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Title
Author(s) ,
Citation . () 11466
Issue Date 2014-03-25
DOI 10.14943/doctoral.k11466
Doc URL http://hdl.handle.net/2115/55543
Type theses (doctoral)
File Information SUGURU_GOTOH.pdf
Hokkaido University Collection of Scholarly and Academic Papers : HUSCAP
https://eprints.lib.hokudai.ac.jp/dspace/about.en.jsp
Development and application of a rheological model for
concentrated flocculated suspensions based on fractal concept
2014 2
Suguru GOTOH
1.1 1
1.2 3
1.2.1
1.2.3
1.2.4
1.2.5
1.3 11
1.4 13
2
21 17
2 2 1 9
2.2.1
2.2.2
2.2.3
2.2.4 Breakup exponent
23 30
2.3.1
2.3.2
24 43
2.4.1
2.4.2
2.4.3
3
31 54
32 54
3.2.1
3.2.2
3.2.3
3.2.4
33 65
3.3.1
3.3.2
3.3.3
3.3.4
3.3.5
34 80
3.4.1
3.4.2
3.4.3
3.4.4
3.4.5
3.5 97
4.1 101
4.2 103
4.2.1
4.2.2
4.2.3
4.2.4
4.3 114
4.4 116
4.4.1
4.4.2
4.5 121
4.6 123
5
5.1 126
5.2 128
5.2.1
5.2.2
5.2.3 K
5.3 132
5.3.1
5.3.2
5.3.3
5.4 141
5.4.1
5.4.2 PC
5.4.3
5.5 148
5.5.1
5.5.2 AFM
5.6 152
155
157
158
1
1.1
1,2)
3)
4) 2)
5)
(Coal Water Mixture,CWM) 6) 2)
7)
8,9)
2
10)
11,12)
13,14,15)
16,17)
3
1.2
1.2.1
Fig.1
10)
1100nm ( 10nm~10m18))100nm(
1m18))
(Solution)
1nm 1000nm 1m
19) 20)
21)
1m
*10)
(, , 1997)
Table 1.1
/
(Solution) /
(Solid
Solution)/
(Colloidal Solid)
(Suspensoid)
(Emulsoid)/
(Form) /
(Suspension)/
(Sol)
(gel)
(Emulsion)/
(Sol)
(gel)
(Macroscopic
Disperse System)
100nm
(1000nm~)
(Dispersed
system)
(Moleculer Disperse
System
1nm
(Colloidal Disperse
System)
1100nm
(1~1000nm)
/
4
1.2.2
G
22)
Fig.1.1 (1)~(7)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(a) (b)
(c) (d)
Fig. 1.1
G
(4)
0
(7)
(5)
(6)
G
0
(7)(4)
(5)
(6)
G
(1)
(2)
(3)
G
(3)
(1)
(2)
5
- -G
-G
Einstein23)
Krieger-Dougherty24)
7
7,10)
1) Bingham
Herschel-Bulkley 10)
Casson25)
0s-1
Krieger-Dougherty
26,27,28)0s-1
7,29,30)
Simha31) Mooney32)Quemada33) Mori-Ototake34)Mills35)
6
1.2.3 36,37)
van der Waals
van der Waals
van der Waals Lifshitz
38van der Waals
van der Waals
van der Waals
Gouy-Chapman
39)
Alexader-de Gennes
39,40)
(2~3nm)
41,42)
43,44)
7
Fig.1.2 DLVO van der Waals Va Vr
DLVO
45,46) van der Waals
V0
Fig. 1.2 DLVO
Interparticle distance [m]
Va
Vr
Vt
8
1.2.4
Quemada,Berli55)
Stokes-Einstein
56)=0.494
0.545
0.58
0.637
0.74
57) 58)
59) 60)
61,62)
9
Fig.1.3 18)
Fig.1.318)
V0
V0
(Transient separated aggregates or particles, )
(Transient percolated
network, )
(Repulsive glass, )
V0
V0
(Non-equilibrium
gel, )
(Equilibrium gel, )(Attractive glass, )
10
Fig.1 (Crystalline)
11
1.3
Eyring47)
Ree,Eyring48)
49) 50) 51)Ogawa
52) Krieger24)
53,54)
Quemada, Berli55)
0s-1
63,64) 35,65,66)
m
12
Fig.1.2
,67)
13
1.4
Mills
14
[1] (2010)
[2]
[3] Th.F. Tadros, Adv. Colloid Interface Sci. 68, pp.97 (1996)
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[8] E. Sakai, Y. Kakinuma, K. Yamamoto and M. Daimon, J.Advanced Concrete
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[11] K. Higashitani, K. Iimura, H. Sanda, Chemical Engineering Science, 56,
2927-2938 (2001)
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1982
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15
[22] K. Umeya, NENRYOU KYOUKAISHI, 64, 9, (1985)(in Japanese)
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(1959)
[26] C.L.A. Berli, D. Quemada, Langmuir, 16, pp.7968-7974(2000)
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[33] D. Quemada, Rheol. Acta 17, 632 (1978)
[34] 204881956
[35] P. Mills, Non-Newtonian behavior of flocculated suspensions. J. Physique Lett.,
46 L301-309 (1985)
[36] J.N.(1996)
[37] (1972)
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Elsevier,Amsterdam(1948)
[47] H.
[48] T. Ree, H. Eyring, J. Appl. Phys. 26, pp.793(1955)
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[51] 558, pp.15-22(2002)
16
[52] A. Ogawa, H. Yamada, S. Matsuda, K. Okajima, M. Doi, J.Rhoel.,41, pp.769(1997)
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(2002)
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Physics:Condensed Matter, 16,pp4831-4839(2004)
[60] H. Tanaka, Y. Nishikawa and T. Koyama, Journal of Physics:Condensed Matter, 17,
pp.143-153(2005)
[61] V. Trappe, V. Prasad, L. Cipelleti, P.N. Segre, D.A. Weitz, Nature, 411,(2001)
[62] H. Tanaka, J. Meunier, D. Bonn, Physical Review E, 69 (2004)
[63] B.B. (1984)
[64] P. Meakin, Advances in Colloid and Interface Science, 28, 249-331(1988)
[65] de Rooij R, Potanin AA, van den Ende D, Mellema J, J. Chem. Phys. 99 (11),
1(1993)
[66] M. Kobayashi, et al., On the steady shear viscosity of coagulated suspensions.
