FLOTATION
(Main feature - hydrophobicity in static approach)
(Main features - hydrophobicity and properties of thin films
in the dynamic approach)
Flotation
water
gas bubble
intergroth
hydrophobic particle
hydrophilic particle
płonna (hydrofilna)
gas bubble

water
particle
Contact angle
flotation
mechanical
stirring
pulp
bubbles
particles
flo ta c ja
Flotation (mechanism) depends on particle size
proper size
coarse
fines
Pease et al., 2006
proper size
Importance of receding and advancing contact angles in flotation
(TPC means three-phase contact)
FLOTATION STEPS
Steps of flotation
Different contact angles
particle
r
1. collision
(R, r, trajectory)
bubble
2. contact
( receding , contact time)
R
3. adhesion
( , contact time)
4. stability
(  advancing, inertia forces)
5. flotation
(buoyancy)
flotacja 2
rc
particle
droga
cząstki
trajectory
zderzenie
collision
sliding
poślizg

rb
rp
stream lines
linia prądu
liquid film
Capillarity: curvature and interfacial free energy of the interface are
related to the pressure jump between the inside and outside of a
liquid drop via
Young-Laplace equation
kinetics and thermodynamics
bubble
thermodynamics
flotation
bubble
film
particle
drop
molecule
ion
contact
angle
aqueous film barrier
attractive forces: dispersion, capillary,
hydrophobic, electrostatic ….
interaction energy
energy increase
due to water
layer resistance
(kinetics)
repulsive forces: disjoinnig pressure
hydrodynamic -liquid viscosity
secondary minimum
(contacless flotation ?)
primary minimum
(bubble-particle attachment)
distance between bubble and particle
energy reduction
due to
hydrophobicity
(thermodynamics)
Contact angle of selected materials
Advancing contact angle (degree units) mesured on polished plates
(after Adamson, 1967; data from other sources denoted as *)
Substance
Teflon
Paraffin
Polystyrene
Human skin
Naphthalene
Stearic acid
Advancing contact angle
112
110
103
90
88
80
Substance
sulfur
graphite
stibnite (Sb2S3)
iodyrite (AgI)
calcite (CaCO3)
glass
Advancing contact angle
86*
86
84
17
~0*
~0
Methods of contact angle measurement
Smoothly polished
surfaces
Capture bubble
Adamson, 1967
heat of immersion
Sessile drop
Adamson, 1967
flotometry
Tilted plate in liquid
Hiemenz, 1986
Force of detachment
Wetting of plate
Drop on a tilted plate
Drop shape
Drop size
Source*
Particles
Source
Neumann and Good, 1979
Drzymała and Lekki, 1989a,b
Drzymała, 1995; 1999a,b,c
shape of border between
Aveyard and Clint, 1995
phases
Hiemenz, 1986
levitation
Li et al., 1993
Heertjes and Kossen, 1967,
Adamson, 1967
pressed disc
He and Laskowski, 1992
rate of penetration of a
Hiemenz, 1986
van Oss et al., 1992
thin layer of particles
Ralson
rate of penetration of a Washburn, 1921, Crowl
i Newcombe, 1992 column of particles
and Wooldridge, 1967
Ralson
captured bubble for
Hanning and Rutter, 1989
i Newcombe, 1992 particles
Clint and Tylor, 1992;
Langmuir through
Aveyard et al., 1944
Huethorst and Leenaars,
centrifuge
1990
capillary rise without
White, 1982
probe liquid
capillary rise in column
of particles with probe Bartell and Whitney, 1933
liquid
Methods of measurement
*Additional source: Neumann i Good (1979).
receding
water
advancing
water
equlilibium
flotacja 4
CONTACT ANGLES
 advancing
 receding
 equilibrium
flotacja 3
CONTACT ANGLES
Laplace-Young Equation and
Dupre-Young Relationship.
R. L. Cerro
Chemical and Materials Engineering
The University of Alabama in Huntsville
Santa Fe, 16 de Abril de 2010
CONTACT ANGLES
Laplace-Young Equation and
Dupre-Young Relationship.
R. L. Cerro
Chemical and Materials Engineering
The University of Alabama in Huntsville
Santa Fe, 16 de Abril de 2010
sg = sc+ cgcos
equilibrium contact angle
is resulting from the
Young equation
s -  = sc+ cgcos
 reflects adsorption of species
at the solid /gas interface
Contact angle determined directly from the Young equation
Contact angle in degrees (Drzymała, 1994)
Substance
Ice
Quartz
Paraffin
Mercury
s, mN/m
e, mN/m
sw, mN/m
cg, mN/m
calculated
measured*
90–120
120–135
50– 68
484
~0
~small
0
~75
22–33
46
51
415
72,8
72,8
72,8
72,8
0
~0
77– 91
95
0
0
110
43–110
There are different models of flotation:
mechanistic, thremodynamic, probabilistic
Mechanistic is based on forces
importance of capillary and excess presure forces
importance of capillary and excess presure forces
will be shown using a single bubble as an example
Bubble in water
water
gas
bubble
pressure net upward force (Fup) on top hemisphere of bubble
(pressure difference (Pi-Po) x area of equatorial circle (r2)
Fpressure, upward = (Pi-Po)r2
surface tension downward force around circle
(surface tension x circumference)
Fsurface tension, downward = 2r
Fpressure, upward = (Pi-Po)r2
equilibrium
Fsurface tension, downward = 2r
Fsurface tension, downward = Fpressure, upward
Laplace equation
Bubble on solid surface
water
Fe
gas

