Minerals Engineering 17 (2004) 847–853This article is also available online at:

www.elsevier.com/locate/mineng

Assessment of true flotation and entrainment in the flotationof submicron particles by fine bubbles

P. George, A.V. Nguyen, G.J. Jameson *

Special Research Centre for Multiphase Processes, University of Newcastle, University Drive, Callaghan, NSW 2308, Australia

Received 27 December 2003; accepted 4 February 2004

Abstract

Entrainment can make an important contribution to recovery in the flotation of fine particles. This paper presents an experi-

mental study into the recovery by true flotation and by entrainment, of colloidal silica and alumina particles with a size range from

40 to 160 nm in diameter. The flotation experiments were carried out in a small laboratory column-type cell with fine bubbles with

typical average diameter of about 150 lm. No wash water was used. Cetyltrimethylammonium bromide and Dowfroth 250 were

used as the collector and frother, respectively. The particle concentration in the pulp was about 1% by weight. In these experiments

the total recovery of particles was low, typically 54% after 50 min. Four techniques, including three previously described in the

literature and one newly developed in this study, were used to assess the true flotation due to the bubble-particle collection

mechanism, and the entrainment. All employed techniques show that the proportion of the colloidal particles recovered by true

flotation was quite high, varying from about 79–86% of the total recovery. The paper also discusses the mechanisms of minimising

the entrainment of the colloidal particles in the laminar flow flotation regime with fine bubbles.

� 2004 Published by Elsevier Ltd.

Keywords: Froth flotation; Fine particle processing; Flotation kinetics; Flotation bubbles; Flotation froths; Entrainment

1. Introduction

The advances currently being made in grinding

technology are allowing large, complex low-grade min-

eral deposits to be exploited economically. The contin-

ual reduction in grade is forcing miners to produce

ultrafine particles in order to liberate mineral particlesfrom the ore, e.g. the McArthur River and Century Zinc

precious metal deposits (Potts, 2003).

The horizontal Isamill (MIM Process Technologies,

Brisbane, Queensland, Australia) is capable of grinding

to P80 of )4 lm at the McArthur River mine (Weller and

Gao, 2003). To fully exploit these deposits, however,

considerable research needs to take place in the area of

ultrafine particle flotation. While the optimum P80 ofmany ores is substantially less than 10 lm, the optimum

particle size for flotation still ranges between 10 and 100

lm in diameter (Jameson, 1984).

*Corresponding author. Tel.: +61-2-4921-6181; fax: +61-2-4960-

1445.

E-mail address: graeme.jameson@newcastle.edu.au (G.J. Jame-

son).

0892-6875/$ - see front matter � 2004 Published by Elsevier Ltd.

doi:10.1016/j.mineng.2004.02.002

Techniques such as carrier flotation, agglomerate

flotation, emulsion flotation and oil-in-water flotation

have been suggested as ways of increasing the flotation

rates of ultrafines. All of these methods have their short-

falls and none have been very widely applicable. These

processes have been discussed and reviewed elsewhere

(Fuerstenau, 1980). It is widely agreed, however, thatadvances in ultrafine flotation technology through

modifications to well-established surface-based methods

is better than developing entirely new processes (Siva-

mohan, 1990).

The recovery of fine particles is a function of true

flotation, entrainment and entrapment. The entrapment

of particles occurs in a poly-disperse system with fine

particles becoming trapped amongst agglomerates ofcoarser particles or trapped amongst agglomerates of

coarser particles and bubbles. The recovery of fine

particles is thus a function of true flotation and

entrainment only, when no coarse particles are added to

the system.

The process of true flotation occurs when a particle

collides with a rising bubble and is attached to its sur-

face. The selected particle is then removed from the cellas part of the froth. On the other hand, particle

Collector

No Collector

Water Recovered (%)

Sol

ids

Rec

over

ed (

%)

Mass recovered

by true flotation

Fig. 1. Illustration of the determination of true flotation by method of

Trahar and Warren (1976).

848 P. George et al. / Minerals Engineering 17 (2004) 847–853

entrainment occurs when particles are dragged from the

pulp into the froth in the interstitial liquid. While true

flotation is a selective process, capture of particles in the

interstitial liquid is non-selective. For a system, of mixed

species, a high level of particle entrainment will result in

a low-grade product.

