adhesion of particles or particles to surfaces

SLIME COATING AND COAGULATION

Slime coating

AFM-images of slime coatings on mineral surface

M.E. Holuszko et al., Minerals Engineering, 21, 2008, 958-966

Slime coating Very important phenomenon

Can be useful and harmful

Ferric oxide slime and flotation of quartz with 10-4 M dodecyl ammonium acetate

Chemistry of flotation , M.C. Fuerstenau, J.D. Miller, M.C. Kuhn, AIMM, 1985

Chemistry of flotation , M.C. Fuerstenau, J.D. Miller, M.C. Kuhn, AIMM, 1985

Alumina as slime on galena and flotation with xanthate

coagulation

homocoagulation heterocoagulation

main parameter: stability ratio W

Process delineation (thermodynamics)

+ =

Gk = Gh – G 

Gk = Gk d + Gk el + Gk s + Gk inne

That is components: dispersion (d), electrical (el),

structural (s), a others

H

RAVGG A

ddk 12

132132,

Dispersion interactions

H – distance between particles, m R – diameter of particle, m A132 – Hamaker constant, J

+ =

phase 1 phase 2phase 3

Dispersion interaction

Interacting objects Formula Units

Two atoms 6H

CGd (C is a constant) J

Two spheres )(6

)(

21

21

RRH

RRAG xd

x J

Two flat parallel slabs 212 H

AG xd

x

J/m2

Sphere and slab H

RAG xd

x 6 J

Two perpendicular cylinders H

RRAG xd

x 621 J

Hamaker constantDispersion interaction .Hamaker constant A11 for selected materials

collected by Drzymala (1994) and other authors

Material A11

(×1020 J)

A11 (×1020 J)

Material A11

(×1020 J) n-pentane (C5H12) 3,8b mica 10,0b MoS2 (molibdenite) 13,3e, 9,1c

Teflon ([C2F4]n) 3,8b MgO (periclase) 10,5c S (sulfur) 23c Acetone (CH3COCH3) 4,1b CaCO3 (calcite) 10,1d Fe2O3 (hematite) 23,2a Ethanol (C2H5OH) 4,2b AsS (realgar) 12c C (graphite) 23,8a

Water (H2O) 4,38a FeS2 (pyrite) 12c SnO2 (cassiterite) 25,6a

n-octane (C8H18) 4,5b CaO (lime) 12,5c Si (silicon) 25,6a

n-dodecane C12H26 5,0b FeCr2O4 (chromite) 14c FeAsS (arsenopyrite) 27c n-tetradecane (C14H30) 5,0b ZnS (sphalerite) 14c As2S3 (auripigment) 28,4a 15c Benzene (C6H6) 5,0b CdS (greenockite) 15,3f C (diamond) 28,4a

n-heksadecane (C16H34) 5,1b Al2O3 (corundum) 15,5a Cu (copper) 28,4a Cyklohexane (C6H12) 5,2b AgI (iodirite) 15,8a Ge (germanium) 30,0a

KCl silvine 6,2a Sb2S3 (metastibnite) 16c TiO2 (rutyl) 31,0a CnH2n +2 (paraffin) 6,3–7,3a SiO2 (quatz) 16,4a PbS (galena) 33c

Polystyrene 6,5b BaSO4 (barite) 16,4a Ag (silver) 40,0a CaF2 (fluorite) 7,2 TiO2 (anatase) 19,7a Hg (mercury) 43,4a Bornite (Cu5FeS4) 7,4c Cu2S (chalcocite) 21c Au (gold) 45,5–50a

Poli(vinyl chloride) 7,5b Fe (iron) 21,2a CuS (covelline) 2,8c (?)

