUBLE-LAYER
EFFECTS IN THE OF FINE PARTICLES
FLOTATION
G L COLLINSt and G J JAMESON Department of Chemical Engmeenng, Imperial College, London, SW7, England (Recerued 9 July 1976, accepted 12 October 1976) Abstrae-Expenments have been conducted III wluch the charges on parkles and bubbles m a flotation process have been measured The partxles were polystyrene latlces of dmmeters between 4 and 20 v The bubbles were of mean dmmeter 53 m A catmmc sutfactant was used to promote ilotatmn, and the charge on the parkles and bubbles was controlled by add~tmnof sodmm sulpbate solutron To measure the charge on bubbles, they were generated electrolyacally IIIa glass electrophmesa cell so that they rose vertxally up a %a~ level” m the cell. whtle at the same bme movmg sideways under the a&on of a honzontal potenti grtient The honzontal velocity, taken with the known potentml went. gave the electromob&y The bubbles were found to carry the same sign as the partxles (posltwe) ami under the same electrolyte concentra~ons, the charge on the parhcles and bubbles was approxunately the same Experzmentally determmed rate constants for flotation were found to depend strongly on the bubble and parhcle charge,decreasmgby an order of magmtt& as the charge mcreasedfrom 30 to 60 mV The data were well correlated by the equation
-In&/d,‘“)=3
9+0 116 U,JJ,
where k. IS the rate constant (mtr-‘k d, 1s the uartxle dmmeter (JUII) and U,, l3, are the ekctmmobties (runls/Vicm)of the pmcle and‘bubbk r&pectweiy
INTRODUtXION Froth flotatzon has been used for many years for the separatton of valuable mmerals from waste matenal Most of the early research was concerned with the chenustry and mode of action of the collectors, flotation agents, activators, depressers, forthers, etc which are added to render the desued mater& hydrophobc wMe leavmg the waste m hydroph&c form There IS a very extensive hterature on these topics [l-4] The physrcal aspects such as the hydrodynamic mtera&ons between bubbles and particles, have received comparatively less attentson, although mention IS made m[l+ and the especial problems encountered unth fine part~les have been reviewed by Trader and Warren[fl There are clearly a large number of physical vanables wbch should be taken mto account when attemptmg to descnbe the collection of parhcIes by bubbles, but the most unportant are probably the size of the particles and the bubbles, the charges they bear, and the “hydrophoblOf these the varrable city” on the surfaces of the pticles on which most work has been done are the pacle sme and charge One of the first stu&es was by Gaudm et al [6] who used a steady state techmque to measure the rate of flotation of galena crystals m a mechamcal cell, and found that for parhcles up to 4 m m dmmeter, the flotation rate was mdependent of pmcle size but m the range 4-20 pm It was dvectly propotional to partrcle dmmeter No mention of bubble SIP was menhoned but it was probably between 0 2 and 2&n, typical figures for a mechamcal cell Other expenmental work on the effect of p&cle size mcludes that of Moms[~, Bushell[8], Tomlmson and Flemmg [91 and Fhnt and Howarth [lo] *Present address CSR Ltd , O’Connell Street, Sydney 2oo0, Austraba CESVol
32. No
LA
Recently, Reay and RatclX[ll, 121 have presented an analysis of the colledon of small pticles by bubbles The results of theu analysis are very mterestmg for they pr&ct a mmunum m the collection efficiency at a parhcle size around 1 firn m dmmeter Below this diameter, collection IS enhanced by Browman Fusion, and for larger pmcles the hydrodynanuc mteractions are more favourable for collection. They also camed out expenments on glass spheres and polystyrene pticles It was found that the rate of flotation of the glass spheres varied approxunately as the 1 5 power of part&e dmmeter but for the polystyrene pmcles the exponent was about 0 5 Recent experunents with polystyrene support the choice of a 15 power dependence [ 131 The effect of particle charge was mvestlgated by Derjagum and Shukaludse[14] who measured the zeta potential of antiomte pticles, wbch are naturally hydrophobic They found that the rate of flotation dropped sharply as the zeta potent& of the pmcles was mcreased beyond a cntical value Jaycock and Otted [lS] studred the adsorption of a catiomc surfactant on to uemvely charged sliver iodide pamcles, and found that the flotation rate measured III a Halhmond tube was west when the zeta potentml of the AgI was zero. De Vlvo and Karger[l6] found a slmllar effect with clay particles However m both cases, coagulation could have taken place because the zeta potenti was zero and rf It had occurred, the mcrease m pticle size could have caused the mcrease rate of flotation The measurement of the charge on a small gas bubble IS not easy to accomphsh and it IS not surpnsmg that few mve@gators have studied bubble zeta potent& Ihbbs, Slrols and Bredm[lfl stu&ed the effect of particle zeta potential the streammg current of ~lsmg bubbles on flotation rate, usmg the method of Bach and Gdman[l81
G L
240
COLL.INS
and G J
and concluded that the double layer mteractions were Important, 111the flotation of quartz m the presence of dodecylamme hydrochlonde It 1s ddiicult to mterpret the results theoretically because the bubbles were well beyond the Stokesian regune of flow, as were those of Samygm, DerJagum and Dakhm[l9] C~chos [20] mvestigated the mfluence of the zeta potential of the bubbles usmg the techmque of McTaggart[21] m whch the bubbles are captured m the centre of a rotatmg tube In some experunents the zeta potenti appeared to be s&cant whereas m others It seemed to have no effect In an earher paper[13] we described experunents in which the effect of parUcle size and charge on the rate of flotation of polystrene par&les was measured The polystyrene was floated m the presence of cetyl trunethylammoruum bromide (CTAB) as collectorjfrother and &he charge was altered by addition of soduun sulphate We found that, mdependently of the pticle charge (for pticles m the range 4-20 *) the flotation rate constant varied as the dmmeter to the 1 5 power However, the particle charge (or rather, the electromoblllty of the pticles whch was the parameter actually measured) appeared to have a very sign&ant effect on the flotation rate constant, which altered almost by an order of magmtude when the mobtity altered from 2 7 to 5 2 pm/slV/cm The evidence so far seems to pomt to the conclusion that m the flotation of small particles, electrical doublelayers could be an nnportant factor However, for this to be estabhshed it must be shown that not only are the pticles charged but so also are the bubbles, for If the latter were uncharged it would be unhkely for the flotation rate to be mfluenced much by the charge on the pticle alone, although thus may be m&catwe of a secondary effect such as the quahty of adsorbed hydrphoblc surfactant ion on the par&le’s surface In thrs paper, we extend ourprevlous work to mclude the effect of the charge on the bubble The sign of the charge and the magnitude of the pa&cle and bubble electromobrlltles, have been measured under conditions sumlar to those existing m the flotation vessel A sunple correlation for the effect of the bubble and pticle charge on the flotation rate constant 1s proposed
&BdESON
the same, 5 x lo-’ M Ethanol (0 5% V/V) was used to promote bubble formation at the smtered disc Sodium sulphate was added m the range 5 x lo-’ to 1 x lo-’ molar to vary the particle charge Addition of the Na2S04 m tlus range caused the double layers to collapse thereby weakenmg the charge The experunental method followed a techruque developed by Reay and Ratchff[l2] Samples taken before and durmg a run were analysed for pticle concentration and size dlstnbution, and the rate of removal of particles of a lpven size could be found by studymg the form of the distibution curve as a function of tune The size tistriiutron of the particles was measured with a Coulter Counter Model ZB The moblllty of the pmcles was measured m a Rank Brothers Part&e mcroElectrophpresrs apparatus Great care was taken m the performance of the flotation experunents and full details can be found m[13] To analyse the results it was assumed that the rate of removal of particles from the flotation cell was first-order v&h respect to the par&le concentration The rate equation 1s therefore - dN/dt = k,Nt
(1)
where N, LSthe number of particles of a gwen dmmeter m the cell at tie t, and kp IS a rate constant If the p&cle concentration at zero at zero tune ISNO,mtegraaon yields In (N,/Nd = kit
(2)
so the rate constant can be obtamed from a plot of In (N,/NO) vs tnne Earher[l3] we showed that the assumption of first-order kmetics was well founded, and that the rate constant vaned approxunately as d, to the 15 power OF
RJBULm
FLCWATION ExpERIhIENTs
The experunentally measured flotation rate constants are shown m Figs 1-6 Each Ggure is for a constant mean parhcle dlarneter, and the rate constant 1s p;lven as a function of the measured electromobfities of the particles (The Coulter Counter can be set to measure the number density of pmcles below a gven threshold, so that by repetitively measurmg the number densities at
FLOTATION EwERlMENTs The flotation experunents were cmed out batchwlse m a 1 dm’ glass filter funnel of base duuneter 12 cm and he&t 1Ocm Nitrogen was passed through the smtered glass base of the filter funnel or cell, at a rate of 3 5 dm3/hr The pore size of the base was m the range 5-15 m and it produced bubbles of mean diameter 53 @, with a standard devmtron of 9 pm The particles were of polystyrene (94% styrene, 6% divmylbenzene co-polymer), of dmmeter between 4 and 2Opm with a mean of 15 pm on a we& basis and 10 pm on a number basis The concentration of polystyrene particles was 0 5 gm/dm3, the same for all runs The surfactant used to float the pticles was cetyl trnnethylammonmm bromide (CTAB), a quaternary ammomum salt yleldmg a surface active cation The uutial CTAB concentration was always
OOll+, 0
’ 2 %
Fu
#
I
I
3
4
5
I
(pmIs/V/cm)
pacle electromobfityon the flotationrate constant Partxle mean dmmeter 6 6 pn
1 The effect of
Double-layer effects m the flotatmn of fine parhcles
241
OOlJ,l
0
2
I
I
I
3
L
5
“E
l+g 2 The effect of partxle electromobtity on the flotation rate constant Parhcle mean dmmeter 8 3 ILL
(pmlslV/cm)
Fig 5 The effect of park+ electromobdlty on the flotation rate constant PaWcle mean dmmcter 16 5 qn
dp = 10 L /un
.2
(pm/s/Vlcm)
"E Fa
“E
3 The effect of parhcle electromobtity on the flotation rate constant Partxle mean dmmeter 10 4 @
0
dP
0.