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[67] H.M. Wyss, E.V. Tervoort, L.J. Gauckler, J. Am. Ceram. Soc., 88, 9,
2337-2348(2005)
17
2
21
Fig.2.1.1
18
Fig.2.1
Input
Output
van der Waals
MillsMori-OtotakeQuemadaKrieger-
Dougherty
nm~ m~ mm~
19
22
2.2.1 1,2, 3)
Fig.2.2
1970 4)
R
r D
D
r
Rj
(2.1)
Fig.2.3 Fig.2.3 (a)~(c)
R0
R0/27 r < R0
1.46
Fig.2.3 (d)RR0/27 < R R0
Fig.2.4
(2.1)
Fig.2.2 5,6)
20
Fig.2.4 Fig.2.3 1)
jlog
-D
-2 Fractal region
0
R
rlog
0
0 27logR
R
0
0logR
R
46.1
3ln
5ln
ln
ln2
2
rR
jD
r=R0/9
0R
(b) r =R0/9, R=R0 , j=25
0R
r=R0/3
(a) r =R0/3, R=R0, j=5
46.1
3ln
5ln
ln
ln
rR
jD
0R
(c) r =R0/27, R=R0, j=125
46.1
3ln
5ln
ln
ln3
3
rR
jD
27/0Rr
30R
27/0Rr
(d) r=R0/27, R=R0/3, N=25
46.1
3ln
5ln
ln
ln2
2
rR
jD
Fig.2.3 1)
21
2.2.2 1,2,7,8,9,10)
(2.1) R
a j
(2.2)
D
fr
Rkj
(2.2)
(-)
Fig.2.4 Meakin 2,7)
DLA(Diffusion limited aggregation, )
2.5 2,7)
1,8,9) (LTA, Linear
Trajectory Aggreagte) EDEN
1,2,10)
D=2.8~3.0
Fig.2.4 off-lattice DLA 7)
22
V
N(0)
i
N )0( (2.3)
i
NReff
)0(
3
4 3
ia
R 3
D
a
R
3
D
effa
Rk
3
1 (2.4)
D
eff R
a
k
3
1
1
(2.5)
D3D=3 R
Fig.2.5 Eirl 11)
D=2.2
3.0 Fig.2.5
D=2.2
23
D=3.0
D=3.0
(2.1)(2.2)Eirl
08.246.4 Dk f (2.6)
Fig.2.5
( 11 )
24
Fig.2.6 (11
), kf,; Sorensen and Robert 12), Lattuada et al., 13) Mountain
and co-workers 14) 15), Wu and Friedlander 16), and Brasil and co-workers 17)18)
2.2.3
shear
thining
19,20,21)
Fig.2.7 22,23)
2.2
3.0
24)
(fracture exponent) 13,14,15,16,17)
Sontagg Russel25,26) 140nm NaCl0.4M
55.2
1Pa 2.2
9Pa20Pa 2.5
25
i
i (2.7)
879.0
0.005M
81.0 0.04M 89.0 0.1M 94.0 0.2M 96.0
0.4M 9.0 0.8 1.0
Horwatt 27)DLA(D=2.47), HCCA(D=1.96,
Hierarchical cluster-cluster aggregation) LTA(D=2.87), EDEN(D=2.96), RLA(2.20~2.93,
Reaction limited aggregation)
-1.0-0.8-2.2-11.3-0.01~-0.75
Eggersdorfer 28) 1.8
-0.74
Harada 22,23) D=2.2 D=3.0 Stokesian dynamics
D=2.2
D=3.0
Harshe 29)
D=1.70
D=2.45 D=2.70
D=2.75
Fig.2.8 2.6
2.6 EDEN
LTA
RLA
EDEN
LTA
26
Fig.2.7 =44.9Pa()D=2.2DLCA
()D=3.0 LTA (S.Harada, et al., 200623,24))
27
Fig.2.8 26) 23) 27) 28) 29)
30)
2.2.4 Breakup exponent
breakup
exponent30) ( the stable floc size exponent20)) breakup
exponent 19,20, 30,32~38)
(2.8)
R(m)G(s-1)mbreakup exponent(-)
75)
(2.9)
-15
-10
-5
0
1.8 2.1 2.4 2.7 3
Fra
ctu
re e
xp
on
en
t,
( -
)
Fractal dimension, D ( - )
Zaccone model(=0.4, 2009)
Zaccone model(=1/(d-D), 2009)
Sim.(Eggersdorfer, et al.,2010)
Sim.(Higashitani,et al.,2001)
Sim.(Harada, et al.,2006)
Sim.(Horwatt et al.,1992)
Exp. (Sonntag and Russel, 1986)
m=0.5
Present model, m=1/(4-D)
EDEN
cluster
RLA cluster
low sticking
RLA cluster
low sticking
LTA
cluster
28
(J/s/kg) (m2/s)
m Yuan 19)0.16 0.82
32)33)Tambo 32)Batche 34)m
Yuan
Tambo
(2.10)
Tensile strength of floc
m
Dm
4
2 (2.11)
Batche 34)
(2.12)
Dm
3
1 (2.13)
Zaccone 30)
breakup exponent
-
Zaccone 30)
D
29
d(-)
m
Fig.2.9 m
m
m
Tambo, Batche Zaccone
Fig.2.9 Breakup exponent 26,28,30,31,32,34,35,36,37,38)
0
0.2
0.4
0.6
0.8
1
0 1 2 3
Bre
ak
up
Ex
po
nen
t, m
( -
)
Fractal dimension, D ( - )
Zaccone model(=1/(d-D),
2009)Zaccone model(=0.4, 2009)
Tambo model (1979)
Bache model (1999)
Eq.[9]
Bache et al., humic
floc+Al2(SO4)3,(1999)Bouyer, bentnite
floc+Al2(SO4)3,(2004)Tao Li, et al.,
Kaolin+Al2(SO4)3,(2006)Tao Li, et al.,
Kaolin+Al2(SO4)3,(2006)Sonntag and Russel, 140nm
PSL, (1986)Kobayashi, et al., PSL,(1999)
Potanin, Sim.,(1993)
Eggersdorfer, Sim., (2010)
30
2.3
2.3.1
~39,40,41,42,
43,44,45,46)
(2.15)
Einstein40)
B=2.5 Batchelor41)
C=6.2 42)
43)
(2.16)
(-)
(2.16) (2.15)
Krieger- Dougherty44)
(2.17)
45) 46)
52.01
31
eff
eff
r
(2.18)
Fig.2.10
(2.4)
31
(2.8)
2.3.2
Lapasin, et al. 47)
Lapasin Quemada48)
(2.19)
(2.20)
(-) (-)
BCCA(Ballistic Cluster-Cluster Aggregation)DA(dense aggregate)
i
(2.21)
Fig. 2.10
32
i
(2.22)
(2.23)
(2.24)
Lapasin
0.15 0.40
2.3 2.95
Lapasin Shear thining
de Rooij et al. 49,50)
de Rooij
Krieger47)
33
dynamic exponentD
Collision radius
D (2.25)
de Rooij D=2.0~2.3
0.011
0.150
Folkersma 51)de Rooij
34
Kobayashi et al.,52)
Kobayashi Mori-Ototake47)
52.01
31
eff
eff
r
(2.18)
(2.4)
D
effa
Rk
3
1 (2.4)
Toress 53) van der Waals
Hamaker (J) (s-1) (m)
Kobayashi (self-consistent theory) 54)
Kobayashi Folkersma 51)
(2.4)(2.18)(2.31)
0.014 0.322
2.2 2.6
35
Mills55), Snable56)
i
Fig.2-12
2-3 Batchelor
5.2 41)
Fig.2-12
Einstein40)
Batchelor41)Brinkman42), Robinson46)
Mills55) 1985
Mills
Mills
Free cell model57)(cell)(shell)
;0 zy uu yux (2.32)
p p p
: Percolated cluster: Isolated particle or cluster
36
a
dy
22
Fig.2-13
(2-32) *
Fig.2-13
*
(2.33)
dy dt
(2.34)
a (m)
* a dy
(2.35)
22a
dy
Rigid
particle
Fluid shell
*
*
*
*
)(
)(
22
2
a
2
* dy
37
1
**
** 1
(2.36)
* ( - )
0
12*
0
2 (2.37)
2*0 11
(2.38)
Fig.2.10 Mills (a)
(2.38)
(2.38)
58) 59) 60)
Fig.2.10(b)
Snabre, Mills55,56) 2.0
R
2.0 2.0
(2-39)
38
2*0 11
eff
eff
(2.39)
ii
eff Fig. 2-10(b)
R D
D
effa
Rk
