Transcript Bez tytułu slajdu - Politechnika Wrocławska

SLIME COATING AND COAGULATION
adhesion of particles or particles to surfaces
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
Alumina as slime on galena and flotation with xanthate
Chemistry of flotation , M.C. Fuerstenau, J.D. Miller, M.C. Kuhn, AIMM, 1985
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
Dispersion interactions
Gk ,d  G
d
132
H
R
A132
A132 R
 VA  
12 H
– distance between particles, m
– diameter of particle, m
– Hamaker constant, J
+
phase 1
phase 3
=
phase 2
Dispersion interaction
Interacting objects
Two atoms
Two spheres
Two flat parallel slabs
Sphere and slab
Two perpendicular cylinders
Formula
C
G d   6 (C is a constant)
H
Ax ( R1R2 )
Gxd  
6H ( R1  R2 )
Gxd  
Ax
12H
AR
Gxd   x
6H
Gxd  
2
Ax R1R2
6H
Units
J
J
J/m2
J
J
Dispersion interaction
Hamaker constant
.Hamaker constant A11 for selected materials
collected by Drzymala (1994) and other authors
A11
(×1020 J)
n-pentane (C5H12)
3,8b
Teflon ([C2F4]n)
3,8b
Acetone (CH3COCH3)
4,1b
Ethanol (C2H5OH)
4,2b
Water (H2O)
4,38a
n-octane (C8H18)
4,5b
n-dodecane C12H26
5,0b
n-tetradecane (C14H30)
5,0b
Benzene (C6H6)
5,0b
n-heksadecane (C16H34)
5,1b
Cyklohexane (C6H12)
5,2b
KCl silvine
6,2a
CnH2n +2 (paraffin)
6,3–7,3a
Polystyrene
6,5b
CaF2 (fluorite)
7,2
Bornite (Cu5FeS4)
7,4c
Poli(vinyl chloride)
7,5b
Pirrothite (FeS)
8,4c
Talc
9,1c
(Mg3[(OH)2Si4O10])
Material
mica
MgO (periclase)
CaCO3 (calcite)
AsS (realgar)
FeS2 (pyrite)
CaO (lime)
FeCr2O4 (chromite)
ZnS (sphalerite)
CdS (greenockite)
Al2O3 (corundum)
AgI (iodirite)
Sb2S3 (metastibnite)
SiO2 (quatz)
BaSO4 (barite)
TiO2 (anatase)
Cu2S (chalcocite)
Fe (iron)
Pb (lead)
Sn (tin)
A11
(×1020 J)
10,0b
10,5c
10,1d
12c
12c
12,5c
14c
14c
15,3f
15,5a
15,8a
16c
16,4a
16,4a
19,7a
21c
21,2a
21,4a
21,8a
A11
(×1020 J)
MoS2 (molibdenite)
13,3e, 9,1c
S (sulfur)
23c
Fe2O3 (hematite)
23,2a
C (graphite)
23,8a
SnO2 (cassiterite)
25,6a
Si (silicon)
25,6a
FeAsS (arsenopyrite)
27c
As2S3 (auripigment)
28,4a 15c
C (diamond)
28,4a
Cu (copper)
28,4a
Ge (germanium)
30,0a
TiO2 (rutyl)
31,0a
PbS (galena)
33c
Ag (silver)
40,0a
Hg (mercury)
43,4a
Au (gold)
45,5–50a
CuS (covelline)
2,8c (?)
[Fe, Ni]9S8) pentlandite 3,3c (?)
CuFeS2 (chalkopyrite) 3,3c (?)
Material
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
Dispersion interaction
A12 
A11 A22
A131  A313  A11  A33  2 A13 
A132 

A11  A33
A132   A131 A132


A11  A33
A22  A33


2
Electrostatic interaction
1  exp(H ) 
 0 R1 R2 ( 12   22 )  2 1 2
Gel  VR 
ln 
 2

2
( R1  R2 )
(



)
1

exp(


H
)


2
 1
 ln 1  exp(2H ) ,
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
Two parallel slabs
limitation
interaction energy VR
overlap
64kTne 1 tanh2 (0,25 ) exp(H )
constant potential
 kT 
2
2 0 
 R ln (1  exp[H ])
 ze 
constant charge
 kT 
2
 2 0 
 R 0 ln (1  exp[H ])
 ze 
2
Two spheres
2
Two spheres
2
Two spheres
linear overlap
R2
 kT 
4 0 
 2 exp(H )

 ze  H  2 R
2
Two spheres
overlap
 kT 
2
32 0 
 R tanh (0,25 ) exp ( H )
 ze 
Structural interaction
For flat particles
 H
 H
0
GS  Kl exp    ES exp  
 l 
 l 
For spherical particles
 H
GS  K lR exp  
 l 
*
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
Total interaction
In teraction en ergy, V
+
DL VO
VR
VS, h
Vt = VR + VA + VS
d ista n ce,H
VS, w
–
VA
Total interaction
in eraction en ergy, Vt
+
Vm a x
d ista n ce,H
VII
Vmax – energy bar r i er
–
VI
VI – pr i mar y mi ni mum
VI I– secondar y mi ni mum
Stability ratio W
Vt
1
W  2R  2 exp dr
r
kT
2R
1
 Vmax 
W
exp

2 R
 kT 
+
in eraction en ergy, Vt

Vm a x
d ista n ce,H
VII
Vmax – energy bar i er
–
VI
VI – pr i mar y mi ni mum
VI I– secondar y mi ni mum
numer of collisions between particles
W
number of collisions leading to coagulation
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)
0
10
15
17.5
20
50
t1/2
0.8 sec
2.0 h
1.3 d
154 d
5.1 y
5.5·1013 y
* Empirical equation of Prieve and Ruckenstein (1980).
Stability ratio
W = exp[0,92{(Vmax/kT) – 1}]
(for (Vmax/kT)  3)*
~2
3.94·103
3.92·105
3.91·106
3.90·107
3.78·1019
Main parameter: stability ratio W
Pa
W
Vm a x
VA ,VR ,VS
A,  ,  , x,  , H
ni,   ,  ,cs, p H,
xc / xj
dh
.....
V *m a x
H, cs
Pz
Pstab
Pk = PzPaPstab
2 × 1 0- 3 Na Cl

t urbi di t y,
130
2 × 1 0- 2 Na Cl
110
90
2 × 1 0- 1 Na Cl
70
Ti O2
50
2
4
6
8
pH
10
x100%
/m t = 0 mi n
st abi l i t y,m t = 5 mi n
150
12
100
Si O 2
80
Fe 2 O 3
60
BaSO 4
40
2
i ep Si O
2
4
6
i ep Fe3O4
8
10
i ep BaSO4
12 p
selective coagulation
s ol i ds c onc e nt r at i on,%
3
2
1
0
i ep Si O
2
i ep Fe
2O3
-1
0
2
4
6
pH
8
10
12
selective coagulation
3
s ol i ds de ns i t y,%
s t abi l i t y
s e l e c t i ve c oagul at i on
of hem at i t e
2
1
he t e r oc oagul at i on
0
Fe 2O3 + Si 2
O
-1
0
2
4
6
pH
8
10
12
selective coagulation
coal coagul at i on
st abi l i t y
100
15
80
12
60
9
40
6
ash

20
3
recovery

0
0
2
4
6
8
pH
10
12
ash content, %
coal recovery, %
het erocoagul at i on