r
131
3
2 “E
l%g
4
5
1:pm/s/V/cm)
4 The effect of partxle electromob&y on the titat~on rate constant ParWle mean duuneter 13 1 m
thresholds one can find the number 111a given size were 5 81,7 32,9 22, 1162,14 63,18 44 and 23 23 pm, g~vmgmean diameters of the respective ranges as 6 6, 8 3, 104, 13 1, 16 5 and
various range
(pm/s/V/cm)
Rg 6 The effect of parkle electromob&y on the flotation rate constant. Partxle mean duuneter 20 8 ,um
20 8 ~UII) The electromobtity was controlled by add&on of sodmm sulphate to the suspension to be floated, and the measured values are shown m Table 1 for the WUIOUS Na2S04 concentrations The results clearly show that there was a rapid mcrease m the flomon rate, by an order of magmtude, as the mob&y was reduced from 5 to about 3 5 gnlslV/cm t At the lower !igure there was a levelhng off or perhaps a maxunum m the rate The graphs bear a str&mg resemblance m shape to those presented by Spielmarr and FWpatnck[23] for the collection of spherical latex parWes m packed beds of umform glass beads The zeta potentials were controlled by ad&t1011of electrolyte to the suspension The data from one of thev experunents were taken and replotted m FU 7, and the slrmlanty uvlthour results IS clear SpIelman and Fltzpatnck suggested that the shape of the curve was due to double layer effects and
The threshold diameters used
tThe ele&romobiUy of the parkles
IS measured m the electrophorests cell, and ISfound by dlvldmgthe observed velocity of the charged parkle by the unposed grad&t of potential The electromobWy IS obviously related to the charge or zeta potenti on the partxle, and for the cond&ons applymg here, the zeta potentud IS &= 12 85 U, mV, where U, IS the mcle electromoblllty m pms/s/V/cm (Shaw [22]) Thus [ ranged from about 30 to 60 mV For bubblesand parkles of the size we are concerned with, 6 and Ue are mdependent of the diameter
Table 1 Electromotittes
of parW1es and bubbles
Conccntratmn of sodmm sulphate (molar) lo-* 10x10-’ 2sx1o-3 50x lo-’ 1ox1o-2
50x
Mean mobd~ty Bubble 48 43 39 if
49 50 39 39
242
G
L C~LLWSand G
J
b
JAMESON
4
’
’
b’
Fig 8 Sidenew of flat electrophoreslscell Oxygenbubblesare generatedat the tip of the platmumwe at a by a 12 V DC pulse They movehonzontallyunderthe steadypotenti apphedacross platmum-blackedelectrodes b,b’ Cell cross sect.~on 1 x 10 mm
Fu 7 Dataof Spielmanaad Fltzpatnck[23] on filtrationof 9 5 e latex parhcles m a bed of glass spheres of dauueter0 25 mm Llqud super6cm.lvelocity 3 5 mm/s The filter coeffrclentIS analogousto the rate umstsnt k, m Figs l-6 Splelman and CukorC241 showed theoretlcally that the collection efliclency (or filter coetliclent) would behave m tbs way d double layer forces became unportant To prove that the presence of double layers on the parhcles and the bubbles IS responsible for the dependence of the flotation rate on the electromobtity of the pmcles, It ISnecessary to show (a) that the bubbles m the flotation cell had the same sign as the parUcles, 1 e they were positively charged, and (b) that the charge on the bubbles mcreased with decreasmg Na2S04 ad&bon, did the charge on the parQcles The expenments undertaken to test these pomts are now descnied DDUWT ME-
NT OF BUBBLE
EWCTROMOBlIXTY
The eqmpment used was a standard Rank Brothers electrophoresls apparatus A sample of the suspension is placed m a Pyrex glass cell across which a potential Merence can be unposed A charged pa&zle m the hqmd wdl move toward one or other of the electrodes, dependmg on the sign of the charge, and its velocity can be measured by v1ewmg it through a travelhng microscope, usmg dark-ground &mum&on A standard flat electrophoresls cell of cross section 1 by IOmm was modtied shghtly by seahng two platmum wves mto the upper and lower walls as m Fu 8, unth Arald~te, au epoxy resm The flotation solution contammg various concentrations of soduun sulphate was first saturated with oxygen then poured mto the moddied cell A short pulse of current from a 12V dry battery was passed through the solution through the wires The bottom we was connected to earth to ensure that the bubble was not charged by the cncmt Bubbles were produced which rose through the solution The electnc field of the instrument was svvltched on and the honzontal velocity of the bubbles was measured at a stationary level The diameter of the bubbles measured was around 35 Frn If they were much smaller they &ssolved, and d they were larger they rose to qu&ly too follow As the bubbles
rose they tended to move out of the field of wew of the nucroscope so to keep them 111mew the nucroscope was racked usmg the verttcal micrometer adjustment A bubble of 35 m dmmeter rises at about 0 5 mm/s and thus IS about the maxuuum speed with which the nucroscope could comfortably be moved The electromobtifies of the bubbles were calculated m the usual way, by d~v~dmgthe homontal component of velocity by the potenti gra&ent of the apphed field The results are presented m Table 1, together unth earher measurements of the mob&ties of the polystyrene par&les The bubble results are less consistent than those of the parWles, au mdication of the much more -cult experunental problems mvolved The results show clearly that the mob&ties of the bubbles and of the pticles were of the same order, and had the same sign, at the same concentration of sodmm sulphate ALTERNATlVE
EXPLANATIONS
The results @ve stroug support to the proposlhon that the charge on both the bubbles and the parhcles has a strong effect on the rate of flotation Smce m the expenments the charge was controlled by addition of sodmm sulphate, the posslbtity exists that the addWon of thus salt had effects other than the sunple alteration of the charge, whch could have changed the flotation rate Accordmgly tests were camed out to lind the effect of the Na2S04 additions on the followmg (a) the adsorption of surfactant on the surface of the bubble, (b) the size of the bubbles, and (c) the contact angle between bubbles and pa&cles The effect on adsorption was tested by measurmg the surface tension of solutions CTAB (5 x lo-’ M) contammg 0 5% V/V ethanol At concentrations 5 x 10W4, lo-‘, 5 x 10e3 and lo-’ molar, the surface tenslons were respectively 54 8, 53 0, 50 7 and 47 5 dyne/cm The Na2S04 clearly reduced the surface tension, as was expected The magmtude of the changes were not large but may have been sticient to alter the bubble sizes m the flotation cell, and possibly the ease unth which the pmcles could attach themselves to the bubbles To test the effect on the bubble size, a run was camed out at a concentration of Na2S04 of lo-’ M Bubbles nsmg m the flotation cell were photographed and their size &stnbution found The mean &eter was 56 Frn with a standard devotion of 11 w Thus cau be compared with
243
Double-layereffects m the flotatmn of line parbcles the mean size of 53 q m the presence of 1 3 x lo-’ M soduuu sulphate The two sets of photographs were taken under Identical con&fions, so although the eqmhbrmm surface tension was lowered by the ad&bon of the sodmm sulphate, the bubble sfze remamed essentially constant An attempt was made to !ind the contact angle between the partxles and the bubbles The latter were generated by electrolysis ti the flat electrophoretic cell, m the presence of polystyrene pmcles and photographs were taken of parhcles attached to bubbles after they had risen to measure to the top of the cell It was very ticult contact angles because of the small size of the latex parQcles Nevertheless, all the contact angles measured were m the range XMO”, and there was no de6mte change m contact angle as the sodnun sulphate concentration was mcreased The contact angle can be regarded as a measure of the hydrophoblclty or wettab&ty of a surface toward a particular solution, and the fact that It &d not change markedly suggests that there was no effect on the ease of attachment of parhcles to bubbles None of these alternative hypotheses appear to have any substance Accordmgly these ad&tional tests strongly support the conclusion that the observed effect of the sodmm sulphate on the rate of flotation was due to the formation of double layers on the parttcles and the bubbles, w& resultmg charges of the same sign and comparable magmtude on their surfaces
m-
3
116 U-Us
(3)