3
1 (2.4)
Mills
Mills
61)
)(FRF (2.40)
62)
RE
DE
DE RE
(N/m2)
(J/m2) R(m) 63)
39
RD
(2.41)
RF Deryaguin
64)
RFR 2
(2.42)
RR RF 2
2RR
(2.43)
D R
2)( DR
(2.44)
D
DK
(2.45)
RS a
2a
2
2
R
aN c
(2.46)
cN RS
R
NaaR
R
NNC
2
3
(2.47)
40
3
3
3
3
R
a
a
R
R
aNf
)1(
3
KRa
Rf
)1(
3
KRa
R
a
R
a
Rf
)1(
4
Kaa
Rf
(2.48)
f
Kaa
R
41
)1(
(2.49)
)1(
1
KA
)4/(1][ f
a
A
a
R
(2.50)
m
Ka
R
1'
(2.51)
'K
a K
Mills 0
a
41
)4/(1
1
f
a
A
a
R
(2.52)
(2.52) Snabre, Mills56)
m
a
R
*1
(2.53)
* (N/m2)(-)
Potanin 65)Boiss 66)
Chougnet, et al. 67)
Chougnet Mills 55)(2-39)
2*0 11
eff
eff
(2-39)
Chougnet
42
van der Waal Kobayashi
(2.30)
Chougnet 0.39~0.49 0.390.51
m=0.3~0.7 2.72.9
43
2.4
2.4.1
m
Kobayashi 52) breakup exponent
m=1/2 Chougnet 67)
m=0.30.7 D=2.72.9
Mills55) Potanin65)Soft m=1/2rigid
m=1/3
22,23,28,29) m
Kobayashi
MillsChougnet
3 4
m
3 3
4
2.4.2
breakup exponent
m Fig.2.9
26,28,68,69)Fig.2.9
Potanin38)Li 35)
Tambo 32)Batche
34)
Zaccone 30)
m
44
70)m
RF R
[N] [N]
[kg/m3] [m/s]
[-] [-]
[m2/s]
G[s-1]
[N]
[N] [-]
[-]
45
z [-]k
[-]
21)
(2.63)-1/(k+1)
54,67)
(2.63)
z
46
(2-61)(2-65) k= ( 3 D ) (2.64) m
Fig.2.8 (2.66) Tambo Batche
(2.66)
m
71,72,73)
26,28,68)(2.66)
Mills (2.50)
breakup exponent
breakup exponent (2.66)
(2.67)
f
a
Ri
(2.67)
m
a aF
a
R
2
(2.68)
m
ka
R
12
(2.69)
fm
ki
12
47
mf
fki
12
(2.70)
m
mf (2.71)
(2.66)(2.72)
m=0.5 52,53)
Fig.2.8 2.5 (2.72)(2.73)
2.5
(2.73)(2.72)(2.72)
EDEN
(RLA)Zaccone
EDEN RLA LTA
(2.72)
m
48
2.4.3
Fig.2.14 Brinkman
42)Mori-Ototake 45)
Mills
Mills,Chougnet 55,67) 0.57
0.550.6474)
Mills55)
2*0 11
eff
eff
(2.50)
D
effa
Rk
3
1 (2.4)
(2-66)
breakup exponent
)4/(12
D
a aF
a
R
(2.74)
Mills (2.52)(2.74)Mills
(2.74)
(2.4)(2.74)
(2.75)
49
(2.50)
(2.75)
3 5
3 3
Fig.2.14 46,76) 42,45,55)
1
10
100
1000
10000
100000
0 0.1 0.2 0.3 0.4 0.5 0.6
Rel
ati
ve
vis
cosi
ty(
-)
Volume fraction( - )
Mills model
Mori-Ototake model
Brinkman model
Exp. (Jones, et al, 1991)
Exp. (Jones, et al, 1991)
Exp. (Robinson, 1949)
50
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54
3
3.1
3.2 2
3.3
3.4
1)
2)
3.2
3.2.1
3)
4,5,6)
Lapasin 4)0.16 0.40 2.3
2.9 Chougnet 5)m=0.3~0.7
0.390.51 2.72.9
Kobayashi 6)m=0.5
Fig.3.1
0.014 0.322 2.2 2.6
2.2 m
Hersh 7)1.72.7
55
breakup exponent 0.350.55
m=1/(4-D) breakup exponent
Mills1)
2*0 11
eff
eff
(2.50)
(2.75)
K
* D
0.550.64
*
K, D
56
Fig.3.1 Kobayashi 6 )
3.2.2
Bushell Amal 8)(DLCA)
Chougnet
5)(1)~(4)
Fig.3 1.0620.0m
2.4mMicrotrac MT3300
SiO2 99.9%
2.29 1.0M NaNO30.15
0.55 0.05
2.0
2.2
2.4
2.6
2.8
0 0.1 0.2 0.3 0.4
Fra
cta
l d
imen
sio
n, D
( -
)
Volume fraction of particles ( - )
57
HAAKE RS150
20.00mm 21.70mm 60mm
120 8.0mm
100ml
2
1 2
2 15
(2-75)
Folkersma 9)
600
0.1Pa
0.001 s-1 300.0 s-1 30
Fig.3.2
0
0.4
0.8
1.2
1.6
2
0.1 1 10 100
dv/
dlo
g2r
(m
3 /m
3 )
2a (m)
Silica in ethanol
58
3.2.3
Fig.3.3 shear
thining
(2.50)(2.75)
0.15
0.9
0.15 1s-1 37 s-1 0.200.30 1s-1 106 s-1
0.35 119 s-1 300 s-1(2-50)
Fig.3.4 0.3 0.57
(2-75)
Fig.3.5 (2-75)
Fig.3.6
2.622.99
Fig.3.6 Folkersma 9)Luckham 10) 11)
(2-50)(2-75)Folkersma
1800nm (PSL)
Luckham
400nm PSL
KCl 0.001mol/l 1620nm
Fig.3.6 0.9
Folkersma 0.1s-1 100 s-1
Luckham 0.250.52 0.012.4s-1 400
s-1 0.55 0.01 s-1 38.2 s-1 0.6s-1
21 s-1 0.6 s-1 42 s-1
Luckham PSL 0.25 0.55
2.83 2.99
Folkersma 0.0310.22 PSL
2.3 2.7
Usui 0.30 0.45 2.89
59
0.30
2.8
(2.50)(2.75)Fig.3.5
0.150.30 0.35
Fig.3.6
Luckham 0.250.45 0.450.55
0.25
Fig.3.7
0100s-1
0.5
0.031-0.071 1.9 2.1
1.8012) 1.8913)
1.9514) DLCA 1.7215) 2.2416)
1.92.1
2.2 de Rooij 17)
2.1
0.1 2.62.9
60
0.3
0.35
0.4
0.45
0.5
0.55
0.6
1 10 100 1000
Eff
ecti
ve
vo
lum
e fr
act
ion
,
eff(
-)
Shear rate, G (s-1)
0.50
0.45
0.40
0.35
0.30
0.25
0.20
0.15
0.55
Fig3.4
1.00E+00
1.00E+01
1.00E+02
1.00E+03
1.00E+04
1.00E+05
1.00E+06
0.01 0.1 1 10 100 1000
Shear rate, G (s-1)
0.50
0.45
0.40
0.35
0.30
0.25
0.20
0.15
0.55
106
105
104
103
102
10
1
Rel
ati
ve
vis
cosi
ty,
r(
-)
10-2 10-1 102 1031 10
Fig. 3.3
61
Fig.3.6
9,10,11)
2.0
2.2
2.4
2.6
2.8
3.0
3.2
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Fra
cta
l dim
ensi
on, D
(-)
Volume fraction, (-)
Silica (This study)Cement (Gotoh and Nawa,2012)Silica (Usui, 2012)PSL (Folkersma, et al.,1999)PSL (Luckham, et al.1999)
c0.55y = 1.074x-0.014
R = 0.971
c0.50y = 1.187x-0.02
R = 0.976c0.45
y = 1.308x-0.032
R = 0.995
c0.15
y = 1.127x-0.277
R = 0.966 c0.20
y = 1.375x-0.241
R = 0.920
c0.25
y = 1.457x-0.23
R = 0.936
c0.35
y = 1.551x-0.094
R = 0.902
c0.30y = 1.559x-0.177
R = 0.934
c0.40
y = 1.420x-0.046
R = 0.982
1
0.01 0.1 1 10 100 1000
0.50
0.45
0.40
0.35
0.30
0.25
0.20
0.15
0.55
5
1
10-2 10-1 10 1021
Shear stress, (Pa)
ef
f/
(
-)
103
Fig.3.5
62
Fig.3.7
3.2.4
DLCA 18,19,20)
15,16,19)Fig.3.7
Matsushita 21)Fig.3.8 s t
D d
DLA
1.8
2
2.2
2.4
2.6
2.8
3
0 100 200 300 400
Fra
cta
l d
imen
sio
n, D
(-)
Shear rate, G (s-1)
Vol.Conc.0.30-0.45(Usui)
0.15-0.35 (This Exp.)
