FLOTATION

1. FLOTATION (Main feature - hydrophobicity)

2. Flotation

3. gas bubble water  particle Contact angle

5. Contact angle of selected materials

6. Methods of measurement

8. There are different models of flotation including mechanistic, thermodynamic and probabilistic models

9. The simplest model of flotation Thermodynamicapproach Gflotation= Gfinal- Ginitial = [sg - (sc+ cg)] A for A = = 1cm2 surface area Gflotation= sg - (sl+ lg) Dupre eq. (1869)

10. 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 isJ/m2

11.  is measured through the aqueous phase The Young Equation sg = sc+ cgcos   - contact angle

12. 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 

13. 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 main feature  „electromagnetic field” of separation (flotation) system

14. More detailed models of flotation Particle and spherical bubble here flotation also depends on  and 

15. other models take into account other parameters such as size of bubble and particle

16. Probabilistic models for instance Schulze (1993) dNp /dt = –k Np. (first order kinetics k = Pc Pa Pstab PtpcZNb c=[2R3p(p+ 1,5)/3]0,5(1,39 – 0,46 ln Rp) i = 3R2FRp/8cbh2crit hcrit = 23,3[ (1 – cos A)]0,16 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 )

18. dN/dt – flotation rate, a – centrifugal acceleration acting on particle-bubble aggregate in a vortex of liquid, Bo´ – Bond’s number, cb – rigidity of bubble surface (cb = 1 for rigid uneven surface, cb < 1 for movable smooth surface), Cb – bubble concentration in pulp (number of bubbles in 1cm3 of pulp), E – efficiency of attachment of particles to bubble surface (number of attached particles divided by the number of particles colliding with considered bubble), E1–energy barrier for adhesion of bubble and particle, Ek – kinetic energy of collision of bubble with particle, Ek´ – kinetic energy of detachment of particle and bubble (calculated from the French–Wilson Eq.), g – acceleration due to gravity, hkryt – critical film thickness on surface of particle, k – rate constant of flotation, Nb – number of bubbles in flotation cell at a considered time, Np – number of particles subjected to flotation at a considered time, Pa – probability of adhesion of particles to a bubble, Pd – probability of detachment of particles from a bubble (Pd = 1 – Pstab), Pstab – probability of stability of particles-bubble aggregate, Ptpc–probability of formation of particle-bubble-water contact, Q – flow of air in flotation machine, m3/s, Rp – particle radius, Rb – bubble radius, Rc – radius of the stream enabling collision of particle with bubble, RF – size of thin film between particle and bubble during collision, Re – Reynolds number, S – cross section area of flotation machine, m2, Sb – area of bubbles leaving flotation cell per time unit and per cross section area ot the cell, V – rate of ascending bubble, m/s, Vb –surface velocity of aeration defined as volume rate of aeration normalized per cross section of the flotation column, U – velocity of particles in relation to velocity of bubble in the pulp, Z – 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, p – particle density,  – contact angle, A – advancing contact angle, v – life time of liquid vortex in flotation cell which destroys the particle–bubble aggregate, tpc – time needed to form permanent three-phase solid-gas-liquid contact, c – collision time of bubble and particle, i – induction time (time of removing liquid film from particle and forming attachment), min – minimal time of contact, = 3.14, * = 180 – /2.

19. Steps of flotation

21. receding qr water advancing qa water q equlilibium flotacja 4

22. sg = sc+ cgcos g cg vapor adsorption liquid drop c scg sg  x x x x x x x x x x x x x x x s s s -  = sc+ cgcos the Young equation

23. FLOTATION depends on hydrophobicity hydrophobicity is measured as contact angle

24. Electrical aspects of flotation naturally hydrophobic

25. 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 • adsorption • chemical potential R gas constant, F Faraday cost. a activity (concentration) • surface charge • surface potential • temperature (d)T = (–idi)T. di = RT d ln ai,

