1. FLOTATION Lecturer Professor Jan Drzymala, Ph.D., D.Sc., Eng.
Room 358, Geocentrum (L-1)

2. Requirements to pass the Flotation class
presence (above 75%)
positive class tests and asignments
- positive laboratory exercises
- positive final test(s)

3. Literature
class notes
book
papers
selected chapters
(free is nice)

4. Other books

6. Jan Drzymala, Mineral Processing, Oficyna Wydawnicza PWr
Jan Drzymala, Mineral Processing, Oficyna Wydawnicza PWr printed and electronic versions
Library
Internet

7. INTRODUCTION TO FLOTATION
goldorecrusher.com

10. (chem. elements production)
Origin of matter
Big Bang
stars
(chem. elements production)

12. 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

13. 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:''' [ Gallery of

14. Future of Universe

15. Fermions (matter carriers) Bosons (force carriers)
Presently known elementary particles of the universe
Elementary particles
Fermions  (matter carriers)
Bosons  (force carriers)
Leptons
Quarks
Weak
(bosons)
Strong
(gluons)
Electro-magnetic (photon)
Gravity (graviton)
electron neutrino up
W- boson
color 1
E1=h1 *
electron
down
W+ boson
color 2
E2=h2
muon neutrino
charm
Zo boson
color 3
muon
strange
E3=h3
tau neutrino
top
En=hn
tau
bottom
Higgs’
boson**
**Nobel Price 2013, Higgs and Englert
* not yet discovered

16. Elements of matter

17. States of matter and flotation
water
gas bubble
particle
Gas
Liquid
Solid

18. 4 basic states of matter

19. QCD matter, Quark–gluon plasma, Supercritical fluid
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
States of matter (classic)
State
Solid
Liquid
Gas / Vapor
Plasma
Low energy
Bose–Einstein condensate
Fermionic condensate
Degenerate matter
Quantum Hall
Rydberg matter
Strange matter
Superfluid
Supersolid
Photonic matter
High energy
QCD matter
Quark–gluon plasma
Supercritical fluid
Other states
Colloid
Glass
Liquid crystal
Quantum spin liquid
Magnetically ordered
Antiferromagnet
Ferrimagnet
Ferromagnet
String-net liquid
Superglass
Transitions
Boiling
Boiling point
Condensation
Critical line
Critical point
Crystallization
Deposition
Evaporation
Flash evaporation
Freezing
Ionization
Lambda point
Melting
Melting point
Recombination
Regelation
Saturated fluid
Sublimation
Supercooling
Triple point
Vaporization
Vitrification
Quantities
Enthalpy of fusion
Enthalpy of sublimation
Enthalpy of vaporization
Latent heat
Latent internal energy
Trouton's ratio
Volatility
Concepts
Binodal
Compressed fluid
Cooling curve
Equation of state
Leidenfrost effect
Mpemba effect
Order and disorder (physics)
Spinodal
Superconductivity
Superheated vapor
Superheating
Thermo-dielectric effect
Lists
List of states of matter

20. Cycle of processes in the Earth crust

21. Solids
(A.Manecki)

22. Crystalline solids
7 elemental cells

23. 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.

24. Solid chemical compounds occurring in Nature are called minerals
Presently we know about 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

25. Remember
Learn by heart names of 100 most important minerals

26. Copper minerals Silver minerals Gold minerals Lead minerals
native copper Cu
chalcopyrite
CuFeS2
bornite
Cu2S(Fe,Cu)S
covelline
CuS
chalcocite
Cu2S
tetrahedrite
Cu3SbS4-5
energite
Cu3AsS4
cuprite
Cu2O
tenorite
CuO
malachite
Cu2(CO3)(OH)2
azurite
Cu3(CO3)2(OH)2
chrysocolla
CuSiO3nH2O
native silver Ag
electrum
(Au, Ag)
argentite
Ag2S
pyrargyrite
Ag3SbS3
chlorargyrite
AgCl
Gold minerals
native gold Au
sylvanite
AuAgTe4
calaverite
(Au,Ag)Te2
Lead minerals
galena
PbS
cerusite
PbCO3
anglesite
PbSO4
betekhtinite
Pb(Cu, Fe)21S15