0.40-0.55 (This Exp.)
0.25-0.45 (data from Luckham and Ukeje)
0.52-0.57 (data from Luckham and Ukeje)
0.031-0.071(Folkersma,et.al.)
Vol.Conc. 0.117-0.322(Folkersma, et.al.)
63
22)Fig.3.9 (3.1) d=3.0 D
(3.1) D
(3.1)DLA
d
1.0
Fig.3.9
Lach-hab 23)
(DLCA)
(3.2)
(3.2)
Fig.3.6 3.0
Fig.3.6 (3.3) 95(3.3)
Mills
24)
64
0.15 25)
Fig.3.6Fig.3.7
0.100.15
Fig.3.8 21)
Fig.3.9 (3.1) dw D
1
1.5
2
2.5
3
1.5 2 2.5 3 3.5
Th
e fr
act
al
dim
ensi
on
of
pa
rtic
le
tra
ject
ory
, d
w(-
)
Fractal dimension of the aggregate, D(-)
s/t=0.5
s/t=1.0
s/t=1.5
s/t=2.0
s/t=3.0
wd
particleswalkrandomofnumberss :
occupiedbetositesperimetert :
65
33
3.3.1 26)
2.4
Krieger-Dougherty
27)
28)
29)
3.3.2 26)
Farris 30)
Farris
(Pas) (Pas)
66
m
Fig.3.10 Farris
8
Fig.3.10 Farris 26,30)
11,31,32,33,34)
31)(CWM)
Lee32)
m10m
11,33)
11,33) 34)
67
35)
m
m CWM 36)
Bull 37)
38)
CWM
3.3.3
(2.50)(2.75) * K
* D
(3.13)50 DLVO
K
50
[3] 17)
68
50
van der Waal
nm Pashley39, 40)AFM mica
(3-4)
(3.4)
(N)
(m)
Na+ mica C1,C2, ,
Na+ mica
40)0.21 Jm-20.06 Jm-20.3 nm 1.0 nm
DLVO 41,42)van der Waals
(3-5)(3-6)
AHamaker (J)
(-)
(Fm-1)
(V)
( (V))
Debye (m-1)
van der Waals 43,44)(3-4)
(3-5) van der Waals
(3-4)(3-5)(3-6) Ft(H)
69
(3.7)
NaNO3 0.35mol/l
Fig.3.11 Hamaker micamica 2.210-20J 40)
25 78.4 Debye 0.35
Fig.3.11
(3.4)(3.5)(3.6)(3.7)
Hamaker Ft /a
(2.74)
Fig.3.12
-5
-20mV van der Waals
van der Waals
(3.4)(3.5)(3.6)Ft /a
Fig.3.11 0.35mol/l NaNO3
-100
-50
0
50
100
0 5 10 15 20
Inte
rpar
ticl
e fo
rce,
F/a
*10
6 N
/m
Interparticle distance, H(nm)
Ft(H)/aFh(H)/aFa(H)/aFr(H)/a (-5mV)Fr(H)/a (-15mV)Fr(H)/a (-40mV)
70
(2-50)
0.550.64 56)
38)
45)
35)
m
k(-)
k(-)
j , k(-)
j (-)
j (-)
k(m)
(3.8)
71
(-)
3.3.4
Microtrac MT3300
Fig.3.12 Fig.3.12
V
50 2a A(2a3.9m)B(2a9.2m)C(2a
29.0m) 2.25 g/cm32.28 g/cm3
2.28 g/cm3
A:B:C=1:2:2 Mix1(2a10.6m), A:B=3:1
Mix6 (2a4.2m)
NaNO3 0.35mol/l 0.55
0.3610.1L2
302
15
HAAKE RS150Z40DIN
250.5Fig.3.13
300s-1 120 120
1s-1 300 s-1120 300 s-1 1 s-1
3
Zetasizer Nano ZS90(Malvern ) NaNO3
0.35mol/l 100ml 0.01g 10
15
72
Fig.3.13
300
1 2
t(s)240 240120
G (s-1)
240
3 4
Fig. 3.12
0
0.5
1
1.5
2
2.5
3
1 10 100
dV/d
(lo
g2a
) (m
3 /m
3)
Particle diameter, 2a (m)
A BC Mix1Mix6
73
3.3.5
Fig.3.14
*
Fig.3.15
C
C
-20
-16
-12
-8
-4
0
0 10 20 30 40
Zeta
po
ten
tial
, (m
V)
Particle diameter, 2a(m)
A BC Mix1Mix6
Fig.3.14 15 NaNO3 0.35mol/l
74
Fig.3.12
(3-8)
38)
88m 1410m
0.3800.394
0.385
(2-50)(2-75)
Table3.1 A,B 18300s-1
2 R2 0.98 C
Mills
18200s-1 R2 0.96
0s-1
Casson 46)
Table 3.1
Fig.3.15
0
20
40
60
80
100
120
140
160
0 100 200 300
Sh
ea
r s
tre
ss
,
(Pa
)
Shear rate, G (s-1)
Silica ASilica BSilica CMix1MIx6
75
Mix1Mix6 Table 3.1
A,B,C K,D
Mix1,Mix6 Table 3.1
Fig.3.16 A,B,C 0.55 0.70
K
()
A,B,C 50 2a Fig.3.16
2a Fig.3.17
50
(3-10)(3-11)(3-12)Mix1, Mix6 K K=1.234(Mix1)
K=1.177 (Mix6)Table 3.1 1
(3-10)
76
Fig.3.16 K
1.00
1.05
1.10
1.15
1.20
1.25
1.30
0.550 0.600 0.650 0.700 0.750 0.800
K (-
)
* (-)
A
B
C
y = 1.818x - 0.0057
R = 1
y = 1.814x - 0.0257
R = 1
y = 1.802x - 0.0552
R = 1
A B C Mix1 Mix6
2a m) 3.9 9.2 29.0 10.6 4.22
* (-) 0.641 0.654 0.678 0.694 0.656
(mV) -14.9 -10.1 -6.4 -15.6 -9.5
* (Pa) 18.8 8.0 2.5 6.9 17.4
(-) 0.0104 0.0100 0.0099 0.0256 0.0145
(Pa) 1.196 1.185 1.177 1.287 1.231
D (-) 2.989 2.990 2.990 2.974 2.985
K (-) 1.151 1.159 1.174 1.225 1.181
R2 0.980 0.988 0.956 0.989 0.987
Casson yield
stress 0c (Pa) 20.50 2.61 0.25 3.42 14.54
Static yield
stress 0 (Pa) 40.67 9.04 1.31 6.92 27.50
Silica fume suspension
Parameters
estimated from
PSD
Interparticle
forces
Parameters in
the rhelogy
model
Table 3.1 A, B, C, Mix1, Mix6
77
3.1 Fig.3.18
D
(3.13)
(3.13) 0.55 D=2.971 Fig.3.19 Mix1Mix6
D=2.971 Mix1
Mix6
Fig.3.19 Mix6
Fig.3.15 Mix1 B
2.974, 2.989
Mix6 Table3.1 D=2.985
K
y = -0.0006x + 1.8196R = 0.9873
y = 0.0017x + 0.0065R = 0.9832
0
0.02
0.04
0.06
1.800
1.805
1.810
1.815
1.820
0 10 20 30 40
q (
-)
p (
-)
Particle diameter, 2a (m)
Fig.3.17 p () q ()
78
3.0
m 1.0 48)
(2-75)
2.8
47) Fig.3.19
0.30
2.9 48)
2.75
Fig.3.18
2.0
2.2
2.4
2.6
2.8
3.0
3.2
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Fra
cta
l d
imen
sio
n, D
(-)
Volume fraction, (-)
Silica (This study)Cement (Gotoh and Nawa,2012)Silica (Usui, 2012)PSL (Folkersma, et al.,1999)PSL (Luckham, et al.1999)
79
0
20
40
60
80
100
120
140
160
0 100 200 300
Sh
ear
stre
ss, (
Pa
)
Shear rate, G(s-1)
Mix1 (exp.)
