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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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Flotation

FLOTATION

(Main feature - hydrophobicity)


Flotation

Flotation


Flotation

gas bubble

water

particle

Contact angle


Flotation

Contact angle of selected materials


Flotation

Methods of measurement


Flotation

There are different models of flotation

including mechanistic, thermodynamic and probabilistic models


Flotation

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)


Flotation

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


Flotation

 is measured through the aqueous phase

The Young Equation

sg = sc+ cgcos 

 - contact angle


Flotation

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 


Flotation

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


Flotation

More detailed models of flotation

Particle and spherical bubble

here flotation also depends on  and 


Flotation

other models take into account other parameters

such as size of bubble and particle


Flotation

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 )


Flotation

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.


Flotation

Steps of flotation


Flotation

receding

qr

water

advancing

qa

water

q

equlilibium

flotacja 4


Flotation

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


Flotation

FLOTATION depends on hydrophobicity

hydrophobicity is measured as contact angle


Flotation

Electrical aspects of flotation

naturally hydrophobic


Flotation

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,


    Flotation

    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


    Flotation

    Electrical aspects of flotation

    -+

    -+

    water

    moving particle

    +

    -

    +

    -

    -+

    -

    +

    -

    -

    +

    -

    +

    +

    slipping plane

    zeta potential

    -+

    -+

    -+


    Flotation

    Structure of electrical double layer


    Flotation

    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


    Flotation

    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


    Flotation

    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


    Flotation

    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


    Flotation

    Flotation reagents

    COLLECTORS

    for hydrophobization

    FROTHERS

    for froth creation

    MODIFIERS

    for enhancing


    Flotation

    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.


    Flotation

    COLLECTORS


    Flotation

    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


    Flotation

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


    Flotation

    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)


    Flotation

    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).


    Flotation

    collector renders the

    surface hydrophobic

    gas

    collector

    particle


    Flotation

    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


    Flotation

    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

    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

    Flotation vs collector dose


    Flotation

    Influence of pH and iep on flotation for various collectors


    Flotation

    Collector as chemicals


    Flotation

    Based on Nagaraj, 1988

    .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


    Flotation

    on Nagaraj, 1988

    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


    Flotation

    Selected chelating collectors. Type S - 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


    Flotation

    COLLECTORS


    Flotation

    Collectors


    Flotation

    FLOTATION METHODS

    Foamseparation

    Frothflotation

    Frothlessseparation

    Microorganisms

    flotation

    Precipitateflotation

    Ionsflotation

    Mineralsflotation

    Flotation with solublecollectors

    Agglomerativeflotation

    Carrier flotation

    Emulsionflotation

    Methods of flotation


    Flotation

    gamma flotation

    (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


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