FLOTATION
water
gas bubble
intergroth
hydrophobic particle
Lecturer
hydrophilic particle
płonna (hydrofilna)
Professor Jan Drzymala, Ph.D., D.Sc., Eng.
Room 358, Geocentrum (L-1)
jan.drzymala@pwr.wroc.pl
Requirements to pass the Flotation class
- presence (above 75%)
- positive class tests and asignments
- positive laboratory exercises
- positive final test(s)
Literature
class notes
book
papers
selected chapters
http://www.dbc.wroc.pl/dlibra/doc
metadata?id=2070&from=&dirids=
1&ver_id=&lp=11&QI=
(free is nice)
Other books
Jan Drzymala, Mineral Processing, Oficyna Wydawnicza PWr. 2007
printed and electronic versions
Library
Internet
http://www.dbc.wroc.pl/dlibra/docmetadata?id=2070&from=&dir
ids=1&ver_id=&lp=11&QI=
INTRODUCTION TO FLOTATION
goldorecrusher.com
mining raw
materials
post-mining
raw materials
secondary raw
materials
EXTRACTIVE METALLURGY
metallurgy
chemical
industry
construction
materials
wastes
EXTRACTIVE METALLURGY
MINERAL PROCESSING
METALLURGY
(separations without chemical changes)(separations with chemical changes)
feed
grinding
screening
flotation & other
tailing
concentrate
ind othe
us r
tri
es
smelting
leaching
electrolysis
tailing
metal
Origin of matter
1s
1 bln ys
3 min 0.3 mln ys
–43
10
s
elemental
particles &
radiation
nucleus
(H, D,
He, (Li)
protons
neutrons
atoms
H, D,
He, (Li)
32
10 K
15 bln ys
larger
atoms
present
Universe
chemical
compounds
10
10 K
Big Bang
w
9
10 K
6000 K
18 K
3K
p r 6
stars
(chem. elements production)
Jacopo Tintoretto's "The Origin of the Milky Way"
In Greek myth, the Milky Way was caused by milk spilt by Hera when suckled by Heracles
Wikipedia
The galactic center harbors a
compact object of very large mass
(named Sagittarius A*), strongly
suspected to be a supermassive
black hole. Most galaxies are
believed to have a supermassive
black hole at their center.
'''Description:''' A Black Hole of ten solar masses as
seen from a distance of 600km with the Milky Way
in the background (horizontal camera opening angle:
90°) '''Source:''' [http://www.tempolimitlichtgeschwindigkeit.de/galerie/galerie.html Gallery
of
https://commons.wikimedia.org/wi
ki/File:Black_Hole_Milkyway.jpg
Future of Universe
Presently known elementary particles of the universe
Elementary particles
Fermions (matter
carriers)
Bosons (force carriers)
Strong
(gluons)
Electromagnetic
(photon)
color 1
E1=h1
Leptons
Quarks
Weak
(bosons)
electron
neutrino
up
W- boson
electron
down
W+ boson
muon
neutrino
charm
Zo boson
muon
strange
E3=h3
tau
neutrino
top
En=hn
tau
bottom
* not yet discovered
color 2
E2=h2
color 3
E2=h2
Gravity
(graviton)
*
Higgs’
boson**
**Nobel Price 2013, Higgs and Englert
Elements of matter
grain
upper quark
gluon
molecule
lower quark
atom
nucleus
proton
neutron
electron
States of matter and flotation
gas bubble
water
particle
Gas
Liquid
Solid
4 basic states of matter
http://en.wikipedia.org/wiki/State_of_matter
Other states of matter
Bose–Einstein condensate, Fermionic condensate,
Degenerate matter, Quantum Hall, Rydberg matter,
Strange matter, Superfluid, Supersolid, Photonic matter
QCD matter, Quark–gluon plasma, Supercritical fluid
Colloid, Glass, Liquid crystal, Quantum spin liquid,
Magnetically ordered, Antiferromagnet, Ferrimagnet,