Fsl
solid
Flg,v
Flg
Fsg
reference plane
balance along Fsl and Fsg forces
Fsg=Fsl + Flg cos  , Fe= 0
for each force F=2a
2asg=2asl + 2alg cos 
sg=sl+γlg cos (Young equation)
correct
incorrect graphical
representation
(literature)
in both cases the Young equation is
sg = sc+ cgcos 
 - contact angle
Thermodynamic approach (static model)
Gflotation= Gfinal- Ginitial = [sg - (sc+ cg)] A
for A =
= 1cm2 surface area
Gflotation= sg - (sl+ lg) Dupre eq. (1869)
Gflotation = sg - (sl+ lg) Dupre eq. (1869)
where
G – thermodynamic potential (free enthalpy,
Gibbs potential)
sg – solid – gas interfacial energy
sl – solid – liquid interfacial energy
lg – liquid – gas interfacial energy
unit of energy  and potential G is J/m2
sg = sc+ cgcos 
Combination of the Dupre
Gflotation = sg - (sl+ lg)
and the Young eq.
sg = sl+ lgcos 
provides the Dupre-Young eq.
G flotation = lg(cos  - 1)
 = 0o, cos = 1, G=0, no flotation,  = 90o, cos = 0,
G= - cg, hipothetically full flotation
Main parameter of separation – contact angle 
main parameter of flotation
(resulting from the simplest flotation model)
contact angle 
( a measure of hydrophobicity )
the Dupre-Young eq.
Gflotation = lg (cos  - 1)
process energy
J/m2, N/m
main feature 
„electromagnetic field” of separation (flotation) system
More detailed models of flotation (Dupre approach)
Particle and spherical bubble
G flotation   cg (1  (sin  )
2/3
1
4
 
1/ 3


2
 (1  cos )  cos 


here flotation also depends on  and 
1/ 3
)
Probabilistic models
for instance Schulze (1993)
dNp /dt = –k Np (first order kinetics)
k = Pc Pa Pstab Ptpc ZNb

