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Table
13. Strength and molar effectiveness for selected frothers, given solid and flotation
device.
Minerals
Strength cγ75, mmol/dm3
(Coal, Lab. Flotation Machine,
[50])
All Article
Example
Types
n-butanol
0.2
Advanced
Search
n-propanol
n-hexanol
Example
Search
Molar Effectiveness, γ1M
(Carbonaceous Shale, Hallimond Cell,
[55])
KPF6
4%
1
NaCl
44%
3
Na2SO4
46%
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
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Introduction



Frothers
in Pure State
Article
Overview
Frother in Aqueous Solutions
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
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in Aqueous Solutions/Gas
Article
Versions
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
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(Liquid/Gas/Solid)
Export
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Conclusions

Acknowledgments
More by Authors Links
Author Contributions

 Conflicts of Interest
Full Article Text
References

×


Table
13. 8(2),
Strength
and molar effectiveness for selected frothers, given solid and flotation
Minerals
2018,
53; https://doi.org/10.3390/min8020053
Open Access
device.
(https://doi.org/10.3390/min8020053)
Article Example
Strength cγ75, mmol/dm3
(Coal, Lab. Flotation Machine,
[50])
Example
0.2
KPF6
Classification of Flotation Frothers
n-butanol
by
Molar Effectiveness, γ1M
(Carbonaceous Shale, Hallimond Cell,
[55])
0
4%
(https://sciprofiles.com/profile/357653) 1
Jan
Drzymala
and
n-propanol
1
NaCl
44%
1,2,*

Przemyslaw B. Kowalczuk (https://sciprofiles.com/profile/255644)
n-hexanol
3
Na2SO4
46%
(mailto:please_login) (https://orcid.org/0000-0002-1432-030X)
1
Faculty of Geoengineering, Mining and Geology, Wroclaw University of Science and Technology,
Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland
2
Department of Geoscience and Petroleum, Norwegian University of Science and Technology, Sem
Sælands vei 1, N-7491 Trondheim, Norway
*
Author to whom correspondence should be addressed.
Received: 23 November 2017 / Accepted: 30 January 2018 / Published: 7 February 2018
Abstract: In this paper, a scheme of flotation frothers classification is presented. The scheme first
indicates the physical system in which a frother is present and four of them i.e., pure state, aqueous
solution, aqueous solution/gas system and aqueous solution/gas/solid system are distinguished. As a
result, there are numerous classifications of flotation frothers. The classifications can be organized
into a scheme described in detail in this paper. The frother can be present in one of four physical
systems, that is pure state, aqueous solution, aqueous solution/gas and aqueous solution/gas/solid
system. It results from the paper that a meaningful classification of frothers relies on choosing the
physical system and next feature, trend, parameter or parameters according to which the Back to TopTop
/

 classification
is performed. The proposed classification can play a useful role in characterizing and
 evaluation of flotation frothers.
Introduction
Abstract




(/)
Frothers in Pure State
Keywords: foam; froth; separation; classification; selectivity; efficiency; power; kinesis
Frother in Aqueous Solutions

Frother in Aqueous Solutions/Gas
System
Three-Phase (Liquid/Gas/Solid)
1. System
Introduction

Conclusions
Frothers are very important reagents playing a multiple role in flotation of particulate matter. The
frothers facilitate formation of either foam or froth and favourably modify the structure of films between
Author Contributions
bubbles as well as solid particles and bubbles [1,2,3,4,5,6,7]. Frothers also interact with collectors
 Conflicts of Interest

resulting in a stronger and faster particle-bubble attachment [8].
References
Although flotation of naturally hydrophobic materials, with a water contact angle greater than zero
[9,10], is possible without any reagent [11], some hydrophobic and slightly hydrophobic materials do
not float in pure water. A good example is molybdenite and different carbonaceous materials, including
metals- and carbon-bearing shales [12]. Their flotation can be induced by application of frothers in the
Table 13. Strength and molar effectiveness for selected frothers, given solid and flotation
form of either organic compounds or inorganic electrolytes [13,14].
device.
Properties of frothers depend on many parameters, including structure, concentration and ability to
Strength cγ75, mmol/dm3
Molar Effectiveness, γ1M
interact with water, solids, collectors
and modifiers. As a result, there are numerous classifications
of
Example
(Coal, Lab. Flotation Machine,
Example
(Carbonaceous Shale, Hallimond Cell,
frothers. For instance, Khoshdast and Sam [15] classified frothers taking into account their (i) pH[50])
[55])
sensitivity; (ii) solubility; (iii) frothing/collecting properties; and (iv) selectivity/frothing power. The 0
n-butanol
0.2
KPF6
4%
classifications considering pH-sensitivity and solubility are
obvious. In the third category frothers can
n-propanol
1
NaCltakes into account ability
44%of frothers to float
also play
the role of a collector. The
fourth classification
n-hexanol
3
Na2SO
46% particles, while
4
particles
according to their size, e.g.,
selective frothers
effectively
recover the fine
powerful frothers float well the coarser ones [16].
Literature survey on frothers, their properties and grouping shows that the issue of frothers
classification is much more complex than that offered in the literature. Therefore, in this work a scheme
for frothers classification is proposed. The scheme first indicates the physical system in which the
frother is present and four groups: (i) pure state; (ii) aqueous solution; (iii) aqueous solution/gas
system; and (iv) aqueous solution/gas/solid system are distinguished (Table 1). Next, within each
physical system, the frothers are classified into five categories, mostly based on the number of
numerical values need for the classification.

Acknowledgments
×


Table 1. Frothers classification system based on four physical systems and number of numerical
values used for classification.
Back to TopTop
/

of

To emphasize that the classification deals with reagents, which are used for separation by flotation
Abstract
(/)
solid particles from water with gas bubbles, in this work these reagents will be referred to as
Introduction
frothers, regardless the fact that sometimes the properties used for the classification involves foam,
Frothers in Pure State
which is a two-phase system without solid particles.
Frother in Aqueous Solutions


Frother in Aqueous Solutions/Gas
System
2. Frothers in Pure State

Three-Phase (Liquid/Gas/Solid)
System
2.1.
Feature-Type (no-Numerical Value) Classification
Conclusions

The simplest classification of frothers in the pure state is based on their elemental composition
Acknowledgments
and
divides
frothers into organic and inorganic [17] (Table 2). Another classification takes into account
Author
Contributions
the


chemical
structure and divides frothers into alcohols and non-alcohols (Table 3). The alcoholic
Conflicts
of Interest

frothers
can be further divided into classes depending on the alcohol structure [18] (Table 3). The nonReferences
alcoholic frothers can also be divided into organic and inorganic. The non-alcoholic organic frothers,
instead of –OH, contain bonded oxygen in their structure. The frother, in its native state, can be solid,
as α-terpineol with melting point of 40 °C [19] and inorganic salts, liquid (most organic frothers
including
polyglycol
ethers)
gaseffectiveness
(ammonia). for selected frothers, given solid and flotation
Table
13. Strength
andand
molar
device.
Table 2. Classification of frothers into organic and inorganic.
×


Example
Strength cγ75, mmol/dm3
(Coal, Lab. Flotation Machine,
[50])
Example
Molar Effectiveness, γ1M
(Carbonaceous Shale, Hallimond Cell,
[55])
0
n-butanol
0.2
KPF6
4%
n-propanol
1
NaCl
44%
n-hexanol
3
Na2SO4
46%
Table 3. Classification of organic frothers into alcohols and non-alcohols ([18], with
modifications).
All these feature-type classifications are descriptive and no numerical value is assigned to the
frother.
2.2. One-Numerical Value Classification
There is also a group of classifications of frothers based on one numerical value of a selected
property of frother in the pure state. One of them takes into account the so-called hydrophilic-lipophilic
balance (HLB) proposed by Davies [20]. The formula for calculation of HLB is: HLB = 7 + 1.3·(O) +
Back to TopTop
/

1.9·(OH)
xHy), where O and OH stand for numbers of hydrophilic oxygen and hydroxyl
Abstract− 0.475·(C
(/)
functional
groups, respectively and CxHy for number of lipophilic (or hydrophobic) –CH, –CH2–, CH3–,
Introduction

=CH–
groups.
TheState
HLB for frothers is between 4 and 10 [21]. The scale of HLB is given in Table 4.
Frothers
in Pure
The
HLB values
for organic
Frother
in Aqueous
Solutionsfrothers can be found in many papers (e.g., [22]).







Frother in Aqueous Solutions/Gas
Table 4. Classification of organic reagents, including frothers, based on numerical value of HLB
System
(after [21], with modifications).
Three-Phase (Liquid/Gas/Solid)
System
Conclusions
Acknowledgments
Author Contributions
 Conflicts of Interest

References
The frothers can also be classified according to their number of carbon in the alkyl chain (n) as
well as molecular mass, historically called molecular weight (MW). The values of MW can be found for
instance in [19].
Table 13. Strength and molar effectiveness for selected frothers, given solid and flotation
2.3. Two-Numerical
Value Classification
device.
3 in the pure state system
The third type of Strength
classification
of frothers
is based
on two numerical
cγ75, mmol/dm
Molar
Effectiveness,
γ1M
values Example
characterizing
(Coal,
theLab.
frother.
Flotation
A good
Machine,
example is
Example
HLB and MW.
(Carbonaceous
These values
Shale,
can
Hallimond
be eitherCell,
[50])as is shown in Figure 1. The frothers can be
[55])
tabulated or presented graphically
grouped into classes,
0
for instance
low
MW/high
HLB
or
high
MW/low
HLB
etc.
n-butanol
0.2
KPF6
4%
×


n-propanol
1
NaCl
44%
n-hexanol
3
Na2SO4
46%
Figure 1. Two-numerical value classification of frothers in pure state according to hydrophobiclipophilic balance (HLB) and molecular weight (MW) (based on [16]).
Back to TopTop
/


3. Abstract
Frother in(/)Aqueous Solutions

Introduction


Frothers
in Pure State
3.1.
Feature-Type
(no Numerical Value) Classification

Frother in Aqueous Solutions
Frothers are used together with water, unless flotation is performed in non-aqueous solutions.

Frother in Aqueous Solutions/Gas
Therefore, there is a classification of frothers based on their ability to dissociate in aqueous solutions.
System
Their
dissociation depends on pH and therefore the frothers are classified into acidic, neutral and
Three-Phase (Liquid/Gas/Solid)
basic, that is cationic, anionic and non-ionic [15,23] (Table 5). This is a no-numerical value
System
classification
type. Assigning numerical values to the frothers, for instance of the dissociation
constants, would turn it into a one-numerical value classification.
Conclusions
Acknowledgments



Author Contributions
Table 5. Classification of frothers according to their pH-sensitivity [15,23].

Conflicts of Interest

References
×


Table 13. Strength and molar effectiveness for selected frothers, given solid and flotation
device.
Solubility of frothers influences the flotation
performance [24]. Crozier [25] divided frothers into
Strength cγ75, mmol/dm3
Molar Effectiveness, γ1M
completely
miscible
and
slightly
soluble.
Such
reagents
as
aliphatic
alcohols,
cresylic
acids, alkoxy
Example
(Coal, Lab. Flotation Machine,
Example
(Carbonaceous Shale,
Hallimond
Cell,
paraffins and non-ionic polypropylene
glycol ethers belong to the slightly soluble
group of frothers,
[50])
[55])
0
while completely
soluble
are
polyglycols
and
polyglycol
ethers
[15].
n-butanol
0.2
KPF
4%
6
n-propanol
1
3.2. One-Numerical
Value Classification
NaCl
44%
n-hexanol
3
Na2SO4
46%
Different
properties of frothers
present in aqueous
solutions can be used for
their one-numerical
value classification. One of them is solubility. The solubility of selected organic frothers is given in
Table 6. Another is the cloud point below which the frother molecules can be dissolved in water. At
higher temperature molecules start to associate and solution becomes cloudy as a result of phase
separation and surface activity loses. The cloud point is observed for frothers containing
polyoxyethylene groups in their structure. Table 7 presents the cloud point for selected
polyoxyethylene-type non-ionic frothers in 0.1 weight fraction aqueous solutions.
Table 6. Solubility in water of selected organic frothers (based on [26,27,28,29]).
Back to TopTop
/









Table 7. Cloud point of selected frothers in 0.1 weight fraction aqueous solutions present in the
Abstract
(/)
polyoxyethylene-type non-ionic frother/water sub-system of frother aqueous solutions system
Introduction

(basedinon
[30]).
Frothers
Pure
State
Frother in Aqueous Solutions
Frother in Aqueous Solutions/Gas
System
Three-Phase (Liquid/Gas/Solid)
System
Conclusions
Acknowledgments
The cloud point can be assigned only to the polyoxyethylenic non-ionic frothers in the aqueous
solution sub-system and therefore for other frothers it is equal to zero.