Mix1
(D=2.971)
Mix6
(Exp.)
Mix6
(D=2.900)
Mix6
(D=2.971)
Mix6
(D=2.985)
Mix6
(D=2.995)
D=2.995
D=2.985
D=2.971
D=2.900
D=2.971
Fig.3.19 () ()
80
34
3.4.1
0.30
2.8 3.0
Fig.2.5
Barthelmess 2)
Mills
3.4.2
(i) 49)
B3
B3
81
2/3
(Ns)
(1/m3)
U3
(ii) 11,33,34)
Simha 54)
82
(3.16) 0 (3.17)(3.18)
n (3.16)
11) 34)
(iii)
2.0
3.4.3
24)
12
50,51,52)
Mills
(2.50)
83
( - )
(2.1)
Mills
Fig.3.10
5)
(2.75)
(3.19)
k(m)
a(m)
k (m-3)
(m-3)
: (-)
84
2
k Barthelmes
2)Barthelmes
k 2k-1
k-1 k
k k-1
Barthelmesk
Barthelmes 4
Fig.3.20
85
k : k ( - )
i (m3 s-1)
k ( s-1)
( - )
(3.20) 1,2 3,4 k
5 k k 6 k+1 k
Fig.3.21
m
k k 2k-1
k-1 2k-2 k-1 2k-3
k-1 2 k-2 2 k-1 k
(3.20) 1,2 k
(3.20) 34 k 2 k-1
(3.20) 5 k+1 (3.20)
6
(3.20)
i k-i Flesch 55)
(3.21)
Pandya Spielman18)
( m-1s -1 )
( - )
( s -1)
86
(3-22)
(2-74)
k
(3.23)
( - )
( - )
2.7
Hersh 7)Hermawan
53) 2.73.0
2k-1 k
(3.23)
k (3.20)1
(3.19)(2.50)
87
Fig.3.21 k
3.4.4
SiO2
99.9%
2.29 NaNO3 1mol/l
0.55( 0.36) 25
HAAKE RS150
Microtrac MT3300
j= 1 j= 2 j= 22
k
j= 2k-1
2Rk
j= 2k-2
K-1
K
K
K
K
1
1
1,1
)1( )()(2),( k
i
kk
ki ikNiNdt
tkdN kk NS
max
,
ki
iiik NS
max
1
, )()(2i
ii
ik kNiN
(b)
(a)
(c)
(d)
)(:' /1 qsmA
)(: q
k
q
k RAS
*'
)(
:
3
, )(31.0 iikkii RRG
88
2
2
15
Fig.3.22 (a)(b)(c)
12(a)(b)
0.01s-1 300 s-1300 s-1 0.01 s-1
60 s-1
200 s-1(c)
60 s-1 18000
300
200
60
(s-1)
240 240 3600 3600300
1 2 3 4
(a)
t(s)
300
60
1 2
(b)
t(s)
240 240 3600
(s-1)
60
18000
1
(c)
t(s)
(s-1)
Fig.3.22
89
3.4.5
(a)1 (b)1
Fig.3.23
(a) (b) 2
(a)1
(b)1
60s-1
Fig.3.24 (a)(c)
60s-1(a)-4 200s-1
Fig.3.23 (b) -1
(a) -1 (b)-2
(a)-2
0
40
80
120
160
200
0 100 200 300 400
Shea
r st
ress
(Pa)
Shear rate(s-1)
(a)-(1)cycle1
(a)-(1)cycle2
(b)-(1)cycle1
(b)-(1)cycle2
Fig.3.23 (a)-1,(b)-1
90
(a)-2(a)-4 (2.50),(3.19)(3.22)
(3.20)
(3.22) q (3.23)
D
Fig.3.25
dV log2R
a=1.2m
0.55
0.64 56) Fig.3.25
38) 0.650
3.3 NaNO3 1.0mol/l van der Waals
3.3
van der
Waals 3.3
Fig.3.26 (a)-1 (2.50)(2.75)
0.995 214
300s-1(2.50)(2.75)
2.97
800
1000
1200
1400
1600
0 1000 2000 3000
Rla
tive
vis
cosi
ty (
-)
Elapsed time, ta2, ta4, tb2, tc1 ( s )
(a)-2
(a)-4
(b)-2
(c)-1
Fig.3.24 60s-1
91
y = 1.142x0.0257
R = 0.9952
1.006
1.008
1.01
1.012
0.0076 0.008 0.0084 0.0088
e
ff/
1/ (Pa-1)
Experimental value
Fig.3.26
0
2
4
6
1 10 100 1000
dv/
dlo
g2R
(m
3/m
3 )
Particle diameter, 2R(m)
Experimental result in Ethanol
Experimental result in
NaNO3 1N
Model prediction
(t=0)
Fig.3.25 (a)-2
92
(a)-2
1051
1051
24
Fig.3.25 NaNO3
1mol/l 100200m
22 (161m)23 (204m)
Fig.3.25
q
Fig.3.23
(b)-1 cycle2 Fig.3.27
(b)-1 cycle2 3.1
Fig.3.27
0
20
40
60
80
100
120
140
0 100 200 300 400
Sh
ear st
ress
, (P
a)
Shear rate, G (s -1)
Model prediction
Continuous Shear Exp.
(At equilibrium)
Constant Shear Exp.
