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FLOTATION Lecturer Professor Jan Drzymala, Ph.D., D.Sc., Eng.
Room 358, Geocentrum (L-1)
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Requirements to pass the Flotation class
presence (above 75%) positive class tests and asignments - positive laboratory exercises - positive final test(s)
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Literature class notes book papers selected chapters (free is nice)
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Other books
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Jan Drzymala, Mineral Processing, Oficyna Wydawnicza PWr
Jan Drzymala, Mineral Processing, Oficyna Wydawnicza PWr printed and electronic versions Library Internet
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INTRODUCTION TO FLOTATION
goldorecrusher.com
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(chem. elements production)
Origin of matter Big Bang stars (chem. elements production)
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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
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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
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Future of Universe
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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=h1 * electron down W+ boson color 2 E2=h2 muon neutrino charm Zo boson color 3 muon strange E3=h3 tau neutrino top En=hn tau bottom Higgs’ boson** **Nobel Price 2013, Higgs and Englert * not yet discovered
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Elements of matter
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States of matter and flotation
water gas bubble particle Gas Liquid Solid
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4 basic states of matter
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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
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Cycle of processes in the Earth crust
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Solids (A.Manecki)
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Crystalline solids 7 elemental cells
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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.
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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
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Remember Learn by heart names of 100 most important minerals
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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 CuSiO3nH2O 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
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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)OMnO2nH2O erythrite – Co3[AsO4]2 nH2O
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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
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Native elements graphite C diamond C fullerite C sulfur S gold Au silver Ag iron Fe copper Cu platinium Pt
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Soluble salts villiaumite NaF sylvit KCl halite NaCl carnalite KMgCl36H2O sal ammoniac NH4Cl bischofite MgCl2H2O kieserite MgSO4 H2O
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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
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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]
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(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 )
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WATER novafiltration.wordpress.com
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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
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(H2O)280 (H2O)1820 ? icosahedron trikontahedron
M.Chaplin, www1.lsbu.ac.uk/water/clusters.html
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icosahedral water cluster consisting of 280 water molecules has a central puckering dodecahedron
M.Chaplin, www1.lsbu.ac.uk/water/clusters.html
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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
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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
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icosahedron M.Chaplin, www1.lsbu.ac.uk/water/clusters.html
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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
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theory and measurements
pH and Eh theory and measurements broadleyjames.com
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Dissociation constants of chemical reactions
A2B3 = 2A3+ + 3B2- Activity = concentration · acticity coefficient a = c· f or ( ) = [ ] ·f
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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
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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
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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-
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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)
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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
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https://www. google. pl/search
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Goreaction = i Gof = Godissociation of water
H2O = H+ + OH- i positive for products (stoichiometric coefficient for reaction) Goreaction = i Gof = Godissociation of water Goreaction = 1Gof, OH- + 1Gof H+ - 1Gof, 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
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SOLUBILITY DIAGRAMS = ATIVITY – pH DIAGRAMS
log OH- = pH H2O = H+ + OH- log H+ = - pH
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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
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pH measurements classical system practical system
IHS Engineering 360)
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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
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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
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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)
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Standard potentials of selected redox reactions
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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
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, , the Nernst equation derivation for reaction
oxidized form (o) + electron (e) = reduced form (r) , , for reactions involving H+ - see futher on
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Eh-pH (the Pourbaix diagrams)
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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)
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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
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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
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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
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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
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Surface tension jeffgreenhouse.com
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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
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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
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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
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BUBBLES
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Bubbles formation methods used in flotation
1. Capillaries d-bubble size, g-gravity, a-capillary size, -density, γ-surface tension 2. Mechanical desintegration
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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
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bubbles can also be produced by:
-applying vacuum to water -dissolving air into pressurized water an then releasing the pressure
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bubble size depends on surfactant concentration
MIBC=methyloizobutylcarbinol characteristic parameter CCC – critical coalescence concentration
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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
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