   c   min   
 R p2  

1 
v
  1  exp(1  ) 1  exp( )
k   2  1  exp   

R

B0 '  
 tpc 
i
  
 b  
 
c=[2R3p(p + 1,5)/3]0,5(1,39 – 0,46 ln Rp)
i = 3R2 Rp/8cbh2crit
h crit = 23,3[ (1 – cos A)]0,16
F
Bo’=4R2p(g + pa) +3Rp(sin2 *) f (Rb)/C
C = 6 sin *sin (* + ), *  180° –  /2
f(Rb) = (2 /Rb) – 2Rbg
v = 0,6(Rp + Rb)2/ (laminar)
v = 13(Rp + Rb)2/3/*1/3 (turbulent )
General models of flotation (dNp/dt = –k Np)
Mao–Yoon (1997)
k = PcPaPstab0.25 Sb
Pc =
Pa =
Pstab = 1 – Pd
Pd
Schulze (1993)
k = Pc Pa Pstab Ptpc ZNb
Pc =
Pa =
c = [2 (p + 1.5)/3]0,5(1.39 –
– 0,46 ln Rp)
i = 3 Rp/8cbh2kryt,
h kryt = 23.3[ (1 – cos A)]0,16
Pstab= 1 – exp(1 – 1/Bo´),
*  180° –  /2,
Bo´ = 4 (g + pa) +
+3Rp(sin2 *) f (Rb)/C
C = 6 sin *sin (* + ),
f (RB) = (2 /RB) – 2Rbg
Ptpc  1 – exp (–v /tpc)
v = 0.6(Rp + Rb)2/ laminar flow
v = 13(Rp + Rb)2/3/*1/3 turbulent flow
Varbanov–Forssberg–
–Hallin (1993)
k = EUCb
 = f (Pc) = RpRb
E = f (Pa)
E = 1 – cos 
Pstab taken into account in
other parts of expression for
k
U =  +2 )/(9)
Cb = 3Q/(4 SV)
dN/dt
a
Bo´
cb
Cb
E
E1
Ek
Ek´
g
hkryt
k
Nb
Np
Pa
Pd
Pstab
Ptpc
Q
Rp
Rb
Rc
RF
Re
S
Sb
V
Vb
U
Z


*




p

A
v
tpc
c
i
min

*
– flotation rate,
– centrifugal acceleration acting on particle-bubble aggregate in a vortex of liquid,
– Bond’s number,
– rigidity of bubble surface (cb = 1 for rigid uneven surface, cb < 1 for movable smooth surface),
– bubble concentration in pulp (number of bubbles in 1cm3 of pulp),
– efficiency of attachment of particles to bubble surface (number of attached particles divided by the number of particles colliding with considered bubble),
– energy barrier for adhesion of bubble and particle,
– kinetic energy of collision of bubble with particle,
– kinetic energy of detachment of particle and bubble (calculated from the French–Wilson Eq.),
– acceleration due to gravity,
– critical film thickness on surface of particle,
– rate constant of flotation,
– number of bubbles in flotation cell at a considered time,
– number of particles subjected to flotation at a considered time,
– probability of adhesion of particles to a bubble,
– probability of detachment of particles from a bubble (P d = 1 – Pstab),
– probability of stability of particles-bubble aggregate,
– probability of formation of particle-bubble-water contact,
– flow of air in flotation machine, m3/s,
– particle radius,
– bubble radius,
– radius of the stream enabling collision of particle with bubble,
– size of thin film between particle and bubble during collision,
– Reynolds number,
– cross section area of flotation machine, m2,
– area of bubbles leaving flotation cell per time unit and per cross section area ot the cell,
– rate of ascending bubble, m/s,
–surface velocity of aeration defined as volume rate of aeration normalized per cross section of the flotation column,
– velocity of particles in relation to velocity of bubble in the pulp,
– number of particle collisions per unit time,
– surface tension of aqueous solution,
– quantity characterizing efficiency of collision between particles and bubbles,
– dissipation energy in flotation cell,
– effective density of particle in water,
– dynamic viscosity,
– kinematical viscosity,
– pulp density,
– particle density,
– contact angle,
– advancing contact angle,
– life time of liquid vortex in flotation cell which destroys the particle–bubble aggregate,
– time needed to form permanent three-phase solid-gas-liquid contact,
– collision time of bubble and particle,
– induction time (time of removing liquid film from particle and forming attachment),
– minimal time of contact,
= 3.14,
= 180 –  /2.
How time (reflection of water film) is introduced to flotation models?
Probabilistic models: with first order kinetics of flotation
dNp /dt = –k Np
DLVO type models: with kinetics of collision and barrier hight
aqueous film barrier
interaction energy
energy increase
due to water
layer resistance
(kinetics)
secondary minimum
(contacless flotation ?)
primary minimum
(bubble-particle attachment)
distance between bubble and particle
energy reduction
due to
hydrophobicity
(thermodynamics)
t 
0.4
4/9
d
7/9
t
 p  f
2/3
 1 / 3  2f / 3
vt particle velocity
 dissipation rate of turbulent kinetic energy per unit mass, W/kg
v kinematic viscosity of fluid, m2/s
f fluid density, kg/m3
p particle density, kg/m3
dt particle diameter, m
Govender, Lelinski, Traczyk, S. Afr. Int. Min. Met., Platinum 2012
Liquid film models: with viscous resistance of the film (to be
derived, some elements are available)
scale up problem in flotation
Carbonaceous copper shale
is hydrophobic with contact angle about 46o
(Peng, 2014)
No native (reagent-free) flotation of carbonaceous
copper shale (only entrainment) in Hallimond tube
(Drzymala,2014)
Froth flotation (C4P3) of shale in a laboratory
flotation machine (Siwiak, 2013)
a
Cu [%]
1.90
Corg [%]
 100%
 100%
1.70
b
CONCENTRATE
FLOTATION MACHINE
TAILINGS
Cu [%] 11.32
 8.1%
 1.36%

