minerals

Article
Influence of Froth Height on Column Flotation of
Kaolin Ore
Fernando Pita 1,2 ID

1 Geosciences Centre, Department of Earth Sciences, Faculty of Sciences and Technology,

University of Coimbra, 3030-790 Coimbra, Portugal; fpita@ci.uc.pt; Tel.: +351-239-860-500
2 Centre for Mechanical Engineering, Materials and Processes, Faculty of Sciences and Technology,
University of Coimbra, 3030-788 Coimbra, Portugal

Received: 17 October 2017; Accepted: 22 November 2017; Published: 26 November 2017

Abstract: The influence of the froth height in the reverse flotation of kaolinitic ore was analyzed
based on the recovery by entrainment and by true flotation of iron, titanium and manganese oxides
(FeO, TiO2 and MnO). Also, the influence of the particle size in the drainage process was analyzed.
The recovery by entrainment and by true flotation of the three oxides is inversely proportional to
the froth height. The entrained particles are drained more easily in the froth phase than the floated
particles since they are not attached to the bubbles. The recovery by entrainment and drainage of
the entrained material is similar for the three oxides. However, the recovery by true flotation and
drainage of the floated material is different for the three oxides. FeO has the lowest recovery, as
a consequence of the minor contribution of its hydrophobic minerals, while MnO has the greatest
recovery values. For the entrained material, the finest fraction is entrained more easily, but it is also
drained more easily, meaning these particles have more mobility in the froth zone. For the true floated
material, the finest fraction is drained more easily, indicating the greater mobility of these particles in
the froth; however, the coarsest fraction is drained more easily than the two intermediate fractions,
indicating the weaker attachment of the larger particles to the bubbles.

Keywords: flotation; froth height; entrainment; true flotation; particle size

1. Introduction
Froth flotation is the most important and versatile separation method used in the mining
industry. It is a physical-chemical process based on the selective adhesion of certain particles to
the air (hydrophobic particles) or the water (hydrophilic particles). The flotation process can be
divided into two distinct phases: one that takes place in the pulp zone (collection zone) and the other
in the froth zone (drainage zone). A successfully flotation process implies the collision of particles
with air bubbles and the formation of particle-bubble aggregates in the pulp zone, and the drainage of
the entrained particles in the froth zone, leading to an enrichment of the floated material. During this
process, the hydrophobic mineral particles enter into the froth zone attached to the surface of bubbles
(true flotation), but the hydrophilic and some hydrophobic mineral particles may enter into the froth
as well.
True flotation is a selective phenomenon contributing to the separation of hydrophobic from
hydrophilic minerals, while entrainment is a problem in flotation because it is non-selective.
Entrainment is responsible for the recovery of hydrophilic particles, especially the finer ones.
A successful flotation process involves minimization of the entrainment and maximization of the
true flotation.
Entrainment is fundamentally conditioned by the operative conditions (pulp dilution, agitation
intensity, aeration rate, stability, and height of the froth) and the nature of the material (density, size,
and shape). The recovery by entrainment decreases with the increased dilution of the pulp and

Minerals 2017, 7, 235; doi:10.3390/min7120235 www.mdpi.com/journal/minerals

Minerals 2017, 7, 235 2 of 13

the froth height, and increases with increased agitation, rate of aeration, and froth stability [1–4].
Also, it decreases with increasing particle size and its density, and depends on the particle shape,
with lamellar shape particles being more easily entrained [5–10]. A large number of studies have
shown that entrainment recovery is proportional to water recovery [5,7,8,11].
The froth is crucial in the flotation process. It can affect both the recovery and the grade, because
it promotes the selective drainage of minerals back to the pulp zone. In spite of the separation between
the hydrophobic and the hydrophilic particles that takes place in the pulp zone (collection zone),
drainage in the froth zone contributes significantly to the increase of selectivity of the flotation process.
Therefore, the froth should have enough stability and height, in order to allow the drainage of the
entrained hydrophilic particles back into the pulp and, simultaneously support the hydrophobic
particles, inhibiting their drainage and contributing to the total selectivity of the process.
Drainage is conditioned by the stability and height of the froth and by the particles’ characteristics
(size, density, shape, and hydrophobicity). Froth stability depends on several factors: type and
concentration of froth, particle size, solid concentration, hydrophobicity, shape and roughness of
particles, and air flow rate [12–17].
The probability of the floated and entrained hydrophilic particles dropping back into the pulp
zone (drained) is greater when the froth zone is higher, since the retention time is longer. Many authors,
including Neethling, Alexander et al., Ross, Schwarz and Grano, and Massinaei et al. [9,15,18–20]
studied the influence of the froth height in flotation. They found a strong dependence of the amount
of hydrophilic particles drained from the froth on the froth residence time. It was observed that the
recovery decreases with the increase in froth height, with the grade of the floated product varying in
the opposite direction. It seems that the drainage of the entrained particles is more intense than the
drainage of the floated particles. However, the drainage is not constant along the height of the froth,
being more pronounced near the pulp–froth interface, where the percentage of water is larger [13,18,20].
In unstable and thick froth, although the drainage is intense and contributes to selective separations,
the recoveries are small. Stable and thin froths lead to larger recoveries, but worse separations since
the entrained hydrophilic particles are less drained. Froths with proper stabilities are essential in the
achievement of good grades and high recoveries.
However, a study by Martínez-Carrillo and Uribe-Salas [21] on the recovery of hydrophilic silica
fines in column flotation tests concluded that the entrainment of hydrophilic fines is not affected
by froth height (within a range of 10 to 30 cm) when wash water is not used. Indeed, Falutsu and
Dobby [22] have developed a column that isolates the froth zone from the collection zone, allowing
the direct measurement of the recovery obtained in each zone and simultaneously the measurement of
the drained material percentage. These authors verified that the recovery in the froth zone was not
influenced by the froth height. The injection of wash water at the pulp-froth interface can produce
an intense drainage of the entrained material, leading to a froth zone composed of particles strongly
attached to the bubbles.
The drainage intensity is affected by the size and density of the particles and by the stability of the
particle-bubble aggregates. In the floated hydrophobic material, it is more difficult to drain particles
with fine size and low density. However, Alexander et al. [15] suggested that the froth is non-selective
in terms of attached particles, i.e., that particles do not break their bonds with air bubbles in the froth
phase due to their hydrophobicity, but rather that the dropping back of particles to the pulp phase is
caused by bubble breakage and coalescence.
In the entrained material, the effect of particle size on the drainage is conditioned by the stability
of the froth. In stable froth, fine particles are drained more easily than coarse particles. In unstable froth,
coarse particles are more easily drained than fine particles. In spite of this, Stevenson et al. [23] found
that the transport of gangue (entrained) through froth is independent of particle size. So, the greater
recovery of the finer particles in the concentrate could be due to physical processes occurring in the
pulp zone rather than the froth zone.
Minerals 2017, 7, 235 3 of 13