It has been a long held view that the predominantcapture mechanism for ultrafine particles is entrainment

(Fuerstenau, 1980). While this may be true for many

systems requiring a high selectivity, no study has been

completed to examine particle entrainment of colloidal

particles floating alone. The aim of this study is to assess

the level of particle entrainment and true flotation in a

system involving colloidal silica and alumina particles.

A novel technique for measuring the entrainment ofcolloidal particles is also introduced.

2. Review of methods and techniques

A number of techniques have been developed to

evaluate the level of true flotation and entrainment. A

brief summary of these methods is given below.

2.1. Method of Trahar

The first technique was proposed by Trahar and

Warren (1976) and compares the water and solids

recovery for two flotation experiments. The first experi-

ment involves a suspension with both a collector and a

frother added, while the second involves just a frother. Itis assumed that all the particles captured in the froth

with no collector added, will be by entrainment only.

The difference between the solids recovered versus water

recovered, for the collector and non-collector tests, gives

an estimate of the mass recovered by true flotation. A

schematic representation of this method was given by

Subrahmanyam and Forssberg (1988), and is shown in

Fig. 1.This first method assumes that entrainment occurs

only when a frother is present. It was argued by Trahar

(1981) that fine particles require only a low hydropho-

bicity, compared to coarser particles, to be captured by

the true flotation process. Hence, Ross (1991) recom-

mended that Trahar’s method would be applicable in

the flotation of coarser particles with a high natural

hydrophobicity.Despite this recommendation, it must be pointed out

that a bubble in distilled, deionised water has a residual

negative zeta potential (Creux, 2000). Assuming the

addition of a frothing agent does not alter the surface

charge on the bubble, fine particles with a negative

surface charge (such as silica) should not attach to the

surface of a bubble without the addition of a cationic

collecting agent. Thus in the absence of a cationic col-

lector, silica particles will be recovered by entrainment

alone.

2.2. Method of Warren

A second technique, proposed by Warren (1985),

assumes that particle entrainment does not take place ina dry froth. A series of experiments are conducted and

the rate of water recovery varied by changing the rate of

froth removal and froth depth. A regression line for the

relationship between total solids recovery and water

recovery is extrapolated to a zero water recovery. The

mass of solids recovered at this point is the recovery by

true flotation alone. This technique may be summarized

as

RðtÞ ¼ F þ eW ðtÞ ð1Þwhere RðtÞ and W ðtÞ are the recoveries of the mineral (by

true flotation and entrainment) and water, respectively,

as a function of time, t. F is the recovery due to true

flotation. The degree of entrainment, e, is equal to the

slope of RðtÞ versus W ðtÞ. A schematic representation of

this technique is given in Fig. 2.

2.3. Method of Ross and Van Deventer

A third method, attributed to Ross and Van Deventer

(1988), assumes the concentration of entrained particles

in the froth and concentrate is identical to the concen-

tration of particles in the pulp. Hence, the recovery by

entrainment can be estimated by multiplying the mass of

water recovered in the froth by the concentration of the

pulp, at that time. This method can estimate the rate offlotation with a single flotation test. Balancing the flo-

tation recoveries gives

RðtÞ ¼ F þ ReðtÞ ð2Þwhere RðtÞ is the (overall) recovery of the mineral by true

flotation and entrainment and F is the recovery by true

True flotation recovery,F

Slope,e

Sol

ids

Rec

over

ed (

%)

Fig. 2. Determination of true flotation by method of Warren (1985).

Hydrophobic particles

Hydrophilic particles

Water Recovered (%)

Sol

ids

Rec

over

ed (

%)

Mass recovered

by true flotation

Fig. 3. Determination of true flotation by the hydrophobic–hydro-

philic particle method.

P. George et al. / Minerals Engineering 17 (2004) 847–853 849

flotation. The recovery due to entrainment, ReðtÞ, is re-lated to the water recovery, W ðtÞ and the initial con-centration, C, of the mineral species in the pulp by

ReðtÞ ¼ W ðtÞðC � btÞ ð3Þwhere b is the slope of the graph of the mineral con-

centration remaining in the pulp phase versus time, t.Substituting Eq. (3) into Eq. (2) gives

F ¼ RðtÞ � W ðtÞðC � btÞ ð4Þ

2.4. New method

A fourth method is now described, which involvestwo separate flotation tests using different colloidal

species of equal size. The two species chosen were silica

and alumina. The silica, which is naturally negatively-

charged, is rendered hydrophobic in the flotation sus-

pension by the attachment of a cationic surfactant. In

contrast, the alumina particles carry a positive charge,

and does not adsorb the cationic collector. Thus in

separate flotation experiments involving a single species,if the solids are conditioned identically with a cationic

collector and a frother, the silica will float by true flo-

tation and entrainment, while alumina will be recovered

only by entrainment in the froth. Thus the difference in

recovery between the two experiments gives a measure

of the true flotation of the hydrophobic species, in this

case, the silica.