Cu [%]
1.77
 91.9%
 98.6%
Corg [%] 1.27
 71.8%
 96.1%
Corg [%] 12.26
 28.2%
 3.91%
Froth flotation in the presence of Corflot in
industrial flotation machine (Konieczny et al.,
2013)
Conclusions
FLOTATION depends of hydrophobicity and film properties
HYDROPHOBICITY provides potential for flotation
(thermodynamics of fotation )
FILM decides about kinetics of flotation
HOME WORK
Prepare a 15-minute long PowerPoint presentation
to be shown in the class on a selected by you topic
Electrical aspects of flotation
flotation recovery, %
100
80
Ge
pHiep = 2.8
naturally hydrophobic
60
40
20
0
0
2
4
6
pH
8
10
12
Electrical aspects of FLOTATION
Main parametr – hydrophobicity (contact angle)
which depends on energetics of three interfaces (Young eq.)
sg = sl+ lgcos 
the Gibbs theory tells that
(d )T = (–idi)T.
di = RT d ln ai,
aM 
RT
o 
ln
F
( a M  ) pzc
 adsorption
 chemical potential
R gas constant, F Faraday cost.
a activity (concentration)
 surface charge
 surface potential
 temperature
FLOTATION
main feature
Hydrophobicity : contact angle
field (el.-mag.)
G = cg (cos  –1)

cg, sg, sc
(cos  =
(sg + sc )/ cg )*
 / E=– 
 , , Y
 = f (Y )
 =–(1/R T) / lna
Potential: electrical E,
Chemical ln a (oraz pH, pX, ....)
electrochemical E h
c
,c
particles
bubbles
*Young eq.
,
c collector , c
frother
f
(activity coeff.
a=fc
csalt , c other
flot
Electrical aspects of flotation
-+
water -+
moving particle
+
-
+
- +
+ +
-
-+
+
-+
-+
slipping plane
zeta potential
-+
Structure of electrical double layer
+ - + - + - +
charged surface
layer
Galvanipotential, 0
+
-
+ + - + - + - +
- +
- - + - + particle
- +- + - +
- +
- + - + +
+
- + - +
- + - +
potential Y
diffusive layer
surface potential Y 0
potential zeta, 
cation concentration
eg. [H+] = [H +] r
exp(Y/RT)
anion concentration
eg. [OH -] = [OH -] r
exp(Y /RT)
Models of electrical double layer
Helmholz
(flat condenser)
Gouy-Chapman
(diffuse layer)
Yo
o -o
H+
OH-
Yo
o d -----
H+
OH-
 0 =  0   0
d 
triple
layer
Stern
(rigid and diffuse layer )
quadruple
layer
Grahame
(binding sites)
Yo
Yi
o i
H+
OH-
d-----
Yo
Yi
Yo
Yi
Yd
Yd
o i d----
H+ K+
OH- A-
Yo
Yo
o i j d
H+ K+ K+H2O
OH- A- A-H2O
Flat condenser
 2 kT 0
 ze  
sinh  0 0 
ze
 2kT 
Diffuse condenser
Formation of electrical double layer
surface charge
negative
positive
metals
ęć