Froth zone recovery is the fraction of material that enters the froth and is transferred to
the concentrate. Savassi et al. [24] gave a definition of froth zone recovery (Rf ) as the quotient
between the mass rate of particles joining the floated material and the mass rate of particles at the
pulp-froth interface.
Direct measurement of froth zone recovery is problematic. Several techniques are
available to determine froth zone recovery, falling predominantly into two categories: (a) the
use of indirect methods that relate froth zone recovery to the first-order flotation rate
constants [14,17,19,25]; and (b) the estimation or direct measurement of bubble loading below the
pulp–froth interface [15,22,24,26–28].
The aims of the present study are: (1) to test and evaluate the influence of the froth height in
column flotation tests, using kaolin ore; (2) to analyze the influence of the particle size in the drainage
phenomena, in terms of entrainment and true flotation.
This paper presents a methodology for the indirect estimation of froth zone recovery based on the
measurement of the effect of froth height on flotation recovery, with the assumption that the froth zone
recovery tends towards 100% when the froth height tends towards zero.

2. Materials and Methods

2.1. Materials
Batch flotation tests were carried out in a column flotation, for mineral processing of kaolin by
reverse froth flotation, in order to float quartz, goethite, ilmenite, rutile and tourmaline, the main
penalty minerals of kaolin. In this case, the floated product concentrates the impurities and the
tailings (sunk) is the improved kaolin. The kaolin samples were obtained from Caulicentro Mine in
Lousã-Coimbra, Portugal. In that mine, a combination of wet screening and hydrocycloning is used to
process the kaolin ore. In the laboratory, the kaolin samples were dried and disaggregated for use in
the flotation tests.
To analyze the effect of the particle size on the flotation process, the size distributions of the
concentrate and tailing products were measured by wet sieving, and the following size fractions were
obtained: <25 µm; +25–45 µm, +45–63 µm; >63 µm.
The mineralogical composition of the four particle size fractions was identified by electronic
microprobe (JEOL JXA 8500F, Freising, Germany) analysis (Table 1). The main minerals are kaolinite,
quartz, feldspar, and muscovite. While kaolinite predominates in the finest fraction, in fractions greater
than 25 µm quartz is the predominant mineral, followed by feldspar and muscovite.

Table 1. Kaolin ore minerals, measured by electronic microprobe (%).

Size Fractions (µm)

Minerals
<25 25–45 45–63 >63
Kaolinite 73.8 9.3 3.6 1.4
Quartz 14.8 56.3 58.1 79.1
Feldspar 6.4 21.8 26.5 13.1
Muscovite 1.1 7.1 7.1 3.5
Goethite 0.4 0.8 0.8 0.6
Hydrated aluminium silicate 1.0 1.0 1.1 0.8
Iron aluminosilicate 1.8 1.5 1.0 0.4
Ilmenite 0.4 0.9 0.5 0.3
Rutile 0.2 0.5 0.3 0.1
Tourmaline 0.1 0.8 1.0 0.7

Because the study was based on the recovery of iron, titanium, and manganese oxides (FeO, TiO2
and MnO) and not on the mineral recovery, it was necessary to determine the contribution of each
oxide to the kaolin ore minerals (Table 2).
Minerals 2017, 7, 235 4 of 13

Table 2. Distribution of FeO, TiO2 , and MnO (%) in minerals, measured by electronic microprobe.