Ferromagnet, String-net liquid, Superglass
Soft matter
transpor- sed
i
tation tati menon
met
am
pho orsis
dia s
esi
gen
post-magmatic
processes wea
ing ther
-
Cycle of processes in the Earth crust
ma
pro gm
thce atic
a
n
ss
es palino- a xis
genesis e
juvenile
flux
Solids
(A.Manecki)
Crystalline solids
System
1
Elemental cell (lattice)
2
1. Regular (C )
7 elemental cells
a=b=c
 =  =  = 90o
2. Tetragonal (Q)
a=bc
 =  =  = 90o
3. Rombic (O)
abc
 =  =  = 90o
4. Hexagonal (H)
a=bc
 =  = 90o,  = 120o
5. Trigonal (T )
(romboedric)
Minerals
3
halite (NaCl)
galena (PbS)
fluorite (CaF2)
sphalerite (ZnS)
rutile (TiO2)
zyrkon (ZrSiO4)
hausmanite
(Mn3O4)
cassiterite (SnO2)
sulfur (S)
barite (BaSO4)
stibnite (Sb2S3)
anhydrite (CaSO4)
graphite (C)
wurzite (ZnS)
corundum (Al2O3)
covellite (CuS)
-quartz (SiO2)
 =  =   90o
calcite (CaCO3)
dolomite
(MgCa(CO3)2)
hematite (Fe3O4)
abc
 =  = 90o,   120o
arsenopyrite (FeSAs)
gipsum (CaSO4
·2H2O)
kriolite (Na3AlF6)
diopside (CaMgSi2O6)
abc
albite (NaAlSi3O8)
microcline (KAl-
a=b=c
6. Monoclinic
(M)
7.Triclinic (A)
A description of the inner structure of crystals makes use of 7
crystallographic systems containing 32 elements of symmetry
combined with 14 translation lattices. The combination of 32
classes of symmetry and 14 translation lattices makes 230 space
groups.
particular crystal must belong to one of the 230 space groups
To distinguish between space groups there are used two different,
international and the Schoenflies, notations. For example, the
symbol of NaCl lattice in the international system is Fm3n while
in the Schoenflies system is O5h.
Solid chemical compounds occurring in Nature are called
minerals
Presently we know about
4 000
minerals
It is recommended to use names endorsed by the Committee on Names
of Minerals and New Minerals of the International Mineralogical
Association
ice is a mineral
water is not a mineral
Remember
Learn by heart names of
100 most important
minerals
Copper minerals
native copper
Cu
Silver minerals
native silver
Ag
electrum
(Au, Ag)
argentite
Ag2S
pyrargyrite
Ag3SbS3
chlorargyrite
AgCl
chalcopyrite
CuFeS2
bornite
Cu2S(Fe,Cu)S
covelline
CuS
chalcocite
Cu2S
tetrahedrite
Cu3SbS4-5
energite
Cu3AsS4
cuprite
Cu2O
tenorite
CuO
native gold
Au
malachite
Cu2(CO3)(OH)2
sylvanite
AuAgTe4
azurite
Cu3(CO3)2(OH)2
calaverite
(Au,Ag)Te2
chrysocolla
CuSiO3nH2O
Gold minerals
Lead minerals
galena
PbS
cerusite
PbCO3
anglesite
PbSO4
betekhtinite
Pb(Cu, Fe)21S15
Zinc minerals
Aluminum minerals
sphalerite
ZnS
diaspore
-AlOOH
smithsonite
ZnCO3
böhmite
-AlOOH
willemite
Zn2(SiO4)
gibbsite
-Al(OH)3
franklinite
ZnFe2O4
leucite
K(AlSi2O6)
Nickel minerals
pentlandite – (Fe,Ni)9S8
millerite –-NiS
gersdorffite – NiAsS
Cobalt minerals
linnaeite – Co3S4
cobaltite –CoAsS
skutterudite –CoAs3
nickiel-skutterudite
asbolane–m(Co, Ni)OMnO2nH2O
(former chloantite)–(Ni,Co)As3-2
erythrite – Co3[AsO4]2  nH2O
nickeline – NiAs
annabergite - Ni3(AsO4)2 8H2O
Iron minerals
magnetite
Fe3O4
hematite
Fe2O3
goethite
-FeOOH
siderite
FeCO3
chamosite
(Fe2+, Mg,Fe3+)5Al[(O,OH)8|AlSi3O10]
native iron
Fe
pyrite
FeS2
markasite (rhom.) FeS2
pirrhotite
FeS
ilmenite
FeTiO3
Native elements
graphite
C
diamond
C
fullerite
C
sulfur
S
gold
Au
silver
Ag