This procedure has a number of advantages over thepreviously discussed methods, principally related to the

effect of the reagents on the bubble size distribution and

the froth properties. The technique of Trahar and

Warren (1976) requires some tests in the absence of a

collector; which has an effect on the bubble size distri-

bution, and hence on liquid entrainment in the froth,

and froth drainage and stability. The new procedure is

more convenient than the Warren (1985) method whichrequires many flotation tests to be conducted (Fig. 3).

3. Experimental

Batch-wise flotation tests were carried out in a 1 l

column-type cell of internal diameter 70 mm and of

height variable in the range 305–405 mm. Bubbles are

produced by introducing gas through a fine frit spargerin the bottom of the column. Nitrogen gas was sparged

through 68 mm pyrex glass sintered disc of porosity

three (Corning Ltd, Artington, Surrey, UK), to produce

an average bubble diameter, determined photographi-

cally, of 150 lm. The volumetric gas flow rate was 80

cm3/min. The height of the froth phase was 285 mm and

was maintained by a constant feed of flotation solution

from a large diameter feed tank. A 10 ml sample wastaken from the pulp every five minutes to determine the

concentration change with time. The froth was collected,

dried and weighed. A mass balance was performed

around the cell and the overall recovery determined. The

total recovery was calculated by dividing the cumulative

mass of particles recovered in the froth by the initial

mass of particles in the flotation cell. Tests were done

using each of the four procedures described above, intriplicate, with a total of twenty five flotation tests being

performed.

The particles used in the flotation tests were silica and

alumina. The silica suspension was composed of 1.5%

Snowtex ZL and 0.5% Snowtex 20 L (Nyacol Chemical

America Corporation, Houston, Texas, USA). The

particle size distribution of this suspension, determined

using transmission electron microscopy, was found torange from 40 to 160 nm. The transmission electron

micrographs were taken using a JEM-1200EX11 trans-

mission electron microscope (Jeol USA, Peabody,

Massachusetts, USA). The alumina suspension was

composed of 0.6% AKP-50 particles (Sumitomo

Chemicals, Tokyo, Japan). The AKP-50 particles have a

mean particle diameter of 150 nm, determined using an

Accoustosizer IIs (Colloidal Dynamics, Warwick,Rhode Island, USA).

850 P. George et al. / Minerals Engineering 17 (2004) 847–853

Prior to conditioning, the alumina and silica particles

were dispersed at 100 W power for 5 min using a So-

nicator 3000 (Misonix incorporated, Farmingdale, New

York, USA). Since the rate of flotation is a function of

particle size, the zeta potentials of the particles were

checked to ensure that the charge they carried was suf-

ficient to ensure a stable suspension. For a quiescentcolloidal pulp a zeta-potential at the mineral interface

greater than 25 mV absolute is generally indicative of

dispersion (Ross and Long, 1969). The zeta potential

was assessed using a ZetaPlus apparatus (Brookhaven

Instrument Corporation, Holtsville, New York, USA).

The zeta potential was )35 mV for the silica particles

and +34 mV for the alumina particles. The pH was

measured as 9.25 and 6.31 for the silica and aluminasuspensions, respectively. A settling test was performed

over a 24 h period, for each suspension, and no sign of

settling occurred. Hence, the suspensions were assumed

to be fully dispersed.

The frother used in the experiments was Dowfroth

250 (Dow Chemical Corporation, Ludington, Michigan,

USA) at a concentration of 30 ppm. The collector used

during the experimental tests was cetyltrimethylammonium bromide (CTAB) (Ajax Chemicals, Sydney,

Australia) at a concentration of 5 · 10�5 M. In these

experiments the total recovery of particles was low,

typically 54% after 50 min.