where kp, the flotation rate constant IS m mm-‘, the parMe deter dP IS m q and the parMe and bubble electromobdrties UE and Us are m pm/slV/cm For mterest, pre&cted rate constants from tlus correlatmn have been plotted m Fig 10, for par&les of various sizes vvlth zero charge The experunental data were obtamed for pticles vvlth zeta potent&s between 30 and 60 mV, so outside this range the curve can only be regarded as an extrapolation However, from comparison vvlth Figs 14 it appears that the rate constant at zero charge nses only a matter of 20 or 30% over the rate constant at a zeta potent& of 20 mV (UB = 15 v/s/V/cm) In our ex-
I
I
I
10
I
I 30
20
Ehg
9 Correlation of data on effect of parkle dmneter
and
pa&cle electromobtity 011the flotation I& constant k, Each pomt IS the mesa of 91~values of &J&“’ The verWal bsrs u&c&e the 95% umfidence lmuts Umts b, mm-‘, 4, ccm,UB, ue, clmls/Vlcm
-I
-i j
2
It now appears to be well estabhshed[l2,13] that for parhcles m the range 4-20 pm m dmmeter the rate constant kp vmes as the pa&cle dmmeter to the 15 power We can use the present results to form an emplncal equation which mcorporates also the effect of charge If we have two bodies carrymg hke charges $1, @z,the repulsive force between them vvlll vary as the product $& The larger the repulswe force, the lower would be the expected rate of flotation so the rate constant should be a func0on of #,&, or of the product of the respective electromobtities, UBUB At zero charge the rate constant would be expected to be a maxmuun and the trend of the results m Figs ld suggests a correlation of the form In (k+/dp’J) = A + BU&. which ISshown m Fig 9, where the data have been replotted The equation on the lme shown, wluch was obtamed by a least-squares fit, IS 3 9+0
I
“E”B
OVERALLCORRELATIONOF RESULTS
-ln(kJdp’5)=
J
0
1
,L 0
E%g
20
10
dp
(pm1
10 Rate constantsprehcted by the empmcal correlation at zero partde charge
penments we dehberately kept c lllgh to prevent coag&tion In a one-component system one would srmply want to maxmuse the rate of removal of that component (e g od pticles m a waste stream, or clay mcles from wash water) However i there are two components whch are to be separated, and both are of colloidal or near-colloidal dunenslons, it 1s hkely that random coagulation of the par&les would occur when they possess zero charge, and although the rate of flotation may then be a maxunum, the floated parhcles of one species may also carry w&h them parWles of the other, reducmg the effectiveness of the separation of the two Accordmgly m nuxed species It would seem undesuable to design for maxunum flotation rate and mstead, the parkles should be charged to the extent of 2&3OmV, thereby preventmg coagulation w&out a drastic redution m the rate of removal -OFGASRATEANDBUBBL.ESUE
descnbmg the flotation process, we have assumed a first-order rate equation m common Hrlth other w01kers[14.10-121 The experunental results described earher[l3] ccrtamly support the assumption of first-order In
G L COLLINS and G J JAMESON
244
kmetnx, as embodred m eqn (1) However, It 1s essentxd to reahze that the rate constant kp IS IIIno way a constant, and depends on a number of vanables not least of which rs the gas flowrate and the bubble size Klassen and Mokrousov[2] ckumed that fine pticles were floated better (faster?) by line bubbles, but this conclusion has been refuted by Traher and Warren[S] who imply that It 1s mconslstent with the work of Flmt and Howarth [ 101and Reay and Rat&E [ll] However, the posslbtity of confusion exists because there are several aspects to the acuon of a smgle bubble, namely the efficiency of collection, ,the volume swept by each bubble and the number density at constant gas rate, wbch all depend on the bubble size To see how the rate of removal of pmcles from the cell depends on the various parameters we shall look more closely at the kmetic model As a bubble rises m the cell it collects par&les, and the collection efficiency EC can be defined as the fraction of mcles m the path of the bubble which actually coalesce wrth it and are removed from the flotation cell In our cell the bubbles are formed at the sintered base and nse freely to the top vvlth only a gentle reclrculafion of the hqmd The cell appeared to be well mixed so the concentration of pticles may be assumed to be umform, and equal to NJV, where N, 1s the total number of partxles m the cell contammg a volume V, of hqmd and pa&cles The total number of partxles removed by a bubble as It nses, through the hqmd of he@t h IS therefore (EmdbzhM) (NV,) If the gas volume&x flowrate IS Q, the number of bubbles formed per second LSQ/(mdb3/6) Thus the rate of removal of particles from the cell IS --=dNl dt From which the rate “constant” 1s k
=
’
3QEch 2dbVc
(5)
Reay and Rat&f [l l] found theoretically that the collection e5clency of a bubble vanes mversely as the bubble duuneter squared, and thus was confumed by experunent for bubbles up to 100 q m dmmeter One IS therefore led to the conclusion, very stnkmg from a pracWal pomt of view, that the rate of flotation vanes mversely as da’at a constant gas flowrate There ISclearly a very s@cant gam m the production of a cell If the bubbles can be made as small as practicable If they are too small, of course, they w5 not float to the top If collectmg par&cles denser than water, but t&s would not apply to oti par0cles In a conventional Aotauon cell of the Denver type, eqns (4) and (5) may not apply exactly because the cell contents are strongly agrtated and the bubbles do not nse mdependent of each other, nor are they m a qmescent hqmd Nevertheless the same general conclusions would apply because the effective volume swept by a bubble would ultitely be related to Its size, and the number of bubbles produced at constant gas rate would vary mversely as the cube of the bubble dmmeter
CONCWSIONS
The results clearly demonstrate that 111the flotation of fine pmcles, the rate of flotation ISstrongly dependent on the charge on both the parhcles and the bubbles When the eiectromobWy of the particles was changed from 2 5 to 5 fl/sM/cm, correspondmg to zeta potential alteration from 30 to 60 mV, the rate of flotation dropped by a factor between 5 for the 6 6 ~UIIparWles and 20 for the 20 8 Frn par&les A new techmque has been described for measurmg the electromobfity of small gas bubbles, by motiymg a standard flat electrophoresls cell A smgle bubble IS generated by electrolysis and nses m the presence of a honzontal potenti gradlent The bubble IS held m the field of Mew of the observatton microscope by manual adlustment of the microscope shde m the vertmal &e&on The method could be unproved s&cantly If the rmcroscope were moved by a motoIlzed dnve The expenments on the bubbles showed that they were posltlvely charged, as were the pmcles, and under the same con&fions, the charge on the bubbles was approxunately the same as on the parhcles Tlus could be 9 very convement result d It IS found to be of general apphcabtity, because the charge on the bubbles IS very d&cult to measure m comparison with that of the pticles The results imply that the maxunum rate of flotation is achieved when the zeta potenti (or mob&y) of the parhcles 1s zero As the charge on the parbcles and the bubbles bmlds up, coalescence between them IStiblted by double-layer rep&Ion Some flotation systems have only one component wbch it ISreqmred to remove as far as practicable, such as a suspension of orl or clay m water In thus case It would obviously be advantageous to keep the charge as near to zero as possible, to promote coagulation pnor to fiotation as well as to help the bubbles and par&les to coalesce However, where there ISmore than one species present, and the reqmrement IS to remove one of them selectively, coagulation of the various species would most certamly be undesuable Accordmgly m flotation of muted speaes, It would probably be necessary to ensure that the parhcles carry sufficient charge to prevent coagulation, but not too much to mhiilt coalescence vvlth bubbles through double-layer repulsion The results suggest that a charge of around 20 mV IS probably optunum A simple correlation for the effect of charge on the flotation rate constant 1s proposed, takmg mto account the effect of pticle allameter It has the form -In(k,/d,“) where kp IS m mn-‘, ccm/slVlcm
= 3 9+0 116 U&B $
m pm
Acknow1edgtmenfs-G L
and UB, US are m