iron
Fe
copper
Cu
platinium
Pt
Soluble salts
villiaumite
NaF
sylvit
KCl
halite
NaCl
carnalite
KMgCl36H2O
sal ammoniac
NH4Cl
bischofite
MgCl2H2O
kieserite
MgSO4 H2O
Sparingly soluble salts
fluorite
CaF2
cryolite
Na3[AlF6]
barite
BaSO4
anhydrite
CaSO4
gypsum
CaSO4 2 H2O
celestine
SrSO4
calcite
CaCO3
dolomite
CaMg (CO3)2
magnesite
MgCO3
quartz
Rock forming minerals
SiO2
opal
SiO2 H2O
orthoclase (monoclinic)
K[AlSi3O8]
microcline (triclinic)
K[AlSi3O8]
albite
Na[AlSi3O8]
anorthite
Ca[Al2Si2O8]
muskovite
K(Al)2(OH)2[AlSi3O10]
biotite
K(Mg,Fe)3(OH)2[AlSi3O10]
olivines
(Mg,Fe)2 [SiO4]
kaolinite
Al4(OH)8[Si4O10]
illite
K(Mg,Fe)3(OH)2[AlSi3O10]
augite
(Ca, Mg, Fe+2, Fe+3, Ti, Al)2[(Si, Al)2O6]
distene
sylimanite
andalusite
garnets
talc
epidote
antygorite
cristobalite
tridymite
stishovite
coesite
lonsdaleite
ice
rodochrosite
rutile, anatase
Others
(find their chemical formula )
WATER
novafiltration.wordpress.com
WATER
(H2O)14
H
(H2O)1
O
H
:
tetrahedral structure of water molecule
(H2O)4
H+ H+
O-
six water molecules on each face, three on each edge, four are
inside tetrahedron
((H2O)14)20
H+
O- H+
O- H+
H+
O- H+
H+
(H2O)280
tetrahedral coordination of water molecules
M.Chaplin, www1.lsbu.ac.uk/water/clusters.html
icosahedral structure
(H2O)280
(H2O)1820
?
icosahedron
trikontahedron
M.Chaplin, www1.lsbu.ac.uk/water/clusters.html
icosahedral water cluster consisting of 280 water molecules has a central puckering dodecahedron
M.Chaplin, www1.lsbu.ac.uk/water/clusters.html
In one 280-molecule water cluster (ES) there are:
80 complete all-gauche chair-form hexamers (a)
(0,3,3), f
360 all-gauche boat-form hexamers (b) (67% 2,2,2
and 33% 0,2,4) of which 90 are made up of partial
bits,
72 all-cis pentamers (c) (5,0,0) of which 36 are
made up of partial bits,
20 all-gauche ten-molecule tetrahedra (d) (0,4,6),
40 all-gauche hexameric boxes (e) (0,6,6) of which
10 are made up of partial bits,
120 all-gauche eight-molecule structures (f) (2,2,4)
of which 30 are made up of partial bits,
48 cis- and gauche-bonded pentameric boxes (g)
(5,5,5) of which 24 are made up of partial bits,
and
M.Chaplin, www1.lsbu.ac.uk/water/clusters.html
4 all-cis dodecahedra (h) (20,0,0) of which 3 are
made up of partial bits (that is,12 quarterdodecahedra)
ES (expanded) structures
Figs a, d, f and h
CS (collapsed) structures
Figs b, c, e, g and i
10-molecule complex (a) after
collapse forms (b) and (c) Those
three structures play the most
imortant role in equlibrium:
ES <-> CS.
20 –molecule dodecahedron (f) is the
central fragment of icosaheral
claster of 280 water molecules
water clasters
struktures (h) and (f) have planes
with five-fold symmetry – impossible
in crystalls. Their elements are 14molecule forms (czworościany!)
M.Chaplin, www1.lsbu.ac.uk/water/clusters.html
icosahedron
M.Chaplin, www1.lsbu.ac.uk/water/clusters.html
CO2 with 18 water
molecules forming
hydration layer
(dodecahedron)
as central part of CO2
(H2O)278 cluster
Note not central location of CO2 (two water molecules form
three, not four, hydrogen bounds)
M.Chaplin, www1.lsbu.ac.uk/water/clusters.html
pH and Eh
theory and measurements
broadleyjames.com
Dissociation constants of chemical reactions
A2B3 = 2A3+ + 3B22
 3   2 - 
A  B 