Author Contributions
 Conflicts of Interest

References
4. Frother in Aqueous Solutions/Gas System
×


4.1. Feature and Trend-Type (no Numerical Value) Classification
Tableand
13.Laskowski
Strength and
effectiveness
for selected
frothers,
given
solid and
Lekki
[31]molar
classified
frothers according
to their
ability
to modify
the flotation
surface tension
device.
of water at concentrations applied in flotation. In their classification frothers can be either surface
3
Strength
cγ75surface
, mmol/dm
Effectiveness,
active, that is changing
the static
tension of water, or surface Molar
inactive
(Table 8). γ1M
Example
(Coal, Lab. Flotation Machine,
[50])
(Carbonaceous Shale, Hallimond Cell,
[55])
Table 8. Classification of frothers according to their surface activity in water
at concentrations
0
n-butanol
0.2
applied
in flotation (after [31]).
Example
KPF6
4%
n-propanol
1
NaCl
44%
n-hexanol
3
Na2SO4
46%
The classification offered in Table 8 is not precise because establishing the limit of surface tension
change for frothers to be called surface inactive is difficult. A better approach is to divide frothers into
surface active and surfactant (Figure 2) based on the trend of surface tension change with increasing
frother concentration. The surface active frothers are those which cause either low or moderate,
positive or negative, surface tension change (Δσ = σsolution − σwater) with increasing concentration of
frother in water, while for surfactants the Δσ parameter is significant and negative (Figure 2).
Back to TopTop
/












Abstract
(/)
Introduction

Frothers in Pure State
Frother in Aqueous Solutions
Frother in Aqueous Solutions/Gas
System
Three-Phase (Liquid/Gas/Solid)
System
Conclusions
Acknowledgments
Author Contributions
 Conflicts of Interest

References
×


Table 13. Strength and molar effectiveness for selected frothers, given solid and flotation
device.
3 on their ability to change
Figure 2. Classification
ofcfrothers,
based
surface
tension of
Strength
Molar
Effectiveness,
γ1Mwater, into
γ75, mmol/dm
Example
Lab. Flotation Machine,
Example
(Carbonaceous
Shale, Hallimond
Cell,
surface
active (Coal,
with characteristic
slope (σ∠) and
surfactants
which significantly
lower surface
[50])
[55])
tension of aqueous solutions.
0
n-butanol
0.2
4.2. One-Numerical
Value Classification
n-propanol
1
n-hexanol
3
KPF6
4%
NaCl
44%
Na2SO4
46%
4.2.1. Surface Tension versus Frother Concentration, σ∠ or cσ50
The surface tension change of surface active reagents and surfactants (Figure 2) can be utilized
for the classification of frothers based on numerical values. Since the surface active reagents change
their static surface tension with the concentration almost linearly, their classification can be based on
the approximated slope of Δσ (or σ) versus frother concentration c plot (Figure 3). Theoretically, there
should exist surface inactive reagents but so far, no reagent with Δσ = 0 in a wide range of
concentrations was reported. In such considerations, the change of surface tension due to mixing of
frother and water, having different pure state surface tension, is neglected. The slopes of Δσ, denoted
as σ∠, can be either negative or positive for both inorganic frothers (salts, Figure 3a; acids, Figure 3b;
bases, Figure 3c) and organic reagents (Figure 3d). The slopes σ∠ of the plots of Δσ versus the
frother concentration for selected frothers are given in Table 9.
Back to TopTop
/












Abstract
(/)
Introduction

Frothers in Pure State
Frother in Aqueous Solutions
Frother in Aqueous Solutions/Gas
System
Three-Phase (Liquid/Gas/Solid)
System
Conclusions
Acknowledgments
Author Contributions
 Conflicts of Interest

References
×


Table 13. Strength and molar effectiveness for selected frothers, given solid and flotation
Figure
device.3. Slope of surface tension of aqueous solution of selected organic and inorganic
reagents, (a) inorganic
salts
(b) inorganic
acids [19]; (c) inorganic
bases [19];γ (d) organic
3
Strength
cγ75[32];
, mmol/dm
Molar Effectiveness,
1M
3).
reagents
([19,33],
assumed
solution
density 1 g/cm
Example
(Coal,
Lab. Flotation
Machine,
Example
(Carbonaceous Shale, Hallimond Cell,
[50])
n-butanol
[55])
Table 9. σ∠ values
for selected surface
active (non-surfactant)4%
frothers.
0.2
KPF
0
6
n-propanol
1
NaCl
44%
n-hexanol
3
Na2SO4
46%
In the case of surfactants, the plot of the surface tension versus concentration is not linear (Figure
4a), although plotting using a logarithmic scale for concentration (Figure 4b) usually provides a linear
part, before it levels off for values characteristic for micellar or pure reagent surface tension.
Back to TopTop
/


Figure 4. Surface tension of aqueous solution of selected surfactants and cσ50 determination.
Abstract
(/)

(a) surfactants (acetals [37]; methyl isobutyl carbinol (MIBC) [38]; dodecyl trimethylammonium
Introduction


bromide
(DTAB):
Frothers
in Pure
State[39]; (b) surfactants (semilog scale) (hexyl ammonium chloride: [35]; Na n-

dodecyl
sulphate:
[40]; diethylene oxide n-decyl ether: [41]).
Frother
in Aqueous
Solutions

Frother in Aqueous Solutions/Gas
The classification of surfactants according to their surface tension can be based on the
System
characteristic
at which the surface tension of aqueous solution drops to an arbitrarily
Three-Phaseconcentration
(Liquid/Gas/Solid)
chosen
value, for instance 50 mN/m. This property will be denoted as cσ50. Any other value can be
System

used.
Table 10 presents the cσ50 values for selected surfactant frothers.
Conclusions

Acknowledgments



Author Contributions

Table 10. cσ50 values of selected surfactant frothers.
Conflicts of Interest

References
×


Table 13. Strength and molar effectiveness for selected frothers, given solid and flotation
4.2.2.device.
Bubble Size versus Frother Concentration, CCC
Strength cγ75, mmol/dm3
Molar Effectiveness, γ1M
Many other properties of frothers in aqueous solutions in the presence of the gas phase can be
Example
(Coal, Lab. Flotation Machine,
Example
(Carbonaceous Shale, Hallimond Cell,
used for their classification. One
of
them,
resulting
from
the
bubble
size versus[55])
concentration plot
[50])
0 the
(Figure 5), is the critical coalescence concentration (CCC) [2]. CCC is a parameter which indicates
n-butanol
0.2
KPF6
4%
frother concentration needed to prevent bubbles coalescence in an aqueous solution. The value of
n-propanol
1
NaCl
44%
CCC can be either read-off from the bubble size-concentration curve or evaluated using HLB and MW
n-hexanol
3 bubble size in theNa
46%usually CCC , that is
2SO4
[2,22,42].
Since the change of the
vicinity
of CCC is not sharp,
95
the frother concentration at which the average bubble size drops 95% is used. The third method of
CCC determination is based on normalization of the bubble size vs. concentration plot using a
mathematical equation approximating the whole curve (CCCt) [43]. The selected values of CCC are
presented in Table 11. The Sauter mean diameter of bubble size is usually used on the y axis.
However, other mean values can also be used.
Back to TopTop
/


Abstract

Introduction

Frother in Aqueous Solutions

Frother in Aqueous Solutions/Gas
System

Three-Phase (Liquid/Gas/Solid)
System

Conclusions

Acknowledgments



Frothers in Pure State


(/)
Author Contributions

Conflicts of Interest

References
Figure 5. Determination of CCC, CCC95 and CCCt from the relation between average bubble
size and frother concentration.
×


Table11.
13.Classification
Strength and of
molar
effectiveness
frothers,
given
solid
Table
frothers
accordingfor
to selected
their values
of CCC,
DFI
andand
GHflotation
0.2. Source of
device.
data: a—[44]; b—[45]; c—[22]; d—[2]; e—[46]; f—[47]; g—[48]; (* denotes CCC95).
Example
Strength cγ75, mmol/dm3
(Coal, Lab. Flotation Machine,
[50])
Example
Molar Effectiveness, γ1M
(Carbonaceous Shale, Hallimond Cell,
[55])
0
n-butanol
0.2
KPF6
4%
n-propanol
1
NaCl
44%
n-hexanol
3
Na2SO4
46%
CCC95 is related to the ratio of HLB and MW by a simple equation shown in Figure 6 [42]. It
means that the two-numerical value classification of frothers based on HLB and MW (Figure 1) can be
replaced by a one-numerical value classification using either HLB/MW or CCC95. The values of CCC
can be also predicted basing on the number of carbon in the alkyl group of the reagent [49].
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/












Abstract
(/)
Introduction

Frothers in Pure State
Frother in Aqueous Solutions
Frother in Aqueous Solutions/Gas
System
Three-Phase (Liquid/Gas/Solid)
System
Conclusions
Acknowledgments
Author Contributions
 Conflicts of Interest

References
×


Figure 6. Relation between CCC and HLB/MW [42].
13. Strength
and
molar Concentration,
effectiveness for
frothers, given solid and flotation
4.2.3.Table
Gas Hold-up
versus
Frother
GHselected
0.2
device.
The
classification of frothers can be also based on the gas hold-up influenced by the frother
Strength
, mmol/dm
γ1M
concentration [48] (Figure
7). cItγ75
can
be done3 by vertical cross-sectionMolar
of theEffectiveness,
plot and determination,
for
Example
(Coal, Lab. Flotation Machine,
Example
(Carbonaceous
Shale,
Hallimond
Cell,
instance the gas hold-up at 0.2 mmol/dm3 of frother or shortly GH0.2. The selected numerical values of
[50])
[55])
GH0.2 are given in Table 11.
0
n-butanol
0.2
KPF6
4%
n-propanol
1
NaCl
44%
n-hexanol
3
Na2SO4
46%
Figure 7. Gas hold-up as a function frother concentration (based on [48]).
4.2.4. Retention Time versus Frother Concentration, DFI
Back to TopTop
/


Another parameter which can be used for classification of frothers is the dynamic foamability index
Abstract
(/)
(DFI)
[1,50,51]. DFI represents the limiting slope of the gas retention time versus frother concentration
Introduction

for
concentration
zero, where the retention time is the slope of the linear part of the
Frothers
in Pure approaching
State
dependence
of the total
gas volume contained in the system (solution + foam) on the gas flow rate
Frother in Aqueous
Solutions
(Figure
values
of DFI for selected frothers were given in Table 11.
Frother8).
in The
Aqueous
Solutions/Gas
System






Three-Phase (Liquid/Gas/Solid)
System
Conclusions
Acknowledgments
Author Contributions
 Conflicts of Interest

References
×


Table 13. Strength and molar effectiveness for selected frothers, given solid and flotation
device.
Example
Strength cγ75, mmol/dm3
Molar Effectiveness, γ1M
(Coal, Lab. Flotation Machine,
Example
(Carbonaceous Shale, Hallimond Cell,
Figure 8. Determination of DFI (based on [50]).
[50])
[55])
0
n-butanol
0.2
KPF6
4%
n-propanol
1
NaCl
44%
4.2.5. Other Parameters Used for Frother Classification
There are many other parameters which could be used for frothers classification resulting from
n-hexanol
3
Na SO4
46%
properties of the frother-in-water/gas system. They are2 concentration
at half of the maximum foam
height (CMH) [52] determined from the foam height—concentration curve; foam time of life [17];
concentration at minimum bubble velocity (CMV) [43,53] based on the bubble velocity-concentration
curve, dynamic stability factor (DSF) [54], Bikerman’s foaminess unit Σ(reference) and Sun’s frothability
index [50].
4.3. Two-Numerical Value Classification
If two classification parameters form a map-type relation as DFI and CCC (Figure 9) a twoparameter classification is possible. The description of the frother class requires two words. The
classes shown in Figure 9 are: high DFI/low CCC, low DFI/low CCC and low DFI/high CCC.
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/












Abstract
(/)
Introduction

Frothers in Pure State
Frother in Aqueous Solutions
Frother in Aqueous Solutions/Gas
System
Three-Phase (Liquid/Gas/Solid)
System
Conclusions
Acknowledgments
Author Contributions
 Conflicts of Interest

References
×


Figure 9. Map-type relation between DFI and CCC and two-numerical value classification of
Table 13.
Strength
and molar solutions/gas
effectiveness system
for selected
frothers
in the
frother/aqueous
(datafrothers,
of [16]). given solid and flotation
device.
Strength cγ75, mmol/dm3
5. Three-Phase
System
Example (Liquid/Gas/Solid)
(Coal, Lab. Flotation
Machine,
[50])
Example
Molar Effectiveness, γ1M
(Carbonaceous Shale, Hallimond Cell,
[55])
0
The
already mentioned classifications
of frothersKPF
are based on either the structure
or ability to
n-butanol
0.2
4%
6
form bubbles and foams in the two-phase (gas/water) systems. However, flotation is a phenomenon
n-propanol
1
NaCl
44%
involving also solids. The main parameters (Figure 10), which are monitored in solids flotation, are
n-hexanol
Na2SO4
yield γ and
recovery ε when two 3or more solids are evaluated,
flotation time and46%
frother dose. Since the
frother concentration influences other parameters such as surface tension of solution and the
maximum yield (or recovery) after a certain or long time of flotation, these properties can also be used
for classification.
Back to TopTop
/


Abstract

Introduction

Frother in Aqueous Solutions

Frother in Aqueous Solutions/Gas
System

Three-Phase (Liquid/Gas/Solid)
System

Conclusions

Acknowledgments



Frothers in Pure State


(/)
Author Contributions

Conflicts of Interest

References
×


Figure 10. Yield (or recovery) of flotation as a function of time at a given frother concentration
Table 13.
Strength
and
molar effectiveness
for selected
given
solid and
provides
various
data
including
yield (or recovery)
trend,frothers,
maximum
flotation
yieldflotation
(or recovery)
device.
(ymax), flotation kinetics (v, k), which can be used for frothers classification in the water/gas/solid
cγ75, mmol/dm
Molar Effectiveness, γ1M
system. The caseStrength
of first order
process 3rate.
Example
(Coal, Lab. Flotation Machine,
[50])
Example
(Carbonaceous Shale, Hallimond Cell,
[55])
0
0.2
KPF6
4%
5.1. Trend-Type Classification
n-butanol
5.1.1. Flotation
Effective, Neutral, Harmful
and Overdosed
n-propanol Yield (Recovery) 1vs. Frother Concentration.
NaCl
44%
Frothers
n-hexanol
3
Na2SO4
46%
The effectiveness of frothers, that is their ability to provide either a desired or the maximum yield
(recovery) in the solid/water/gas flotation system, depends on the particle hydrophobicity, frother type
(inorganic or organic), surface tension change and many other parameters. Therefore, it is useful to
divide the solid/water/gas flotation systems into sub-systems, because of similar properties observed
within these groups. Such classification is based on (i) particle hydrophobicity θ, which can be high,
medium and low; (ii) frother type, which can be inorganic or organic; and (iii) surface tension change,
which can be increasing (Δσ+), decreasing (Δσ-), constant (Δσ0), or significantly decreasing in the
case of surfactant (Δσs). Basing on the yield or recovery change with the frother concentration, the
frothers can be divided into effective, neutral, harmful and overdosed (Figure 11). This type of
classification is presented in Table 12.
Back to TopTop
/