FeO (% Weight) TiO2 (% Weight) MnO (% Weight)

Minerals
<25 25–45 45–63 >63 <25 25–45 45–63 >63 <25 25–45 45–63 >63
Kaolinite 49.8 7.2 3.5 2.6 48.1 3.6 2.8 2.2 40.8 2.4 1.3 0.7
Quartz 0.3 1.4 1.9 4.9 1.1 2.5 5.1 14.5 8.3 14.0 21.1 41.4
Feldspar 0.1 0.6 0.9 0.8 0.5 0.9 2.3 2.4 3.6 5.5 9.7 6.9
Muscovite 0.8 5.8 7.5 6.9 0.7 2.7 5.4 5.5 0.6 1.8 2.6 1.8
Goethite 9.3 29.5 38.0 43.1 0.1 0.1 0.3 0.3 5.0 6.3 9.2 7.9
Hydrated aluminium silicate 0.6 0.7 0.9 1.3 0.1 0.1 0.1 0.2 0.7 0.3 0.5 0.5
Iron aluminosilicate 34.2 32.0 27.6 20.8 0.6 0.3 0.4 0.3 1.4 0.5 0.7 0.3
Ilmenite 4.5 18.4 11.0 10.3 24.3 51.8 47.7 49.3 39.6 65.5 43.9 31.3
Rutile 0.4 1.4 0.8 0.5 24.5 37.8 35.0 24.1 - - - -
Tourmaline - 3.1 8.0 8.8 - 0.2 0.9 1.1 - 3.8 11.0 9.2

There are two types of minerals in kaolin ore in terms of floatability: hydrophobic minerals
(quartz, goethite, ilmenite, rutile and tourmaline); and hydrophilic minerals (kaolinite, feldspar,
muscovite, hydrated aluminium silicate and aluminosilicates). The degree of hydrophobicity of the
minerals was not determined (for example, by measuring the contact angle). However, the analysis
of the floated material by electronic microprobe, using only one of the tests, allowed us to verify a
higher content of quartz, ilmenite, goethite, rutile and tourmaline in the concentrate. The percentage
of each oxide in the kaolin minerals determined by electronic microprobe was then combined into
hydrophobic and hydrophilic minerals (Table 3).

Table 3. Distribution of FeO, TiO2 , and MnO (%) in hydrophobic and hydrophilic minerals.

Size Fractions (µm)

Oxide Mineral Type
<25 25–45 45–63 >63
Hydrophobic minerals 14.5 53.8 59.7 67.6
FeO
Hydrophilic minerals 85.5 46.2 40.3 32.4
Hydrophobic minerals 50.0 92.4 89.0 89.3
TiO2
Hydrophilic minerals 50.0 7.6 11.0 10.7
Hydrophobic minerals 52.9 89.5 85.2 89.8
MnO
Hydrophilic minerals 47.1 10.5 14.8 10.2

In the size fraction lower than 25 µm only 15% of FeO and about 50% of TiO2 and MnO come
from the hydrophobic minerals. The hydrophobic minerals contribute more of the three oxides in the
three coarser fractions, contributing nearly 60% of those minerals for FeO and about 90% for the other
two oxides (Table 3).
The particle size distribution of the kaolin ore and the grade of the three oxides in four
size fractions determined by AAS (atomic absorption spectrometry, Solaar M2 Thermo Scientific,
Cambridge, MA, USA) are presented in Table 4.

Table 4. Particle size and grades of FeO, TiO2 , and MnO in four size fractions.

Size Fractions Weight Grade of Oxide (%)

(µm) (%) FeO TiO2 MnO
<25 96.27 1.902 0.397 0.010
25–45 1.66 0.861 0.504 0.061
45–63 0.68 0.704 0.366 0.049
>63 1.39 0.763 0.300 0.024
Minerals 2017, 7, 235 5 of 13

2.2. Flotation Experiments

The column flotation has a height of 3.40 m and a diameter of 7.2 cm and was operated with the
recycling of the tailings in a closed circuit. The column is made of acrylic material and porous discs
have 0.5 mm pore size. The froth height varied between 6 and 35 cm, systematically with a near 5 cm
increment. No wash water was used in order to maintain the stable chemical conditions and enable
the operation of the column for a longer period of time.
The optimum working conditions, i.e., those that would produce a more enriched concentrate and
a more impoverished tailings (processed kaolin) in penalty minerals, were determined in the planning
of experimental tests. After performing multiple tests altering the operating conditions, the reagents
and conditions that provided the best results were: concentration of solids in the pulp: 17.5%; pH of
the pulp: adjusted to around 9.5 by adding sodium hydroxide; sodium silicate (dispersant) was added
at a dosage of 1.2 kg/ton and the pulp was conditioned for 5 min; then kerosene activator was added at
a dosage of 0.5 kg/ton and conditioned during 2 min; next oleic acid collector was added, at a dosage
of 2 kg/ton, and conditioned during 5 min; after 2 min of froth conditioning (Cyanamid aerofroth 65)
with dosage of 30 × 10−3 g/L air was introduced. After performing flotation tests at three aeration
rates (2.4, 3.6 and 4.8 L/min), it was verified that the aeration rate of 3.6 L3 /min led to the highest
recovery of the three oxides in the floated material. In the present study, the aeration rate used
was 3.6 L/min. All reagents used in the experiments were chemically pure and were obtained from
Chem-Lab Company (Zedelgem, Belgium). The experiments were carried out at room temperature
and tap water was used in all tests. The tests were performed three times under similar operating
conditions and the coefficients of variation were less than 0.05.
The flotation tests were carried out for 8 min. Size distributions of four fractions (<25 µm;
+25–45 µm, +45–63 µm; >63 µm) were determined in the concentrate and tailing products by wet
sieving. For all fractions, the chemical assays in FeO, TiO2 , and MnO were determined by atomic
absorption spectrometry. The results were compared against the percentage of each oxide in the kaolin
minerals determined by electronic microprobe.
Since the influence of froth height may be different in the entrained and floated materials, the effect
of the froth height in the recovery by entrainment and by true flotation is analyzed separately,
giving more precise information about the effect of the froth height in both processes. The total
recovery was not considered because its behaviour can be masked by those two types of recoveries.
The recovery by true flotation and by entrainment of the three oxides was quantified by the method of
Ross and Van Deventer [29].