(At equilibrium)
Fig.3.27
93
30s-1
Table3.2
q, Fig.3.27
60s-1
Fig.3.24(a)-2(a)-4(b)-23600 (a)-2
(a)-4 G
(a)Table3.2 Fig.3.25
60s-1 3600 200s-1
300 60s-1 3600 Fig.3.29
Fig.3.28
(a)-2
2m 200m
2m 200m
(3-9)~(3-13)
Table 3.2 (2.50),(3-19)(3-23)
Volume
fraction
Random packing
fraction
Radious of
a Particle
Fractal
dimension
Fragmentation
exponent
Fragmentation
constant
Order of the
largest aggregate
Interparticle
attractive force
( - ) * ( - ) a (m) D ( - ) q ( - ) A'( m-1 s-1 ) max ( - ) f/a2 ( Pa )
0.55 0.65 1.2 2.97 2.0 88360 40 18.8
94
40
44
48
52
56
60
0 1200 2400 3600
Sh
ear
stre
ss,
(P
a)
Time (s)
Exp.
Model prediction
Fig.3.29
(a)-2
(a)-4
Fig.3.28 (a)-2,(a)-4
()
0
1
2
3
4
5
6
1 10 100 1000
dv/
dlo
g2R
(m3)
Particle diameter, 2R (m)
Model (a)-2 (t=0)
Model (a)-2 (t=3600s)
Model (a)-4 (t=0s)
Model (a)-4 (t=3600)
95
(a) 60s-1
60s-1q, A
(c)
(c) 1545
Fig.3.30
Fig.3.31 (c)-1 6000
Fig.3.31
1800
Fig.3.30 0 1800 6000
Fig.3.30 (c)()
0
2
4
6
1 10 100 1000
dv/
dlo
g2
R (
m3)
Particle diameter, 2R (m)
Model (c) (t=0s)
Model (c) (t=1800s)
Model (c) (t=6000s)
Model (c) (t=18000s)
96
40
50
60
70
80
90
0 6000 12000 18000
Sh
ear
stre
ss,
(
Pa
)
Time (s)
Model prediction
Exp.
Fig.3.31 (c)60s-1
97
3.5
3.2 2.4
3.0
50s-1
3.3
DLVO
50
50
3.4
Barthlmes
Mills
98
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pp.629-632 (2008)
101
4
4.1
Mills1), Chougnet 2)
3)
3.0
DLCA(diffusion limited cluster aggregation,D=1.7)
RLCA(Reaction limited cluster aggregation, D=2.1)
4)
Harmawan 5)Harmawan
25nm
D=1.72.2
D=2.53.0
Fig.4.1(a)(b)
90s-1
6)Spicer 300s-1 50s-1
2.65 2.4
7)
Kobayashi 8)
2.5
102
Kobayashi
Fig.4.1 (a)
(b).
(b)Over the yield stressIn dilute system
R2
(a)Below the yield stressIn dilute system
R1
103
4.2
4.2.1
R
a
(4.1)
(4.2)
() (m) (m)
() ()
9)
Snabre10),
Mills1)
Fig.4.2(A)
(Fig.4.2(B))
Fig.4.2(C)
10)
Shih 11)
Wessel12)
104
Fig.4.2
4.2.2
11,13,14)
Potanin 13)
Fig.4.3
Fig.4.3
Fig.4.3 Shih
backbone
Potanin 13)de Rooij 14)
de Rooij 14)
(C) Packing of fractal
blobs(aggregates) and
formation of gel network
(B) At the percolation
threshold
(A) Aggregates
dispersed in liquid
Dilute Concentrated
105
Hook
(4.3)
(m)
Kantor Webman15)
(Pam3) (-)
(m)
Fig.4.3(c)
Fig.4.3 (a), (b)
(a)
(b)
106
chemical dimension(-)
U (J)
(N)
de Rooij
107
Fig.4.4 Bond stretching
14,16)
Fig.4.4 Bond bending
14,16)
Bond bendingIsotropic chain
gR
Bond stretchingStraight chain
gR
Fig.4.4 16) (Wyss, et al. , 2005)
108
4.2.3 17,18,19)
Fig.4.5
(a)(c)(d)
n 1/2
Flory
Fig.4.5 17)
(a) Dilute solution (b) Overlapped
(d) Concentrated solution
(c) Semi-dilute solution
109
3
n 3/5
Chemical dimension
(m) (m)
(Fig.4.5(b))
110
Fig.4.6
5/3
2.0
n
n
( =5/3)
111
( =2.0)
n
4.2.4
Fig.4.3
Fig.4.4
Bond stretching 14,16)Fig.4.4
Bond bending 14,16)
112
()
113
Chemical dimension
(4.10)(4.27)
de Rooij
114
4.3
Bushell 20)
Chougnet 2)(2.50)(2.75)
Usui21)
9,10)
P2
NaNO3 0.35mol/l NIKKISO
Microtrac MT3300
NIKKISO USVR 6mm
8mm
12.5ml/s
1.25 ml/s P2
Fig.4.6 50 2a 2.8m
P2 3.68 g/cm3Fig.4.6
22)
0.615 0.663
NaNO3 0.35mol/l
0.25,0.30,0.35,0.40,0.45,0.49, 0.52, 0.55, 0.58100ml
230
2
HAAKE RS150 Z40DIN
20.00mm 21.70mm 60mm
120 8.0mm
25
1, 3, 5, 7, 10, 15, 20, 25, 50, 100, 300s-1 180 180
23)
pH 7.3 7.4 pH
Malvern Mastersiazer 3000
633nm10mW He-Ne
NaNO3 0.35mol/l
115
500ppm
5 1500rpm 300
Fig.4.6 NaNO3
0.35mol/l
0
0.5
1
1.5
2
2.5
3
0.1 1 10 100 1000 10000
dv
/dlo
g2r
(m
3/m
3)
2a (m)
10-1 10-2 10-3 10-4
In ethanol
In NaNO3350mM
(Low speed)
In NaNO3350mM
(High speed)
116
4.4
4.4.1
Fig.4.7
Casson 24)
Fig.4.8 Casson 0s-1
Fig.4.9 Casson
0.40
Casson
Fig.4.7 ()
0.1
1
10
100
1000
0.1 1 10 100 1000
Sh
ear
stre
ss,
(
Pa
)
Shear rate, G(s-1)
c0.25
c0.30
c0.35
c0.4
c0.45
c0.49
c0.52
c0.55
c0.58
117
Fig.4.8 () Casson ()
0
4
8
12
16
20
0 5 10 15 20
0
.5(P
a0
.5)
G0.5 (s-0.5)
c0.25
c0.30
c0.35
c0.40
c0.45
c0.49
c0.52
c0.55
Fig.4.9 Casson
ca = 44047.9948
R = 0.9989
ca= 312.494.9342
R = 0.9983
0.1
1
10
100
0.1 1
ca
(Pa
)
(-)
c0.45-0.58
c0.25-0.40
118
Zhou 25) 0.42 0.42
de Rooij 26)
0.01 0.15
Channell 27) 0.10 0.40
Buscall 28)
dch=1.67, /
=1.0, =0
Table 4.1
1 D1 D1 D1
0.25-0.40 4.93
0.45-0.58 7.99 2.75 2.69 2.62
(=0) (=0.5) (=1.0)
2.59 2.49 2.39
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3
0 0.5 1 1.5
fra
cta
l dim
ensi
on
, D(-
)
(-)
=4.93
=7.99
Table 4.1 (4.28)
Fig.4.10 (4.28) D1
119
4.4.2
(2.50)(2.75)
Fig.4.7m(2.66)m=1/(4-D)
3~15s-1
Table 4.2
2.88 2.99 Harshe 29) Spicer 7)
D=2.42.7
Harshe Spicer
Fig.4.11
Table 4.2 (2.50)(2.75)
D2
(m= 1/(4-D))G (s
-1) R
2 ca
P2 0.25 0.1057 2.368 2.882 3-100 0.976 0.3
0.3 0.0977 2.137 2.892 3-300 0.955 0.8
0.35 0.0901 1.980 2.901 3-300 0.995 1.7
0.4 0.0861 1.842 2.906 5-300 0.989 3.5
0.45 0.0648 1.672 2.931 5-300 0.992 7.5
0.49 0.0475 1.526 2.950 7-300 0.973 14.1
0.52 0.0252 1.374 2.974 7-300 0.942 24.2
0.55 0.0148 1.267 2.985 10-300 0.945 37.7
0.58 0.0099 1.187 2.990 15-300 0.963 55.6
120
Fig.4.12
0.0
1.0
2.0
3.0
4.0
5.0
-6.0 -5.0 -4.0 -3.0 -2.0 -1.0 0.0
logI
(-)
logq (nm-1)
0min.
