1. PHYSICAL ASPECTS OF FLOTATION

2. Contents Particle shape & texture Bubble formation
Bubble/particle interactions
Mixing
Kinetics
Effects of bubble size and particle size
Froth drainage
Effects of cell geometry

3. Particle Shape & Texture (1)
Particles are formed by breakage
The breakage is random so that the resulting particles are of complex shape and structure
Particles after crushing are angular & elongated
After grinding generally reasonably compact
Few elongated or concave particles except eg crusher products, molybdenum concentrates, etc
Broken shapes have advantage for flotation - they have sharp edges and points – thus more likely to penetrate a liquid film around a bubble

4. Particle Shape & Texture (2)
Also breakage gives complex internal structures
Breakage rarely occurs at the grain boundaries
Breakage pattern is independent of ore texture
Particles are of one or of many mineral phases
Breakage generally aimed at liberating one particular mineral – hence structure often described as particle composition distribution relative to that mineral
The mean particle composition is the composition of the unbroken ore
Shape of particle composition distribution describes the extent of liberation
The cumulative liberation yield at particle composition x is the proportion of the sample contained in particles of composition  x.

10. Particle Shape & Texture (3)

11. Particle Shape & Texture (4)

12. Particle Shape & Texture (5)
Another way to describe particle structure is in terms of particle types, eg liberated, binary with specific minerals, ternary particles, etc.
Can define many such locking types
But practically it is common to specify binaries then lump all other locked particles together
eg., a lead/zinc ore with all gangue minerals lumped together (3 phases) gives 7 particle types
Liberated – galena, sphalerite, gangue
Binary – gal/sphal, gal/gangue, sphal/gangue
Ternary – all particles with more than two phases

13. Particle Shape & Texture (6)
This classification useful for processing as nature of locked minerals will affect flotation behaviour
But number of particle types increases quite rapidly with number of phases
4 phases – 11 particle types
5 phases – 16 particle types
Particle structure important for 2 main reasons:
It determines whether or not the particle will float
After separation it determines the contribution of impurities to concentrate or losses of values to tailing

14. Particle Shape & Texture (7)
Must have mineral on surface for flotation
How much needed depends on many factors – particle size, reagent conditions, cell agitation, etc.
There is evidence that quite a low surface exposure can induce flotation in some situations
Increasing the extent of the surface exposure increases the effectiveness of the flotation
But it is the total composition , not surface exposure, that determines how it affects separation performance

15. Particle Shape & Texture (8)

16. Particle Shape & Texture (8 cont.)

17. Bubble Formation (1)
The flotation process requires a continuous stream of small bubbles
They must be stable enough to give plenty of opportunity for particle bubble collisions
The froth phase which overflows the cell lip should then break down for easy transport
Sizes of a few mm have proved the best in general.
Smaller sizes have advantages for very small particles.

18. Bubble Formation (2)
Bubbles can be generated in liquids by forcing gas through some orifice.
 Single bubbles in water vary in shape, depending on size
Small spheres (4 – 6mm)
Oblate spheroids (6 – 40mm)
Large spherical caps (>88mm)
They rise in the water, expand as hydrostatic head falls and break immediately at the surface.

19. Bubble Formation (3)
A stream of bubbles in water are unstable and rapidly coalesce, grow, rise to the surface where they break
Lowering the surface tension means smaller bubbles
Frothers lower surface tension and also give higher viscosity to the liquid films – this increases the stability
When the rate of generation of bubbles exceeds the rate of breakage at the surface a froth layer forms.

20. Bubble Formation (4)
Smaller bubbles are also generated by shearing larger bubbles to beak them up. This is one aspect of the rotor mixing mechanisms in a flotation cell.
Induced air systems suck air into the rotor vortex and break up the bubbles in the high shear rotor region. This air supply is less controllable than a forced air system

21. Bubble Formation (5)
The use of frothers is essential for the operation of a flotation system
When frothers is added to a cell bubbles of about 2mm are generated and stable froths are formed
In the early cells where particle loading is high froths are stable.
In later cells, as reagents deplete and particle loading falls, the bubble size increases through coalescence and the stability of the froths falls significantly.