27. nickiel-skutterudite (former chloantite)–(Ni,Co)As3-2 nickeline – NiAs
Zinc minerals
Aluminum minerals
sphalerite
ZnS
smithsonite
ZnCO3
willemite
Zn2(SiO4)
franklinite
ZnFe2O4
diaspore
-AlOOH
böhmite
-AlOOH
gibbsite
-Al(OH)3
leucite
K(AlSi2O6)
Nickel minerals
Cobalt minerals
pentlandite – (Fe,Ni)9S8
millerite –-NiS
gersdorffite – NiAsS
nickiel-skutterudite
(former chloantite)–(Ni,Co)As3-2
nickeline – NiAs
annabergite - Ni3(AsO4)2 8H2O
linnaeite – Co3S4
cobaltite –CoAsS
skutterudite –CoAs3
asbolane–m(Co, Ni)OMnO2nH2O
erythrite – Co3[AsO4]2  nH2O

28. 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

29. Native elements
graphite C
diamond C
fullerite C
sulfur S
gold Au
silver Ag
iron Fe
copper Cu
platinium Pt

30. Soluble salts
villiaumite NaF
sylvit KCl
halite NaCl
carnalite KMgCl36H2O
sal ammoniac NH4Cl
bischofite MgCl2H2O
kieserite MgSO4 H2O

31. 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

32. Rock forming minerals
quartz 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]

33. (find their chemical formula )
distene
sylimanite
andalusite
garnets
talc
epidote
antygorite
cristobalite
tridymite
stishovite
coesite
lonsdaleite
ice
rodochrosite
rutile, anatase
Others
(find their chemical formula )

34. WATER
novafiltration.wordpress.com

35. WATER (H2O)14 (H2O)1 (H2O)4 ((H2O)14)20 (H2O)280 H O :
tetrahedral structure of water molecule O- H+
tetrahedral coordination of water molecules
WATER
(H2O)14
(H2O)1
six water molecules on each face, three on each edge, four are inside tetrahedron
(H2O)4
((H2O)14)20
(H2O)280
M.Chaplin, www1.lsbu.ac.uk/water/clusters.html
icosahedral structure

36. (H2O)280 (H2O)1820 ? icosahedron trikontahedron
M.Chaplin, www1.lsbu.ac.uk/water/clusters.html

37. icosahedral water cluster consisting of 280 water molecules has a central puckering dodecahedron
M.Chaplin, www1.lsbu.ac.uk/water/clusters.html

38. 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 
4 all-cis dodecahedra (h) (20,0,0) of which 3 are made up of partial bits (that is,12 quarter-dodecahedra)
M.Chaplin, www1.lsbu.ac.uk/water/clusters.html

39. 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
struktures (h) and (f) have planes with five-fold symmetry – impossible in crystalls. Their elements are 14- molecule forms (czworościany!)
water clasters
M.Chaplin, www1.lsbu.ac.uk/water/clusters.html

40. icosahedron
M.Chaplin, www1.lsbu.ac.uk/water/clusters.html

41. 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

42. theory and measurements
pH and Eh
theory and measurements
broadleyjames.com

43. Dissociation constants of chemical reactions
A2B3 = 2A3+ + 3B2-
Activity = concentration · acticity coefficient
a = c· f or ( ) = [ ] ·f

44. K=1.8·10-16 Electrolytic dissociation of water molecules in water
(real reaction)
2H2O = H3O+ + OH-
hydronic ion
oxonic ion
(simplified form)
H2O = H+ + OH-
hydronic ion
(hydrogen)
hydroxyl ion
proton
Water dissociation constant
K=1.8·10-16
55 kmol/m3

45. pH ionic product for water 1 ·10-14
Kw = Ir = K·[H2O]= [H+][OH-]=1.8·10-16 ·55 = 1 · (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 = neutral solution
pH > alkaline solution
pH < acidic solution

46. Substances dissolved in water
Acids and bases theories
Acids
Bases
Salts
Complex compounds
Nonionic substances
Arrhenius
Brönsted-Lowry
Solvent
Lewis
Usanovitch
Arrheniusa theory
Acids - produce hyrogen ions
Bases – produce hydroxyl ions
HA = H+ + A , MOH = M+ +OH-

47. 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)

48. stanadard Gibbs’ formation potential values
Substance
State
ΔfG°(kJ/mol)
C2H6 g
-32.0
C3H8
-23.4
C6H6
-124.5 l
-129.7
CH4
-50.5 CO
-137.2
CO2
-394.4
H2O
-228.6
-237.1
N2O
-103.7 NO
-87.6
NO2
-51.3