5min. with shear
Slope =2.34
Slope =1.53
2.20
2.40
2.60
2.80
3.00
0.00 0.10 0.20 0.30 0.40 0.50 0.60
Frac
tal d
ime
nsi
on
(-)
Volume concentration, (-)
Polydisperse alumina (Present study)polydisperse silica (data from Gotoh and Nawa)Polydisperse PSL (data from Luckham and Ukeje)Monodisperse PSL ( data from Folkersma, et al.)Monodisperse silica( data from Usui )
Fig.4.11 (2.50)(2.66)(2.75)
121
4.5
( i )
Fig.4.12
logq= -21
-5.57
122
(iii)
Fig.4.10
1.0 =2.39 (ii)
0
=2.59
2.88 2.91
(iV)
2.93 2.99
=1.0 =2.62
=0 =2.75
123
4.6
0.250.58
2.882.99
0.40 2.392.59
0.45 2.622.75
0.40
124
4
[1] P. Mills, Non-Newtonian behavior of flocculated suspensions, J. Physique Lett.,
Vol.46, L-301-L309(1985)
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1297-1301 (2008)
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126
5
PC AE
Fig.5.1 PC
(PGM)(MAA)
PC (MAA)(PGM)
PC
PC
1,2,3) 4) 5)
Napper 1) PC
PC
PC
de Gennes6,7)PC
8)PC(L)2
3
PC 7)PC
PC
(AFM)
9,10,11)
AFM PC
AFM
127
pHPC
12,13,14)
PC
PC
PC
Fig.5.1 PC
128
.
PC van
der Waals
H
Pt(H)=Pa(H)+Pr(H)+Pstr(H)
Pt(H)Pa
Pa(H)van der Waals Pa
Pr(H)Pa
Pstr(H)Pa
Pa(H)Pr(H) van der Waals Pa=J/m3(Pa=J/m3)
(J/m2) 15,16) H
)exp(100064)( 2 HCRTHPr
333
22
2
2
1
2
1
48)(
HHH
AHPa
kT
enz
222 8
)2
tanh(kT
ze
AHamaker J
(m)
V
F/m
nions/m3
eC
Cmol/l
129
Fig. 5.2 Fig. 5.2
PC DLVO
Pag
Pstr(H)Alexander-de Gennes 3,17)
H
130
sPC
Pa(H)Pr(H)
Pstr s
PCHPag
Mills18)
2*0 11
eff
eff
(2.50)
2
Chougnet 19)
1/
K
DLVO
Pag L
K
Pag K
Chougnet
K
Pag
131
K
PC Pstr(H)
PDLVO(H)
PDLVO(H) = Pa(H) + Pr(H)
PC KPag
PagPDLVO(H)K
sec
DLVOPK
PDLVOsec PDLVO(H)(Pa)
m(3-D )
KPagm(3-D)
PC
( NS )K
132
CC
CC CC
2.77N2BET 13.0m2/gXRD
CaCO3 93.5%
PC
PC (MPEG)
(MAA)1 MAAMPEG pq
p/(p+q)0.8 PC
(PEG) n 3 p=62.8q=15.7n=23
PC PC(1-1) PC PC(1-1) PC()
PC(0.5-1)PC(1-1)PC(2-1)
20)EOn=71.93nm
PC(0.5-1)PC(1-1)PC(2-1)2.5nm6.3nm12.4nm
C-C-C 2.51 20)
PC(1-1)19.6nm
PC Fig.5.1
GPC Table 5.1
GPC TSKguraecolumn TSKgel -5000TSKgel -4000
TSKgel -3000 40
//
/ 124.8g/286.5g/15588.7g/4000g
0.8mL/min 1wt% 250L
Viscotek Model302 670nm
SE-8
40
CC PC
Ca >CO3Ca+
Ca Ca Ca(NO3)2[Ca2+]=20mmol/l
Ca20mM 2 Na+NO3- CC
NaNO3 0.35mol/l
NaOH pH 12 PC CC
133
PC
[11] K NSNS
0.3%0.4%0.5% 4
CC0.254
HAKKE Rheo Stress RS150
Z40DIN 30 120 0.01(s-1)
300(s-1) 120 300(s-1) 0.01(s-1) 2
2300(s-1)
TOC () CC
CC PC PC
CC PC CC PC
CC CC 30
5C
0.45m
TOC
Malvern Zetasizer NanoCC CC
8.8cm 12000rpm 5 24 CC
Table 5.1 PC
PC
Polyethylene
oxide chain
n(mol)
p q
Side chain
length
S (nm)
Backbone
length
B (nm)
Weight-average
molecular
weight
PC(0.5-1) 9 67.3 16.9 2.5 21.0 15700
PC(1-1) 23 62.8 15.7 6.3 19.6 24300
PC(2-1) 45 66.4 16.9 12.4 20.8 42500
134
2 25V
10 1 1 8~10
(1)(2)(3)25
Fig.5.3Fig.5.4 Ca Ca20mM PCCC
PC
Ca20mM PC
Ca
Fig.5.5Fig.5.6 Ca Ca20mM PCCC
PC (mg/g) PC
PC(0.5-1)PC(1-1)PC(2-1)PC
PC(1-0.5)PC(1-1)PC(1-2)PCPC
PCCa20mM
PCPCPC
Fig.5.7~5.8 PC CC
PCPC
CC MPEG(/100nm2)MPEG
MPEG
PC
PC MPEG
PC
135
0
500
1000
1500
0 0.05 0.1 0.15 0.2 0.25 0.3
Ap
par
ent
visc
osi
ty (
mP
as)
Dosage of PC(wt%)
PC(0.5-1)
PC(1-1)
PC(2-1)
0
200
400
600
800
1000
1200
0 0.05 0.1 0.15 0.2 0.25 0.3
Ap
par
ent
visc
osi
ty (
mP
as)
Dosage of PC(wt%)
PC(0.5-1)
PC(1-1)
PC(2-1)
Fig. 5.4 Ca20mM PC
(300s-1)
Fig. 5.3 Ca0mM PC
(300s-1)
136
Fig. 5.6 Ca20mM PC
Fig. 5.5 Ca0mM PC
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 0.05 0.1 0.15 0.2 0.25 0.3
Ad
sorb
ed a
mo
un
t of P
C(m
g/g)
Dosage of PC(wt%)
PC(0.5-1)
PC(1-1)
PC(2-1)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 0.05 0.1 0.15 0.2 0.25 0.3
Ad
sorb
ed a
mo
un
t of P
C(m
g/g
)
Dosage of PC(wt%)
PC(0.5-1)
PC(1-1)
PC(2-1)
137
Fig. 5.7 Ca0mM
MPEG
Fig. 5.8 Ca20mM
MPEG
0
200
400
600
800
1000
1200
0 3 6 9 12 15
Ap
par
ent
visc
osi
ty (
mP
as)
Adsorbed amount of PC(MPEGs/100nm2)
PC(0.5-1)
PC(1-1)
PC(2-1)
0
200
400
600
800
1000
1200
0 3 6 9 12 15
Ap
par
ent
visc
osi
ty (
mP
as)
