1. FLOTATION KINETICS A flotation model is similar to chemical kinetics
dN/dt =-k1 N1a- k2 N2b
N - species (1 and 2) concentration
t- time
k - rate constant(s)
a, b – process order
-negative sign indicates that the concentration is diminishing due to the loss
of particles being floated.
-exponents a and b signify the order of the process
Since flotation seems to depend only on particles concentration
dN/dt =-k1 N1a

2. Flotation kinetics models
Relation
Classic first order
 =  [1 – exp (–k1t)]
Modified first order
 =  {1 – 1/(k2t)[1 – exp (–k2t)]}
For reactor with ideal mixing
 =  [1 – 1/(1 + t/k3)]*
Modified for gas–solid adsorption
 =  k4t/(1 + k4t)*
Kinetics of second order
 = ()2 k5t/(1 +  k5t)
Modified second order
 =  {1 – [ln (1 + k6t)]/(k6t)}
Two rate constants
 =  [1– { exp (–k7t) + (1 –  ) exp(–k8t)}
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.

3. more
A. Bakalarz, J. Drzymala, 2013, Interrelation of the Fuerstenau upgrading curve parameters with kinetics of separation, Physicochemical Problem of Mineral Processing, 49(2),

4. product (yield vs time)
Flotation kinetics of the whole mass and components
product (yield vs time)
components (recovery vs time)
Flotation results plotted as a relationship between recovery of each component in concentrate and separation time (a), yield of components forming concentrate vs. separation time (b)
A. Bakalarz, J. Drzymala, 2013, Interrelation of the Fuerstenau upgrading curve parameters with kinetics of separation, Physicochemical Problem of Mineral Processing, 49(2),

5. relation between flotation kinetics and upgrading curves
The kinetics of separation of feed components (a) provide separation results in the form of the Fuerstenau upgrading curve (b).
A. Bakalarz, J. Drzymala, 2013, Interrelation of the Fuerstenau upgrading curve parameters with kinetics of separation, Physicochemical Problem of Mineral Processing, 49(2),

6. ugrading curves (here Fuerstenau’s) equations based on kinetics of flotation4 7 9 13
c,1 recovery of component 1 in concentrate
c,2 recovery of component 2 in concentrate

7. Theoretical shape of the separation data in the Fuerstenau plot4 * 7 9
Remeber: for characterizing separation results we need either two parameter or a law governing separation and then you can use one parameter which can be called selectivity as in these plots selectivity k 13
*for a suitable equation see previous slide
(more plots in A. Bakalarz, J. Drzymala, 2013, Interrelation of the Fuerstenau upgrading curve parameters with kinetics of separation, Physicochemical Problem of Mineral Processing, 49(2),

8. Polish copper ore – lab tests with xanthate
An example of separation results approximation using the Fuerstenau plot
a=~110
a=100
a=~1000
Polish copper ore – lab tests with xanthate

9. Homework
Calculate the rate constant and order of a set of yield flotation data

10. FLOTATION DEVICES Microlaboratory cells Laboratory cells
Laboratory machines
Industrial machines
Mechanical
Pneumo-mechanical
Pneumatic
Pressurized (DAF)
Other (sparged hydrocyclone, ASH)

13. Laboratory cells Other laboratory flotation devices
Other laboratory flotation devices
cylindrical cell equipped with magnetic stirrer (Fuerstenau, 1964)
laboratory flotation device of Partridge and Smith, 1971

14. Laboratory Mechanobr flotation machine

15. Laboratory Denver flotation machine

16. Industrial flotation
EIMCO Product Leaflets, 2000

17. Flotation machines are used individually and as a group (bank)

18. Flotation machines are rectangular and circular
Svedala Product Handbook, 1996

19. Constructions and impellers of flotation machines are different

20. pressurized mechanical injection pneumo-mechanical
Mechanical (self air aspiration)
Pneumo-mechanical (air is forced and mechanically dispersed
Pneumatic (air is forced)
Injection ( air and slurry go together)
Pressurized (dissolved air flotation DAF)
Other (air sparged hydrocyclone, ASH)
pressurized
mechanical
injection
pneumo-mechanical
XCELL™ Flotation Machines. FLSmidth Mineralss brochure 2008.
Comparison of pneumo-mechanical (FLSmidth Minerals) and mechnical flotation machines (WEMCO) )