3. Results and Discussion

Recovery of FeO, TiO2 , and MnO by true flotation (TF) and by entrainment (ENT) after 8 min
is given as a function of froth height for different size fractions (Figure 1). Water recovery is also
presented for comparison (Figure 1).
Froth height has a significant effect on the recovery of the three oxides, as well as on the water
recovery. Recovery by entrainment, by true flotation and water recovery decreases with increasing froth
height. That is attributed to a longer froth retention time, which leads to an increased drainage time.
True flotation is more effective for coarse particles, but entrainment recovery increases with
decreasing particle size, being more visible for the finer size fraction. Since the finer fraction weighs 96%
of the total sample of kaolin ore (Table 4), this feature plays an important role in the flotation process.
The entrainment results are similar for the three oxides, which illustrates the non-selectivity of
the entrainment, being independent of the mineral species. However, FeO shows a slightly greater
value for entrainment. FeO has the lowest recovery by true flotation, as a consequence of the minor
contribution of its hydrophobic minerals, making this oxide more susceptible to being entrained.
The recovery by entrainment of the three oxides decreases with decreasing water recovery for all
size fractions (Figure 1). The entrainment recovery, in all size fractions, is less than the corresponding
water recovery, although the recovery of the finer size fraction (i.e., under 25 µm) closely approaches
Minerals 2017, 7, 235 6 of 13

the water recovery value. These results are comparable to those of most of the previous works on this
subject, taking into 7,account
Minerals 2017, 235 the water recovery range and the particles size studied [5–9,21]. 6 of 13

70
(a) < 25 µm (b) < 25 µm
25-45 µm 25-45 µm
15 60
FeO Recovery (ENT) (%) 45-63 µm 45-63 µm

FeO Recovery (TF) (%)

> 63 µm > 63 µm
50
Water Water
10 40

30

5 20

10

0 0
0 10 20 30 40 0 10 20 30 40
Froth Height (cm) 70 Froth Height (cm)
(c) < 25 µm (d) < 25 µm
25-45 µm 25-45 µm
15 45-63 µm 60 45-63 µm
TiO2 Recovery (ENT) (%)

> 63 µm

TiO2 Recovery (TF) (%)

> 63 µm
50

10 40

30

5 20

10

0 0
0 10 20 30 40 0 10 20 30 40
Froth Height (cm) 70
Froth Height (cm)
< 25 µm < 25 µm
(e) (f)
25-45 µm 25-45 µm
15 45-63 µm 60 45-63 µm
> 63 µm > 63 µm
MnO Recovery (ENT) (%)

MnO Recovery (TF) (%)

50

10 40

30

5 20

10

0 0
0 10 20 30 40 0 10 20 30 40
Froth Height (cm) Froth Height (cm)

Effect 1.
Figure 1.Figure ofEffect
frothofheight on theon
froth height water recovery
the water (a, b)
recovery (a,and onon
b) and thethe
recovery
recoverybybyentrainment (ENT)
entrainment (ENT)
of iron (a),
of titanium (c) and manganese
iron (a), titanium (e) oxides
(c) and manganese and on
(e) oxides theonrecovery
and by true
the recovery flotation
by true (TF)(TF)
flotation of iron (b),
of iron
titanium (b),
(d) titanium
and manganese (f) oxides,(f)
(d) and manganese inoxides,
four size fractions.
in four size fractions.