Abstract

Introduction

Frother in Aqueous Solutions

Frother in Aqueous Solutions/Gas
System

Three-Phase (Liquid/Gas/Solid)
System

Conclusions

Acknowledgments



Frothers in Pure State


(/)
Author Contributions

Conflicts of Interest

References
×


Table 13. Strength and molar effectiveness for selected frothers, given solid and flotation
Figure
device.11. Classification of frothers into effective, neutral, harmful and overdosed (a). Examples:
3
(b) medium hydrophobicity
material
(coal)/different
surfactants (yield
effectiveness
Strength cγ75
, mmol/dm
Molarand
Effectiveness,
γ1M increase
with
frother concentration)
(data after
[50], flotation
2.5 min); (c) medium
hydrophobicity
Example
(Coal, Lab. Flotation
Machine,
Exampletime (Carbonaceous
Shale, Hallimond
Cell,
[50])
material (carbonaceous shale)/different
inorganic salts (based on data [55])
of [55]); (d) differently
0
hydrophobic
materials/surfactant
(based
on
data
of
[56,57]).
n-butanol
0.2
KPF6
4%
n-propanol
1
NaCl
44%
Table 12. Classification of frothers into effective, neutral, harmful and overdosed, based on
n-hexanol
3
Na2SO4
46%
flotation yield (or maximum yield) change caused by increasing concentration of frother and
taking into account particle hydrophobicity θ, frother type (inorganic or organic) and surface
tension change (increase Δσ+, decrease Δσ-, constant Δσ0, significant decrease by surfactant
Δσs) (s: solid; w: water; g: gas).
Figure 11a illustrates the classification of frothers into effective (Δγ+), neutral (Δγ0), harmful (Δγ-)
and overdosed (Δγ-) due to the maximum yield change with the frother concentration for different
systems. In the medium hydrophobic solid/surfactants/water/gas system (Figure 11b) the yield
increases with the frother concentration, indicating that frothers are always effective. However, it
should be kept in mind that too much surfactant eventually reduces the flotation yield due to a
significant surface tension drop leading to a hydrophilization of the solid known as the Zisman plot [58].
Back
In some systems, especial with inorganic frothers, low concentration diminishes flotation due
to to
theTopTop
/

Jones-Ray
caused by electrical double layer changes [59,60]. The most desire range of flotation
Abstract effect,
(/)
system
response due to application of the frother is called in this work the Lyster effect because he
Introduction

introduced
first
frothers
Frothers in
Pure
State to flotation [61].
In theincase
of medium
hydrophobic solid/inorganic salts/water/gas sub-systems (Figure 11c) the
Frother
Aqueous
Solutions

maximum
increases
also when the surface tension increases, no change of yield occurs when the
Frother inyield
Aqueous
Solutions/Gas
saltSystem
does not change the surface tension and the yield increases when the surface tension increases.
For
medium hydrophobic
solids yield increases and the frothers are effective and no yield change is
Three-Phase
(Liquid/Gas/Solid)
observed
System for very weakly hydrophobic and hydrophilic solids (neutral frothers). In other systems, for

instance
differently hydrophobic solid/surfactant/water/gas (Figure 11d), for highly hydrophobic
Conclusions
materials
surfactants can be easily overdosed and too high concentration diminished the flotation
Acknowledgments

performance.
Flotation of highly hydrophobic solids in the presence of inorganic salts requires more
Author Contributions

investigations
to establish the yield response to different frothers.
Conflicts of Interest




References
5.1.2. Flotation Performance Versus Surface Tension. Surface Tension Effective, Neutral and Harmful
Inorganic Frothers
×


Pugh et al. [32] investigated flotation of graphite, which is a medium hydrophobic material, in the
presence
of13.
different
inorganic
salts.effectiveness
Their data, replotted
by Ratajczak
and Drzymala
(Figure 12)
Table
Strength
and molar
for selected
frothers, given
solid and [62]
flotation
as thedevice.
yield after a certain flotation time and the surface tension of aqueous solution caused by the
frother evidently shows,
that there are groups of inorganic frother: effective,
neutral, and harmful,
Strength cγ75, mmol/dm3
Molar Effectiveness, γ1M
resulting
from positive
(Δσ
= +),
negative
(Δσ = −) and
none (Δσ
≅ 0) change Shale,
of the Hallimond
surface tension
Example
(Coal,
Lab.
Flotation
Machine,
Example
(Carbonaceous
Cell,
with the inorganic frother concentration,
respectively. This type of flotation was[55])
confirmed in other
[50])
0
papers n-butanol
[63,64].
0.2
KPF6
4%
n-propanol
1
NaCl
44%
n-hexanol
3
Na2SO4
46%
Figure 12. Influence of aqueous solution surface tension of inorganic salts and electrolytes on
yield of graphite flotation (based on [62,65,66]).
5.2. One Numerical Value Classification
Back to TopTop
/


Abstract
5.2.1.
Maximum
(/) Flotation Yield versus Frother Concentration. Frother Strength cγ75 and Molar
Effectiveness
Introduction γ1M



Frothers
in Pure
Stateconcentration plots are able to provide not only general classification of frothers
The yield
versus
Frother
in Aqueous
into
effective,
neutral,Solutions
harmful and overdosed but also various numerical values which can be used for


Frother
in Aqueous Solutions/Gas
further
classifications
of frothers. This can be accomplished by performing different cross-sections of
System
the yield-frother concentration plots. Two of them, which are the most obvious, are presented in Figure

(Liquid/Gas/Solid)
13.Three-Phase
The horizontal
cross-section provides a specific parameter which can be called the frother strength,
System
while vertical cross-section gives molar effectiveness of the frother (Table 13). Since the yield (and
Conclusions
also recovery) depends on the type of solid and flotation device, these parameters are not universal
Acknowledgments
but rather specific, depending on the solid properties and the type of flotation device. In addition, the
Author Contributions
position of the crossing line must be carefully selected. We propose for the horizontal cross-section the
 Conflicts of Interest

yield of 75% as the most practical and therefore the symbol of frother strength is cγ75. In the case of
References
inorganic frothers the practical vertical cross-section is at 1 mol/dm3 and the proposed symbol is γ1M.
×


Table 13. Strength and molar effectiveness for selected frothers, given solid and flotation
device.
Example
Strength cγ75, mmol/dm3
(Coal, Lab. Flotation Machine,
[50])
Example
Molar Effectiveness, γ1M
(Carbonaceous Shale, Hallimond Cell,
[55])
0
n-butanol
0.2
KPF6
4%
n-propanol
1
NaCl
44%
n-hexanol
Na2SOfrother
Figure
13. Cross sections3 of the yield versus
concentration46%
plot for creation of
4
parameters useful for specific classification of frothers. (a) horizontal cross-section of Figure 13a
providing frother strength; (b) vertical cross-section of Figure 13b providing molar effectiveness
of the frother.
Table 13. Strength and molar effectiveness for selected frothers, given solid and flotation device.
5.2.2. Maximum Yield (Recovery) versus Kinetic Constant, k50
More precise characterization and classification of flotation systems and hence frothers, can be
achieved taking into account the maximum yield (or recovery) and kinetics of process already shown in
Figure 10. The horizontal cross-section of the maximum yield versus kinetic constant plot, called the
Back to[68].
TopTop
limits kinetic curves [67] (Figure 14), provides a parameter which is called kinesis of the process
/

When
the cross section is performed at the maximum yield equal to 50%, kinesis is denoted as k50.
Abstract
(/)
The
selected values of k50 are given in Table 14. The horizontal cross-sections can be performed at
Introduction

other
of
values
of k, State
for instance 75%, providing k75. The data show that flotation of shale in the presence
Frothers
in Pure
hexylamine
is much
less efficient than that of coal with di(propylene glycol) methyl ether, because
Frother
in Aqueous
Solutions
the
value in
of Aqueous
1st orderSolutions/Gas
kinetic constant of the first process is much smaller. Figure 14b shows that when
Frother
theSystem
data are replotted as the maximum yield vs. k/k50, all the experimental points form one universal
line
indicating the
generic properties of the investigated flotation frothers. This procedure is called
Three-Phase
(Liquid/Gas/Solid)
normalization.
The generic trend means that frothers exhibit similar foaming/frothing behaviour but at
System

different
concentrations expressed as either DFI, CCC, CMH, CMV etc. or any other frother
Conclusions
characterization
parameters e.g., k50.
Acknowledgments




Author Contributions

Conflicts of Interest

References
×


Table 13. Strength and molar effectiveness for selected frothers, given solid and flotation
device.
Strength cγ75, mmol/dm3
(Coal, Lab. Flotation Machine,
[50])
Molar Effectiveness, γ1M
Example
Example
(Carbonaceous Shale, Hallimond Cell,
[55])
0
Figure 14. (a) Limits kinetic curves; and (b) universal limits kinetic curves after normalization
n-butanol
0.2
KPF6
4%
n-propanol
1
NaCl
44%
against kinetic constant for maximum yield of 50% [67].
n-hexanol
3
Na2SO4
46%
Table
14. Values k50 for different
separation systems.
Symbols in the parenthesis
denote the
type of flotation device: MHT—monobubble Hallimond tube; MM—Mechanobr type laboratory
machine; FC—flotation column; DM—Denver type laboratory machine; LFM—laboratory flotation
machine; MFC—mechanical flotation cell; MIBC—methyl isobutyl carbinol; C4E3—tri(ethylene
glycol) butyl ether, C1P2—di(propylene glycol) methyl ether.
5.2.3. Power P and Selectivity F of Frothers Based on Upgrading Curves
In the case when more than one solid is present in the flotation system and their recoveries are
available, additional one-parameter classification of frothers can be performed [76]. It is based on the
Fuerstenau upgrading curve [77,78] used for evaluation of the process efficiency. From the Fuerstenau
upgrading curve, which relates recovery of the useful component in the concentrate versus the
Back to TopTop
/

recovery
remaining solid components in the tailing, selectivity F and independently power P, are
Abstractof the
(/)
read-off
from the graph as shown in Figure 15. The power of frother P is defined as the dose
Introduction
in mmol/dm3, mg/dm3 or g/Mg) of frother needed to reach a certain degree of
Frothers ineither
Pure State
(expressed
separation.
mostSolutions
convenient is the point when the recovery of the useful component in the
Frother in The
Aqueous

concentrate
is equal Solutions/Gas
to the recovery of the remaining components in the tailing. Selectivity F, is
Frother in Aqueous
determined
System by the point at which the upgrading curve crosses the ascending diagonal. Selectivity F
can
also be determined
mathematically by approximation of the experimental data with suitable
Three-Phase
(Liquid/Gas/Solid)
equations
System [79].

Conclusions

Acknowledgments



Author Contributions

Conflicts of Interest

References
×


Table 13. Strength and molar effectiveness for selected frothers, given solid and flotation
device.
Example
Strength cγ75, mmol/dm3
(Coal, Lab. Flotation Machine,
[50])
Example
Molar Effectiveness, γ1M
(Carbonaceous Shale, Hallimond Cell,
[55])
0
n-butanol
0.2
KPF6
4%
n-propanol
1
NaCl
44%
n-hexanol
3
Na2SO4
46%
Figure 15. Procedure of determination of selectivity F (%) and separately power P (expressed in
frother dose) of flotation frothers using the Fuerstenau upgrading curve [76]. Collector, if used,
regulates hydrophobicity and its concentration is constant.
The values of selectivity F and power P of selected alkyl polypropoxy CnPm and alkyl polyetoxy
CnEm frothers used for flotation of a copper ore [76] utilizing the Fuerstenau upgrading curve are given
in Table 15.
Table 15. Selectivity F and power P of alkyl polypropoxy CnPm and polyetoxy CnEm frothers
used for flotation of copper ore [76].
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/






Abstract
(/)
Introduction

Frothers in Pure State
Frother in Aqueous Solutions
Frother in Aqueous Solutions/Gas
System
5.3.
Two-Numerical Value Classification
Three-Phase (Liquid/Gas/Solid)
System
5.3.1.
Maximum Yield versus Specific Rate Constant. Slow/Powerful, Fast/Powerful, Slow/Powerless,
Fast/Powerless Frothers
Conclusions
Acknowledgments

The maximum
yield versus specific rate constant relation for many materials provides a twoAuthor
Contributions
numerical


map-type relation which can be used for the classification into slow/powerful, fast
Conflicts values
of Interest

/powerful,
slow/powerless and fast/powerless [67] (Figure 16). This type of classification can also be
References
used for systems involving two or more solids. In such cases the maximum yield is replaced with the
maximum recovery.
×