Colhas IS grateful to CSR Ltd, Sydney, Australia,for financialsupport We WE&to thankProf J T Dawes of Blrmmgham Umverslty for his helpfulsuggestions regardmg the correlation of the results
245
Double-layer effects m the tlotat~on of tie parUes NOTATlON
A surface area of bubble C concentration of surfaclant db dkmeter of bubble D d~@usi~ty of surfactant m water EC collect~n efficEncy of bubble h depth of hqmd m flotatin cell kL. mass transfer coellklent rc, flotation rate constant number of moles of surfactant N* No uutml number concentrauon of particles N* number concentration of parOcles at tune t Q gas volumetic flowrate gas constant R Reynolds number of nsmg bubble Re Schrmdt number of dlfEusmg surfactant SC Sh Sherwood number of nsmg bubble t tune T temperature, K ZJ nse velocity of bubble UB electrophoretic moblllty of bubble, &s/V/cm electrophorek mobMy of par&le. elm/s/V/cm ue VC volume of hqt.ud 111flotation cell Greek symbols y surface tension
r l p p #
surface excess of surfactant zeta potential, = 12 85 Ue mV hqwd vlscoslty hqud density charge on parUe or bubble
REFESENCES
[l] Sutherland K L and Wark J W, PnnczpIes of mot&on Australasian Institute of Mmmg and Metallurgy, Melbourne 1955 [2] Klassen V I and Mokrousov V A , An Introduction to the Theory of Flotation, Butterworths, London 1%3 [3] Joy A S and Robmson A J , III Recent Progress m S&ace Scrence(Ed~tedbyJ F Damelh, K G A PankhurstandA C mdtiord), Vol 2 Acadenuc Press, New York 1964 [4] Fuerstenau D W and Healy T W , 111Adsotptlue Bubble Separarron Technrques (E&ted by R Lemhch) Acadenuc Press, New York 1972 151 _ _ Traher W J and Warren L J , Int J Muter Process 1976 3 103 [6] Gaudm A M , Schulunarm R and Schlecbten A W , .7 P hys Chem 1942 46901 [fl Moms T M , Trans A I M E 1952 193 794 [8] BushellC H G, Trans AIME 1%2223 266 [9] Tomlmson H S and Flemmg M G , m Mineral Processrng (E&ted by A Roberts) Pergamon Press, London 1963 [IO] Flmt L R and Howarth W J , Chem Engng Scr 1971 26 11.55 [l l] Reay D and Ratclti G A , Canad J Chem Engng 1973 51 178 1121 Reay D and Rat&f G A, Chad J Chem Engng 1975 53 481 1131 Collins G L and Jameson G J , Chem Engng Scz 1976 31 985 1141 Derlagum B V and Shukaladse N D , Tmns IMM 1%170 569 [15l Jaycock M J and OttetiR H , Trans IMM 1963 72497 [16] DeV~vo D G and Karger B L Sep SCL 1970 5 145 [17] Gibbs H P , S~OISL L and Bredm R ,Research Rep R248
zex
Mmes and Resources, Mmes Branch,
Bach N’and Gilman A, Actu Physlcochzmrca V.R S S 1938 9 27 SamygmV D,DerJagumB V andDukhmS S,Koll ZA 196426424 Clchos C , Fretb~~ Forschungs 1973 513 7 McTaggariH A,& hfag 192244386 Shaw D J . E~ectroDhonsrs AcadermcPress, London 1969 Spielman i A ani Fltzpatnck J A, J Coli Interface Sci 1973 43 350 Spielman L A and Cukor P M , .T Co11 Inter/ace Scl 1973 43 51 Harper J H , Adv Appl Mech 1972 12 59 Calderbank P H , The Chemrcal Engmeer, No 212, CE209 1967 Petica B A, Trans Faraday Sot 1954 60 413 Perry J H , Chemical Engmeers Handbook, 4th Edn McGraw-Hill. New York 1963 APmNDlx
Equdlbnum between bubble surface and surfactant sol&on If a gas bubble ISsuddenly formed m a soltion of a surf-t, Its surface Hrlllbe clean, and a limte bme ~IU be needed for surfactant to Muse to the surface and reach eqmhbrmm anth the solutton In our expenments we need to be sure that each bubble reaches eqmhbnum m the flotation vessel and m the electrophoresls cell, and that the tune needed to reach eqtibrmm IS only a small fractmn of the total residence ixme As soon as the bubble forms rt begms to me. so the transfer of molecules to the surface ISby convective d&~sion Because the bubble IS nsmg, the eqmhbrmm surface concentration (mollcm’) of surfactant ISunbkelyto be that of a surface m a stagnant hqmd (Harper [25]) but we can obtam a good appromtion to the mass transfer problem d we e&mate the tie to eqmliium by assummg that mass transfer occurs as d to a sphere nsmg with steady velocity, and the surface concentration at eqmhbrmm ISthe cflbbs surface excess Smce the bubbles are small(around 50 mdlameter m the flotation vessel and 30 m m the electrophoresls cell), the flow field about them ISStokeslan (Re < 1) and the mass transfer equation for low Reynolds number around a sphere can be used[26] Sh = 0 99 Re”3Sc”3
(AU
where Sh = Sherwood number (k&,/D) Re = Reynolds number (& Q/p) SC = Schrmdt number (&II) From the defimbon of the mass transfer coefficient, the number of moles NA whch are transferred from the bulk to the surface of the bubble m tune t IS N.+=krAhc
t
W)
where A is the area of the bubble and AC 1s the concentration tierence At eqmliirmm, the number of moles on the surface of the bubble ISI’A where r ISthe surface excess (moles/cm’) Hence the tie requued for eqml&n_un IS of order I = I-/k,Ac
WV
To calculate the surface excess the equation
r=-L-42
BRT dc
(A41
was used, m wluch c ISthe bulk concentration of surfactant and y is the surface temuon The constant j3 was grven a value of 2,
246
G L CousandG
foilowmg aryments of Pe&za[27] A plot of the measured values of the surface tenslon of our CTAB solution was constructed from whch drJdc was estimated to be -3 3 x 10’dynes cm’/mole at a Thus r= 5 x lo+ molar CTAB wncentrat~on of 3 5 x lo-‘* mole/cm* For the drffusivrty D of CTA3 m water we use 5 x 10dcm*/s wbch appears to be typti for large molecules[28] The concentration drfference AC obviously decreases with tune but as a g&e we use the bulk concentration c = 5 x lo-” molar, smce at t = 0 the bubble surface contams no smfactant For a 50~ &meter bubble, the Stokes nsmg velocity IS
J JAMJWN 0 137 cm/s, and from (Al) the Sherwood number IS 5 09. g~vmg k, = 5 1 x lo-’ cm/s Hence from (A3), t = 0 137 set A sun&u calctiti for a 30 + bubble ylcldcd t = 0 137 W-Calso These “tunes to equiliinum” are obviously only rou& gmdes but taken with the nse velocities (0 137 and 0 049 cm/s for 50 and 30 q bubbles respectively) they suggest that the bubbles reach equibbnum after movmg only a few bubble dmmeters from the pomt of formation Accordmgly we conclude that the bubbles are essentmlly m equihbnum vvlth the bulk flotation salmon almost from the tune they are formed
EFFECTS IN THE OF FINE PARTICLES
FLOTATION
G L COLLINSt and G J JAMESON Department of Chemical Engmeenng, Imperial College, London, SW7, England (Recerued 9 July 1976, accepted 12 October 1976) Abstrae-Expenments have been conducted III wluch the charges on parkles and bubbles m a flotation process have been measured The partxles were polystyrene latlces of dmmeters between 4 and 20 v The bubbles were of mean dmmeter 53 m A catmmc sutfactant was used to promote ilotatmn, and the charge on the parkles and bubbles was controlled by add~tmnof sodmm sulpbate solutron To measure the charge on bubbles, they were generated electrolyacally IIIa glass electrophmesa cell so that they rose vertxally up a %a~ level” m the cell. whtle at the same bme movmg sideways under the a&on of a honzontal potenti grtient The honzontal velocity, taken with the known potentml went. gave the electromob&y The bubbles were found to carry the same sign as the partxles (posltwe) ami under the same electrolyte concentra~ons, the charge on the parhcles and bubbles was approxunately the same Experzmentally determmed rate constants for flotation were found to depend strongly on the bubble and parhcle charge,decreasmgby an order of magmtt& as the charge mcreasedfrom 30 to 60 mV The data were well correlated by the equation
-In&/d,‘“)=3
9+0 116 U,JJ,
where k. IS the rate constant (mtr-‘k d, 1s the uartxle dmmeter (JUII) and U,, l3, are the ekctmmobties (runls/Vicm)of the pmcle and‘bubbk r&pectweiy