49. https://www. google. pl/search

50. Goreaction = i Gof = Godissociation of water
H2O = H+ + OH-
i positive for products (stoichiometric coefficient for reaction)
Goreaction = i Gof = Godissociation of water
Goreaction = 1Gof, OH- + 1Gof H+ - 1Gof, H2O
From tables
Gof, H+ = 0 kJ/mol
Gof, OH- = kJ/mol
Gof, H2O = 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 =0
log K= log H+ + log OH- - log H2O = -14.0
log H+ = - pH
log OH- = pH
and

51. SOLUBILITY DIAGRAMS = ATIVITY – pH DIAGRAMS
log OH- = pH
H2O = H+ + OH-
log H+ = - pH

52. Gof = from tables in kJ/mol
Possible reactions
Cu2O
tenorite
CuO + 2H+ = Cu2+ + H2O
Goreaction = i Gof
i positive for products, negative for substrates (reaction stoichiometric coefficient)
Gof = from tables in kJ/mol
Go reaction = -RT ln K,
R =8.314 JK-1mol-1
K =….
log Cu2+ = pH

54. pH measurements classical system practical system
IHS Engineering 360)

55. Eo www2.ucdsb.on.ca REDOX half –reaction 2H+ + 2e = H2
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

56. system to measure redox potental of a solution
chromservis.cz
REDOX
burkert.com Eh
calomel reference electrode
contact with measured solution
Pt electrode
system to measure redox potental of a solution

57. Eo normal (standard) potential – difference between an electrode working under standard conditions and normal hydrogen electrode
For chemical elements
Reduction ability
Oxidation ability
Eo (in volts, V)

58. Standard potentials of selected redox reactions

59. Calculation of redox potential
The Nernst equation
absolute temperature
activity of oxidized form
gas constant
electrode potential
activity of reduced form
standard potential
Faraday constant
number of electrones exchanged
Cell potential
(electromotoric force):
Ecell = Eright - Eleft

60. , , the Nernst equation derivation for reaction
oxidized form (o) + electron (e) = reduced form (r) , ,
for reactions involving H+ - see futher on

61. Eh-pH (the Pourbaix diagrams)

62. Eh–pH diagram for Cu–H2O system at 25 °C (298 K)
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 – pH); Cu = Cu2+ + 2e (E = lg [Cu2+]); Cu2O + 2H+ = 2Cu2+ + H2O + 2e (E = ,0591 pH + 0,0591 lg [Cu2+]); Cu2+ + H2O = CuO + 2H+ (pH = 3,44 – 0,5 lg [Cu2+]) (Łętowski, 1975)

63. Eh-pH DIAGRAMS CALCULATIONS
Write reaction (always electrons on your left hand side)
WATER STABILITY REGION
H2O activity =1
2H O2 +2e = H2O
Half reaction
Equlibrium constant
DGof Gibbs potential of a species formation (available in tables)
DGo of reaction
Go = i Gof
DGof values
Gof, H+ = 0 kJ/mol
Gof, O2 = 0 kJ/mol
Gof, H2O = kJ/mol
Gof, e = 0 kJ/mol
Go = kJ/mol
DGo of reaction

64. Eo = -(-237200 )J mol-1/(2·96484.56 Cmol-1) = 1.229 V
Eo value
Eo = -( )J mol-1/(2· Cmol-1) = V
2H O2 +2e = H2O
Nernst’s eq.
Eh-pH relation:
Eh = log PO2 – pH
In comparison to hydrogen electrode which E= 0 V

65. water stability region
for hydrogen
2H+ + 2e = H2
Go = 0 kJ/mol, Eo = 0
E = log PH2 – pH
hydrogen line
Eh = log PO2 – pH
oxygen line
water stability region
(between lines for H2 and O2) usually for pressure PH2 and PO2 pressure = 0.1 MPa

66. 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

67. Surface tension
jeffgreenhouse.com

68. 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) (density 0.14 g/cm3 at 3 K)
water
ice
quartz
mercury
diamond ~ 4000

70. 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

71. methyl isobutyl carbinol (MIBC) surface tension vs concentration
b) surfactants
methyl isobutyl carbinol (MIBC) surface tension vs concentration
CMC = critical micelle concentration, CCC = critical coalescence concentration

72. BUBBLES

73. Bubbles formation methods used in flotation
1. Capillaries
d-bubble size, g-gravity, a-capillary size, -density, γ-surface tension
2. Mechanical desintegration

74. Mechanical desintegration
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

75. bubbles can also be produced by:
-applying vacuum to water
-dissolving air into pressurized water an then releasing the pressure

76. bubble size depends on surfactant concentration
MIBC=methyloizobutylcarbinol
characteristic parameter
CCC – critical coalescence concentration

77. 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): DOI: /j.jcis