Table 13. Strength and molar effectiveness for selected frothers, given solid and flotation
device.
Example
Strength cγ75, mmol/dm3
(Coal, Lab. Flotation Machine,
[50])
Example
Molar Effectiveness, γ1M
(Carbonaceous Shale, Hallimond Cell,
[55])
0
n-butanol
0.2
KPF6
4%
n-propanol
1
NaCl
44%
n-hexanol
3
Na2SO4
46%
Figure 16. A map-type classification for the three-phase (liquid/gas/solid) system according to
achieved maximum yield and n-order kinetic constant k values (based on [67]).
5.3.2. Special Trend–Type Classifications Based on Relationship between Selectivity and Other
Parameters
Special trend–type classifications based on relationship between selectivity and additional
parameters for frothers present in the solids/gas/liquid systems was proposed by Laskowski [16,45].
They are based on the relation between trends in solids flotation and either pure state (MW and HLB)
or liquid/gas system parameters such as DFI and CCC. First, the plot relating MW and HLB (Figure 1)
as well as DFI and CCC (Figure 9) are created and next their numerical values are somehow
related
Back to TopTop
/
to

the selectivity of flotation of either fine or coarse particles. According to Laskowski [16], frothers with
Abstract
(/)
low
values of CCC and high DFI produce stable foams and can be used in flotation of coarse particles.
Introduction

They
were innamed
powerful. On the other hand, the frothers with high values of CCC and low DFI float
Frothers
Pure State
well
fine particles.
They
were named selective (Figure 17a). The same procedure can be applied for
Frother
in Aqueous
Solutions
HLB
versus
MW plotSolutions/Gas
and fine and coarse particles flotation selectivity data (Figure 17b).
Frother
in Aqueous
System

Three-Phase (Liquid/Gas/Solid)
System

Conclusions

Acknowledgments



Author Contributions

Conflicts of Interest

References
×


Figure 17. Classification of a frother into selective and powerful category resulting from a
relation
between
either
DFI/CCC
or (b) HLB/MW
and frothers,
a trend ingiven
selectivity
of fine
and coarse
Table 13.
Strength
and(a)
molar
effectiveness
for selected
solid and
flotation
particles
device. flotation, respectively ([45] with modification).
Strength cγ75, mmol/dm3
Molar Effectiveness, γ1M
The
trend-type(Coal,
correlative
classification of frothers
in the liquid/gas/fine,
medium and coarse
Example
Lab. Flotation Machine,
Example
(Carbonaceous Shale, Hallimond Cell,
particles system is presently not
precise because the selectivity and power of frothers
are not directly
[50])
[55])
0
visible from plots and no numerical values are given. Therefore, the classification of frothers into
n-butanol
0.2
KPF6
4%
powerful and selective based DFI versus CCC and HLB versus MW requires further development.
n-propanol
1
NaCl
44%
The trend-type correlative classifications of frothers shown in Figure 17 are equivalent because
n-hexanol
3
Na2SO4
46%
HLB/MW
and CCC (Figure 7) are
well related [22,42].
5.4. Three-Numerical Value Classification
Many parameters of the liquid/solids/gas systems allow to use more than two parameters
simultaneously for the classification of frothers. It could be for instance flotation selectivity, froth height
and kinetic constant. When three numerical values are considered for the classification, the graphical
representation of such approach can be made in the form of a Cartesian x-y plot with data points in the
graph amended with numerical values of the third parameter. Another option is the Gibbs triangle [80].
Both are shown schematically in Figure 18.
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









Abstract
(/)
Introduction
Frothers in Pure State
Frother in Aqueous Solutions

Frother in Aqueous Solutions/Gas
System
Three-Phase (Liquid/Gas/Solid)
System
Conclusions
Acknowledgments
Figure 18. Possible three-numerical value classification of frothers. (a) Cartesian x-y plot; (b) the
Author
GibbsContributions
triangle plot.
 Conflicts of Interest

References
6. Conclusions
×


The flotation frothers can be considered as either pure or part of different physical systems
resulting
from
combination
solid,
liquid and gas
pure state,
Table
13.aStrength
and of
molar
effectiveness
for phases
selectedi.e.,
frothers,
givenaqueous
solid andsolution,
flotationaqueous
solution/gas
device. system and aqueous solution/gas/solid system. Once the physical system is defined, the
frothers can be classified according to the number
of numerical values used for this purpose and five of
Strength cγ75, mmol/dm3
Molar Effectiveness, γ1M
them are
discussed
in
the
paper.
The
first
classification
category
does
not use any numerical value and
Example
(Coal, Lab. Flotation Machine,
Example
(Carbonaceous Shale, Hallimond Cell,
is based on a feature expressed
in words or as it changes, which can be either[55])
increasing, constant or
[50])
0
decreasing. The second category is based on one numerical value and uses such parameters as
n-butanol
0.2
KPF6
4%
solubility, dissociation constant, critical coalescence concentration (CCC), dynamic foaming index (DFI)
n-propanol
1
NaCl
44%
and many others. The third category uses two parameters leading to double terms of frother class such
n-hexanol
3
Na2SO4
46%
as low DFI/high
CCC or slow (small
kinetic constant)/powerful
(high maximum yield).
In a graphical
form the category is a map type of classification. The fourth type is based on three numerical values
and leads to a 2D map with isolines. The last category is based on two numerical values, which by
means of a relation with another parameter such as flotation of coarse or fine particles, are turned into
a single descriptive term. Each proposed classification can play a useful role in characterizing and
evaluation of flotation frothers.
Acknowledgments
The work was financed by the Polish Statutory Research Grant No. 0401/0129/17.
Author Contributions
Both authors created the classification system and wrote the paper.
Conflicts of Interest
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/



The authors declare no conflict of interest.
Abstract
(/)
Introduction


Frothers in Pure State
References







Frother in Aqueous Solutions
Frother
in Aqueous
1. Czarnecki,
J.;Solutions/Gas
Malysa, K.; Pomianowski, A. Dynamic frothability index. J. Colloid Interface Sci.
System
1982,
86,
570–572.
[Google
Scholar
(https://scholar.google.com/scholar_lookup?
Three-Phase (Liquid/Gas/Solid)
title=Dynamic+frothability+index&author=Czarnecki,+J.&author=Malysa,+K.&author=Pom
System
ianowski,+A.&publication_year=1982&journal=J.+Colloid+Interface+Sci.&volume=86&pag
es=570–572&doi=10.1016/0021-9797(82)90101-1)]
[CrossRef
Acknowledgments
(https://dx.doi.org/10.1016/0021-9797(82)90101-1)]
Conclusions
Author Contributions
2. Cho, Y.S.; Laskowski, J.S. Effect of flotation frothers on bubble size and foam stability. Int. J.

Miner.
Process.
2002,
64,
69–80.
[Google
Scholar
References
(https://scholar.google.com/scholar_lookup?
title=Effect+of+flotation+frothers+on+bubble+size+and+foam+stability&author=Cho,+Y.S.
&author=Laskowski,+J.S.&publication_year=2002&journal=Int.+J.+Miner.+Process.&volu
me=64&pages=69–80&doi=10.1016/S0301-7516(01)00064-3)]
[CrossRef
Table
13. Strength and molar effectiveness for selected frothers, given solid and flotation
(https://dx.doi.org/10.1016/S0301-7516(01)00064-3)]
device.
 Conflicts of Interest

×


3
Strength
cγ75, mmol/dm
Molar Effectiveness,
γ1M
3. Mobius, D.; Miller,
R. Studies
in Interface
Science. Novel Methods
to Study Interfacial
Layers;
Example
(Coal,
Lab.
Flotation
Machine,
Example
(Carbonaceous
Shale,
Hallimond
Cell,
Elsevier Science: Amsterdam, The Netherlands, 2001; Volume 11, pp. 1–521. [Google Scholar
[50])
[55])
(https://scholar.google.com/scholar_lookup?
0
n-butanol
0.2
KPF6
4%
title=Studies+in+Interface+Science.+Novel+Methods+to+Study+Interfacial+Layers&autho
r=Mobius,+D.&author=Miller,+R.&publication_year=2001)]
n-propanol
1
NaCl
44%
n-hexanol
3
Na2SO
46% of Innovation; SME
4
4. Fuerstenau,
M.C.; Jameson,
G.J.; Yoon, R-H.
Froth
Flotation: A Century
Inc.:
Littleton,
CO,
USA,
2007.
[Google
Scholar
(https://scholar.google.com/scholar_lookup?
title=Froth+Flotation:+A+Century+of+Innovation&author=Fuerstenau,+M.C.&author=Jam
eson,+G.J.&author=Yoon,+R-H.&publication_year=2007)]
5. Drzymala, J. Mineral Processing. Foundations of Theory and Practice of Minerallurgy, 1st ed.;
Oficyna Wydawnicza Politechniki Wroclawskiej: Wroclaw, Poland, 2007. [Google Scholar
(https://scholar.google.com/scholar_lookup?
title=Mineral+Processing.+Foundations+of+Theory+and+Practice+of+Minerallurgy&autho
r=Drzymala,+J.&publication_year=2007)]
6. Kosior, D.; Zawala, J.; Krasowska, M.; Malysa, K. Influence of n-octanol and α-terpineol on thin
film stability and bubble attachment to hydrophobic surface. Phys. Chem. Chem. Phys. 2013,
15,
2586–2595.
[Google
Scholar
(https://scholar.google.com/scholar_lookup?
title=Influence+of+n-octanol+and+αterpineol+on+thin+film+stability+and+bubble+attachment+to+hydrophobic+surface&auth
or=Kosior,+D.&author=Zawala,+J.&author=Krasowska,+M.&author=Malysa,+K.&publicati
on_year=2013&journal=Phys.+Chem.+Chem.+Phys.&volume=15&pages=2586–Back to TopTop
/



2595&doi=10.1039/c2cp43545d&pmid=23322074)]
Abstract
(/)
(https://dx.doi.org/10.1039/c2cp43545d)]
Introduction
[CrossRef
[PubMed


(https://www.ncbi.nlm.nih.gov/pubmed/23322074)]
Frothers
in Pure State

Frother
in Aqueous
Solutions
7. Wills,
B.A.; Finch,
J.A. Wills’ Mineral Processing Technology: An Introduction to the Practical

Frother
in Aqueous
Solutions/Gas
Aspects
of Ore
Treatment and Mineral Recovery, 8th ed.; Elsevier Ltd.: Amsterdam, The
System
Netherlands, 2016. [Google Scholar (https://scholar.google.com/scholar_lookup?



Three-Phase
(Liquid/Gas/Solid)
title=Wills’+Mineral+Processing+Technology:+An+Introduction+to+the+Practical+Aspect
System
s+of+Ore+Treatment+and+Mineral+Recovery&author=Wills,+B.A.&author=Finch,+J.A.&p
Conclusions
ublication_year=2016)]
Acknowledgments
8. Leja, J.; Schulman, J.H. Flotation Theory: Molecular interactions between frothers and collectors
at solid-liquid-air interfaces. Trans. AIME 1954, 199, 221–228. [Google Scholar

Conflicts of Interest


(https://scholar.google.com/scholar_lookup?

References
title=Flotation+Theory:+Molecular+interactions+between+frothers+and+collectors+at+sol
id-liquidair+interfaces&author=Leja,+J.&author=Schulman,+J.H.&publication_year=1954&journal
=Trans.+AIME&volume=199&pages=221–228)]
Table
13. Strength and molar effectiveness for selected frothers, given solid and flotation

Author Contributions
×


9. device.
Nguyen, A.; Schulze, H.J. Colloidal Science of Flotation; Surfactant Science Series; Marcel
3USA,
Dekker:
New
York,
NY,
2004;
Volume
[Google
Scholar
Strength
cγ75, mmol/dm
Molar 118.
Effectiveness,
γ1M
Example
(Coal, Lab. Flotation Machine,
Example
(Carbonaceous Shale, Hallimond Cell,
(https://scholar.google.com/scholar_lookup?
[50])
[55])
title=Colloidal+Science+of+Flotation&author=Nguyen,+A.&author=Schulze,+H.J.&publica
0
tion_year=2004)]
n-butanol
0.2
KPF6
4%
n-propanol
1 J. Some remarks NaCl
44%
10. Kowalczuk,
P.B.; Drzymala,
on attachment of a gas bubble
to another phase
both
immersed in a water.
Process. 2016,46%
52, 147–154. [Google
n-hexanol
3 Physicochem. Probl.
Na2SOMiner.
4
Scholar
(https://scholar.google.com/scholar_lookup?
title=Some+remarks+on+attachment+of+a+gas+bubble+to+another+phase+both+immers
ed+in+a+water&author=Kowalczuk,+P.B.&author=Drzymala,+J.&publication_year=2016&j
ournal=Physicochem.+Probl.+Miner.+Process.&volume=52&pages=147–
154&doi=10.5277/ppmp160113)] [CrossRef (https://dx.doi.org/10.5277/ppmp160113)]
11. Drzymala, J. Hydrophobicity and collectorless flotation of inorganic materials. Adv. Colloid
Interface
Sci.
1994,
50,
143–186.
[Google
Scholar
(https://scholar.google.com/scholar_lookup?
title=Hydrophobicity+and+collectorless+flotation+of+inorganic+materials&author=Drzym
ala,+J.&publication_year=1994&journal=Adv.+Colloid+Interface+Sci.&volume=50&pages=
143–186&doi=10.1016/0001-8686(94)80029-4)] [CrossRef (https://dx.doi.org/10.1016/00018686(94)80029-4)]
12. Kowalczuk, P.B.; Drzymala, J. Contact angle of bubble with an immersed-in-water particle of
different materials. Ind. Eng. Chem. Res. 2011, 50, 4207–4211. [Google Scholar
(https://scholar.google.com/scholar_lookup?
title=Contact+angle+of+bubble+with+an+immersed-inBack to TopTop
/



water+particle+of+different+materials&author=Kowalczuk,+P.B.&author=Drzymala,+J.&p
Abstract
(/)
ublication_year=2011&journal=Ind.+Eng.+Chem.+Res.&volume=50&pages=4207–
Introduction


4211&doi=10.1021/ie102264s)]
[CrossRef (https://dx.doi.org/10.1021/ie102264s)]
Frothers
in Pure State

Frother
in Aqueous
Solutionsion effect of chloride salts on collectorless flotation of coal. Physicochem.
13. Ozdemir,
O. Specific

Frother
in Aqueous
Solutions/Gas
Probl.
Miner.
Process.
2013,
49,
System
(https://scholar.google.com/scholar_lookup?