INTRODUtXION Froth flotatzon has been used for many years for the separatton of valuable mmerals from waste matenal Most of the early research was concerned with the chenustry and mode of action of the collectors, flotation agents, activators, depressers, forthers, etc which are added to render the desued mater& hydrophobc wMe leavmg the waste m hydroph&c form There IS a very extensive hterature on these topics [l-4] The physrcal aspects such as the hydrodynamic mtera&ons between bubbles and particles, have received comparatively less attentson, although mention IS made m[l+ and the especial problems encountered unth fine part~les have been reviewed by Trader and Warren[fl There are clearly a large number of physical vanables wbch should be taken mto account when attemptmg to descnbe the collection of parhcIes by bubbles, but the most unportant are probably the size of the particles and the bubbles, the charges they bear, and the “hydrophoblOf these the varrable city” on the surfaces of the pticles on which most work has been done are the pacle sme and charge One of the first stu&es was by Gaudm et al [6] who used a steady state techmque to measure the rate of flotation of galena crystals m a mechamcal cell, and found that for parhcles up to 4 m m dmmeter, the flotation rate was mdependent of pmcle size but m the range 4-20 pm It was dvectly propotional to partrcle dmmeter No mention of bubble SIP was menhoned but it was probably between 0 2 and 2&n, typical figures for a mechamcal cell Other expenmental work on the effect of p&cle size mcludes that of Moms[~, Bushell[8], Tomlmson and Flemmg [91 and Fhnt and Howarth [lo] *Present address CSR Ltd , O’Connell Street, Sydney 2oo0, Austraba CESVol
32. No
LA
Recently, Reay and RatclX[ll, 121 have presented an analysis of the colledon of small pticles by bubbles The results of theu analysis are very mterestmg for they pr&ct a mmunum m the collection efficiency at a parhcle size around 1 firn m dmmeter Below this diameter, collection IS enhanced by Browman Fusion, and for larger pmcles the hydrodynanuc mteractions are more favourable for collection. They also camed out expenments on glass spheres and polystyrene pticles It was found that the rate of flotation of the glass spheres varied approxunately as the 1 5 power of part&e dmmeter but for the polystyrene pmcles the exponent was about 0 5 Recent experunents with polystyrene support the choice of a 15 power dependence [ 131 The effect of particle charge was mvestlgated by Derjagum and Shukaludse[14] who measured the zeta potential of antiomte pticles, wbch are naturally hydrophobic They found that the rate of flotation dropped sharply as the zeta potent& of the pmcles was mcreased beyond a cntical value Jaycock and Otted [lS] studred the adsorption of a catiomc surfactant on to uemvely charged sliver iodide pamcles, and found that the flotation rate measured III a Halhmond tube was west when the zeta potentml of the AgI was zero. De Vlvo and Karger[l6] found a slmllar effect with clay particles However m both cases, coagulation could have taken place because the zeta potenti was zero and rf It had occurred, the mcrease m pticle size could have caused the mcrease rate of flotation The measurement of the charge on a small gas bubble IS not easy to accomphsh and it IS not surpnsmg that few mve@gators have studied bubble zeta potent& Ihbbs, Slrols and Bredm[lfl stu&ed the effect of particle zeta potential the streammg current of ~lsmg bubbles on flotation rate, usmg the method of Bach and Gdman[l81
G L
240
COLL.INS
and G J
and concluded that the double layer mteractions were Important, 111the flotation of quartz m the presence of dodecylamme hydrochlonde It 1s ddiicult to mterpret the results theoretically because the bubbles were well beyond the Stokesian regune of flow, as were those of Samygm, DerJagum and Dakhm[l9] C~chos [20] mvestigated the mfluence of the zeta potential of the bubbles usmg the techmque of McTaggart[21] m whch the bubbles are captured m the centre of a rotatmg tube In some experunents the zeta potenti appeared to be s&cant whereas m others It seemed to have no effect In an earher paper[13] we described experunents in which the effect of parUcle size and charge on the rate of flotation of polystrene par&les was measured The polystyrene was floated m the presence of cetyl trunethylammoruum bromide (CTAB) as collectorjfrother and &he charge was altered by addition of soduun sulphate We found that, mdependently of the pticle charge (for pticles m the range 4-20 *) the flotation rate constant varied as the dmmeter to the 1 5 power However, the particle charge (or rather, the electromoblllty of the pticles whch was the parameter actually measured) appeared to have a very sign&ant effect on the flotation rate constant, which altered almost by an order of magmtude when the mobtity altered from 2 7 to 5 2 pm/slV/cm The evidence so far seems to pomt to the conclusion that m the flotation of small particles, electrical doublelayers could be an nnportant factor However, for this to be estabhshed it must be shown that not only are the pticles charged but so also are the bubbles, for If the latter were uncharged it would be unhkely for the flotation rate to be mfluenced much by the charge on the pticle alone, although thus may be m&catwe of a secondary effect such as the quahty of adsorbed hydrphoblc surfactant ion on the par&le’s surface In thrs paper, we extend ourprevlous work to mclude the effect of the charge on the bubble The sign of the charge and the magnitude of the pa&cle and bubble electromobrlltles, have been measured under conditions sumlar to those existing m the flotation vessel A sunple correlation for the effect of the bubble and pticle charge on the flotation rate constant 1s proposed
&BdESON
the same, 5 x lo-’ M Ethanol (0 5% V/V) was used to promote bubble formation at the smtered disc Sodium sulphate was added m the range 5 x lo-’ to 1 x lo-’ molar to vary the particle charge Addition of the Na2S04 m tlus range caused the double layers to collapse thereby weakenmg the charge The experunental method followed a techruque developed by Reay and Ratchff[l2] Samples taken before and durmg a run were analysed for pticle concentration and size dlstnbution, and the rate of removal of particles of a lpven size could be found by studymg the form of the distibution curve as a function of tune The size tistriiutron of the particles was measured with a Coulter Counter Model ZB The moblllty of the pmcles was measured m a Rank Brothers Part&e mcroElectrophpresrs apparatus Great care was taken m the performance of the flotation experunents and full details can be found m[13] To analyse the results it was assumed that the rate of removal of particles from the flotation cell was first-order v&h respect to the par&le concentration The rate equation 1s therefore - dN/dt = k,Nt
(1)
where N, LSthe number of particles of a gwen dmmeter m the cell at tie t, and kp IS a rate constant If the p&cle concentration at zero at zero tune ISNO,mtegraaon yields In (N,/Nd = kit
(2)
so the rate constant can be obtamed from a plot of In (N,/NO) vs tnne Earher[l3] we showed that the assumption of first-order kmetics was well founded, and that the rate constant vaned approxunately as d, to the 15 power OF
RJBULm
FLCWATION ExpERIhIENTs
The experunentally measured flotation rate constants are shown m Figs 1-6 Each Ggure is for a constant mean parhcle dlarneter, and the rate constant 1s p;lven as a function of the measured electromobfities of the particles (The Coulter Counter can be set to measure the number density of pmcles below a gven threshold, so that by repetitively measurmg the number densities at
FLOTATION EwERlMENTs The flotation experunents were cmed out batchwlse m a 1 dm’ glass filter funnel of base duuneter 12 cm and he&t 1Ocm Nitrogen was passed through the smtered glass base of the filter funnel or cell, at a rate of 3 5 dm3/hr The pore size of the base was m the range 5-15 m and it produced bubbles of mean diameter 53 @, with a standard devmtron of 9 pm The particles were of polystyrene (94% styrene, 6% divmylbenzene co-polymer), of dmmeter between 4 and 2Opm with a mean of 15 pm on a we& basis and 10 pm on a number basis The concentration of polystyrene particles was 0 5 gm/dm3, the same for all runs The surfactant used to float the pticles was cetyl trnnethylammonmm bromide (CTAB), a quaternary ammomum salt yleldmg a surface active cation The uutial CTAB concentration was always
OOll+, 0
’ 2 %
Fu
#
I
I
3
4
5
I
(pmIs/V/cm)
pacle electromobfityon the flotationrate constant Partxle mean dmmeter 6 6 pn
1 The effect of
Double-layer effects m the flotatmn of fine parhcles
241
OOlJ,l
0
2
I
I
I
3
L
5
“E
l+g 2 The effect of partxle electromobtity on the flotation rate constant Parhcle mean dmmeter 8 3 ILL
(pmlslV/cm)
Fig 5 The effect of park+ electromobdlty on the flotation rate constant PaWcle mean dmmcter 16 5 qn
dp = 10 L /un
.2
(pm/s/Vlcm)
"E Fa
“E
3 The effect of parhcle electromobtity on the flotation rate constant Partxle mean dmmeter 10 4 @
0
dP
0.