 

K
A 2 B3 
3
Activity = concentration · acticity coefficient
a = c· f
or ( ) = [ ] ·f
Electrolytic dissociation of water molecules in water
(real reaction)
2H2O = H3O+ + OH-
hydronic ion
oxonic ion
(simplified form)
H2O = H+ + OH-
hydronic ion
(hydrogen)
proton
hydroxyl ion
Water dissociation constant

H  OH 
K


H 2O
K=1.8·10-16
55 kmol/m3
pH
Kw = Ir = K·[H2O]= [H+][OH-]=1.8·10-16 ·55 = 1 ·10-14 (298 kelwin)
ionic product for water 1 ·10-14
- log [H+] - log [OH-] = 14
pH = - log [H+]
pOH = - log [OH-]
pH + pOH = 14
For pure water [H+] = [OH-] = 1 ·10-7
pH = 7
neutral solution
pH > 7
alkaline solution
pH < 7
acidic solution
Substances dissolved in water
Acids
Bases
Salts
Complex compounds
Nonionic substances
Acids and bases theories
Arrhenius
Brönsted-Lowry
Solvent
Lewis
Usanovitch
Arrheniusa theory
Acids - produce hyrogen ions
Bases – produce hydroxyl ions
HA = H+ + A-
,
MOH = M+ +OH-
pH calculations
M = kmol/m3
calculate pH for:
0.001 M HCl
0.001 M H2SO4
2 M HCl
0.001 M NaOH
0.001 M Ca(OH)2
2M KOH
(we assume that activity coefficient is 1)
stanadard Gibbs’ formation potential values
Substance
State
ΔfG°(kJ/mol)
C2H6
g
-32.0
C3H8
g
-23.4
C6H6
g
-124.5
C6H6
l
-129.7
CH4
g
-50.5
CO
g
-137.2
CO2
g
-394.4
H2O
g
-228.6
H2O
l
-237.1
N2O
g
-103.7
NO
g
-87.6
NO2
g
-51.3
https://www.google.pl/search?q=standard+gibbs+free+energ
y+table&sa=X&biw=1360&bih=634&tbm=isch&imgil=94b
XvF2mQpgpM%253A%253BO_EcbVKScPAE_M%253Bht
tps%25253A%25252F%25252Fwww.safaribooksonline.com
%25252Flibrary%25252Fview%25252Ffundamentals-ofchemical%25252F9780132693158%25252Fapp03.html&so
urce=iu&pf=m&fir=94bXvF2mQpgpM%253A%252CO_EcbVKScPAE_M%252C_
&usg=__GFvy73Dw90nheKoiiqw7YpWRny8%3D&ved=0
ahUKEwiUl73m2tHJAhXJVRQKHYSqCGYQyjcIJw&ei=z
6dpVtTzA8mrUYTVorAG#imgdii=94bXvF2mQpgpM%3A%3B94bXvF2mQpgpM%3A%3BKhCfPJLo4zlLM%3A&imgrc=94bXvF2mQpgpM%3A&usg=__GFvy73Dw90nheKoiiqw7Yp
WRny8%3D
i positive for products
H2O = H+ + OH-
Goreaction
(stoichiometric coefficient
= i Gof = Godissociation of water for reaction)
Goreaction = 1Gof, OH- + 1Gof H+ - 1Gof, H2O
From tables
Gof, H+ = 0 kJ/mol Gof, OH- = -157.3 kJ/mol
Gof, H2O = -237.2 kJ/mol
Gof, reaction = 79.9 kJ/mol
Go reaction = -RT ln K, log K = -Gr/5.708, log K = -79.9/5.708 = -14.0