511–524.
[Google
Scholar
Three-Phase
(Liquid/Gas/Solid)
title=Specific+ion+effect+of+chloride+salts+on+collectorless+flotation+of+coal&author=
System
Ozdemir,+O.&publication_year=2013&journal=Physicochem.+Probl.+Miner.+Process.&vol
Conclusions
ume=49&pages=511–524&doi=10.5277/ppmp130212)]
[CrossRef
Acknowledgments
(https://dx.doi.org/10.5277/ppmp130212)]
Author Contributions
14. Kowalczuk, P.B.; Buluc, B.; Sahbaz, O.; Drzymala, J. In search of an efficient frother for preflotation of carbonaceous shale from the Kupferschiefer stratiform copper ore. Physicochem. 
References
Probl.
Miner.
Process.
2014,
50,
835–840.
[Google
Scholar
(https://scholar.google.com/scholar_lookup?
title=In+search+of+an+efficient+frother+for+preflotation+of+carbonaceous+shale+from+the+Kupferschiefer+stratiform+copper+ore&aut
Table
13. Strength and molar effectiveness for selected frothers, given solid and flotation
hor=Kowalczuk,+P.B.&author=Buluc,+B.&author=Sahbaz,+O.&author=Drzymala,+J.&publ
device.
ication_year=2014&journal=Physicochem.+Probl.+Miner.+Process.&volume=50&pages=8
Strength cγ75, mmol/dm3
Molar Effectiveness, γ1M
35–840&doi=10.5277/ppmp140233)]
[CrossRef
(https://dx.doi.org/10.5277/ppmp140233)]
Example
(Coal, Lab. Flotation Machine,
Example
(Carbonaceous Shale, Hallimond Cell,
Conflicts of Interest
×


[50])Flotation frothers: Review of their classifications,
[55])
15. Khoshdast, H.; Sam, A.
properties
and
0
preparation.
Open
Miner.
Process. KPF
J. 6 2011,
4,
25–44.4% [Google
Scholar
n-butanol
0.2
(https://scholar.google.com/scholar_lookup?
n-propanol
1
NaCl
44%
title=Flotation+frothers:+Review+of+their+classifications,+properties+and+preparation&a
n-hexanol
3
Na2SO4
46%
uthor=Khoshdast,+H.&author=Sam,+A.&publication_year=2011&journal=Open+Miner.+Pr
ocess.+J.&volume=4&pages=25–44&doi=10.2174/1874841401104010025)]
[CrossRef
(https://dx.doi.org/10.2174/1874841401104010025)]
16. Laskowski, J.S. Testing flotation frothers. Physicochem. Probl. Miner. Process. 2004, 38, 13–22.
[Google
Scholar
(https://scholar.google.com/scholar_lookup?
title=Testing+flotation+frothers&author=Laskowski,+J.S.&publication_year=2004&journal
=Physicochem.+Probl.+Miner.+Process.&volume=38&pages=13–22)]
17. Gaudin, A.M. Flotation, 2nd ed.; McGraw-Hill Book Company, Inc.: New York, NY, USA, 1957.
[Google
Scholar
(https://scholar.google.com/scholar_lookup?
title=Flotation&author=Gaudin,+A.M.&publication_year=1957)]
18. Laskowski, J. Frothers and frothing. In Frothing in Flotation II; Laskowski, J.S., Woodburn, E.T.,
Eds.; Gordon and Breach: Amsterdam, The Netherlands, 1998; pp. 1–49. [Google Scholar
(https://scholar.google.com/scholar_lookup?
title=Frothers+and+frothing&author=Laskowski,+J.&publication_year=1998&pages=1–
49)]
Back to TopTop
/






19. Chain(/)Reaction Cycles (CRC). Handbook of Chemistry AND Physics, 67th ed.; CRC Press:
Abstract
Boca
Introduction
Raton,
FL,
USA,
1986–1987.
[Google
(https://scholar.google.com/scholar_lookup?
Frothers
in Pure State
title=Handbook+of+Chemistry+AND+Physics&author=Chain+Reaction+Cycles+
Frother
in Aqueous Solutions
(CRC)&publication_year=1986–1987)]
Frother
in Aqueous Solutions/Gas
Scholar

System

20. Davies, J.T. A quantitative kinetic theory of emulsion type, I. Physical chemistry of the
Three-Phase (Liquid/Gas/Solid)
emulsifying agent, Gas/Liquid and Liquid/Liquid Interface. In Proceedings of the International
System
Congress of Surface Activity, London, UK, 20–31 July 1957; pp. 426–438. [Google Scholar
(https://scholar.google.com/scholar_lookup?

Acknowledgments
title=A+quantitative+kinetic+theory+of+emulsion+type,+I.+Physical+chemistry+of+the+e

Author Contributions
mulsifying+agent,+Gas/Liquid+and+Liquid/Liquid+Interface&conference=Proceedings+of

Conflicts of Interest

+the+International+Congress+of+Surface+Activity&author=Davies,+J.T.&publication_yea 

References
r=1957&pages=426–438)]

Conclusions
×


21. Tanaka, K.; Igarashi, A. Determination of nonionic surfactants. In Handbook of Detergents Part
C: Analysis; Waldhoff, H., Spilker, R., Eds.; CRC Press: Boca Raton, FL, USA, 2005; pp. 149–
214. 13. Strength
[Google
Scholar
(https://scholar.google.com/scholar_lookup?
Table
and molar effectiveness
for selected
frothers, given solid and flotation
title=Determination+of+nonionic+surfactants&author=Tanaka,+K.&author=Igarashi,+A.&p
device.
ublication_year=2005&pages=149–214)]
Strength c , mmol/dm3
Molar Effectiveness, γ
γ75
1M
Example W.;(Coal,
Lab. Flotation
Machine,
Example
(Carbonaceous Shale,
Hallimond
22. Zhang,
Nesset,
J.E.; Rao,
R.; Finch,
J.A. Characterizing
frothers
throughCell,
critical
[50])
[55])
coalescence concentration (CCC)95-hydrophile-lipophile balance (HLB) relationship. Minerals
0
n-butanol 2,
4%
6
2012,
208–227. 0.2
[Google Scholar KPF
(https://scholar.google.com/scholar_lookup?
title=Characterizing+frothers+through+critical+coalescence+concentration+(CCC)95n-propanol
1
NaCl
44%
hydrophile-lipophile+balance+
n-hexanol
3
Na2SO4
46%
(HLB)+relationship&author=Zhang,+W.&author=Nesset,+J.E.&author=Rao,+R.&author=Fi
nch,+J.A.&publication_year=2012&journal=Minerals&volume=2&pages=208–
227&doi=10.3390/min2030208)] [CrossRef (https://dx.doi.org/10.3390/min2030208)]
23. Dudenkov, S.V.; Galikov, A.A. Theory and Practice of Application of Flotation Reagents; Nedra:
Moscow, Russia, 1969. [Google Scholar (https://scholar.google.com/scholar_lookup?
title=Theory+and+Practice+of+Application+of+Flotation+Reagents&author=Dudenkov,+S.
V.&author=Galikov,+A.A.&publication_year=1969)]
24. Bulatovic, S.M. Handbook of Flotation Reagents: Chemistry, Theory and Practice; Elsevier
Science:
Amsterdam,
The
Netherlands,
2007.
[Google
Scholar
(https://scholar.google.com/scholar_lookup?
title=Handbook+of+Flotation+Reagents:+Chemistry,+Theory+and+Practice&author=Bulat
ovic,+S.M.&publication_year=2007)]
25. Crozier, R.D. Properties of Flotation Froths: Flotation—Theory, Reagent and Ore Testing;
Pergamon:
New
York,
NY,
USA,
1992.
[Google
Scholar
(https://scholar.google.com/scholar_lookup?
Back to TopTop
/



title=Properties+of+Flotation+Froths:+Flotation—
Abstract
(/)
Theory,+Reagent+and+Ore+Testing&author=Crozier,+R.D.&publication_year=1992)]
Introduction


Frothers
in Pure
26. Yaws,
C.L.;State
Hopper, J.R.; Sheth, S.D.; Han, M.; Pike, R.W. Solubility and Henry’s law constant

Frother
for in Aqueous
alcoholsSolutions
in water.




Waste Manag. 1997, 17, 541–547. [Google Scholar
Frother
in Aqueous Solutions/Gas
(https://scholar.google.com/scholar_lookup?
System
title=Solubility+and+Henry’s+law+constant+for+alcohols+in+water&author=Yaws,+C.L.&a
Three-Phase
(Liquid/Gas/Solid)
uthor=Hopper,+J.R.&author=Sheth,+S.D.&author=Han,+M.&author=Pike,+R.W.&publicatio
System
n_year=1997&journal=Waste+Manag.&volume=17&pages=541–547&doi=10.1016/S0956Conclusions
053X(97)10057-5)] [CrossRef (https://dx.doi.org/10.1016/S0956-053X(97)10057-5)]
Acknowledgments
27. Li, J.; Perdue, E.M. Physicochemical properties of selected monterpenes. Environ. Int. 1998, 24,
353–358.
[Google
Scholar
(https://scholar.google.com/scholar_lookup?

Conflicts of Interest

title=Physicochemical+properties+of+selected+monterpenes&author=Li,+J.&author=Per 

References
due,+E.M.&publication_year=1998&journal=Environ.+Int.&volume=24&pages=353–
358&doi=10.1016/S0160-4120(98)00013-0)] [CrossRef (https://dx.doi.org/10.1016/S01604120(98)00013-0)]

Author Contributions
×


13.S.Strength
andReagents:
molar effectiveness
for selected
frothers,
solidFlotation
and flotation
28.Table
Wang,
Flotation
Applied Surface
Chemistry
on given
Minerals
and Energy
device.
Resources
Beneficiation;
Springer:
Singapore,
2016.
[Google
Scholar
(https://scholar.google.com/scholar_lookup?
Strength cγ75, mmol/dm3
Molar Effectiveness, γ1M
title=Flotation+Reagents:+Applied+Surface+Chemistry+on+Minerals+Flotation+and+Ener
Example
(Coal, Lab. Flotation Machine,
Example
(Carbonaceous Shale, Hallimond Cell,
[50])
[55])
gy+Resources+Beneficiation&author=Wang,+S.&publication_year=2016)]
0
n-butanol
0.2
KPF6
4%
29. Technical
Data & Safety Bulletin.
2017. Available
online: http://www.monumentchemical.com/
n-propanol
1
NaCl (http://www.monumentchemical.com/docu
44%
documents/MIBC-Data_and_Safety_Sheet.pdf
ments/MIBC-Data_and_Safety_Sheet.pdf)
(accessed
on 1 November 46%
2017).
n-hexanol
3
Na
2SO4
30. Inoue, T.; Ohmura, H.; Murata, D. Cloud point temperature of polyoxyethylene–type nonionic
surfactants and their mixtures. J. Colloid Interface Sci. 2003, 258, 374–382. [Google Scholar
(https://scholar.google.com/scholar_lookup?
title=Cloud+point+temperature+of+polyoxyethylene–
type+nonionic+surfactants+and+their+mixtures&author=Inoue,+T.&author=Ohmura,+H.&
author=Murata,+D.&publication_year=2003&journal=J.+Colloid+Interface+Sci.&volume=2
58&pages=374–382&doi=10.1016/S0021-9797(02)00162-5)]
[CrossRef
(https://dx.doi.org/10.1016/S0021-9797(02)00162-5)]
31. Lekki, J.; Laskowski, J. A new concept of frothing in flotation systems and general classification
of flotation frothers. In Proceedings of the XIth International Mineral Processing Congress,
Cagliari,
Italy,
20–26
April
1975;
pp.
429–448.
[Google
Scholar
(https://scholar.google.com/scholar_lookup?
title=A+new+concept+of+frothing+in+flotation+systems+and+general+classification+of+f
lotation+frothers&conference=Proceedings+of+the+XIth+International+Mineral+Processi
ng+Congress&author=Lekki,+J.&author=Laskowski,+J.&publication_year=1975&pages=4
29–448)]
Back to TopTop
/









32. Pugh,(/)R.J.; Weissenborn, P.; Paulson, O. Flotation in inorganic electrolytes: The relationship
Abstract
between recovery of hydrophobic particles, surface tension, bubble coalescence and gas
Introduction
solubility.
Int.
Frothers
in Pure State

J.
Miner.
Process.
1997,
51,
125–138.
[Google
Scholar
(https://scholar.google.com/scholar_lookup?
Frother
in Aqueous Solutions
title=Flotation+in+inorganic+electrolytes:+The+relationship+between+recovery+of+hydro
Frother
in Aqueous Solutions/Gas
System
phobic+particles,+surface+tension,+bubble+coalescence+and+gas+solubility&author=Pu
Three-Phase
gh,+R.J.&author=Weissenborn,+P.&author=Paulson,+O.&publication_year=1997&journal
(Liquid/Gas/Solid)
System
=Int.+J.+Miner.+Process.&volume=51&pages=125–138&doi=10.1016/S0301Conclusions
7516(97)00021-5)] [CrossRef (https://dx.doi.org/10.1016/S0301-7516(97)00021-5)]
Acknowledgments
33. DeWitt, C.C.; Roper, E.E. The surface relations of potassium ethyl xanthate and pine oil. J. Am.
Chem.
Soc.
1932,
54,
444–455.
[Google
Scholar

Conflicts of Interest


(https://scholar.google.com/scholar_lookup?