As expected, the recovery by true flotation is generally greater than the recovery by
As expected, the recovery by true flotation is generally greater than the recovery by entrainment,
entrainment, with the exception of the finer fraction of the FeO.
with the exception of the finer fraction of the FeO.
For all size fractions, MnO presents the greatest recovery by true flotation, a consequence of the
For largest
all sizecontribution
fractions, MnO
of thepresents
hydrophobic the greatest recovery
minerals in this oxide by(Table
true flotation,
3). FeO has a the
consequence of the
lowest recovery
largest contribution of the hydrophobic minerals in this oxide (Table 3). FeO has the
values, as a result of the smallest contribution of the hydrophobic minerals (Table 3), while TiO2 lowest recovery
values, as a resultpresents
recovery of the smallest
intermediatecontribution of theTiO
values. Since hydrophobic
2 and MnO minerals
have similar(Table 3), while TiO
contributions of 2
recoveryhydrophobic
presents intermediate values.
minerals (Table Since
3), the TiOrecovery
worse 2 and MnOof have
TiO 2 similar
may be duecontributions
to the lower of hydrophobic
hydrophobicity
mineralsof rutile3),
(Table versus ilmenite
the worse and quartz
recovery of TiO(Table
2 may2).be
Less
due significant recovery
to the lower of the three of
hydrophobicity oxides byversus
rutile true
flotation is observed for the size fraction lower than 25 µm, an outcome of the smaller
ilmenite and quartz (Table 2). Less significant recovery of the three oxides by true flotation is observed contribution of
hydrophobic minerals and of the particle size.
for the size fraction lower than 25 µm, an outcome of the smaller contribution of hydrophobic minerals
Regression analyses (linear, logarithmic, cubic, power and exponential) of the recovery results
and of the particle size.
versus froth height were made for all size fractions, and the goodness of fit and their statistical
Regression analyses (linear, logarithmic, cubic, power and exponential) of the recovery results
significance calculated. The best results were obtained when a linear model was used. The goodness
versus froth
of fit height were made
was measured by the Ffor
testalland
size
thefractions,
significanceand thewere
levels goodness ofup
generally fittoand their statistical
0.001.
significance calculated. The best
A linear equation results
of the followingwereform
obtained when a linear model was used. The goodness
was used:
of fit was measured by the F test and the significance levels were generally up to 0.001.
Minerals 2017, 7, 235 7 of 13

A linear equation of the following form was used:

R = a+b×h (1)

where R is the recovery at the end of the flotation test; h is the froth height; a is the y-intercept; and b is
the slope of the linear regression line.
For all linear regressions, the R-squared (R2 ) presents high values and the significance level
presents low values, giving reliability to the influence of the froth height in the recovery by entrainment
and by true flotation of the three oxides. The goodness of fitting of the FeO, TiO2 and MnO recovery
versus froth height revealed linear regressions with correlation coefficients significant at the 0.001 level
(Table 5).

Table 5. Linear regression coefficients (a and b), critical froth heights (hc ), Standard error associated
with the calculation of the slope and the intercept of the curve between parentheses, R-squared (R2 ) and
significance levels * of the oxides recovery by entrainment and true flotation of the four size fractions.

Fraction Entrainment True Flotation

Oxide
(µm) a b hc (cm) R2 A b hc (cm) R2
<25 13.89 −0.291 47.7 0.986 * 4.91 −0.082 59.9 0.913 *
(0.34) (0.015) (0.251) (0.082)
25–45 8.26 −0.160 51.6 0.968 * 33.68 −0.283 119.0 0.885 **
(0.29) (0.013) (1.02) (0.046)
FeO
45–63 7.92 −0.156 50.8 0.961 * 41.20 −0.595 69.2 0.960 *
(0.31) (0.014) (1.30) (0.058)
>63 7.83 −0.155 50.5 0.980 * 41.06 −0.614 66.8 0.933 *
(0.22) (0.010) (1.64) (0.074)
<25 12.18 −0.252 48.3 0.952 * 14.64 −0.247 59.3 0.918 *
(0.56) (0.025) (0.74) (0.033)
25–45 6.21 −0.119 52.2 0.923 * 55.29 −0.444 124.5 0.937 *
(0.34) (0.015) (1.55) (0.051)
TiO2
45–63 6.02 −0.116 51.9 0.950 * 59.68 −0.716 83.4 0.919 *
(0.26) (0.012) (2.13) (0.095)
>63 5.57 −0.105 53.0 0.925 * 64.74 −0.947 68.4 0.938 *
(0.29) (0.013) (2.44) 0.109)
<25 10.41 −0.212 49.1 0.970 * 24.38 −0.247 98.7 0.982 *
(0.37) (0.016) (0.33) (0.014)
25–45 5.53 −0.102 54.2 0.976 * 62.51 −0.466 134.1 0.897 *
(0.16) (0.007) (1.64) (0.073)
MnO
45–63 5.28 −0.098 53.9 0.981 * 65.66 −0.679 96.7 0.894 *
(0.13) (0.006) (2.34) (0.0104)
>63 5.14 −0.096 53.5 0.978 * 67.95 −0.868 78.3 0.925 *
(0.14) (0.006) (2.48) (0.111)
* Significance level of 0.001; ** significance level of 0.002.

