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

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
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)
The particle texture is classified based on mineral association and liberation
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

5. Particle Shape & Texture (3)
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
Must have hydrophobic 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

6. Particle Shape & Texture (4)

7. 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.

8. 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 (1 – 2mm)
Oblate spheroids (6 – 40mm)
Large spherical caps (>88mm)
They rise in the water, expand as hydrostatic head falls and break immediately at the surface.

9. 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

10. 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

11. 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.

12. Anglo Platinum Bubble Sizer (APBS)
Collection tube
1st ball valve
2nd ball valve
Battery
Camera
Light
Collection chamber

14. Images of Air Bubbles

15. 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 center 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

16. Bubble-Particle Interactions (2)

17. Induction Time
Induction Time:The time required to penetrate the water film around the bubble.
Induction time decreases with increasing particle hydrophobicity
If induction time is higher than the contact time, particle will not attach

18. Probability of Collision
Flow stream lines deflect the particles and reduce the probability of collision
Probability of collision is the actual number of particle collide relative to the number in the path of the bubble.
The probability of collision is small (one in hundred)
Large number of bubbles is required to increase probability of collision

19. Attachment Hydrophobic particle breaks the water film and attach
Hydrophilic particles slides

20. Contact Time
Contact time is the time takes a particle to slide around a bubble.
Contact time of a particle depends on its weight
The speed of the larger particle is higher and does not have enough time to attach

21. Bubble-Particle Interactions (3)
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 or with decreasing bubble size.

22. Bubble-Particle Interactions (4)

23. Bubble-Particle Interactions (5)
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.

24. Mixing (1) 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

25. 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.

26. 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

29. 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

30. 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.

31. 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.

34. 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

35. Froth Drainage (3)

36. 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.