r
131
3
2 “E
l%g
4
5
1:pm/s/V/cm)
4 The effect of partxle electromob&y on the titat~on rate constant ParWle mean duuneter 13 1 m
thresholds one can find the number 111a given size were 5 81,7 32,9 22, 1162,14 63,18 44 and 23 23 pm, g~vmgmean diameters of the respective ranges as 6 6, 8 3, 104, 13 1, 16 5 and
various range
(pm/s/V/cm)
Rg 6 The effect of parkle electromob&y on the flotation rate constant. Partxle mean duuneter 20 8 ,um
20 8 ~UII) The electromobtity was controlled by add&on of sodmm sulphate to the suspension to be floated, and the measured values are shown m Table 1 for the WUIOUS Na2S04 concentrations The results clearly show that there was a rapid mcrease m the flomon rate, by an order of magmtude, as the mob&y was reduced from 5 to about 3 5 gnlslV/cm t At the lower !igure there was a levelhng off or perhaps a maxunum m the rate The graphs bear a str&mg resemblance m shape to those presented by Spielmarr and FWpatnck[23] for the collection of spherical latex parWes m packed beds of umform glass beads The zeta potentials were controlled by ad&t1011of electrolyte to the suspension The data from one of thev experunents were taken and replotted m FU 7, and the slrmlanty uvlthour results IS clear SpIelman and Fltzpatnck suggested that the shape of the curve was due to double layer effects and
The threshold diameters used
tThe ele&romobiUy of the parkles
IS measured m the electrophorests cell, and ISfound by dlvldmgthe observed velocity of the charged parkle by the unposed grad&t of potential The electromobWy IS obviously related to the charge or zeta potenti on the partxle, and for the cond&ons applymg here, the zeta potentud IS &= 12 85 U, mV, where U, IS the mcle electromoblllty m pms/s/V/cm (Shaw [22]) Thus [ ranged from about 30 to 60 mV For bubblesand parkles of the size we are concerned with, 6 and Ue are mdependent of the diameter
Table 1 Electromotittes
of parW1es and bubbles
Conccntratmn of sodmm sulphate (molar) lo-* 10x10-’ 2sx1o-3 50x lo-’ 1ox1o-2
50x
Mean mobd~ty Bubble 48 43 39 if
49 50 39 39
242
G
L C~LLWSand G
J
b
JAMESON
4
’
’
b’
Fig 8 Sidenew of flat electrophoreslscell Oxygenbubblesare generatedat the tip of the platmumwe at a by a 12 V DC pulse They movehonzontallyunderthe steadypotenti apphedacross platmum-blackedelectrodes b,b’ Cell cross sect.~on 1 x 10 mm
Fu 7 Dataof Spielmanaad Fltzpatnck[23] on filtrationof 9 5 e latex parhcles m a bed of glass spheres of dauueter0 25 mm Llqud super6cm.lvelocity 3 5 mm/s The filter coeffrclentIS analogousto the rate umstsnt k, m Figs l-6 Splelman and CukorC241 showed theoretlcally that the collection efliclency (or filter coetliclent) would behave m tbs way d double layer forces became unportant To prove that the presence of double layers on the parhcles and the bubbles IS responsible for the dependence of the flotation rate on the electromobtity of the pmcles, It ISnecessary to show (a) that the bubbles m the flotation cell had the same sign as the parUcles, 1 e they were positively charged, and (b) that the charge on the bubbles mcreased with decreasmg Na2S04 ad&bon, did the charge on the parQcles The expenments undertaken to test these pomts are now descnied DDUWT ME-
NT OF BUBBLE
EWCTROMOBlIXTY
The eqmpment used was a standard Rank Brothers electrophoresls apparatus A sample of the suspension is placed m a Pyrex glass cell across which a potential Merence can be unposed A charged pa&zle m the hqmd wdl move toward one or other of the electrodes, dependmg on the sign of the charge, and its velocity can be measured by v1ewmg it through a travelhng microscope, usmg dark-ground &mum&on A standard flat electrophoresls cell of cross section 1 by IOmm was modtied shghtly by seahng two platmum wves mto the upper and lower walls as m Fu 8, unth Arald~te, au epoxy resm The flotation solution contammg various concentrations of soduun sulphate was first saturated with oxygen then poured mto the moddied cell A short pulse of current from a 12V dry battery was passed through the solution through the wires The bottom we was connected to earth to ensure that the bubble was not charged by the cncmt Bubbles were produced which rose through the solution The electnc field of the instrument was svvltched on and the honzontal velocity of the bubbles was measured at a stationary level The diameter of the bubbles measured was around 35 Frn If they were much smaller they &ssolved, and d they were larger they rose to qu&ly too follow As the bubbles
rose they tended to move out of the field of wew of the nucroscope so to keep them 111mew the nucroscope was racked usmg the verttcal micrometer adjustment A bubble of 35 m dmmeter rises at about 0 5 mm/s and thus IS about the maxuuum speed with which the nucroscope could comfortably be moved The electromobtifies of the bubbles were calculated m the usual way, by d~v~dmgthe homontal component of velocity by the potenti gra&ent of the apphed field The results are presented m Table 1, together unth earher measurements of the mob&ties of the polystyrene par&les The bubble results are less consistent than those of the parWles, au mdication of the much more -cult experunental problems mvolved The results show clearly that the mob&ties of the bubbles and of the pticles were of the same order, and had the same sign, at the same concentration of sodmm sulphate ALTERNATlVE
EXPLANATIONS
The results @ve stroug support to the proposlhon that the charge on both the bubbles and the parhcles has a strong effect on the rate of flotation Smce m the expenments the charge was controlled by addition of sodmm sulphate, the posslbtity exists that the addWon of thus salt had effects other than the sunple alteration of the charge, whch could have changed the flotation rate Accordmgly tests were camed out to lind the effect of the Na2S04 additions on the followmg (a) the adsorption of surfactant on the surface of the bubble, (b) the size of the bubbles, and (c) the contact angle between bubbles and pa&cles The effect on adsorption was tested by measurmg the surface tension of solutions CTAB (5 x lo-’ M) contammg 0 5% V/V ethanol At concentrations 5 x 10W4, lo-‘, 5 x 10e3 and lo-’ molar, the surface tenslons were respectively 54 8, 53 0, 50 7 and 47 5 dyne/cm The Na2S04 clearly reduced the surface tension, as was expected The magmtude of the changes were not large but may have been sticient to alter the bubble sizes m the flotation cell, and possibly the ease unth which the pmcles could attach themselves to the bubbles To test the effect on the bubble size, a run was camed out at a concentration of Na2S04 of lo-’ M Bubbles nsmg m the flotation cell were photographed and their size &stnbution found The mean &eter was 56 Frn with a standard devotion of 11 w Thus cau be compared with
243
Double-layereffects m the flotatmn of line parbcles the mean size of 53 q m the presence of 1 3 x lo-’ M soduuu sulphate The two sets of photographs were taken under Identical con&fions, so although the eqmhbrmm surface tension was lowered by the ad&bon of the sodmm sulphate, the bubble sfze remamed essentially constant An attempt was made to !ind the contact angle between the partxles and the bubbles The latter were generated by electrolysis ti the flat electrophoretic cell, m the presence of polystyrene pmcles and photographs were taken of parhcles attached to bubbles after they had risen to measure to the top of the cell It was very ticult contact angles because of the small size of the latex parQcles Nevertheless, all the contact angles measured were m the range XMO”, and there was no de6mte change m contact angle as the sodnun sulphate concentration was mcreased The contact angle can be regarded as a measure of the hydrophoblclty or wettab&ty of a surface toward a particular solution, and the fact that It &d not change markedly suggests that there was no effect on the ease of attachment of parhcles to bubbles None of these alternative hypotheses appear to have any substance Accordmgly these ad&tional tests strongly support the conclusion that the observed effect of the sodmm sulphate on the rate of flotation was due to the formation of double layers on the parttcles and the bubbles, w& resultmg charges of the same sign and comparable magmtude on their surfaces