From Equation (1) it appears that the phenomenon that takes place in the pulp zone produces
effects mostly at intercept a (when the froth height is null the recovery tends to be the collection zone
recovery), and the phenomenon that takes place in the froth zone (drainage) influences the magnitude
of slope b.
The recovery becomes null for a certain froth height, known as the critical froth height (hc ),
which can be determined by the relationship between the y-intercept and the absolute value of the
slope (hc = a/b). For values of froth height greater than hc , all the material transferred from the pulp
zone to the froth zone is drained, and there is no output of the floated material. Therefore, the higher
the values of hc the lower the probability of drainage.
Linear regression coefficients and critical froth heights obtained from experimental data
concerning the recovery of the FeO, TiO2 and MnO in the four size fractions are presented in Table 5.
Minerals 2017, 7, 235 8 of 13

For recovery by entrainment of the three oxides, the finer fraction (<25 µm) has a greater
y-intercept of the linear regression than coarser fractions (Table 5). Since the y-intercept depends only
on what happens in the pulp zone, the fine material can be more easily entrained, moving from the
pulp zone to the froth zone. In fact, for the three coarser fractions the y-intercept of the linear regression
decreases slightly with increasing particle size. These results are in agreement with previous studies
by Subrahmanyam and Forssberger [6], Kirjavainen [7], Zheng et al. [8], and Warren [11], in which
they concluded that fine particles are more easily entrained.
For recovery by true flotation of the three oxides, a finer size fraction presents a smaller y-intercept
(Table 5), meaning lower collection zone recovery as a consequence of the smaller contribution
of hydrophobic minerals for the amounts of the three oxides and of the lower probability of
collision between fine particles and bubbles. For the three coarse fractions, the regression intercepts
(collection zone recovery) increase slightly with increasing particle size (Table 5). Since in this size range,
for each oxide, the contribution of hydrophobic minerals is similar (Table 3), this behavior is likely to
result from differences in the particle size, increasing the probability of collisions between particles and
bubbles. Linear regression of FeO presents lower y-intercepts than the other two oxides, a consequence
of the smaller contribution of the hydrophobic minerals to the FeO or of their smaller hydrophobicity.
Froth zone recovery is defined as the ratio between the mass of the particles passing from the
froth to the floated material and the mass of the particles passing from the pulp to the froth. When the
froth height is null, the recovery of solids in the flotation process is merely a result of the collection
zone phenomena and the recovery tends to be equal to the collection zone recovery. The estimation of
the froth zone recovery (Rf ) could be made by changing the froth height, measuring the recovery at
each height and extrapolating to zero froth height, in a way that is similar to the Schwarz and Grano
method (Equation (2)) [19]:

recovery at h = x (cm)
R f (%) = × 100% (2)
recovery at h = 0(cm)

Based on this assumption, the recovery at h = 0 could be estimated by the a parameter (the intercept
of the recovery versus froth height regression line) and the froth zone recovery (Rf ) could be estimated
by Equation (2). The drainage (drop back) is estimated by the difference between 100% and Rf .
The froth zone recovery and the drop back of the three oxides recovered by entrainment and by
true flotation are presented in Tables 6 and 7, respectively. Froth recovery decreases with increasing
froth height, whereas the drop back increases with increasing froth height. Small variations in the froth
height have a large impact on the froth zone recovery.

Table 6. Froth zone recovery by entrainment of the three different oxides of the four size fractions for
four froth heights (cm).

Fraction Froth Zone Recovery (%) Drop Back (%)

Oxide
(µm) h = 10 h = 20 h = 30 h = 40 h = 10 h = 20 h = 30 h = 40
<25 79.0 58.1 37.1 16.2 21.0 41.9 62.9 83.8
25–45 80.6 61.3 41.9 22.5 19.4 38.7 58.1 77.5
FeO
45–63 80.3 60.6 40.9 21.2 19.7 39.4 59.1 78.8
>63 80.2 60.4 40.6 20.8 19.8 39.6 59.4 79.2
<25 79.3 58.6 37.9 17.2 20.7 41.4 62.1 82.8
25–45 80.8 61.7 42.5 23.5 19.2 38.3 57.5 76.7
TiO2
45–63 80.7 61.5 42.2 22.9 19.3 38.5 57.8 77.1
>63 81.1 62.3 43.4 24.6 18.9 37.7 56.6 75.4
<25 79.6 59.3 38.9 18.5 20.4 40.7 61.1 81.5
25–45 81.6 63.1 44.7 26.2 18.4 36.9 55.3 73.8
MnO
45–63 81.4 62.9 44.3 25.7 18.6 37.1 55.7 74.2
>63 81.3 62.7 44.0 25.3 18.7 37.4 56.0 74.7
Minerals 2017, 7, 235 9 of 13

Table 7. Froth zone recovery by true flotation of the three different oxides of the four size fractions for
four froth heights (cm).