22. Bubble-Particle Interactions (1)
For particle capture by a bubble we need
Collision between a particle & a bubble
The fluid film between them must thin down
Then rupture of film to give a gas-solid interface
In a conventional cell, collection occurs by different mechanisms in different parts of the cell
Near the impellor collisions are by a shearing mechanism. Velocity gradients high. Bubbles will be at centre of opposing streams of liquid bearing particles
In quieter regions of cell the relative motion between particles and bubbles is due to gravity with bubbles rising at a terminal velocity appropriate to their size

27. Bubble-Particle Interactions (2)

28. Bubble-Particle Interactions (2)
Theoretical attempts to describe capture
Calculate path of particle as it passes a bubble
Particles within a distance R of the centre line of the bubble will touch the bubble as it passes
The efficiency of capture E is then the ratio of the area of the collision tube to the bubble cross sectional area
E = (πR2)/(πrb2)   or
E = (dp/db)N where N is about 2.
Thus capture rate increases strongly with increasing particle size.

29. Bubble-Particle Interactions (3)

30. Bubble-Particle Interactions (4)
This is a highly idealised situation. The problem of calculating from first principles the rate of collision of particles and bubbles in a turbulent stirred vessel is still too difficult to be solved.
The increase in capture as particle size increases is counteracted at large sizes by detachment mechanisms.
Particles are too large to be firmly held by the bubbles and can be broken away by the agitation
To break attachment, work must be done to overcome the surface tension forces. This work is supplied by the turbulent eddies in the agitated vessel.

31. Mixing in a cell is designed to do many things:
Suspend the mineral particles
Distribute the flotation chemicals evenly
Provide high shear conditions near the air sparge so that small bubbles are generated
Promote particle bubble contacts
Maintain a quieter region at top of cell where separation can occur between froth and pulp
Mixing efficiency (cost) is also important

32. Mixing (2)
The time particles spend in the cell is also very important - there must be time for capture
In a cell of volume V (m3) with an exit flow of v (m3/s), the mean residence time  in the cell is given by  = V/v (s). On average particle will spend time  in the cell
The most efficient cell would have all particles spending the same time  in the cell, eg like a pipe
In practice there will be a spread of times defined by the residence time distribution.

33. Mixing (3) A single cell has a wide range of residence times
Thus flotation cells are connected together in banks to get satisfactory overall efficiency
Countercurrent operation is the most efficient giving maximum oportunity for purifying concentrate and exhausting tailings
Achieved by arranging cells in banks, then banks in countercurrent arrangements
The flotation column, where bubbles rise from the bottom to the top, and particles fall from near the top, gives maximum oportunities for capture

36. Kinetics (1) Contact angle and hydrophobicity are equilibrium concepts
But industial flotation involves rate processes - the faster the process the cheaper the operation
It is commonly accepted that flotation can be simply represented by first order kinetics:
dc/dt = -kt , where
c = floatable material left in batch cell
t = time
k = flotation rate constant

37. Kinetics (2)
Then ∫(dc/c) = -∫kdt and c = coe-kt where co is the initial concentration of flotable material in a batch cell The problem is that k is only constant for that set of conditions. It is affected by many factors such as the chemical conditions, the particle size, the bubble size and air rate, the agitation, etc, etc.

38. Effects of Bubble & Particle Size (1)
The capture efficiency E of particles by bubbles in a column of liquid is
E = (dp/db)N
With N about 2. E increases as db decreases.
 E  (1/db)2
The overall flotation rate is proportional to E, to the bubble frequency bf, and to the bubble projected area bpa

39. Effects of Bubble & Particle Size (2)
For a fixed air rate bf  1/(db)3 (ie no. of bubbles inversely proportional to bubble vol)
bpa  (db)2
Flotation rate  1/(db)2 * 1/(db)3 * (db)2 = 1/(db)3
Thus for small particles and bubbles flotation rate increases strongly as the bubble size is decreased
This has been confirmed by experiment
But note that it is for rather unrealistic conditions, very different from those in an agitated flotation cell.