 Me  Me  Me 
Me 




 Me  Me  Me 
Me 




 Me  Me  Me 
Me 
oxides








 Me  O  Me  O





 O  Me  O 
Me 




 Me  O  Me  O





salts
H2O
H2O




 Me  X  Me  X H2O





 X  Me  X 
Me 




 Me  X  Me  X

 placeof particle
 breakage



 Me
Me

 Me 
 Me
Me




 Me 
+ n Me+ or Me


 Me 
Me



 Me 
Me




O
 O  MeO
 Me  OH

+ n H+ or
 O  MeO

 Me  X

X 
 Me  X

+ electrons
MeOH2+

 Me  OH

O
+ n OH-
MeOH2+

+n
Me+
particle /water interface
or

X 
Me

 Me+

X 
Me

+n
X-
Formation of electrical double layer
lad



 Me  S  Me 



 S  Me  S 



 Me  S  Me 




S 

H 2O
Me 

S 


 S  Me  OH

 Me  SH

 S  Me  OH

other

 S  Me  OH 2

 Me  SH

+
 S  Me  OH 2

+
+ n OH
-

 S  Me  OH

 Me  S 
 S  Me  OH

+H
+
surface electrical charge, µC/cm 2
60
40
pzc
20
0
-20
0.001M NaCl
0.010M NaCl
-40
0.100M NaCl
-60
2
4
6
pH
8
10
60
zeta potential, mV
40
iep
20
0
-20
0.100M NaCl
0.010M NaCl
-40
0.001M NaCl
-60
2
4
6
pH
8
10
interpretation: preferential adsorption of -OH groups
20
zeta potentia, mV
0
-20
D2O-ice ( n) (0.0001M)
diamond (  )
-40
air ( w),Nocardia sp.( )
-60
hexadecane
D2O-ice (0.001M)
-80
2
4
6
8
10
12
pH
zeta potential and iep for materials without
functional groups
Point of zero charge (pzc) and isoelectric point (iep)
for selected substances in aqueous solution. A collection of pzc and iep
for a great number of solids can be found in a work Parks (1965)
Substance
Quartz, SiO2
Oleic acid, C17H33COOH
Cassiterite, SnO2
Sulfur, S
Sulfides, MeS
Ice, D2O
Hydrocarbons, CnH2n+2
Air, O2+N2+CO2
Diamond, C
Bacteria (Nocardia)
Rutile, TiO2
Ilmenite, FeTiO3
Hematite, Fe2O3
Barite, BaSO4
Tenorite, CuO
Dolomite, (Ca,Mg)CO3
Magnesite, MgCO3
Corundum, Al2O3
Periclase, MgO
pHpzc
<5
<5.5
–
–
7.0 0.5
6.3
–
–
–
4.8–5.3
5.6
6.5–8.5
–
6.5–8.5
–
pHiep
1.54
2.0
2.0–5.5
2.1
2.1–7.0
3.0–3.5
3.3
3.5
3.5
3.5
4.8–8.7
6.0–8.1
6.0–7.6
7.5
7.5
9.1
12.0
hydrophobization: with all possible chemical bondings
b
oil
a
-O-H -O
d
c
Me
S
Me
S
S
Possible modes of adsorption of collectors at particle-water interface:
a – adsorption of oil on hydrophobic particle with van der Waals forces,
b – adsorption of apolar molecule of collector by means of hydrogen bonding,
c – adsorption of polar collector by means of simple chemical bond
or electrostatic attraction, d – adsorption with formation of chelating bond.
Hydrophobic part of the collector is shown in white while hydrophilic as black
Not to scale.
collectors
non-polarne
ionic
chelating
simple
sulfur
compounds
hydrocarbons
and derivatives
alcohols
typu S-S
xanthates
cationic
typu O-O
fatty acids
typu N-N
diamines
typu S-N
carbamines
anionic
amphoteric
typu O-S
monothiocarbonates
typu O-N
oximes
amines
merkaptans
aminoalkylacids
Structure of collector
–
CH3CH2CH2CH2 CH2CH2CH2CHCOO
2
tail
(hydrophobic)
head
(hydrophilic)
CMC
a
b
c
Collector ions can be present in aqueous solution as free ions (a), premicellar species (b)
spherical micelles (c). The structures appear with increasing concentration of collector in aqueous solution.
Symbol o denotes ion appositively charged to the collector ion
100
recovery, %
80
CMC
CMC
SOS
SDS
60
40
20
alumina
0 -7
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
3
collector concentration, kmol/m
An example of lack of correlation between CMC and flotation (after Freund and Dobias, 1995).
SOS – sodium octyl sulfate, SDS – sodium dodecyl sulfate
a
b
c
Adsorption of ionic collector on the surface of particle with the formation of hemimicelle (a),
monolayer (b) and a second layer leading to hydrophilicity (c)
Collector
Chain length*
ethyl
butyl
Dithiocarbaminate
60
77
Mercaptane
60
74
Xanthate
60
74
Dithiophosphate
59
76
Trithiocarbonate
61
74
Monothiocarbonate
61
73
Maximum contact angle for different collectors with ethyl and butyl chain. After Gaudin, 1963
* For methyl chain (C1)   50°, propyl (C3) 68°, C5 78°, C6 81°, for greater about 90°, and for C16 98°
(Aplan and Chander, 1988).
collector renders the
surface hydrophobic
gas
collector
particle
100
100
80
60
60
20
40
-20
20
-60
0
-100
0.80
30
20
0.90
10
0 -6
10
-5
10
-4
10
-3
10
-2
zeta potential, mV
40
flotation recovery
quartz-dodecylamine
cos 
adsorption density, mol/m2 x1011
50
10
collector concentration, kmol/m 3
Flotation of particles increases with increasing concentration of collector in the system
and is proportional to collector adsorption and hydrophobicity caused by the adsorption.
Collector adsorption is manifested by the increase of zeta potential of particles (after
Fuerstenau et al., 1964 and Fuerstenau and Urbina, 1988), pH = 6–7
Which interface is responsible for hydrophobicity increase with
collector addition?
450
90