4. Results and discussion

4.1. Results obtained by the technique of Trahar

The solids recovered versus water recovered, for a

system with and without collector, obtained for silica

particles with the method of Trahar and Warren (1976)

is shown in Fig. 4. The collector CTAB, was added to

render the surface of the silica hydrophobic, to enable

the particles to be captured by true flotation. It is as-sumed that particle entrainment is the only method for

0

10

20

30

40

50

0 5 10 15 20

Water Recovered (%)

Sol

idid

s R

ecov

ered

(%

)

20mm FH 30mm FH40mm FH 60mm FH100mm FH 120mm FHNoCollector

Fig. 4. Recoveries of silica particles versus water recovery obtained

with and without collector by the technique of Trahar and Warren

(1976). The numbers in the legend shows the froth heights (FH) and

the data obtained with CTAB. During the experiment in the absence of

the collector the froth height was maintained at 60 mm.

particle capture when no collector is added. The differ-

ence in overall solids recovery for flotation froths, with

and without collector, for a fixed water recovery, gives a

measure of the true flotation taking place. Fig. 4 indi-

cates that the overall water recovery decreased as the

froth height increased. As the drainage of liquid from

the foam increased, so did the proportion of particlescaptured by true flotation. The total fraction of particles

recovered by true flotation was determined to be 76%±

3% for a 20 mm froth height and 83%±3% for a froth

height of 120 mm.

One benefit of Trahar’s method over that of Warren

(1985), is that only two flotation tests are required to

estimate the level of true flotation taking place. It must

be noted however that the froth character changedsubstantially when the CTAB collector was added. For

the system with no collecting agent, no particles were

captured by true flotation and hence the concentration

of particles remaining in the interstitial liquid increased.

An increase in particle concentration causes a linear

increase in the effective fluid viscosity (Einstein, 1906).

Hence the rate of drainage from the froth decreased

significantly. This low rate of drainage ensured the frothremained wet with small bubble sizes and mobile inter-

faces, accordingly.

4.2. Results obtained by the technique of Warren

The rates of true flotation and entrainment were as-

sessed using the technique of Warren (1985). A plot of

the recovery of silica particles versus overall waterrecovery, obtained with CTAB collector, is given in Fig.

5. The overall water recovery was changed for each test

by altering the froth depth from between 20 and 120 mm

in height.

The procedure of Warren assumes that entrainment

occurs when particles are transported in the interstitial

liquid. When the line of best fit is extrapolated to zero

water recovery, for a 60 mm froth height, the interceptsuggests that over 79%±2% of the solids are recovered

15

25

35

45

2 3 4 5 6 7

Water Recovery (%)

Sol

ids

Rec

over

y (%

)

Fig. 5. Recovery of silica particles versus water recovery obtained

after 20 min of flotation, using the technique of Warren (1985).

P. George et al. / Minerals Engineering 17 (2004) 847–853 851

by true flotation. The overall recovery for the 120 mm

froth height is 26%±2%, indicating that around

75%±9% of all recovered particles are captured by true

flotation. When the test is performed for a froth height

of 20 mm, over 32%±6% of all particles are recovered,

revealing around 66%±1% are captured by true flota-

tion. The reduction in recovery as the froth depth in-creases is presumably due to coalescence of the bubbles,

as the froth drains while rising up the column.

This labor-intensive method requires many flotation

tests to be carried out to obtain an accurate estimate of

the true flotation and entrainment rates. Tests must be

conducted with a wide range of froth heights, to obtain a

range of water recoveries. As the froth height is in-

creased the character of the froth changes. The upperlayers of the froth in the column tend to be drier than

those at the bottom. For a three-phase system, the

bubble size increases significantly as coalescence takes

place in the froth. This coalescence improves froth grade

by dislodging entrapped particles and detaching weakly

held true flotation particles. Hence the problem of the

Warren (1985) technique is that it does not distinguish

between particles captured by true flotation in the pulpand improvements made in the froth.

4.3. Results obtained by the technique of Ross and Van

Deventer

A flotation test was performed for a froth height of 60

mm and a mass balance was completed around the cell.

The technique of Ross and Van Deventer (1988) wasused to estimate the rate of entrainment and true flota-

tion. The flotation test was performed over 28 min and

the results for recovery are shown in Fig. 6.

In this technique, it is assumed that the concentration

of entrained particles in the interstitial liquid is the same

as the concentration of particles in the pulp. Flotation

tests were performed with froth heights ranging from 20

to 120 mm. The level of true flotation was determinedusing Eq. (4). The true flotation was found, using the

0

10

20

30

40

50

60

0 10 2 0 3 0 4 0 5 0 6 0

Flotation Time (minutes)

Rec

over

y (%

)

Overall Flotation

True Flotation

Entrainment

Fig. 6. Recoveries by true flotation and entrainment obtained with the

technique of Ross and Van Deventer (1988).