21. FLOTATION MACHINES MECHANICAL
Denver
Mechanobr
Fagergreen (WEMCO-EIMCO)

22. DENVER

23. Wemco-Fagergreen (V=0.085 ÷ 85m3)
Kelly E.G., Spottiswood D.J., Introduction to mineral processing. J.Wiley& Sons, N.Jork 1985

24. Wemco-Fagergreen (WEMCO-EIMCO) mechanical flotation machines
EIMCO Product Leaflets, 2000

25. FLOTATION MACHINES PNEUMO-MECHANICAL
Denver
Agitair
Metso RCS (Metso Minerals)
Outotec (Outokumpu)
X-Cell (FLSmidth Minerals)
Humbolt-Wedag
IMN Gliwice

26. Industrial flotation machine (mechano-pneumatic, Agitair)
Pressurized air
froth product
rotor’s shaft
rotor
Kelly E.G., Spottiswood D.J., Introduction to mineral processing. J.Wiley& Sons, N.Jork 1985

27. Maszyna flotacyjna mechaniczno-pneumatyczna AS (Svedala/Metso Minerals), V=0,21 ÷ 16 m3
Svedala Product Handbook, 1996

28. Wills B.A., Mineral processing technology. Pergamon Press 1983
Fragment of mechano-pneumatic flotation machine (continueous, multi-impeller tankless Denver D-R
Wills B.A., Mineral processing technology. Pergamon Press 1983

29. Pneumo-mechanic multi-tank (15m3 each) (Aker FM – Humbold Wedag)
feed
tailing
Humbold-Wedag Product Leaflets, 1998

30. Maszyna przepływowa wielowirnikowa Maszyna jednowirnikowa
Pneumo-mechanical flotation machines IMN
Maszyna przepływowa wielowirnikowa
Maszyna jednowirnikowa

31. New machines: large volume and output, saving energy
Historyczny rozwój pojemności maszyn flotacyjnych
Flotation technologies. Outotec Leaflets 2007

32. (Outokumpu OK-100, V= 100m3 TankCell 300 300m3
Outokumpu Oy Leaflets 2000
Flotation technologies, Outotec Oyj. Leaflets 2007

33. Outotec TankCell 500 (500m3)
© 2012 Outotec Oyj.

34. RCS™ (Reactor Cell System) from 5 to 200 m3 (Metso Minerals/Svedala)
1-radial flow of slurry to tank wall
2-primary slurry stream to benith impeller
3-secondary recirculation towards upper part of tank
Basics in mineral processing. Metso Minerals 2003

35. RCS™ (Reactor Cell System) from 5 to 200 m3 (Metso Minerals)
Basics in mineral processing. Metso Minerals 2003

36. RCS™ (Reactor Cell System) from 260 m3 (Metso Minerals)

37. XCELL (FLSmidth Minerals)
pneumo-machanic
XCELL (FLSmidth Minerals)
XCELL™ Flotation Machines. FLSmidth Mineralss brochure 2008.

38. PNEUMATIC FLOTATION MACHINES
FLOTATION COLUMNS
Metso
Outotec (Outokumpu)

40. INJECTION FLOTATION MACHINES
Jameson Cell
Imhoflot
Pneuflot (Humbolt-Wedag)

41. Injection Jameson Cell

43. Pneumatic PNEUFLOT
Pneumatic flotation with PNEUFLOT® cells HUMBOLDT WEDAG leaflet 2009

44. pneumatic PNEUFLOT
Pneumatic flotation with PNEUFLOT® cells HUMBOLDT WEDAG leaflet 2009

45. Injection Imhoflot 2 Distributor of air and suspennion feed air
flotation froth
concentrate
product
middlings to recirculation
tailing
Distributor of air and suspennion
Pneumatic cell Imhoflot. Maelgwyn Mineral Service leaflet 4/06 Chile 2006

47. Multi-injection Imhoflot 3 (centrifugal flotation)
feed
compressed air
air plus suspension
feed
reagents
concentrate
tailing
feed pump
tailing pump
Pneumatic cell Imhoflot. Maelgwyn Mineral Service leaflet 4/06 Chile 2006

48. Injection column Siemens SIMINE Hybrid Flot
Metals and Mining, Siemens VAI, No. 1, 2011

49. PRESSURIZED FLOTATION MACHINES Dissolved air flotation (DAF)

50. Dissolved air flotation (DAF)

51. Pressurized flotation (separation of coal from sulfides)
FGR - Flocs Generator Reactor
Rodrigues & Rubio, International Journal Of Mineral Processing. V. 82, P. 1-13, 2007.

53. Flotation, ZWR Polkowice