References
title=The+surface+relations+of+potassium+ethyl+xanthate+and+pine+oil&author=DeWitt,
+C.C.&author=Roper,+E.E.&publication_year=1932&journal=J.+Am.+Chem.+Soc.&volum
e=54&pages=444–455&doi=10.1021/ja01341a006)]
[CrossRef
(https://dx.doi.org/10.1021/ja01341a006)]
Table 13. Strength and molar effectiveness for selected frothers, given solid and flotation
34.device.
Tuckermann, R. Surface tension of aqueous solutions of water-soluble organic and inorganic
compounds. Strength
Atmos.c , mmol/dm
Environ. 3 2007,
41,
6265–6275.
[Google
Scholar
Molar Effectiveness, γ1M
γ75
(https://scholar.google.com/scholar_lookup?
Example
(Coal, Lab. Flotation Machine,
Example
(Carbonaceous Shale, Hallimond Cell,
title=Surface+tension+of+aqueous+solutions+of+water[50])
[55])
0
soluble+organic+and+inorganic+compounds&author=Tuckermann,+R.&publication_year
n-butanol
0.2
KPF6
4%
=2007&journal=Atmos.+Environ.&volume=41&pages=6265–
n-propanol
1
NaCl
44%
6275&doi=10.1016/j.atmosenv.2007.03.051)]
[CrossRef
n-hexanol
3
Na2SO4
46%
(https://dx.doi.org/10.1016/j.atmosenv.2007.03.051)]

Author Contributions
×


35. Tamaki, K. The surface activity of the lower homologues of n-alkylammonium chlorides in
aqueous solutions. Effect of hydrophobic hydration. Colloid Polyme. Sci. 1974, 252, 547–550.
[Google
Scholar
(https://scholar.google.com/scholar_lookup?
title=The+surface+activity+of+the+lower+homologues+of+nalkylammonium+chlorides+in+aqueous+solutions.+Effect+of+hydrophobic+hydration&a
uthor=Tamaki,+K.&publication_year=1974&journal=Colloid+Polyme.+Sci.&volume=252&p
ages=547–550)]
36. Lyklema, J. Fundamentals of Interface and Colloid Science; Academic Press: London, UK,
1993; Volume 1. [Google Scholar (https://scholar.google.com/scholar_lookup?
title=Fundamentals+of+Interface+and+Colloid+Science&author=Lyklema,+J.&publication
_year=1993)]
37. Burczyk, B.; Sokolowski, A. Relations between chemical structure and surface activity—1.
Synthesis and properties of aqueous solutions of acetals formed from aliphatic aldehydes and
monoalkyl ethers of ethylene glycols. Tenside Deterg. 1978, 15, 68–71. [Google Scholar
(https://scholar.google.com/scholar_lookup?
Back to TopTop
/





title=Relations+between+chemical+structure+and+surface+activity—
Abstract
(/)
1.+Synthesis+and+properties+of+aqueous+solutions+of+acetals+formed+from+aliphatic
Introduction

+aldehydes+and+monoalkyl+ethers+of+ethylene+glycols&author=Burczyk,+B.&author=S
Frothers
in Pure State
okolowski,+A.&publication_year=1978&journal=Tenside+Deterg.&volume=15&pages=68–
Frother
in Aqueous Solutions
71)]in Aqueous Solutions/Gas
Frother
System
38. Aston, J.R.; Drummond, C.J.; Scales, F.J.; Healy, T.W. Frother chemistry in fine coal processing.

Three-Phase
(Liquid/Gas/Solid)
In Proceedings
of the 2nd Australian Coal Preparation Congress, Brisbane, Australia, 10–14
System
October 1983; Whitmore, R.I., Ed.; Westminster Press: Brisbane, Australia, 1983; pp. 148–160.


Conclusions
[Google
Scholar
(https://scholar.google.com/scholar_lookup?
Acknowledgments
title=Frother+chemistry+in+fine+coal+processing&conference=Proceedings+of+the+2nd

Author
Contributions
+Australian+Coal+Preparation+Congress&author=Aston,+J.R.&author=Drummond,+C.J.

of Interest
&author=Scales,+F.J.&author=Healy,+T.W.&publication_year=1983&pages=148–160)]
 Conflicts



References
39. Takata, Y.; Tagashira, H.; Hyono, A.; Ohshima, H. Effect of counterion and configurational
entropy on the surface tension of aqueous solution of ionic surfactants and electrolyte mixtures.
Entropy 2010, 12, 983–995. [Google Scholar (https://scholar.google.com/scholar_lookup?
title=Effect+of+counterion+and+configurational+entropy+on+the+surface+tension+of+aq
Table
13. Strength and molar effectiveness for selected frothers, given solid and flotation
ueous+solution+of+ionic+surfactants+and+electrolyte+mixtures&author=Takata,+Y.&aut
device.
hor=Tagashira,+H.&author=Hyono,+A.&author=Ohshima,+H.&publication_year=2010&jou
Strength cγ75, mmol/dm3
Molar Effectiveness, γ1M
rnal=Entropy&volume=12&pages=983–995&doi=10.3390/e12040983)]
[CrossRef
Example
(Coal, Lab. Flotation Machine,
Example
(Carbonaceous Shale, Hallimond Cell,
(https://dx.doi.org/10.3390/e12040983)]
[50])
[55])
×


0
40. Warszynski,
P.W.; Barzyk,
Fruhner, H. Surface
n-butanol
0.2 W.; Lunkenheimer,
KPFK.;
4% tension and surface
6
potential of Na n-dodecyl1 sulfate at the air−solution
interface: Model and
n-propanol
NaCl
44% experiment. J. Phys.
Chem.
B
1998,
102,
10948–10957.
[Google
Scholar
n-hexanol
3
Na2SO4
46%
(https://scholar.google.com/scholar_lookup?
title=Surface+tension+and+surface+potential+of+Na+ndodecyl+sulfate+at+the+air−solution+interface:+Model+and+experiment&author=Warszy
nski,+P.W.&author=Barzyk,+W.&author=Lunkenheimer,+K.&author=Fruhner,+H.&publicati
on_year=1998&journal=J.+Phys.+Chem.+B&volume=102&pages=10948–
10957&doi=10.1021/jp983901r)] [CrossRef (https://dx.doi.org/10.1021/jp983901r)]
41. Karraker, K.A.; Radke, C.J. Disjoining pressure, zeta potential and surface tension of aqueous
non-ionic surfactant/electrolyte solution: Theory and comparison to experiment. Adv. Colloid
Interface
Sci.
2002,
96,
231–264.
[Google
Scholar
(https://scholar.google.com/scholar_lookup?
title=Disjoining+pressure,+zeta+potential+and+surface+tension+of+aqueous+nonionic+surfactant/electrolyte+solution:+Theory+and+comparison+to+experiment&author=
Karraker,+K.A.&author=Radke,+C.J.&publication_year=2002&journal=Adv.+Colloid+Interf
ace+Sci.&volume=96&pages=231–264&doi=10.1016/S0001-8686(01)00083-5)]
[CrossRef
(https://dx.doi.org/10.1016/S0001-8686(01)00083-5)]
Back to TopTop
/







42. Kowalczuk,
P.B. Determination of critical coalescence concentration and bubble size for
Abstract
(/)
surfactants used as flotation frothers. Ind. Eng. Chem. Res. 2013, 52, 11752–11757. [Google
Introduction

Scholar
Frothers
in Pure State
(https://scholar.google.com/scholar_lookup?
title=Determination+of+critical+coalescence+concentration+and+bubble+size+for+surfac
Frother
in Aqueous Solutions
tants+used+as+flotation+frothers&author=Kowalczuk,+P.B.&publication_year=2013&jour
Frother
in Aqueous Solutions/Gas
nal=Ind.+Eng.+Chem.+Res.&volume=52&pages=11752–11757&doi=10.1021/ie401263k)]
System
Three-Phase
[CrossRef
(Liquid/Gas/Solid)
(https://dx.doi.org/10.1021/ie401263k)]
System
43. Kowalczuk, P.B.; Zawala, J.; Drzymala, J. Concentration at the minimum bubble velocity (CMV)
for various types of flotation frothers. Minerals 2017, 7, 118. [Google Scholar

Acknowledgments
(https://scholar.google.com/scholar_lookup?

Author Contributions
title=Concentration+at+the+minimum+bubble+velocity+

Conflicts of Interest

(CMV)+for+various+types+of+flotation+frothers&author=Kowalczuk,+P.B.&author=Zawal 

References
a,+J.&author=Drzymala,+J.&publication_year=2017&journal=Minerals&volume=7&pages=
118&doi=10.3390/min7070118)] [CrossRef (https://dx.doi.org/10.3390/min7070118)]

Conclusions
×


44. Sweet, C.; van Hoogstraten, J.; Harris, M.; Laskowski, J.S. The effect of frothers on bubble size
and frothability
of and
aqueous
In Processing
the Complex
Ores,and
Proceedings
Table
13. Strength
molar solutions.
effectiveness
for selectedoffrothers,
given solid
flotation of the
2nd UBC-McGill International Symposium, Montreal, QC, Canada, 17–19 August 1997; Finch,
device.
J.A., Rao, S.R.,
Holubec, I., Eds.; Metallurgical Society of CIM:
Montreal, QC, Canada, 1997;
Strength cγ75, mmol/dm3
Molar Effectiveness, γ1M
pp.
235–245.
Scholar Example
(https://scholar.google.com/scholar_lookup?
Example
(Coal, Lab.[Google
Flotation Machine,
(Carbonaceous Shale, Hallimond Cell,
title=The+effect+of+frothers+on+bubble+size+and+frothability+of+aqueous+solutions&a
[50])
[55])
0
uthor=Sweet,+C.&author=van+Hoogstraten,+J.&author=Harris,+M.&author=Laskowski,+J
n-butanol
0.2
KPF6
4%
.S.&publication_year=1997&pages=235–245)]
n-propanol
1
NaCl
44%
45. Laskowski,
J.S.; Tlhone,
T.; Williams, Na
P.;2SODing,
K. Fundamental
n-hexanol
3
46% properties of the
4
polyoxypropylene alkyl ether flotation frothers. Int. J. Miner. Process. 2003, 72, 289–299.
[Google
Scholar
(https://scholar.google.com/scholar_lookup?
title=Fundamental+properties+of+the+polyoxypropylene+alkyl+ether+flotation+frothers&
author=Laskowski,+J.S.&author=Tlhone,+T.&author=Williams,+P.&author=Ding,+K.&publi
cation_year=2003&journal=Int.+J.+Miner.+Process.&volume=72&pages=289–
299&doi=10.1016/S0301-7516(03)00105-4)] [CrossRef (https://dx.doi.org/10.1016/S03017516(03)00105-4)]
46. Gupta, A.K.; Banerjee, P.K.; Mishra, A.; Satish, P.; Pradip. Effect of alcohol and polyglycol ether
frothers on foam stability, bubble size and coal flotation. Int. J. Miner. Process. 2007, 82, 126–
137.
[Google
Scholar
(https://scholar.google.com/scholar_lookup?
title=Effect+of+alcohol+and+polyglycol+ether+frothers+on+foam+stability,+bubble+size+
and+coal+flotation&author=Gupta,+A.K.&author=Banerjee,+P.K.&author=Mishra,+A.&aut
hor=Satish,+P.&author=Pradip&publication_year=2007&journal=Int.+J.+Miner.+Process.&
volume=82&pages=126–137&doi=10.1016/j.minpro.2006.09.002)]
[CrossRef
(https://dx.doi.org/10.1016/j.minpro.2006.09.002)]
Back to TopTop
/







47. Finch,(/)J.; Zhang, W. Frother function-structure relationship: Dependence of CCC95 on HLB and
Abstract
H-ratio.
Introduction
Miner.
Eng.
2014,
61,
1–8.
[Google
Scholar
(https://scholar.google.com/scholar_lookup?title=Frother+functionFrothers
in Pure State
structure+relationship:+Dependence+of+CCC95+on+HLB+and+HFrother
in Aqueous Solutions
ratio&author=Finch,+J.&author=Zhang,+W.&publication_year=2014&journal=Miner.+Eng.
Frother
in Aqueous Solutions/Gas
&volume=61&pages=1–8&doi=10.1016/j.mineng.2014.02.006)]
[CrossRef
System
(https://dx.doi.org/10.1016/j.mineng.2014.02.006)]
Three-Phase
(Liquid/Gas/Solid)

System
48. Azgomi, F.; Gomez, C.O.; Finch, J.A. Characterizing frothers using gas hold-up. Can. Metall. Q.
2007, 46, 237–242. [Google Scholar (https://scholar.google.com/scholar_lookup?