Ross and Van Deventer (1988) technique, to account for

between 75%±3% and 85%±1% of all particles floated.

A mass balance was performed around the flotation cell

and only 3% of the silica was unaccounted for.

The linear behaviour of the recovery curve is due to

the low overall recovery of solids, to be expected in the

flotation of particles of the size used here. Total recoverycould have been increased by increasing the flotation

time, or the gas flowrate. The recovery can also be en-

hanced by using another frother capable of forming

finer bubble sizes in the pulp. A preliminary test revealed

that reagent-grade ethanol at 0.5% concentration, in

conjunction with CTAB, was capable of achieving an

overall recovery greater than 85% after 20 min of flo-

tation. However, ethanol is unable to form a stable frothwhen no collector is added. Hence Dowfroth 250 was

chosen as the preferred frothing agent as it was able to

produce stable froth with and without collector and

could be used to examine all four models.

4.4. Results obtained by the new technique

This technique involved comparing the flotation ofhydrophilic alumina particles, against a system of hy-

drophobised silica particles, conditioned with the same

reagents. The addition of the cationic collector, 30 ppm

CTAB, rendered the silica hydrophobic while leaving

the alumina particles hydrophilic in the slurry. Hence,

all particles captured during the flotation of alumina

with a cationic surfactant were entrained. The flotation

tests were carried out at a 60 mm froth height. Theoverall solids recovered versus water recovered, for a

system with hydrophobic silica and a system with

hydrophilic alumina is given in Fig. 7.

This technique indicates that true flotation accounts

for 82%±3% of all the particles recovered for a 60 mm

froth height. This figure compares to 86%±3% using the

technique of Ross and Van Deventer (1988), 79%±2%

using the technique of Warren (1985) and 82%±3%using the technique of Trahar and Warren (1976). One

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14

Water Recovery (%)

Sol

ids

Rec

over

y (%

)

Silica

Alumina

Fig. 7. Recoveries of hydrophobised silica particles by true flotation

and of hydrophilic alumina particle by entrainment using the hydro-

phobic–hydrophilic particle technique.

Fig. 8. CFD simulation of the formation of wakes travelling with a

rising bubble with Re ¼ 50. The lines show the liquid streamlines

passing the bubble.

852 P. George et al. / Minerals Engineering 17 (2004) 847–853

possible difficulty with this technique, however, is that it

does not take account of different particle morphologies.

A particle with angular surfaces has a higher specific

surface energy (Fuerstenau, 1980) and is more able to

attach to a bubble surface upon collision. The silica and

alumina particles were both examined under a trans-

mission electron microscope and the morphology wasshown to be markedly different. The silica particles,

formed by precipitation, had a uniform spherical shape,

where as the alumina particles were very angular. The

effect of the morphology of the hydrophilic solids on li-

quid entrainment and drainage in the froth is not known.

4.5. Mechanisms of minimising the entrainment of colloi-

dal particles in the laminar flow flotation regime with fine

bubbles

The recovery of colloidal silica by true flotation was

found to be very high ranging between 79% and 86%,depending on the technique used to measure this value.

This is a very significant portion considering the froth

height was only 60 mm and no wash-water was added to

flush the mechanically entrained particles back into the

pulp. It is known that the entrained particles can enter

the pulp-froth interface by the pulp agitation (mechani-

cal entrainment), and/or by the bubble wake and the

bubble swarm (crowding) effects (hydraulic entrain-ment). Since no mechanical agitation was used in our

experiments, the contribution of mechanical entrainment

was insignificant. The formation of a wake behind a

rising bubble is limited by the hydrodynamic conditions.