Adsorbed amount of PC(MPEGs/100nm2)
PC(0.5-1)
PC(1-1)
PC(2-1)
138
Fig.5.9Fig.5.10PC Langmuir
PC
0.99
Fig.5.11 Fig.5.12 Ca20mM PC
Ca PC
Ferrari 21)3 Si3N4
PC PC PC
PC
PC PC
PC
PC
22) CC PC>CO3Ca+
>CO3H2+>CO3Ca+
Ca20mM Ca Ferrari 21)
PC
PC(1-0.5)PC(1-1)PC(1-2)
MPEG
MPEG
PC
PC(0.5-1)PC(1-1)PC(2-1)CC PC
CC PC PC
139
Fig. 5.10 Ca20mM
()
Fig. 5.9 Ca0mM
()
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 100 200 300 400 500
Ad
sorb
ed n
um
ber
of P
C
(PC
s/1
00
nm
2)
Concentration of PC(mol/l)
PC(1-1)
PC(0.5-1)
PC(2-1)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 100 200 300 400 500
Ad
sorb
ed n
um
ber
of P
C
(PC
s/1
00
nm
2)
Concentration of PC(mol/l)
PC(1-1)
PC(0.5-1)
PC(2-1)
140
Fig. 5.12 Ca20mM
MPEG
Fig. 5.11 Ca0mM
MPEG
-15
-10
-5
0
5
10
15
0 2 4 6 8 10
Zeta
po
ten
tial
(mV
)
Adsorbed amount of PC(MPEGs/100nm2)
PC(0.5-1)
PC(1-1)
PC(2-1)
-15
-10
-5
0
5
10
15
0 2 4 6 8 10
Zeta
po
ten
tial
(mV
)
Adsorbed amount of PC(MPEGs/100nm2)
PC(0.5-1)
PC(1-1)
PC(2-1)
141
5.4
5.4.1
PC
van der WaalsHamakerCaCO3
23) 2.2310-20(J) K
DLVO
NS
Fig.5.13 NS NS PC
SO42-
Pr(H) NS
1.4nm
Fig.5.14
NS Ca Ca20mM
K 2.061.81 K Table
5.2 K PC Lpredicted
Fig.5.15 Fig.5.16 Lpredicted MPEG
PC(0.5-1) Lpredicted
PC PC Lpredicted S
NS Ca20mM
PC dosage
(wt%)(-) (-) D(-) G(s
-1) R
2 G=300 (mV) Pag K
0.3 0.0366 2.69 2.96 100-250 0.989 178 -4.68 -293296 1.70
0.4 0.0342 2.67 2.96 100-250 0.986 184 -8.19 -43812 1.85
0.5 0.0383 2.71 2.96 100-250 0.995 166 -10.9 -16090 1.87
average K 1.81
Table 5.2 K NS
142
Fig.5.13
Fig.5.14 NS
-20000
-15000
-10000
-5000
0
5000
10000
15000
20000
0 5 10 15 20
Inte
r p
arti
cel f
orc
es
(Pa)
Interparticle distance, H(nm)
Ca20mM NS 0.50wt%
Pr(H)
Pa(H)
Pt(H)
143
0
2
4
6
8
10
12
14
16
0 2 4 6 8 10
Pre
dic
ted
Lb
y m
od
el(n
m)
Adsorbed amount of PC(MPEGs/100nm2)
PC(0.5-1)
PC(1-1)
PC(2-1)
0
2
4
6
8
10
12
14
16
0 2 4 6 8 10
Pred
icte
d L
by
mo
del
(nm
)
Adsorbed amount of PC(MPEGs/100nm2)
PC(0.5-1)
PC(1-1)
PC(2-1)
Fig. 5.15 Ca0mM
Fig. 5.16 Ca20mM
144
5.4.2 PC
CC PC
PC
Fig.5.95.10 PC PC1
CC Q(nm2)
dA
Q100
QPC1 CC (nm2/PC)
AdPC (PCs/100nm2)
PC1 CC D (nm2)
QD
4
[2]D PC D
PC CC
PC
CC PC
145
Fig. 5.18 CC PC
Lmax 12 X
D
2d
L
effective cationic site
D
d
CaCO3
D
side chain
backbone
S
+
side chain
effective cationic site
backbone
aggregated PC
L
L
(a)long side chain
(b)short side chain
Fig. 5.17
146
5.4.3
CCPC
22) 24)
(PHREEQC)PC CC
PC Ca
Ca20mM CC PC [Adsite]
[Adsite] PC d(nm)
siteAd
d
1
CC PC d PC
(0.3nm) PC
CC
CCPC1D d x =D
/d D Dd x
PC L
2
2
12
1d
x
DL
L S
PC Lmax
SLL max
Fig.5.17 Table 5.3
LpredictedLmaxLpredicted
Ca PC 0.3wt%Ca20mM PC
0.2wt%PC(2-1) Ca
PC(0.5-1)PC(1-1)
Lmax
Lpredicted
147
Table 5.3 D,d,L,Lmax
PC
D (nm) d (nm) L (nm) Lmax (nm) Lpredicted (nm)
No Ca*1 20mM
Ca*2 No Ca
20mM
Ca No Ca
20mM
Ca No Ca
20mM
Ca
No Ca 20mM
Ca
PC(0.5-1) 12.7 10.2 1.0 0.8 0.7 0.8 3.2 3.3 9.4 15.1
PC(1-1) 14.9 11.5 1.1 0.9 0.6 0.7 6.9 7.0 8.7 12.9
PC(2-1) 18.8 13.5 1.3 0.9 0.4 0.6 12.8 13.0 7.5 14.3
*1: Ca(NO3)2 not added condition, *2: 20mM Ca(NO3)2 added condition
148
PC CC Fig.5.18
PC(2-1)Ca Lmax Lpredicted
Fig.5.18a
PC(0.5-1)PC(1-1) Ca20mM
PC(2-1)Lmax Lpredicted
Dominguez25)
SDS
SDS
Dominguez
Fig.5.19
PC PEG
PC(0.5-1)PC(1-1) Ca20mM PC(2-1)
CC PC
Fig.5.18bLmax Lpredicted
PC PC(0.5-1)PC(1-1)PC(2-1)
CC PC
Langmuir (Fig.5.95.10)Dominguez9)
SDSLangmuir
Langmuir
149
Fig.5.19 Dominguez25) SDS
AFM
Fig.5.16 Fig.5.19
nm AFM
AFM PC
S-image Nanonavi Real
SN-AF01 0.08N/m
DFM(Dynamic Force Mode) 0.5nm
Crystal Base Ca20mM HD-3
1ppm(1mg/l)60 PC
0.25 0.11wt% PC
Fig.5.20
1nm 5nm
Fig.5.21 nm
Fig.5.21 15nm
10nm
PC Fig.5.19
150
nmFig.5.16
PC
PC
PC
Fig.5.20 AFM
151
Fig.5.21 Ca20mM HD-3 1ppm AFM
669nm
14.9nm
152
5.6
PC PC
2nm 15nm
PC 13
20nm100~300nm
PC
Pt(D)
FaK
K
153
AFM
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2.2 3.0
156
D=2.88
2.99 0.40
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10