Acknowledgments
title=Characterizing+frothers+using+gas+hold
Author Contributions
up&author=Azgomi,+F.&author=Gomez,+C.O.&author=Finch,+J.A.&publication_year=200

Conflicts of Interest


7&journal=Can.+Metall.+Q.&volume=46&pages=237–

References
242&doi=10.1179/cmq.2007.46.3.237)]
[CrossRef
(https://dx.doi.org/10.1179/cmq.2007.46.3.237)]

Conclusions
×


49. Tan, Y.H.; Finch, J.A. Frother structure–property relationship: Effect of alkyl chain length in
alcohols
and polyglycol
ethers
on bubble for
rise
velocity.frothers,
Miner. given
Eng. 2016,
95, flotation
14–20. [Google
Table
13. Strength
and molar
effectiveness
selected
solid and
Scholar
(https://scholar.google.com/scholar_lookup?title=Frother+structure–
device.
property+relationship:+Effect+of+alkyl+chain+length+in+alcohols+and+polyglycol+ether
Strength cγ75, mmol/dm3
Molar Effectiveness, γ1M
s+on+bubble+rise+velocity&author=Tan,+Y.H.&author=Finch,+J.A.&publication_year=201
Example
(Coal, Lab. Flotation Machine,
Example
(Carbonaceous Shale, Hallimond Cell,
6&journal=Miner.+Eng.&volume=95&pages=14–20&doi=10.1016/j.mineng.2016.05.012)]
[50])
[55])
0
[CrossRef
(https://dx.doi.org/10.1016/j.mineng.2016.05.012)]
n-butanol
0.2
KPF6
4%
50. Malysa,
J. A method
frothing and collecting
n-propanol E.; Malysa, K.; Czarnecki,
1
NaCl of comparison of the44%
properties
of frothers.3 Colloids Surfaces
23, 29–39.
Scholar
n-hexanol
Na2SO4 1987,
46% [Google
(https://scholar.google.com/scholar_lookup?
title=A+method+of+comparison+of+the+frothing+and+collecting+properties+of+frothers
&author=Malysa,+E.&author=Malysa,+K.&author=Czarnecki,+J.&publication_year=1987&j
ournal=Colloids+Surfaces&volume=23&pages=29–39&doi=10.1016/0166-6622(87)802470)] [CrossRef (https://dx.doi.org/10.1016/0166-6622(87)80247-0)]
51. Khoshdast, H.; Mirshekari, S.; Zahab-Nazouri, A. A model for predicting dynamic frothability
index value for dual-frother blends. J. Min. Environ. 2015, 6, 119–124. [Google Scholar
(https://scholar.google.com/scholar_lookup?
title=A+model+for+predicting+dynamic+frothability+index+value+for+dualfrother+blends&author=Khoshdast,+H.&author=Mirshekari,+S.&author=ZahabNazouri,+A.&publication_year=2015&journal=J.+Min.+Environ.&volume=6&pages=119–
124&doi=10.22044/jme.2015.368)] [CrossRef (https://dx.doi.org/10.22044/jme.2015.368)]
52. Kowalczuk, P.B.; Siedlarz, M.; Szczerkowska, S.; Wojcik, M. Facile determination of foamability
index of non-ionic and cationic frothers and its effect on flotation of quartz. Sep. Sci. Technol.
2017,
38,
1–9.
[Google
Scholar
(https://scholar.google.com/scholar_lookup?
title=Facile+determination+of+foamability+index+of+nonBack to TopTop
/





ionic+and+cationic+frothers+and+its+effect+on+flotation+of+quartz&author=Kowalczuk,
Abstract
(/)
+P.B.&author=Siedlarz,+M.&author=Szczerkowska,+S.&author=Wojcik,+M.&publication_y
Introduction
ear=2017&journal=Sep.+Sci.+Technol.&volume=38&pages=1–
Frothers
in Pure State
9&doi=10.1080/01496395.2017.1293100)]
Frother
in Aqueous Solutions

[CrossRef
(https://dx.doi.org/10.1080/01496395.2017.1293100)]
Frother
in Aqueous Solutions/Gas
System
53. Tan, Y.H.; Rafiei, A.A.; Elmahdy, A.; Finch, J.A. Bubble size, gas holdup and bubble velocity

Three-Phase
profile of(Liquid/Gas/Solid)
some alcohols and commercial frothers. Int. J. Miner. Process. 2013, 119, 1–5.
System
[Google
Scholar
(https://scholar.google.com/scholar_lookup?






Conclusions
title=Bubble+size,+gas+holdup+and+bubble+velocity+profile+of+some+alcohols+and+co
Acknowledgments
mmercial+frothers&author=Tan,+Y.H.&author=Rafiei,+A.A.&author=Elmahdy,+A.&author=
Author
Contributions
Finch,+J.A.&publication_year=2013&journal=Int.+J.+Miner.+Process.&volume=119&page
of Interest
s=1–5&doi=10.1016/j.minpro.2012.12.003)]
 Conflicts
References
(https://dx.doi.org/10.1016/j.minpro.2012.12.003)]
[CrossRef 
×


54. Barbian, N.; Ventura-Medina, E.; Cilliers, J.J. Dynamic froth stability in froth flotation. Miner.
Eng. 2003, 16, 1111–1116. [Google Scholar (https://scholar.google.com/scholar_lookup?
title=Dynamic+froth+stability+in+froth+flotation&author=Barbian,+N.&author=VenturaTable
13. Strength and molar effectiveness for selected frothers, given solid and flotation
Medina,+E.&author=Cilliers,+J.J.&publication_year=2003&journal=Miner.+Eng.&volume=
device.
16&pages=1111–1116&doi=10.1016/j.mineng.2003.06.010)]
[CrossRef
Strength cγ75, mmol/dm3
Molar Effectiveness, γ1M
(https://dx.doi.org/10.1016/j.mineng.2003.06.010)]
Example
(Coal, Lab. Flotation Machine,
Example
(Carbonaceous Shale, Hallimond Cell,
[50])T. Flotacja mechaniczna łupka miedzionośnego
[55])
55. Smolska, M.; Ratajczak,
we flotowniku
0
Hallimonda
w
roztworach
soli
podwyzszających
i
obnizajacych
napiecie
powierzchniowe
wody.
n-butanol
0.2
KPF6
4%
In Lupek Miedzionosny III;1 Kowalczuk, P.B., Drzymala,
J., Eds.; WGGG44%
PWr: Wroclaw, Poland,
n-propanol
NaCl
2017; pp. 97–102. (In Polish) [Google Scholar (https://scholar.google.com/scholar_lookup?
n-hexanol
3
Na2SO4
46%
title=Flotacja+mechaniczna+łupka+miedzionośnego+we+flotowniku+Hallimonda+w+rozt
worach+soli+podwyzszających+i+obnizajacych+napiecie+powierzchniowe+wody&author
=Smolska,+M.&author=Ratajczak,+T.&publication_year=2017&pages=97–102)]
56. Kowalczuk, P.B.; Mroczko, D.; Drzymala, J. Influence of frother type and dose on collectorless
flotation of copper-bearing shale in a flotation column. Physicochem. Probl. Miner. Process.
2015, 51, 547–558. [Google Scholar (https://scholar.google.com/scholar_lookup?
title=Influence+of+frother+type+and+dose+on+collectorless+flotation+of+copperbearing+shale+in+a+flotation+column&author=Kowalczuk,+P.B.&author=Mroczko,+D.&au
thor=Drzymala,+J.&publication_year=2015&journal=Physicochem.+Probl.+Miner.+Proces
s.&volume=51&pages=547–558&doi=10.5277/ppmp150215)]
[CrossRef
(https://dx.doi.org/10.5277/ppmp150215)]
57. Kowalczuk, P.B.; Zawala, J.; Kosior, D.; Drzymala, J.; Malysa, K. Three-phase contact formation
and flotation of highly hydrophobic polytetrafluoroethylene in the presence of increased dose of
frothers.
Ind.
Eng.
Chem.
Res.
2016,
55,
839–843.
[Google
Scholar
(https://scholar.google.com/scholar_lookup?title=Threephase+contact+formation+and+flotation+of+highly+hydrophobic+polytetrafluoroethylene
Back to TopTop
/





+in+the+presence+of+increased+dose+of+frothers&author=Kowalczuk,+P.B.&author=Za
Abstract
(/)
wala,+J.&author=Kosior,+D.&author=Drzymala,+J.&author=Malysa,+K.&publication_year
Introduction
=2016&journal=Ind.+Eng.+Chem.+Res.&volume=55&pages=839–
Frothers
in Pure State
843&doi=10.1021/acs.iecr.5b04293)]
Frother
in Aqueous Solutions

[CrossRef
(https://dx.doi.org/10.1021/acs.iecr.5b04293)]
Frother
in Aqueous Solutions/Gas
System
58. Lyklema, J. Fundamentals of Interface and Colloid Science: Liquid-Liquid Interfaces; Academic

Three-Phase
Press: (Liquid/Gas/Solid)
London,
UK,
2000;
Volume
III.
[Google
Scholar
System
(https://scholar.google.com/scholar_lookup?





Conclusions
title=Fundamentals+of+Interface+and+Colloid+Science:+LiquidAcknowledgments
Liquid+Interfaces&author=Lyklema,+J.&publication_year=2000)]
Author Contributions
59. Deschenes, L.; Lyklema, J.; St-Germain, F. Entropy of aqueous surfaces. Application to
of Interest
 Conflicts
polymeric Langmuir films. Adv. Colloid Interface Sci. 2017, 247, 149–162. [Google Scholar 

References
(https://scholar.google.com/scholar_lookup?
title=Entropy+of+aqueous+surfaces.+Application+to+polymeric+Langmuir+films&author
=Deschenes,+L.&author=Lyklema,+J.&author=StGermain,+F.&publication_year=2017&journal=Adv.+Colloid+Interface+Sci.&volume=247&
Table
13. Strength and molar effectiveness for selected frothers, given solid and flotation
pages=149–162&doi=10.1016/j.cis.2017.04.004&pmid=28501099)]
[CrossRef
device.
(https://dx.doi.org/10.1016/j.cis.2017.04.004)]
[PubMed
Strength cγ75, mmol/dm3
Molar Effectiveness, γ1M
(https://www.ncbi.nlm.nih.gov/pubmed/28501099)]
Example
(Coal, Lab. Flotation Machine,
Example
(Carbonaceous Shale, Hallimond Cell,
×


[50]) D.M.; Roke, S. The Jones-Ray effect reinterpreted:
[55])
60. Okur, H.I.; Chen, Y.; Wilkins,
Surface 0tension
minima
electrolyte solutions
n-butanol of low ionic strength
0.2
KPF6 are caused by electric
4% field induced waterwater correlations. Chem.
Phys. Lett. NaCl
2017, 684, 433–442.
Scholar
n-propanol
1
44% [Google
(https://scholar.google.com/scholar_lookup?title=The+Jonesn-hexanol
3
Na2SO4
46%
Ray+effect+reinterpreted:+Surface+tension+minima+of+low+ionic+strength+electrolyte+
solutions+are+caused+by+electric+field+induced+waterwater+correlations&author=Okur,+H.I.&author=Chen,+Y.&author=Wilkins,+D.M.&author=
Roke,+S.&publication_year=2017&journal=Chem.+Phys.+Lett.&volume=684&pages=433–
442&doi=10.1016/j.cplett.2017.06.018)]
[CrossRef
(https://dx.doi.org/10.1016/j.cplett.2017.06.018)]
61. Lynch, A.J.; Watt, J.S.; Finch, J.A.; Harbort, G.E. History of flotation technology. In Froth
Flotation: A Century of Innovation; Fuerstenau, M.C., Jameson, G.J., Yoon, R.-H., Eds.; SMME
Inc.:
Littleton,
CO,
USA,
2007.
[Google
Scholar
(https://scholar.google.com/scholar_lookup?
title=History+of+flotation+technology&author=Lynch,+A.J.&author=Watt,+J.S.&author=Fi
nch,+J.A.&author=Harbort,+G.E.&publication_year=2007)]
62. Ratajczak, T.; Drzymala, J. Flotacja Solna; Oficyna Wydawnicza Politechniki Wrocławskiej:
Wroclaw,
Poland,
2003.
(In
Polish)
[Google
Scholar
(https://scholar.google.com/scholar_lookup?
Back to TopTop
/



title=Flotacja+Solna&author=Ratajczak,+T.&author=Drzymala,+J.&publication_year=2003)
Abstract
(/)
]
Introduction


Frothers
in Pure State
63. Grabowski,
B.; Drzymala, J. Graphite flotation in the presence of sodium acetate. Ann. UMCS

Frother
in Aqueous
Chem.
2008,Solutions
6, 58–72. [Google Scholar (https://scholar.google.com/scholar_lookup?