surface or interfacial
tension, mN/m
425
H2O
400
Hg/air
50
375
Hg/H2O
350
surface tenion, mN/m
contact angle, degree
70
30
-7
-6
-5
-4
-3
-2
-1
log (collector concentration, mol/dm3)
Dependence of contact angle and the state of mercury at interfaces on concentration of collector
Data by Smolders (1961) taken from various sources: contact angle in dodecyl sulfate solution and
 H2O (dodecyl sulfate) (Leja, 1982),  Hg /H2O(decyl sulfonate) and  Hg (decyl sulfonate) (de Bruyn i Agar, 1962))
collector

contact angle ,

 sg,  sc  cg
initial
contact angle
0
sg   sc
cos =  
--------------
 cg

 cg  sc  sg

 sc  cg  sg
electrolytes
(pH regulators and
salts)
modifying
reagents
hydrophilization
reagents
Flotation is influenced by reagents modifying the interfaces. Collectors strongly change the solidgas, surfactants water–gas, and electrolytes (pH reagents and salts) solid–water interfaces. The
extent of modification is expressed by the height of symbol
gamma flotation
(flotation in water mixed with soluble organic liquid)
1
100
cos
0,75
75
cos
0,5
0,25
50
25
surface tension
of wetting
0
0
0
20
40
60
flotation recovery,  , %