m-
3
116 U-Us
(3)
where kp, the flotation rate constant IS m mm-‘, the parMe deter dP IS m q and the parMe and bubble electromobdrties UE and Us are m pm/slV/cm For mterest, pre&cted rate constants from tlus correlatmn have been plotted m Fig 10, for par&les of various sizes vvlth zero charge The experunental data were obtamed for pticles vvlth zeta potent&s between 30 and 60 mV, so outside this range the curve can only be regarded as an extrapolation However, from comparison vvlth Figs 14 it appears that the rate constant at zero charge nses only a matter of 20 or 30% over the rate constant at a zeta potent& of 20 mV (UB = 15 v/s/V/cm) In our ex-
I
I
I
10
I
I 30
20
Ehg
9 Correlation of data on effect of parkle dmneter
and
pa&cle electromobtity 011the flotation I& constant k, Each pomt IS the mesa of 91~values of &J&“’ The verWal bsrs u&c&e the 95% umfidence lmuts Umts b, mm-‘, 4, ccm,UB, ue, clmls/Vlcm
-I
-i j
2
It now appears to be well estabhshed[l2,13] that for parhcles m the range 4-20 pm m dmmeter the rate constant kp vmes as the pa&cle dmmeter to the 15 power We can use the present results to form an emplncal equation which mcorporates also the effect of charge If we have two bodies carrymg hke charges $1, @z,the repulsive force between them vvlll vary as the product $& The larger the repulswe force, the lower would be the expected rate of flotation so the rate constant should be a func0on of #,&, or of the product of the respective electromobtities, UBUB At zero charge the rate constant would be expected to be a maxmuun and the trend of the results m Figs ld suggests a correlation of the form In (k+/dp’J) = A + BU&. which ISshown m Fig 9, where the data have been replotted The equation on the lme shown, wluch was obtamed by a least-squares fit, IS 3 9+0
I
“E”B
OVERALLCORRELATIONOF RESULTS
-ln(kJdp’5)=
J
0
1
,L 0
E%g
20
10
dp
(pm1
10 Rate constantsprehcted by the empmcal correlation at zero partde charge
penments we dehberately kept c lllgh to prevent coag&tion In a one-component system one would srmply want to maxmuse the rate of removal of that component (e g od pticles m a waste stream, or clay mcles from wash water) However i there are two components whch are to be separated, and both are of colloidal or near-colloidal dunenslons, it 1s hkely that random coagulation of the par&les would occur when they possess zero charge, and although the rate of flotation may then be a maxunum, the floated parhcles of one species may also carry w&h them parWles of the other, reducmg the effectiveness of the separation of the two Accordmgly m nuxed species It would seem undesuable to design for maxunum flotation rate and mstead, the parkles should be charged to the extent of 2&3OmV, thereby preventmg coagulation w&out a drastic redution m the rate of removal -OFGASRATEANDBUBBL.ESUE
descnbmg the flotation process, we have assumed a first-order rate equation m common Hrlth other w01kers[14.10-121 The experunental results described earher[l3] ccrtamly support the assumption of first-order In
G L COLLINS and G J JAMESON
244
kmetnx, as embodred m eqn (1) However, It 1s essentxd to reahze that the rate constant kp IS IIIno way a constant, and depends on a number of vanables not least of which rs the gas flowrate and the bubble size Klassen and Mokrousov[2] ckumed that fine pticles were floated better (faster?) by line bubbles, but this conclusion has been refuted by Traher and Warren[S] who imply that It 1s mconslstent with the work of Flmt and Howarth [ 101and Reay and Rat&E [ll] However, the posslbtity of confusion exists because there are several aspects to the acuon of a smgle bubble, namely the efficiency of collection, ,the volume swept by each bubble and the number density at constant gas rate, wbch all depend on the bubble size To see how the rate of removal of pmcles from the cell depends on the various parameters we shall look more closely at the kmetic model As a bubble rises m the cell it collects par&les, and the collection efficiency EC can be defined as the fraction of mcles m the path of the bubble which actually coalesce wrth it and are removed from the flotation cell In our cell the bubbles are formed at the sintered base and nse freely to the top vvlth only a gentle reclrculafion of the hqmd The cell appeared to be well mixed so the concentration of pticles may be assumed to be umform, and equal to NJV, where N, 1s the total number of partxles m the cell contammg a volume V, of hqmd and pa&cles The total number of partxles removed by a bubble as It nses, through the hqmd of he@t h IS therefore (EmdbzhM) (NV,) If the gas volume&x flowrate IS Q, the number of bubbles formed per second LSQ/(mdb3/6) Thus the rate of removal of particles from the cell IS --=dNl dt From which the rate “constant” 1s k
=
’
3QEch 2dbVc
(5)
Reay and Rat&f [l l] found theoretically that the collection e5clency of a bubble vanes mversely as the bubble duuneter squared, and thus was confumed by experunent for bubbles up to 100 q m dmmeter One IS therefore led to the conclusion, very stnkmg from a pracWal pomt of view, that the rate of flotation vanes mversely as da’at a constant gas flowrate There ISclearly a very s@cant gam m the production of a cell If the bubbles can be made as small as practicable If they are too small, of course, they w5 not float to the top If collectmg par&cles denser than water, but t&s would not apply to oti par0cles In a conventional Aotauon cell of the Denver type, eqns (4) and (5) may not apply exactly because the cell contents are strongly agrtated and the bubbles do not nse mdependent of each other, nor are they m a qmescent hqmd Nevertheless the same general conclusions would apply because the effective volume swept by a bubble would ultitely be related to Its size, and the number of bubbles produced at constant gas rate would vary mversely as the cube of the bubble dmmeter
CONCWSIONS