40. Effects of Bubble & Particle Size (3)
Nevertheless, similar results were found for experiments in a laboratory flotation cell. Particle sizes 4 to 42 micron at different densities floated by bubbles ranging in size from 75 to 655 micron. The following conclusions were drawn:
 Flotation rate is strongly dependent on bubble size. When the bubble diameter reduced from 655 to 75 μ the flotation rate increased by about 50 % for fine particles
Increasing agitation improves performance of large bubbles, but worse for small bubbles. The range of improvement with fine particles is reduced to about 5 %.

41. Froth Drainage (1)
Bubbles loaded with mineral rise in pulp, enter froth layer and rise through the froth to the top where they finally overflow the cell lip
Bubbles entering the base of the froth will entrain liquid containing hydrophilic gangue material
To produce a high concentrate grade this entrained material must drain from froth before discharge
The concentrate purity increases with height in the froth. It is important to have effective drainage of the froth to achieve good enrichment.

44. Froth Drainage (2)
Particles in froth affect froth stability and drainage
Particle size and hydrophobicity are both important
Hydrophilic particles may act as a buffer between opposing air-liquid interfaces thus reducing drainage
Rough hydrophobic particles and smoothe spheres of low contact angle can form stable contact lines with the surfaces of the films, and thus stabilise the films
Orthorhombic particles like galena, will cause rupture as soon as they bridge both film surfaces
Smoothe spheres at high contact angle, will destabilise a film when both surfaces are pierced

45. Froth Drainage (3)

46. Froth Drainage (4) Possible methods of froth stabilisation:
Froth heavily mineralised with fine particles. The films are prevented from collapsing by the high concentrations of hydrophobic particles
hydrophillic particles
Froth film with a large hydrophobic particle of roughly spherical shape, with a low contact angle.

48. Effects of Cell Geometry (1)
The flotation cell has many functions:
Materials handling – feed entry, tailings discharge, froth support & removal
Flotability effects – dissolution & dispersion of reagents, promotion of reagent surface interactions
Separation effects – particle suspension, air entrainment & dispersion, particle bubble collisions, froth separation

49. Effects of Cell Geometry (2)
Materials handling
Has become simpler and simpler
Generally just a feed box at the head of the bank and gravity flow between cells, with exit from the end cell controlled by an adjustable weir
Scraper arrangements for froth removal are also less common except where large proportions of coarse mineral must be removed, eg coal, potash, phosphate or some cleaning banks.

50. Effects of Cell Geometry (3)
Flotability effects
Reactions in sulphide systems are reasonably fast so that surprisingly little conditioning time is needed
But the intense agitation promotes various chemical and surface reactions
Also oxidation reactions can affect the floatability of sulphide minerals
Many systems require more time than is available in the flotation cell itself – thus conditioning tanks are needed to allow time for surfaces to be adjusted for flotation.

52. Effects of Cell Geometry (4)
Separation effects
The power required to stir a baffled tank has been well studied - power relationships are of the following type
Np = P / (N3d5) = 1 (Nd2/) = 1 NRe , where
Np = Power number
NRe = Reynolds number
P = power
r     = fluid density
N = rotational speed
d = impeller diameter
m    = fluid viscosity
1 = function depending on tank and impeller geometry

53. Effects of Cell Geometry (5)
For Reynolds number less than 10 (laminar flow) Np* NRe is constant
For Reynolds number greater than 104 (fully turbulent) Np is constant
When air is added the power drops significantly – the air lowers the fluid density in the region of the rotor. Several correlations exist to account for the fall in power draw for aerated systems.

54. Effects of Cell Geometry (6)
The suspension of a particle in a stirred tank depends mainly on:
the weight (and shape) of the particle
the impellor speed
As impellor speed is increased a particle will remain on the bottom until a critical speed is reached, then it will progressively move higher in the vessel towards the mid point.

55. Effects of Cell Geometry (7)
This means for a typical flotation feed with a wide range of particle sizes there will be a range of behaviour – except at an unrealistically high stirring speed when all particles are well suspended (too expensive in practice and will break-up bubble particle aggregates)
So fine particles will be well dispersed. Larger particles should be suspended, but not dispersed throughout the entire vessel.

56. Effects of Cell Geometry (8)
Much of the development of flotation cell design has been aimed at balancing the suspension requirements
keeping larger particles off bottom
minimising power requirements
allowing a quiet zone to develop at the top of the cell so a froth zone can separate.