80
surface tension,  wg, mN/m
Typical shape of the cos  = f (surface tension of liquid) relationship also called the Zisman
plot, and flotation of naturally hydrophobic materials
Flotation vs collector dose
100
contact angle,  , degree
contact angle, degree
80
60
40
galena
20
80
pH = 7
pH = 9
60
pH = 10
40
pH = 10.5
20
hematite - NaOl
0
0
2
4
6
8
10
concentration of potassium ethyl xanthate, g/m3
0 -07
10
10
-06
10
-05
10
-04
-03
10
concentration of sodium oleate, kmol/m3
Influence of pH and iep on flotation for various collectors
100
100
goethite
80
kyanit
(collector: oleic acid)
60
recovery, %
recovery, %
80
40
iep 6.9
20
collector
RSO4Na
60
iep 6,7
40
20
0
0
0
2
4
6
8
10
12
2
14
4
6
100
8
10
12
pH
pH
100
coal
80
quartz
80
(collector: tridecane)
(collector: octylphenylpolyethoksyethanol)
recovery, %
recovery, %
collector
RNH3Cl
60
40
60
40
iep 2 3
20
iep 2 3
20
0
0
2
4
6
8
pH
10
12
2
4
6
8
pH
10
12
Collector as chemicals
Ionic collectors
Collector
Example
Cationic
Primary amines* R–NH2
n-dodecylamine C12H25–NH2 or C12H25–NH2·HCl
(C12H25–N+H3Cl–)
Secondary amines* R–(R´)N–H
di-n-amylamine, (C5H11)2–NH
Tertiary amines* R–(R´)N–R´´
tri-n-amylamine, (C5H11)3–N
R'
Cl
N+
Quarternary ammonium salts
R
Diamines and triamines
R''
-
R''
diamine R–NH–(CH2)x–NH2
N+
Pyridinium salts
C lR
CH 2 -CH 2
Morpholinium salts
+ O Cl
R NH
CH 2 -CH 2
R'
R''
S+
Sulfonium salts
R
Cl
Anionic
Mercaptans, R–SH
Due to unpleasant smell mercaptans are not used
by industry
amphoteric
N-dodecyl-2-aminopropionic acid
C12H25–N+H2–(CH2)2–COO–
other
C12H25–NH–CH2–COONa,
C12H25–N(CH2–COONa)2, R–(CH3)2N+–CH2–
COO– (alkyl betaines)
Selected chelating collectors. Type O–O. Based
on Nagaraj, 1988
Collector
Formula
Carbonic acid derivatives
R–COOH
(fatty acids)
Sulfuric acid derivatives
R–O–SO3H
(sulfates)
Sulfuric acid derivatives
R–SO3H
(sulfonates)
Phosphoric acid derivatives
(RO)2–P(O)–OH
(phosphates)
Phosphonic acid derivatives
(phosphonates, diphosphonates)
Phosphinic acid derivatives
(phosphinate)
Nitrosophenylhydroxylamine
(ammonium salt)
Salicylaldehyde
Nitrosonaphthols
Nitrosophenols
Organic dyes
Hydroxamic acids
(RO)–(R)P(O)–OH
R–(PO3H2)2
(R)2–P(O)–OH
(Ar–N(O–)–N=O)NH4
OH–Ar–CHO
ON–nA–OH
R–(OH)Ar(OH)–NO
R–CO–NH–OH
Example
oleic, linoleic, linolenic, stearic acids
dodecyl sulfate
dodecyl sulfonates
dialkyl phosphoric acid
dialkyl phosphonic acid
Flotol-7,9 (1-hydroxyalkylidene-1,1diphosphonic acid)
dialkyl phosphinic acid
Cupferron
Salicylaldehyde
a-nitroso-b-naphthol,
b-nitroso-anaphthol
nitroso alkyl resorcinol
alizarin and derivatives
Benzohydroxamic acid, potassium
octylhydroxamate, IM-50 (C7-C9)
.Selected chelating collectors. Type S – S
Collector
Based on Nagaraj, 1988
Formula
S
Dithiocarbonates (xanthate)
- C - OS
Trithiocarbonates (tioxanthate)
Example
Potassium ethyl xanthate
(R–OCSSK)
S
- C - SS
S
Dithiophosphates
- P(OR) 2
Aerofloat ((RO)2 P(=S)–SK)
S
S
Dithiophosphinates
- PR
2
Aerofins
S
S
Dithiocarbamates
- C - NR2
S
Sodium diethyldithiocarbamate
Selected chelating collectors. Type O–N. Based on Nagaraj, 1988
collector
formula
Example
a- benzoin oxime
CH
Oximes
OH
C
CH
N OH
C
OH
N OH
LIX65N
C9 H1 9
Hydroxyoximes (LIX series)
C
OH
N
OH
8- hydroxyquinoline and derivatives
N
OH
8- hydroxyquinoline (oxine)
Selected chelating collectors. Type S - N
Collector
Based on Nagaraj, 1988
Formula
C S
C SH
C N
(flotagen)
R C N
C SH
N S
C NH
C SH
N
C
S
Mercaptobenzothiazols
Mercaptothiodiazoles
Thiotertrahydroglyoxaline
Mono-and dithiocarbamates
C4H9O
NH
C
N
Phenylthiourea
S
C
N
H
H
C2H5
Apolar collectors
Collector
Hydrocarbons and derivatives
Sulfur compounds
Alcohol and derivatives
Example
fuel oil, naphtha, heptane, benzene, halogen derivatives
of hydrocarbons
dixantogen (R–O–C(=S)–S–)2
formic xanthate R–O–C(=S)–S–C(=O)–O–R´, alkyl
disulfides R–S–S–R
alkylfenyl(polyethoxy) alcohols (Triton, Tergitol, Brij),
alkylphenols, higher alcohols
Collectors
ANIONIC
Alkyl mercaptan
R-S-H
Alkyl dithiocarbonate (xanthate)
R-O-CS-S-Na
Dialkyl disufide (dixanthogen)
R-O-CS-S-S-CS-O-R
Xanthogen formates
R-O-CS-S-CO-O-R’
Dialkyl dithiocarbamate
RR-N-CS-S-Na
Dialkyl dithiophosphate
RO(RO)-PS-S-Na
Carboxylate (fatty acids)
R-CO-O-H
Alkyl sulfate
R-O-SO3H
Alkyl sulfonate
R-SO3H
CATIONIC
Amine
R-NH2, RR-NH, RRR-N
Quaternary Amine
Cl- R+RRR-N
FLOTATION
METHODS
Foam
separation
Minerals
flotation
Flotation with
soluble
collectors
Emulsion
flotation
Froth
flotation
Precipitate
flotation
Agglomerative
flotation
Frothless
separation
Ions
flotation
Carrier
flotation
Methods of flotation
Microorganisms
flotation
gamma flotation
(flotation in water mixed with soluble organic liquid)
1
100
cos
0,75
75
cos
0,5
0,25
50
25
surface tension
of wetting
0
0
0
20
40
60
flotation recovery,  , %