Fraction Froth Zone Recovery (%) Drop Back (%)

Oxide
(µm) h = 10 h = 20 h = 30 h = 40 h = 10 h = 20 h = 30 h = 40
<25 83.3 66.6 49.9 33.2 16.7 33.4 50.1 66.8
25–45 91.6 83.2 74.8 66.4 8.4 16.8 25.2 33.6
FeO
45–63 85.6 71.1 56.7 42.2 14.4 28.9 43.3 57.8
>63 85.0 70.1 55.1 40.2 15.0 29.9 44.9 59.8
<25 83.1 66.3 49.4 32.5 16.9 33.7 50.6 67.5
25–45 92.0 83.9 75.9 67.9 8.0 16.1 24.1 32.1
TiO2
45–63 88.0 76.0 64.0 52.0 12.0 24.0 36.0 48.0
>63 85.4 70.7 56.1 41.5 14.6 29.3 43.9 58.5
<25 89.9 79.7 69.6 59.5 10.1 20.3 30.4 40.5
25–45 92.5 85.1 77.6 70.2 7.5 14.9 22.4 29.8
MnO
45–63 89.7 79.3 69.0 58.6 10.3 20.7 31.0 41.4
>63 87.2 74.5 61.7 48.9 12.8 25.5 38.3 51.1

Froth zone recovery of the entrained material is similar for the three oxides and is slightly smaller
for the finer fraction, indicating an easier drainage of the finer particles through the channels between
the bubbles (Table 6).
For the three oxides, the froth zone recovery by true flotation is greater than by entrainment
because floated particles are attached to the bubbles. Froth zone recovery of the three oxides by
true flotation is different as a consequence of the discriminatory effect on the minerals (Table 7).
Froth recovery decreases with increasing froth height, an effect that is more pronounced for iron
and titanium oxides. Several authors verified that froth zone recovery decreases as the froth height
increases and that it varies with the particle size [14,17,20,24,26,28,30].
For the three oxides, the froth zone recovery by true flotation is smaller for the finer fraction.
However, the coarser fraction is more easily drained than the two intermediate fractions. This means
that the coarse particles are more weakly attached to the bubbles, a characteristic that overlaps with
the entrapment of the coarse particles between the bubbles.
For the coarser fraction, the hydrophobic mineral carriers of manganese oxide are quartz and
ilmenite, while in the other three fractions it is ilmenite with minor amounts of quartz (Table 2).
A probable lower hydrophobicity of quartz may generate less stable particle-bubble aggregates, and
thus justify the easier drainage of the coarser particles.
For the three oxides, the two coarser fractions have greater intercepts indicating greater floatability,
but they present smaller froth recoveries than the 25–45 µm fraction, indicating low stability
of the particle-bubbles aggregates and more intense drainage. The lower drainage of the size
fraction 25–45 µm (high froth zone recoveries) can be explained by the large contribution of ilmenite
(hydrophobic mineral) (Table 2), which leads to the formation of more stable particle-bubble aggregates,
which hampers the drainage.
For all size fractions, MnO presents the greatest froth zone recovery by true flotation,
a consequence of the major contribution of its hydrophobic minerals, mainly ilmenite, which hampers
its detachment and diminishes drainage. It seems that drainage phenomena are more sensitive to the
hydrophobicity of minerals than the collection phenomena that occur in the pulp.
The influence of the particle size on the collision is confirmed by the intercept’s increase with
increasing particle size in the coarser fractions, where the amount of hydrophobic minerals is similar.
In the pulp zone, the different behavior of titanium and manganese oxides, illustrated by the
y-intercept, is more evident for the finer fraction (Table 5). Since these two oxides have similar
contributions in hydrophobic minerals but a much larger contribution of rutile in the TiO2 and ilmenite
in the MnO, it can be argued that the flotation of extremely fine particles is more sensitive to the degree
Minerals 2017, 7, 235 10 of 13

of mineral hydrophobicity than the flotation of coarser ones. This behavior may indicate an easier
separation of finer particles with respect to coarser ones, because they need higher hydrophobicity
in order to float. On the contrary, Trahar [5] found that it was easier to separate coarser particles
with small hydrophobic differences than fine particles. Fine particles require lower hydrophobicity to
achieve flotation. In addition, Finch and Dobby [1] verified that differences in the collection of two or
more minerals that have different attachment times increase with particle size and that the collection
efficiency is independent of particle size when the size is less than 5 µm. However, these assumptions
cannot explain why recoveries of TiO2 and MnO in the finer fraction are different from in the
coarser fractions.
Attachment time is defined as the time needed for the attachment of particles to an air
bubble. A long attachment time corresponds to weak hydrophobicity or low floatability of minerals,
while a short attachment time indicates strong hydrophobicity or high floatability of minerals.
Attachment time depends on the nature of the material, such as the mineralogy, density, shape and
roughness of the particle; the solution chemistry (pH, ionic strength, concentrations of reagents, etc.);
the bubble size; and the conditioning time.
Attachment time, contact time and particle size are related. For the particle-bubble attachment
to occur it is necessary that the particle-bubble contact time be higher than the attachment time.
The contact time varies with the motion of particles and bubbles, the hydrodynamic conditions and the
particle size, being independent of the degree of hydrophobicity of minerals. However, the attachment
time is determined by the chemical surface characteristics of the particles and is changed by the
addition of reagents.
In a flotation cell, the particle-bubble contact time decreases with decreasing particle size; however,
in a column the contact time (evaluated by the sliding time) increases with decreasing particle size [31].
Assuming that the stability of particle-bubble aggregates is related to the degree of hydrophobicity
(and also the attachment time), froth zone recovery can be used as an indicator of the stability of the
aggregates and, indirectly, can also be used to evaluate the hydrophobicity and the attachment time.
The froth recoveries calculated in this study point to the possibility that the particle–bubble
aggregates of rutile are more unstable than those of ilmenite and quartz, since the froth zone recovery
of TiO2 is lower than that of MnO. Rutile is composed of TiO2 , while ilmenite has almost equal
contributions of MnO and TiO2 (Table 2). Also, it is probable that rutile has a lower hydrophobicity
and a greater attachment time than ilmenite and quartz, requiring greater contact time in order to
promote its flotation.
Since the contribution of hydrophobic minerals is similar for TiO2 and MnO (Table 3), the flotation
results should be similar, unless the carrier minerals of each oxide have different attachment times.
The overall results of the TiO2 and MnO recovery are almost the same for the coarser fractions,
but the finer fraction TiO2 gives worse results. Although the contact time is greater in the finer fraction,
the TiO2 recoveries are smaller than those of MnO, which is probably a consequence of the need for
longer attachment times in the finer particles, especially for the fine particles of rutile.
Several researchers have analyzed the effect of particle size on attachment time. Using five
different coal types with a particle size range of approximately 40–500 µm, Ye and Miller [32] show
that the attachment time increases with increasing particle size. Similar observations were also made
by Wang et al. [33] and Ozdemir et al. [34] for coal samples.
Experimental results of Yoon and Yordan [35] for quartz particles with sizes between 90 and
400 µm, and of Albijanic et al. [36] for quartz particles of 147–300 µm, suggest that the attachment
time increases with increasing particle size. Also, Ye et al. [37] verified that for molybdenite with
particle sizes between 50 and 200 µm, sulfur with particle sizes between 700 and 1500 µm, and resin
with particle sizes between 40 and 500 µm, the attachment time increases with increasing particle size.
This behaviour is ascribed to the displacement of the liquid film on the surface of large particles.
Also, Ralston et al. [38] observed that for quartz particles with sizes between 10 and 60 µm the
Minerals 2017, 7, 235 11 of 13