The results clearly demonstrate that 111the flotation of fine pmcles, the rate of flotation ISstrongly dependent on the charge on both the parhcles and the bubbles When the eiectromobWy of the particles was changed from 2 5 to 5 fl/sM/cm, correspondmg to zeta potential alteration from 30 to 60 mV, the rate of flotation dropped by a factor between 5 for the 6 6 ~UIIparWles and 20 for the 20 8 Frn par&les A new techmque has been described for measurmg the electromobfity of small gas bubbles, by motiymg a standard flat electrophoresls cell A smgle bubble IS generated by electrolysis and nses m the presence of a honzontal potenti gradlent The bubble IS held m the field of Mew of the observatton microscope by manual adlustment of the microscope shde m the vertmal &e&on The method could be unproved s&cantly If the rmcroscope were moved by a motoIlzed dnve The expenments on the bubbles showed that they were posltlvely charged, as were the pmcles, and under the same con&fions, the charge on the bubbles was approxunately the same as on the parhcles Tlus could be 9 very convement result d It IS found to be of general apphcabtity, because the charge on the bubbles IS very d&cult to measure m comparison with that of the pticles The results imply that the maxunum rate of flotation is achieved when the zeta potenti (or mob&y) of the parhcles 1s zero As the charge on the parbcles and the bubbles bmlds up, coalescence between them IStiblted by double-layer rep&Ion Some flotation systems have only one component wbch it ISreqmred to remove as far as practicable, such as a suspension of orl or clay m water In thus case It would obviously be advantageous to keep the charge as near to zero as possible, to promote coagulation pnor to fiotation as well as to help the bubbles and par&les to coalesce However, where there ISmore than one species present, and the reqmrement IS to remove one of them selectively, coagulation of the various species would most certamly be undesuable Accordmgly m flotation of muted speaes, It would probably be necessary to ensure that the parhcles carry sufficient charge to prevent coagulation, but not too much to mhiilt coalescence vvlth bubbles through double-layer repulsion The results suggest that a charge of around 20 mV IS probably optunum A simple correlation for the effect of charge on the flotation rate constant 1s proposed, takmg mto account the effect of pticle allameter It has the form -In(k,/d,“) where kp IS m mn-‘, ccm/slVlcm
= 3 9+0 116 U&B $
m pm
Acknow1edgtmenfs-G L
and UB, US are m
Colhas IS grateful to CSR Ltd, Sydney, Australia,for financialsupport We WE&to thankProf J T Dawes of Blrmmgham Umverslty for his helpfulsuggestions regardmg the correlation of the results
245
Double-layer effects m the tlotat~on of tie parUes NOTATlON
A surface area of bubble C concentration of surfaclant db dkmeter of bubble D d~@usi~ty of surfactant m water EC collect~n efficEncy of bubble h depth of hqmd m flotatin cell kL. mass transfer coellklent rc, flotation rate constant number of moles of surfactant N* No uutml number concentrauon of particles N* number concentration of parOcles at tune t Q gas volumetic flowrate gas constant R Reynolds number of nsmg bubble Re Schrmdt number of dlfEusmg surfactant SC Sh Sherwood number of nsmg bubble t tune T temperature, K ZJ nse velocity of bubble UB electrophoretic moblllty of bubble, &s/V/cm electrophorek mobMy of par&le. elm/s/V/cm ue VC volume of hqt.ud 111flotation cell Greek symbols y surface tension
r l p p #
surface excess of surfactant zeta potential, = 12 85 Ue mV hqwd vlscoslty hqud density charge on parUe or bubble
REFESENCES
[l] Sutherland K L and Wark J W, PnnczpIes of mot&on Australasian Institute of Mmmg and Metallurgy, Melbourne 1955 [2] Klassen V I and Mokrousov V A , An Introduction to the Theory of Flotation, Butterworths, London 1%3 [3] Joy A S and Robmson A J , III Recent Progress m S&ace Scrence(Ed~tedbyJ F Damelh, K G A PankhurstandA C mdtiord), Vol 2 Acadenuc Press, New York 1964 [4] Fuerstenau D W and Healy T W , 111Adsotptlue Bubble Separarron Technrques (E&ted by R Lemhch) Acadenuc Press, New York 1972 151 _ _ Traher W J and Warren L J , Int J Muter Process 1976 3 103 [6] Gaudm A M , Schulunarm R and Schlecbten A W , .7 P hys Chem 1942 46901 [fl Moms T M , Trans A I M E 1952 193 794 [8] BushellC H G, Trans AIME 1%2223 266 [9] Tomlmson H S and Flemmg M G , m Mineral Processrng (E&ted by A Roberts) Pergamon Press, London 1963 [IO] Flmt L R and Howarth W J , Chem Engng Scr 1971 26 11.55 [l l] Reay D and Ratclti G A , Canad J Chem Engng 1973 51 178 1121 Reay D and Rat&f G A, Chad J Chem Engng 1975 53 481 1131 Collins G L and Jameson G J , Chem Engng Scz 1976 31 985 1141 Derlagum B V and Shukaladse N D , Tmns IMM 1%170 569 [15l Jaycock M J and OttetiR H , Trans IMM 1963 72497 [16] DeV~vo D G and Karger B L Sep SCL 1970 5 145 [17] Gibbs H P , S~OISL L and Bredm R ,Research Rep R248
zex
Mmes and Resources, Mmes Branch,
Bach N’and Gilman A, Actu Physlcochzmrca V.R S S 1938 9 27 SamygmV D,DerJagumB V andDukhmS S,Koll ZA 196426424 Clchos C , Fretb~~ Forschungs 1973 513 7 McTaggariH A,& hfag 192244386 Shaw D J . E~ectroDhonsrs AcadermcPress, London 1969 Spielman i A ani Fltzpatnck J A, J Coli Interface Sci 1973 43 350 Spielman L A and Cukor P M , .T Co11 Inter/ace Scl 1973 43 51 Harper J H , Adv Appl Mech 1972 12 59 Calderbank P H , The Chemrcal Engmeer, No 212, CE209 1967 Petica B A, Trans Faraday Sot 1954 60 413 Perry J H , Chemical Engmeers Handbook, 4th Edn McGraw-Hill. New York 1963 APmNDlx
Equdlbnum between bubble surface and surfactant sol&on If a gas bubble ISsuddenly formed m a soltion of a surf-t, Its surface Hrlllbe clean, and a limte bme ~IU be needed for surfactant to Muse to the surface and reach eqmhbrmm anth the solutton In our expenments we need to be sure that each bubble reaches eqmhbnum m the flotation vessel and m the electrophoresls cell, and that the tune needed to reach eqtibrmm IS only a small fractmn of the total residence ixme As soon as the bubble forms rt begms to me. so the transfer of molecules to the surface ISby convective d&~sion Because the bubble IS nsmg, the eqmhbrmm surface concentration (mollcm’) of surfactant ISunbkelyto be that of a surface m a stagnant hqmd (Harper [25]) but we can obtam a good appromtion to the mass transfer problem d we e&mate the tie to eqmliium by assummg that mass transfer occurs as d to a sphere nsmg with steady velocity, and the surface concentration at eqmhbrmm ISthe cflbbs surface excess Smce the bubbles are small(around 50 mdlameter m the flotation vessel and 30 m m the electrophoresls cell), the flow field about them ISStokeslan (Re < 1) and the mass transfer equation for low Reynolds number around a sphere can be used[26] Sh = 0 99 Re”3Sc”3
(AU
where Sh = Sherwood number (k&,/D) Re = Reynolds number (& Q/p) SC = Schrmdt number (&II) From the defimbon of the mass transfer coefficient, the number of moles NA whch are transferred from the bulk to the surface of the bubble m tune t IS N.+=krAhc
t
W)
where A is the area of the bubble and AC 1s the concentration tierence At eqmliirmm, the number of moles on the surface of the bubble ISI’A where r ISthe surface excess (moles/cm’) Hence the tie requued for eqml&n_un IS of order I = I-/k,Ac
WV
To calculate the surface excess the equation
r=-L-42
BRT dc
(A41
was used, m wluch c ISthe bulk concentration of surfactant and y is the surface temuon The constant j3 was grven a value of 2,
246
G L CousandG
foilowmg aryments of Pe&za[27] A plot of the measured values of the surface tenslon of our CTAB solution was constructed from whch drJdc was estimated to be -3 3 x 10’dynes cm’/mole at a Thus r= 5 x lo+ molar CTAB wncentrat~on of 3 5 x lo-‘* mole/cm* For the drffusivrty D of CTA3 m water we use 5 x 10dcm*/s wbch appears to be typti for large molecules[28] The concentration drfference AC obviously decreases with tune but as a g&e we use the bulk concentration c = 5 x lo-” molar, smce at t = 0 the bubble surface contams no smfactant For a 50~ &meter bubble, the Stokes nsmg velocity IS
J JAMJWN 0 137 cm/s, and from (Al) the Sherwood number IS 5 09. g~vmg k, = 5 1 x lo-’ cm/s Hence from (A3), t = 0 137 set A sun&u calctiti for a 30 + bubble ylcldcd t = 0 137 W-Calso These “tunes to equiliinum” are obviously only rou& gmdes but taken with the nse velocities (0 137 and 0 049 cm/s for 50 and 30 q bubbles respectively) they suggest that the bubbles reach equibbnum after movmg only a few bubble dmmeters from the pomt of formation Accordmgly we conclude that the bubbles are essentmlly m equihbnum vvlth the bulk flotation salmon almost from the tune they are formed