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# FLOTATION - PowerPoint PPT Presentation

FLOTATION. ( Main feature - hydrophobicity). Flotation. gas bubble. water. . particle. Contact angle. Contact angle of selected materials. Methods of measurement. There are different models of flotation including mechanistic, thermodynamic and probabilistic models.

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## PowerPoint Slideshow about ' FLOTATION' - stone-fischer

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Presentation Transcript

(Main feature - hydrophobicity)

water

particle

Contact angle

including mechanistic, thermodynamic and probabilistic models

Thermodynamicapproach

Gflotation= Gfinal- Ginitial = [sg - (sc+ cg)] A

for A = = 1cm2 surface area

Gflotation= sg - (sl+ lg) Dupre eq. (1869)

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

is measured through the aqueous phase

The Young Equation

sg = sc+ cgcos 

 - contact angle

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 

(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

Particle and spherical bubble

here flotation also depends on  and 

such as size of bubble and particle

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 )

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,

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,

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.

qr

water

qa

water

q

equlilibium

flotacja 4

sg = sc+ cgcos

g

cg

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

hydrophobicity is measured as contact angle

naturally hydrophobic

Main parametr – hydrophobicity (contact angle)

which depends on energetics of three interfaces (Young eq.)

sg = sl+ lgcos 

the Gibbs theory tells that

• 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,

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

-+

-+

water

moving particle

+

-

+

-

-+

-

+

-

-

+

-

+

+

slipping plane

zeta potential

-+

-+

-+

layer

Helmholz

(flat condenser)

Stern

(rigid and diffuse layer )

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

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

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

20

0

-20

D

O-ice (

)

(0.0001M)

n

2

·

diamond (

)

zeta potentia, mV

-40

air (

),

(

)

Nocardia sp.

w

«

-60

D

O-ice

(0.001M)

2

-80

2

4

6

8

10

12

pH

zeta potential and iep for materials without functional groups

COLLECTORS

for hydrophobization

FROTHERS

for froth creation

MODIFIERS

for enhancing

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.

CH3CH2CH2CH2 CH2CH2CH2CH2

COO–

tail

(hydrophobic)

(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

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

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)

Maximum contact angle for different collectors with the formation of hemimicelle (a), monolayer (b) and a second layer leading to hydrophilicity (c) with 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).

collector renders the with the formation of hemimicelle (a), monolayer (b) and a second layer leading to hydrophilicity (c)

surface hydrophobic

gas

collector

particle

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

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))

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

Flotation vs collector dose 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

Influence of pH and iep on flotation for various collectors 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

Collector as chemicals 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

Based on Nagaraj, 1988 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

.Selected chelating collectors. Type S

– S

Collector

Formula

Example

S

Potassium ethyl xanthate

-

Dithiocarbonates (xanthate)

C - O-

(R

OCSSK)

S

S

-

Trithiocarbonates (tioxanthate)

C - S-

S

S

-

P(OR)

Dithiophosphates

Aerofloat ((RO)

P(=S)

SK)

2

2

S

S

-

PR

Dithiophosphinates

Aerofins

2

S

S

-

Sodium diethyldithiocarbamate

Dithiocarbamates

C - NR

2

S

on Nagaraj, 1988 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

Selected chelating collectors.

Type O

N.

Based

collector

formula

Example

a

-

benzoin oxime

C

H

C

C

H

C

O

ximes

O

H

O

H

N

O

H

O

H

N

LIX65N

C

H

9

1

9

Hydroxyoximes (LIX series)

C

N

O

H

O

H

8

-

hydroxyquinoline (oxine)

8

-

hydroxyquinoline and derivatives

N

O

H

Selected chelating collectors. Type S 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 - N

Based on Nagaraj, 1988

Collector

Formu

la

S

C

S

H

C

Mercaptobenzothiazols

C

N

(flotagen)

N

R

C

Mercaptothiodiazoles

S

H

C

N

S

N

H

C

S

H

Thiotertrahydroglyoxaline

C

N

C

S

Mono

-

and dithiocarbamates

N

H

C

H

C

H

O

C

2

5

4

9

N

H

S

C

Phenylthiourea

H

N

COLLECTORS 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

Collectors 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

FLOTATION METHODS 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

Foamseparation

Frothflotation

Frothlessseparation

Microorganisms

flotation

Precipitateflotation

Ionsflotation

Mineralsflotation

Flotation with solublecollectors

Agglomerativeflotation

Carrier flotation

Emulsionflotation

Methods of flotation

gamma flotation 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

(flotation in water mixed with soluble organic liquid)

and

Typical shape of the cos  = f (surface tension of liquid) relationship also called the Zisman plot, and flotation of naturally hydrophobic materials