The wake volume is a function of the velocity, U , of the

bubble rise, the bubble radius, Rb, and the liquid vis-

cosity, l, and density, q. The wake volume decreases with

decreasing the bubble Reynolds number, Re ¼ 2qRbU=l(Batchelor, 1967; Clift et al., 1978). Indeed, Miyahara

et al. have reported that bubbles rising with a Reynolds

number between 600 and 5000 form a helical vortex wake

with a wake-to-bubble volume ratio of 2.5. The bubbles

rising with a Reynolds number greater than 5000 form a

symmetrical wake with a wake-to-bubble volume diam-

eter of 4.7 (Miyahara et al., 1988). In this work the

numerical computation fluid dynamics (CFD) program(FLUENT, Fluent Inc., Lebanon, New Hampshire,

USA) was used to study the wake formation behind

rising bubbles. An example for the liquid streamlines and

the wake is shown in Fig. 8. The numerical study shows

that no wake can be formed if the bubble Reynolds

number is smaller than about 20. The wake volume,

Volw, can be correlated with the bubble volume, Volb,

and the Reynolds number. The following correlation wasempirically obtained from the numerical data:

Volw ¼ Volb½0:045Re0:649 � 0:314� 206Re6 400 ð5ÞTherefore the reduction in the bubble diameter sig-

nificantly reduces the size of the associated wake, by

reducing the Reynolds number and terminal velocity.

The reduction in the size of the wake in-turn reduces the

number of fine particles captured behind the bubblewhich are later transferred hydraulically to the froth.

For fine bubbles with a mean diameter of 150 lm,

produced in this study by sparging nitrogen gas through

a fine glass frit, the rise velocity determined by the

available predictions (Nguyen, 1998) is about 16 mm/s,

and the bubble Reynolds number is about 3. Clearly, for

such small Reynolds numbers the entrainment due to

the bubble wake mechanism is insignificant and can beneglected in our experiments. However, when bubbles of

the size generated in mechanical cells are used, typically

1–3 mm in diameter, entrainment of solids in the wakes

of the bubbles could be very significant.

The small degree of entrainment in the flotation tests

can be due to the bubble swarm crowding effect, which is

a function of the bubble concentration. In flotation cells,

bubbles rise through the pulp, slow down as they ap-proach the pulp-froth interface and then crowd together

at the interface. The liquid cannot be rapidly squeezed

out between the rising swarm of bubbles, due to the

restricted paths for drainage through the bubble swarm.

As each layer crosses the interface, another layer of

bubbles will form and push more liquid upwards in a

continuous process and entrain particles into the froth

phase. Further work needs to be conducted relatingentrainment rates to the bubble size and gas holdup in

order to verify this mechanism.

5. Conclusion

Batch flotation tests were conducted in a small labo-

ratory column-type cell using fine bubbles to assess therate of true flotation and entrainment using four different

techniques. The four techniques employed were those of

Trahar and Warren (1976), Warren (1985), Ross and

Van Deventer (1988), and the new hydrophilic–hydro-

phobic particle technique introduced here. Tests were

conducted in triplicate with a total of twenty five flota-

P. George et al. / Minerals Engineering 17 (2004) 847–853 853

tion tests being performed. The average bubbles size of

sparged nitrogen was 150 lm. A 1% suspension of silica

particles ranging in diameter from 40 to 150 nm was used

as the floatable species, while alumina particles with a d50of 150 nm were used as the hydrophilic species. A mass

balance was performed around the cell for each test and

the level of true flotation and entrainment determined.The level of true flotation and entrainment was found

to vary linearly with froth height. The true flotation was

found to account for 76%±3% of all silica particles

recovered for a froth height of 20 mm, and over

83%±3% for a froth height of 120 mm, using the tech-

nique of Trahar and Warren (1976). This indicates that

the proportion of particles captured by entrainment is

relatively small, despite the absence of any wash-water.The four techniques were compared and were found

to reveal highly consistent results. For a constant 60 mm

froth height, the level of true flotation was found to be

82%±3% for the method of Trahar and Warren (1976),

79%±2% for the method of Warren (1985), 86%±3%

for the method of Ross and Van Deventer (1988), and

82%±3% for the method of hydrophilic–hydrophobic

particles. Each of these techniques has their drawbacksincluding changing froth structure for the methods of

Warren (1985), Trahar and Warren (1976) and the

hydrophilic–hydrophobic particle technique. The

changing particle morphology and surface chemistry for

the hydrophilic–hydrophobic technique affects the

measured rate of entrainment, along with changing

particle concentrations in the interstitial liquid for the

Ross and Van Deventer (1988) method.The high efficiency of true flotation obtained with

colloidal silica is due to the fine bubble size, 150 um,

used in the experiments. As the bubble collides with the

froth it rapidly decelerates causing the particles en-

trained in its wake to wash over its surface and entrain

hydraulically into the froth. A smaller bubble size has a

smaller associated wake and hence fewer particles are

entrained into the froth.

Acknowledgements

The authors gratefully acknowledge the financial

support of the Australian Research Council.

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