Frother
in Aqueous Solutions/Gas
title=Graphite+flotation+in+the+presence+of+sodium+acetate&author=Grabowski,+B.&au
System
thor=Drzymala,+J.&publication_year=2008&journal=Ann.+UMCS+Chem.&volume=6&pag


Three-Phase
(Liquid/Gas/Solid)
es=58–72&doi=10.2478/v10063-008-0029-0)]
[CrossRef (https://dx.doi.org/10.2478/v10063System
008-0029-0)]
Conclusions
64. Lipniarski, M.; Ratajczak, T.; Drzymała, J. Weryfikacja hipotez o roli soli we flotacji na
przykładzie węgla kamiennego w wodnych roztworach NaCl I KPF6. In Proceedings of the III

Author Contributions
Polski Kongres Gorniczy, Mineralurgia I Wykorzystanie Surowcow Mineralnych, Wroclaw,

Conflicts of Interest

Poland, 14–16 September 2015; Drzymała, J., Kowalczuk, P.B., Eds.; WGGG PWr: Wroclaw, 

References
Poland,
2015;
pp.
35–39.
(In
Polish).
[Google
Scholar
(https://scholar.google.com/scholar_lookup?
title=Weryfikacja+hipotez+o+roli+soli+we+flotacji+na+przykładzie+węgla+kamiennego+w
+wodnych+roztworach+NaCl+I+KPF6&conference=Proceedings+of+the+III+Polski+Kongr
Table
13. Strength and molar effectiveness for selected frothers, given solid and flotation
es+Gorniczy,+Mineralurgia+I+Wykorzystanie+Surowcow+Mineralnych&author=Lipniarski,
device.
+M.&author=Ratajczak,+T.&author=Drzymała,+J.&publication_year=2015&pages=35–39)]
3

Acknowledgments
×


Strength cγ75, mmol/dm
Molar Effectiveness, γ1M
Example
(Coal,
Flotation
Machine,tension
Example
(Carbonaceous
Hallimond
Cell,
65. Weissenborn,
P.K.;Lab.
Pugh,
R.J. Surface
of aqueous
solutions of Shale,
electrolytes:
Relationship
[50]) solubility, and bubble coalescence. J. Colloid
[55]) Interface Sci. 1996,
with ion hydration, oxygen
0
184,
[Google
Scholar KPF
(https://scholar.google.com/scholar_lookup?
n-butanol 550–563.
0.2
4%
6
title=Surface+tension+of+aqueous+solutions+of+electrolytes:+Relationship+with+ion+hy
n-propanol
1
NaCl
44%
dration,+oxygen+solubility,+and+bubble+coalescence&author=Weissenborn,+P.K.&autho
n-hexanol
3
Na2SO4
46%
r=Pugh,+R.J.&publication_year=1996&journal=J.+Colloid+Interface+Sci.&volume=184&p
ages=550–563&doi=10.1006/jcis.1996.0651&pmid=8978559)]
[CrossRef
(https://dx.doi.org/10.1006/jcis.1996.0651)]
[PubMed
(https://www.ncbi.nlm.nih.gov/pubmed/8978559)]
66. Paulson, O.; Pugh, R.J. Flotation of inherently hydrophobic particles in aqueous solutions of
inorganic
electrolytes.
Langmuir
1996,
12,
4808–4813.
[Google
Scholar
(https://scholar.google.com/scholar_lookup?
title=Flotation+of+inherently+hydrophobic+particles+in+aqueous+solutions+of+inorgani
c+electrolytes&author=Paulson,+O.&author=Pugh,+R.J.&publication_year=1996&journal
=Langmuir&volume=12&pages=4808–4813&doi=10.1021/la960128n)]
[CrossRef
(https://dx.doi.org/10.1021/la960128n)]
67. Drzymala, J.; Ratajczak, T.; Kowalczuk, P.B. Kinetic separation curves based on process rate
considerations. Physicochem. Probl. Miner. Process. 2017, 53, 983–995. [Google Scholar
(https://scholar.google.com/scholar_lookup?
title=Kinetic+separation+curves+based+on+process+rate+considerations&author=Drzym
ala,+J.&author=Ratajczak,+T.&author=Kowalczuk,+P.B.&publication_year=2017&journal=
Back to TopTop
/



Physicochem.+Probl.+Miner.+Process.&volume=53&pages=983–
Abstract
(/)
995&doi=10.5277/ppmp170224)] [CrossRef (https://dx.doi.org/10.5277/ppmp170224)]
Introduction


Frothers
in Pure State
68. Drzymala,
J.; Stodulski, M. Moc i kineza heksyloaminy we flotacji lupka miedzionosnego. In

Frother
in Aqueous
SolutionsIII; Kowalczuk, P.B., Drzymala, J., Eds.; WGGG PWr: Wroclaw, Poland,
Lupek
Miedzionosny

Frother
in Aqueous Solutions/Gas
2017;
pp.
167–171.
(In
System
(https://scholar.google.com/scholar_lookup?


Polish)
[Google
Scholar
Three-Phase
(Liquid/Gas/Solid)
title=Moc+i+kineza+heksyloaminy+we+flotacji+lupka+miedzionosnego&author=Drzymala
System
,+J.&author=Stodulski,+M.&publication_year=2017&pages=167–171)]
Conclusions
69. Szajowska, J.; Wejman, K.; Kowalczuk, P.B. Froth flotation of shale and quartz the in
Hallimonda tube. In Kupferschiefer; Kowalczuk, P.B., Drzymala, J., Eds.; WGGG: Wroclaw,

Author Contributions
Poland,
2014;
pp.
91–97.
(In
Polish)
[Google
Scholar

Conflicts of Interest


(https://scholar.google.com/scholar_lookup?

References
title=Froth+flotation+of+shale+and+quartz+the+in+Hallimonda+tube&author=Szajowska,
+J.&author=Wejman,+K.&author=Kowalczuk,+P.B.&publication_year=2014&pages=91–
97)]

Acknowledgments
×


13. Strength
and molar
effectiveness
for selected
frothers, given solid
70.Table
Kudlaty,
T. Maximum
Size of
Floating Particles
of Copper-Bearing
Shaleand
in flotation
the Presence of
device.
Frothers. Bachelor’s Thesis, Wroclaw University of Science and Technology, Wroclaw, Poland,
January 2016.Strength
(In Polish).
[Google3 Scholar (https://scholar.google.com/scholar_lookup?
cγ75, mmol/dm
Molar Effectiveness, γ1M
Example
(Coal, Lab. Flotation Machine,
Example
(Carbonaceous Shale, Hallimond Cell,
title=Maximum+Size+of+Floating+Particles+of+Copper[50])
[55])
Bearing+Shale+in+the+Presence+of+Frothers&author=Kudlaty,+T.&publication_year=201
0
6)]
n-butanol
0.2
KPF6
4%
n-propanolP.; Drzymala, J. 1Influence of sodium
NaCl
71. Merta,
chloride and sodium 44%
acetate on flotation of
anthracite
coal as a model
substance rich Na
in 2kerogen.
In Kupferschiefer
n-hexanol
3
SO4
46% II; Kowalczuk, P.B.,
Drzymala, J., Eds.; WGGG PWR: Wroclaw, Poland, 2016; pp. 195–200. (In Polish) [Google
Scholar
(https://scholar.google.com/scholar_lookup?
title=Influence+of+sodium+chloride+and+sodium+acetate+on+flotation+of+anthracite+co
al+as+a+model+substance+rich+in+kerogen&author=Merta,+P.&author=Drzymala,+J.&pu
blication_year=2016&pages=195–200)]
72. Kowalczuk, P.B.; Zawala, J. A relation between time of the three-phase contact formation and
flotation kinetics of naturally hydrophobic solids. Colloids Surfaces A Phys. Eng. Asp. 2016, 506,
371–377.
[Google
Scholar
(https://scholar.google.com/scholar_lookup?
title=A+relation+between+time+of+the+threephase+contact+formation+and+flotation+kinetics+of+naturally+hydrophobic+solids&aut
hor=Kowalczuk,+P.B.&author=Zawala,+J.&publication_year=2016&journal=Colloids+Surf
aces+A+Phys.+Eng.+Asp.&volume=506&pages=371–
377&doi=10.1016/j.colsurfa.2016.07.005)]
[CrossRef
(https://dx.doi.org/10.1016/j.colsurfa.2016.07.005)]
73. Kalinowski, K.; Kaula, R. Verification of flotation kinetics model for triangular distribution of
density function of floatabilities of coal particles. Arch. Min. Sci. 2013, 58, 1279–1287.
Back[Google
to TopTop
/






Scholar
Abstract
(/)
(https://scholar.google.com/scholar_lookup?
title=Verification+of+flotation+kinetics+model+for+triangular+distribution+of+density+fu
Introduction
nction+of+floatabilities+of+coal+particles&author=Kalinowski,+K.&author=Kaula,+R.&pu
Frothers
in Pure State
blication_year=2013&journal=Arch.+Min.+Sci.&volume=58&pages=1279–
Frother in Aqueous Solutions
1287&doi=10.2478/amsc-2013-0088)]
[CrossRef (https://dx.doi.org/10.2478/amsc-2013Frother
in Aqueous Solutions/Gas
0088)]
System


Three-Phase
(Liquid/Gas/Solid)
74. Chipfunhu,
D.; Zanina, M.; Grano, S. Flotation behaviour of fine particles with respect to contact
System
angle.
Chem.
Eng.
Res.
Des.
2012,
90,
26–32.
[Google
Scholar

Conclusions
(https://scholar.google.com/scholar_lookup?




Acknowledgments
title=Flotation+behaviour+of+fine+particles+with+respect+to+contact+angle&author=Chi
Author
Contributions
pfunhu,+D.&author=Zanina,+M.&author=Grano,+S.&publication_year=2012&journal=Che
of Interest
m.+Eng.+Res.+Des.&volume=90&pages=26–32&doi=10.1016/j.cherd.2011.06.021)]
 Conflicts

References
[CrossRef (https://dx.doi.org/10.1016/j.cherd.2011.06.021)]
×


75. Janicki, M.; Bartkowicz, L.; Zakrecki, B.; Kowalczuk, P.B. Collectorless coal flotation in the
presence of foaming agents. In Proceedings of the III Polish Mining Congress, Minerallurgy and
Utilization
of Mineral
Resources,
Wroclaw,
Poland, frothers,
14–16 September
2015;
Drzymala, J.,
Table
13. Strength
and molar
effectiveness
for selected
given solid and
flotation
Kowalczuk, P.B., Eds.; WGGG PWR: Wroclaw, Poland, 2015; pp. 52–60. (In Polish). [Google
device.
Scholar
(https://scholar.google.com/scholar_lookup?
Strength cγ75, mmol/dm3
Molar Effectiveness, γ1M
title=Collectorless+coal+flotation+in+the+presence+of+foaming+agents&conference=Pro
Example
(Coal, Lab. Flotation Machine,
Example
(Carbonaceous Shale, Hallimond Cell,
ceedings+of+the+III+Polish+Mining+Congress,+Minerallurgy+and+Utilization+of+Mineral
[50])
[55])
0
+Resources&author=Janicki,+M.&author=Bartkowicz,+L.&author=Zakrecki,+B.&author=K
n-butanol
0.2
KPF6
4%
owalczuk,+P.B.&publication_year=2015&pages=52–60)]
n-propanol
1
NaCl
44%
76. Kowalczuk, P.B.; Drzymala, J. Selectivity and power of frothers in copper ore flotation.
n-hexanol
3
Na2SO4
46%
Physicochem. Probl. Miner. Process. 2017, 53, 515–523. [Google Scholar
(https://scholar.google.com/scholar_lookup?
title=Selectivity+and+power+of+frothers+in+copper+ore+flotation&author=Kowalczuk,+P.
B.&author=Drzymala,+J.&publication_year=2017&journal=Physicochem.+Probl.+Miner.+P
rocess.&volume=53&pages=515–523&doi=10.5277/ppmp170140)]
[CrossRef
(https://dx.doi.org/10.5277/ppmp170140)]
77. Fuerstenau, D.W. Coal Surface Control for Advanced Fine Coal Flotation; Final Report
DOE/PC/88878-T12; University of California: Berkeley, CA, USA, July 1991. [Google Scholar
(https://scholar.google.com/scholar_lookup?
title=Coal+Surface+Control+for+Advanced+Fine+Coal+Flotation&author=Fuerstenau,+D.
W.&publication_year=1991)]
78. Drzymala, J. Atlas of upgrading curves used in separation and mineral science and technology.
Part I. Physicochem. Probl. Miner. Process. 2006, 40, 19–29. [Google Scholar
(https://scholar.google.com/scholar_lookup?
title=Atlas+of+upgrading+curves+used+in+separation+and+mineral+science+and+techn
Back to TopTop
/

ology.+Part+I&author=Drzymala,+J.&publication_year=2006&journal=Physicochem.+Prob
Abstract
(/)

l.+Miner.+Process.&volume=40&pages=19–29)]
Introduction



Frothers
in Pure State
79. Drzymala,
J.; Ahmed, H.A.M. Mathematical equations for approximation of separation results

Frother
in Aqueous
Solutions upgrading curves. Int. J. Miner. Process. 2005, 76, 55–65. [Google
using
the Fuerstenau

Frother
in Aqueous Solutions/Gas
Scholar
(https://scholar.google.com/scholar_lookup?
System
title=Mathematical+equations+for+approximation+of+separation+results+using+the+Fuer

Three-Phase
(Liquid/Gas/Solid)
stenau+upgrading+curves&author=Drzymala,+J.&author=Ahmed,+H.A.M.&publication_ye
System
ar=2005&journal=Int.+J.+Miner.+Process.&volume=76&pages=55–

Conclusions
65&doi=10.1016/j.minpro.2004.10.002)]

Acknowledgments
(https://dx.doi.org/10.1016/j.minpro.2004.10.002)]


[CrossRef
Author Contributions


80. Raghavan, V. On the Gibbs Triangle. J. Phase. Equilib. Diff. 2008, 29, 213–215. [Google
Scholar
(https://scholar.google.com/scholar_lookup? 
References
title=On+the+Gibbs+Triangle&author=Raghavan,+V.&publication_year=2008&journal=J.+
Phase.+Equilib.+Diff.&volume=29&pages=213–215&doi=10.1007/s11669-008-9308-x)]
[CrossRef (https://dx.doi.org/10.1007/s11669-008-9308-x)]
Conflicts of Interest
×


Table 13. Strength and molar effectiveness for selected frothers, given solid and flotation
device.
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(Carbonaceous
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Hallimond
Cell,
(https://creativecommons.org/licenses/by/4.0/)http://creativecommons.org/licenses/by/4.0/
[50])
[55])
(http://creativecommons.org/licenses/by/4.0/)).
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0.2
KPF6
4%
1
NaCl
44%
3
Na2SO4
46%
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