26. FLOTATION main feature field (el.-mag.) Hydrophobicity : contact angle g D q G = (cos –1) q cg ( g g g q (cos = + )/ ) sg sc cg * g g g dg d s / E= – cg, sg, sc G s Y , , s ( Y = f ) G d g /d =–(1/R T ) ln a Potential: electrical E , Chemical ln a (oraz pH, pX, ....) f (activity coeff. electrochemical E h a = f c c c c c c c , , , , bubbles collector frother salt other particles *Young eq. flot

27. Electrical aspects of flotation -+ -+ water moving particle + - + - -+ - + - - + - + + slipping plane zeta potential -+ -+ -+

28. Structure of electrical double layer

29. triple layer Helmholz (flat condenser) Stern (rigid and diffuse layer ) quadruple layer Gouy-Chapman (diffuse layer) Grahame (binding sites) o o o i o i d o i d o o oijd H+ K+ K+H2O OH- A- A-H2O od ----- H+ OH- o id----- H+ OH- o -o H+ OH- oid---- H+ K+ OH- A- Models of electrical double layer 0 =  0  0 Flat condenser Diffuse condenser

30. Formation of electrical double layer surface charge negative positive metals ęć   Me  Me  Me  Me    Me  Me  Me  Me    Me  Me  Me  Me     Me Me   Me -   Me Me    Me  Me   Me  Me   Me  Me   H2O + n Me+ + electrons or  oxides   Me  O  Me  O    O  Me  O  Me    Me  O  Me  O     O  MeO-   Me  OH   O  MeO-    O  MeOH2+   Me  OH   O  MeOH2+  H2O + n H+ + n OH- or salts   Me  X  Me  X    X  Me  X  Me    Me  X  Me  X     Me  X   X -   Me  X    X  Me   Me+   X  Me  H2O + n X- + n Me+ or place of particle breakage particle /water interface

31. lad ½ ½ ½ ½ ½ ¾ ¾ ¾ ¾ ¾ ¾ ¾ ¾ S Me OH Me S Me S ½ ½ ½ ½ ½ H O 2 ¾ ¾ ¾ ¾ ¾ ¾ ¾ Me SH S Me S Me ½ ½ ½ ½ ½ ¾ ¾ ¾ ¾ ¾ ¾ ¾ ¾ S Me OH Me S Me S ½ ½ ½ ½ ½ other ½ ½ + ¾ ¾ ¾ S Me OH ¾ ¾ ¾ S Me OH 2 ½ ½ - + - ¾ ¾ Me S + n OH + H ¾ ¾ Me SH ½ ½ ¾ ¾ ¾ S Me OH + ¾ ¾ ¾ S Me OH ½ 2 ½ Formation of electrical double layer

34. interpretation: preferential adsorption of -OH groups 20 0 -20 D O-ice ( ) (0.0001M) n 2 · diamond ( ) zeta potentia, mV -40 air ( ), ( ) Nocardia sp. w « -60 hexadecane D O-ice (0.001M) 2 -80 2 4 6 8 10 12 pH zeta potential and iep for materials without functional groups

36. Flotation reagents COLLECTORS for hydrophobization FROTHERS for froth creation MODIFIERS for enhancing

37. hydrophobization: with all possible chemical bondings COLLECTORS 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.

38. COLLECTORS

39. CH3CH2CH2CH2 CH2CH2CH2CH2 COO– tail (hydrophobic) head (hydrophilic) Structure of collector CMC 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

40. An example of lack of correlation between CMC and flotation (after Freund and Dobias, 1995). SOS – sodium octyl sulfate, SDS – sodium dodecyl sulfate

41. 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)

42. Maximum contact angle for different collectorswith 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).

43. collector renders the surface hydrophobic gas collector particle

44. 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

45. Which interface is responsible for hydrophobicity increase with collector addition? 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))

46. Flotation is influenced by reagents modifying the interfaces. Collectors strongly change the solid-gas, surfactants water–gas, and electrolytes (pH reagents and salts) solid–water interfaces. The extent of modification is expressed by the height of symbol

47. Flotation vs collector dose

48. Influence of pH and iep on flotation for various collectors

49. Collector as chemicals