Pirrothite (FeS) 8,4c Pb (lead) 21,4a [Fe, Ni]9S8) pentlandite 3,3c (?) Talc (Mg3[(OH)2Si4O10])

9,1c Sn (tin) 21,8a CuFeS2 (chalkopyrite) 3,3c (?)

a) Visser (1972), b) Israelachvili (1985), c) Lins i współ. (1995), d) Hunter (1987), e) Ebaadi (1981), f) Krupp et al., (1972). Symbol ? denotes uncertain data

221112 AAA

23311133311313131 2 AAAAAAA

33223311132 AAAAA

132131132 AAA

Dispersion interaction

Electrostatic interaction

,)2exp(1ln

)exp(1)exp(1

ln)(

2)(

)(22

21

21

21

22

21210

el

H

HH

RRRR

VG R

1 – particle electrostatic potential, V, 2 – the other particle electrostatic potential, V, R1

– particle radius, m, R2 – the other particle radius, m, – dielectric constant (usually water)0 – dielectric permeability in vacuum, 8,854187817·10–12 C2 N–1 m–2 1/ – Debye radius (thickness of ewp), m,

H – distance between interacting objects, m.

Electrostatic interaction

Approximate formulas for energy of electrostatic interactions Gel = VR between objects having different geometry in medium of a given dielectric constant

(Russel i et al., 1989)

Geometry limitation interaction energy VR

Two parallel slabs overlap )exp()25,0(tanh64 21 HkTne

Two spheres constant potential ])exp[1(ln2 22

0 HRze

kT

Two spheres constant charge ])[exp1(ln2 20

2

0 HRze

kT

Two spheres linear overlap )(exp2

4 222

0 HRH

R

ze

kT

Two spheres overlap )(exp)25,0(tanh32 22

0 HRze

kT

l

HE

l

HKlG SS expexp 0

l

HlRKGS exp*

For flat particles

For spherical particles

K , K* , Eso- constants

l - parameter correlating standing for thickness of oriented water molecules at the surface of particle

H - distance between particles

R - radius of particles

Structural interaction

Total interaction In

tera

ctio

n e

ner

gy, V

+

–

VR

VA

distance, H

VS, w

VS, h Vt = VR + VA + VS

DLVO

iner

acti

on e

ner

gy, V

t

+

–

Vmax

VI

VII

Vmax – energy barrier

VII– secondary minimum

VI – primary minimum

distance, H

Total interaction

Stability ratio W

R

t drkTV

rRW

22 exp

12

kTV

RW maxexp

21

ncoagulatio toleading collisions ofnumber particlesbetween collisionsofnumer W

iner

acti

on e

ner

gy, V

t

+

–

Vmax

VI

VII

Vmax – energy barier

VII– secondary minimum

VI – primary minimum

distance, H

Time of half-life t1/2 of hypothetical emulsion containing 1 m droplet and having energy barrier Vmax one radius apart from the

droplet surface (after Friberg, 1991)

Energy barrier Vmax /kT

(in kT units) t1/2

Stability ratio W = exp[0,92{(Vmax/kT) – 1}]

(for (Vmax/kT) 3)*

0 0.8 sec ~2

10 2.0 h 3.94·103 15 1.3 d 3.92·105

17.5 154 d 3.91·106

20 5.1 y 3.90·107

50 5.5·1013 y 3.78·1019

* Empirical equation of Prieve and Ruckenstein (1980).

Pstab

Vmax

W

VA,VR,VS

A, , , x, , H

ni, , ,cs,pH,

.....

Pa

Pz

xc / xj hd

V*max H, cs

Pk = PzPaPstab

Main parameter: stability ratio W

2 4 6 8 10 12

pH

50

70

90

110

130

150

turb

idit

y,

TiO2

2×10-3 NaCl

2×10-2 NaCl

2×10-1 NaCl

2 4 6 8 10 1240

60

80

100

stab

ilit

y, m

t = 5

min

/ mt =

0 m

inx1

00%

iep SiO2 iep Fe3O4 iep BaSO4

SiO2

BaSO4

Fe2O3

pH

selective coagulation

0 2 4 6 8 10 12

pH

-1

0

1

2

3

soli

ds

con

cen

trat

ion

, %

iep SiO2 iep Fe2O3

selective coagulation

0 2 4 6 8 10 12

pH

-1

0

1

2

3so

lid

s d

ensi

ty, %

Fe2O3 + SiO2

selective coagulation of hematite

heterocoagulation

stability

selective coagulation

2 4 6 8 10 12pH

0

20

40

60

80

100

coal

rec

over

y, %

0

3

6

9

12

15

ash con

tent, %

stability

recovery

ash

heterocoagulation

coal coagulation