80
surface tension,  wg, mN/m
Typical shape of the cos  = f (surface tension of liquid) relationship also called the Zisman
plot, and flotation of naturally hydrophobic materials


0
Flotation kinetics
Model
Relation
 =  [1 – exp (–k1t)]
Classic first order
Modified first order
 =  {1 – 1/(k2t)[1 – exp (–k2t)]}
 =  [1 – 1/(1 + t/k3)]*
For reactor with ideal mixing
 =  k4t/(1 + k4t)*
Modified for gas–solid adsorption
 = ()2 k5t/(1 +  k5t)
Kinetics of second order
Modified second order
 =  {1 – [ln (1 + k6t)]/(k6t)}
 =  [1– { exp (–k7t) + (1 –  ) exp(–k8t)}
Two rate constants
Distributed rate constants
 =  [1 – exp(–kt) f (k, 0) dk]
* Equivalent models because k3 = 1/k4.
 – flotation recovery after time t,
 – maximum recovery,
 – fraction of particles having lower flotation rate constant, k7,
k – flotation rate constant.
FLOTATION
classification
upgrading
splitting
sorting, etc.
evaluation

analysis

c
me
rm
th
e
o
od
er
th
y
ch nam
an
ic
phy ics s
sics
delineation
P1
Cs
x1
chemistry of flotation
x2
x4
x3
xn
Cp
P2