H  OH 
K


H 2O
log OH- = -14.0 + pH
log K= log
and
H+
+ log
OH-
log H+ = - pH
=0
- log H2O = -14.0
SOLUBILITY DIAGRAMS = ATIVITY – pH DIAGRAMS
log OH- = -14.0 + pH
H2O = H+ + OH-
= - pH
0
H2O
-2
H+
-4
log C, kmol/m3
log
H+
OH-
-6
-8
-10
-12
-14
0
2
4
6
8
pH
10
12
14
Possible reactions
Cu2O tenorite
Goreaction = i Gof
CuO + 2H+ = Cu2+ + H2O
0
i positive for products, negative
R =8.314 JK-1mol-1
K =….
H+
-4
log C, kmol/m3
Go reaction = -RT ln K,
OH-
-6
-8
-10
-12
-14
0
log Cu2+ = 7.74 - 2pH
CuO - H2O
-2
for substrates (reaction
stoichiometric coefficient)
Gof = from tables in kJ/mol
Cu++
2
4
6
8
pH
10
12
14
0
0
Cu++
-2
-2
OH-
-6
-8
-10
CuOH+
-12
-14
4
6
-6
Cu(OH)3-8
-10
CuOH+
8
10
12
CuO - H2O
-14
14
0
pH
2
4
6
8
pH
0
Cu++
CuO - H2O
-2
H+
-4
log C, kmol/m3
2
OH-
-12
CuO - H2O
0
H+
-4
log C, kmol/m3
H+
-4
log C, kmol/m3
Cu++
OHCu(OH)3-
-6
-8
Cu(OH)2 aq
-10
CuOH+
-12
-14
0
2
4
6
8
pH
10
12
14
10
12
14
pH measurements
classical system
http://www.globalspec.com/learnmore/sensors_transducers_d
etectors/analytical_sensors/oxidation_reduction_potential_or
p_instruments
IHS Engineering 360)
practical system
https://www.google.pl/search?q=ph+measurement+device&source=lnms&tbm=isch
&sa=X&ved=0ahUKEwiR9q3e0tHJAhWEbxQKHQskBB4Q_AUIBygB&biw=1360
&bih=634#imgrc=Z9-0kJMk9oW37M%3A
REDOX
www2.ucdsb.on.ca
Eo
for reaction Zn2+ + 2e = Zn
under standard conditions
1 kmol/m3 Zn2+
half –reaction 2H+ + 2e = H2
half –reaction Zn2+ + 2e = Zn
system to measure redox potental of a Zn electrode in Zn2+ 1mol/m3 solution
against hydrogen electrode
chromservis.cz
REDOX
burkert.com
Eh
calomel reference electrode
contact with measured solution
Pt electrode
system to measure redox potental of a solution
Eo normal (standard) potential – difference between an
electrode working under standard conditions and normal
hydrogen electrode
For chemical elements
Eo
Reaction
Eo
Reaction
Li+/Li
-3.045
Ni2+/Ni
-0.236
K+/K
-2.925
Pb2+/Pb
-0.126
Ca2+/Ca
-2.840
H+/H
0
Na+/Na
-2.714
Cu2+/Cu
0.345
Mg+/Mg
-2.380
I2/I-
0.536
Al+3/Al
-1.662
Ag+/Ag
0.799
Zn2+/Zn
-0.763
O2/O2-
1.228
S/S2-
-0.510
Cl2/Cl-
1.359
Fe2+/Fe
-0.440
Au+/Au
1.692
Eo (in volts, V)
Standard potentials of selected redox reactions
Reaction
Abbreviated form
2
S2O82  + 2e = 2 SO 4
S2O82  / SO 24 
ClO– + 2H+ + 2e = Cl– + H2O
ClO–/Cl–
MnO4 + 8H+ +5e = Mn2+ + 12H2O
MnO4 /Mn2+
Cl2 +2e = 2Cl–
O2 + 4H+ + 4e = 2H2O
Fe3+ + e = Fe2+
O2 + 2e + 2H+ = H2O2
(CN)2 + 2H+ + 2e = 2HCN
Cl2/2Cl–
O2/O2–
Fe3+/Fe2+
O2/H2O2
(CN)2/HCN
Fe(CN)36 + e = Fe(CN)64 
Fe(CN)36 / Fe(CN)64 
Cu2+ + e = Cu+
2H+ + 2e = H2
Cu2+/Cu+
H+/H2
SO 24  + 2H+ + 2e = SO 32  + H2O
SO 24  / SO 32 
N2 + 4H+ + 4e = N2H4 (hydrazine)
S + 2e = S2–
Zn2+ + 2e = Zn
N2 /N2–
S/S2–
Zn2+/Zn
Normal potential
Eo(V)
2.050
1.640
1.510
1.360
1.228
0.771
0.680
0.370
0.363
0.167
0.000
–0.103
–0.333
–0.510
–0.763
Calculation of redox potential
The Nernst equation
absolute temperature
activity of oxidized form
gas constant
electrode potential
Eh  E 0 
standard potential
RT o
ln
nF r 
activity of reduced form
Faraday constant
number of electrones exchanged
Cell potential
(electromotoric force):
Ecell = Eright - Eleft
the Nernst equation derivation for reaction
oxidized form (o) + electron (e) = reduced form (r)