attachment efficiency increases with decreasing particle size, but for stronger hydrophobic particles
the attachment efficiency is less dependent on the particle size.
However, Crawford and Ralston [39] found that the attachment time of quartz particles with a
size of 15 µm is much greater than size fractions with 46 µm and with 99 µm. Also, Nguyen et al. [40]
verified that the attachment time of quartz particles smaller than 80 µm increases with decreasing
particle size.
In the present study, it seems that fine particles (<25 µm) can have an attachment time greater
than the coarser fractions, mainly for rutile, a floatable mineral with low hydrophobicity, resulting in a
greater difficulty of flotation of the fine fraction, reflected in the lower recoveries of titanium oxide
compared to manganese oxide.

4. Conclusions
The column flotation tests promoted the flotation of the main penalty hydrophobic minerals of
kaolin ore, specially ilmenite, quartz, tourmaline, goethite and rutile, measured by the presence of
FeO, TiO2 and MnO. The separation efficiency of MnO had better results as a consequence of the major
contribution and floatability of its hydrophobic minerals. TiO2 achieved good recovery performances
in the coarser fractions, nevertheless, in the finer fraction the recovery was lower than the recovery of
MnO, which can be justified by the greater difficulty of floating the rutile, the main carrier mineral of
TiO2 . The performance of the FeO in the flotation tests was the lowest as a consequence of the minor
contribution of hydrophobic minerals.
The entrainment phenomenon and the drainage of entrained material are independent of the
mineralogy. The degree of entrainment depends on the particle size, being greater for fractions lower
than 25 µm, and similar for the other three coarser fractions.
The recoveries by true flotation and by entrainment decrease linearly with the increase of froth
height, as an outcome of the increased drainage of particles. The effect of the froth height in drainage
depends on how the particles are transferred to the froth, and their size and hydrophobicity, with the
entrained particles draining more easily than the floated ones. Floated material has greater froth
recovery than entrained material since floated particles are attached to bubbles, which makes them
more difficult to drain. Drainage depends on the effect of the particle size on the mobility and the
stability of the particle–bubble aggregates. For the three oxides, the finest fraction entrained presents
the smallest froth zone recovery as a consequence of the greater mobility of the fine particles in
the froth.
For true flotation in the three oxides, the finest fraction presents the smallest froth zone recovery.
However, the coarser fraction is more easily drained than the two intermediate fractions. This means
that particles of greater size are more weakly attached to the bubbles, a feature that overlaps with the
effect of the entrapment of the coarser particles between the bubbles.
The drainage phenomenon is more sensitive to the degree of hydrophobicity than the phenomenon
that occurs in the pulp zone for particles greater than 25 µm. However, for fine particles,
the phenomenon that occurred in the pulp zone presents as much or more sensitivity to the degree of
hydrophobicity of the particles than the phenomenon that occurred in the froth zone.

Acknowledgments: This work was supported by the Portuguese Foundation for Science and Technology
(FCT-MEC) through national funds and, when applicable, co-financed by FEDER in the ambit of the partnership
PT2020, through the following research projects: UID/Multi/00073/2013 of the Geosciences Center and
UID/EMS/00285/2013 of the Centre for Mechanical Engineering of the University of Coimbra.
Conflicts of Interest: The author declares no conflict of interest.

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