r
K
,
o e
 G
0

r
 RT ln
o e ,

r
RT ln K  RT ln
o e

 G 0 RT
r

ln
nF
nF o e

RT
r
RT o RT
RT o
E 
ln

ln

ln e  
ln
E
nF o e
nF r  nF
nF r 
0
RT o
EE 
ln
nF r 
0
for reactions involving
H+ - see futher on
Eh-pH (the Pourbaix diagrams)
Eh
http://en.wikipedia.org/wiki/Pourbaix_diagram
2-
10
HCuO , CuO 2
Cu 2+
0.8
CuO
10
0.4
-
0.6
0
2
Eh potential, V
10 -6
1
10
-4
10
10
0
-2
1.2
-6
1.4
0.2
10
0
-2
10
-4
10
Cu 2O
-6
-0.2
-0.4
Cu
-0.6
-0.8
-1
0
2
4
6
8
pH
10
12
14
Eh–pH diagram for Cu–H2O system at 25 °C (298 K). Diagram is based on
reactions: Cu2O + H2O = 2CuO + 2H+ + 2e (E = 0,747 – 0,0591 pH); 2Cu + H2O =
Cu2O + 2H+ + 2e (E = 0,471 – 0.0591 pH); Cu = Cu2+ + 2e (E = 0.337 + 0.0295
lg [Cu2+]); Cu2O + 2H+ = 2Cu2+ + H2O + 2e (E = 0.203 + 0,0591 pH + 0,0591
lg [Cu2+]); Cu2+ + H2O = CuO + 2H+ (pH = 3,44 – 0,5 lg [Cu2+]) (Łętowski, 1975)
Eh-pH DIAGRAMS CALCULATIONS
Write reaction (always electrons on your left hand side)
WATER STABILITY REGION
H2O activity =1
Half reaction
Equlibrium constant
Go of reaction
Gof values
2H+ + 0.5O2 +2e = H2O
K
O2 
H 2O
0.5
H  e
 2
2
Go = i Gof
Gof Gibbs potential
of a species formation
(available in tables)
Gof, H+ = 0 kJ/mol Gof, O2 = 0 kJ/mol Gof, H2O = -237.2 kJ/mol
Go of reaction
Go = -237.2 kJ/mol
Gof, e = 0 kJ/mol
G
Eo value
o
 nFE
o
Eo  
G o
nF
Eo = -(-237200 )J mol-1/(2·96484.56 Cmol-1) = 1.229 V
Nernst’s eq.
Eh  E 0 
RT
ln(1 / K )
nF
2H+ + 0.5O2 +2e = H2O
2.303 RT
Eh  1.229 
(log[ H  ]2  log( PO2 ) 0.5 ), V
nF
Eh-pH relation:
2.303 RT
nF

0.0591
[V ]
n
Eh = 1.229 + 0.0148 log PO2 – 0.0591 pH
In comparison to
hydrogen electrode
which E= 0 V
for hydrogen
2H+ + 2e = H2
Go = 0 kJ/mol, Eo = 0
E = -0.0591 log PH2 – 0.0591 pH
Eh = 1.229 + 0.0148 log PO2 – 0.0591 pH
water stability
region
(between lines
for H2 and O2)
usually for
pressure PH2 and
PO2 pressure =
0.1 MPa
hydrogen line
oxygen line
Potential redox calculations
broadleyjames.com
calculate redox potential Eh for redox reaction given in the
previous tables and insert it to the Eh-pH diagram
Surface tension
jeffgreenhouse.com
Surface and interfacial phenomena
Surface forming molecules are more strongly
attracted by their own phase than by the
surrounding phase
Surface tension of selected substances (mN/m)
hellium (liquid -270oC)
0.24
water
72.8
ice
90-120
quartz
120
mercury
484
diamond
~ 4000
(density 0.14 g/cm3 at 3 K)
Interfacial (capillary) phenomena
plants
surface
tension
drops
capillary raise
spreading
juice
meniscus
liquid
bubble
walking on
water
flotation
cooking
Surface tension of aqueous solutions
a) salts, acids, bases
Surface tension as a function of activity for selected electrolytes at 25oC.
Drzymala and Lyklema, 2012
b) surfactants
80
surface tenion, mN/m
Aston et al., 1983
MIBC
60
40
20
Laskowski, 2004
CCC
CMC
0
0.1
1
10
100
frother concentration, mmol/dm 3
1000
methyl isobutyl carbinol (MIBC) surface tension vs concentration
CMC = critical micelle concentration, CCC = critical coalescence
concentration
BUBBLES
http://www.superbwallpapers.com/abstract/bubbles-20111/
Bubbles formation methods used in flotation
1. Capillaries
dp  3
6a wg
g ( c   g )
d-bubble size, g-gravity, a-capillary size, density, γ-surface tension
2. Mechanical desintegration
Mechanical desintegration

_
  lg  0.4
d B ,max  We 
  D
  
0.6
0.6
c
dB, max= bubble diameter in a two phase system produced mechanically
We = Weber number (1 may be inserted for critical Weber number in a water –air system)
 =surface tension of solution
 = fluid density
D = dissipation in the dispersion zone around the impeller ( =P/m)
_

= average dissipation energy=P/m
P = power input
m = mass
(fluid's inertia compared to its surface tension)
v = fluid velocity
l = characteristic length, typically the droplet diameter
bubbles can also be produced by:
-applying vacuum to water
-dissolving air into pressurized water an then
releasing the pressure
bubble size depends on surfactant concentration
2
Tucker et al., 1994
bubble size, mm
1.6
MIBC
MIBC=methyloizobutylcarbinol
1.2
0.8
0.4
Laskowski, 2004
CCC
0
0
4
8
12
16
surfactant concentration, ppm
characteristic parameter
CCC – critical coalescence concentration
20
zeta potential of bubble
(the issue of zeta potentail of bubble will be disscussed later)
A novel method of measuring electrophoretic mobility of gas bubbles Aref Seyyed Najafi · Jaroslaw
Drelich · Anthony Yeung · Zhenghe Xu · Jacob Masliyah · Journal of Colloid and Interface Science 05/2007;
308(2):344-50. DOI:10.1016/j.jcis.2007.01.014