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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)

[4] C. Ye, D. Wang, B. Shi, J. Yu, J. Qu, M. Edwards, H. Tang, Colloid and Surfaces A:

Physicochem. Eng.Aspects, 294, pp.163-173(2007)

[5] No793(2013)

[6]

294pp.526-533 (2003)

[7] (2003)

[8] E. Sakai, Y. Kakinuma, K. Yamamoto and M. Daimon, J.Advanced Concrete

Technology, vol.7(1), pp.13-20(2009)

[9] Journal of Ceramics

Society of Japan, 106,11,1110-1113(1998)

[10] (1997)

[11] K. Higashitani, K. Iimura, H. Sanda, Chemical Engineering Science, 56,

2927-2938 (2001)

[12] S. Harada, et al., Dependence of fragmentation behavior of colloidal aggregates on

their fractal structure. Journal of colloid and interface science, 301, (2006) 123-129

[13] R.J. Flatt, I. Schober, E. Raphael, C. Plassard, E. Lesniewska, Langumuir, 25,

845-855(2009)

[14] C. J. Rueb and C. F. Zukoski, Viscoelastic properties of colloidal gels, Journal of

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[16]

-J.Soc.Powder Technol., Japan, 48,

456-463(2011)

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[18] M. Roth, Rheology of arrested colloids: A parameter study using novel

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[19] NIHON

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[20] 48 6 402-408 (1984)

1982

[21]G.K. Batchelor, J.T. Green, J. Fluid Mech, 56, 401 (1972)

15

[22] K. Umeya, NENRYOU KYOUKAISHI, 64, 9, (1985)(in Japanese)

[23] A. Einstein, Vol.19, pp.289-306 (1906)

[24] I.M. Krieger, T.J. Dougherty, Trans. Soc. Rheol., 3, pp.137 (1959)

[25] W. Casson, Rheology of dispersed systems, ed. Mill CC, 84-104, London : pergamon

(1959)

[26] C.L.A. Berli, D. Quemada, Langmuir, 16, pp.7968-7974(2000)

[27] B.E. Rodriguez, E.W.Kaler and M.S.Wolfe, Langmuir, 8, pp.2382-2389(1992)

[28] P.F. Luckham, M.A. Ukeje, J. of Colloid and Interface Sci., 220, 347-356(1999)

[29] J.S.Chong and E.B. Christiansen and A.D. Baer, J.Appl. Polymer Sci., 15, pp2007

(1971)

[30] K. Miyahara, Y. Adachi and K. Nakanishi, Colloids Surfaces A, 131, 69 (1998)

[31] R. Simha, J.Phys.Chem., 53, 1042 (1949)

[32] M. Mooney, J.Colloid and Interface Science., 6, 2, 162-170(1951)

[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)

[38] E.M. Lifshitz, Soviet Phys. JETP, 2, pp73-83(1956)

[39] S.J. Alexander, Journal de Physique,Vol.38,pp.983-987(1977)

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Colloid Interface Sci. Vol.27,pp.189-209(1987)

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[43]

41,4,(1994)

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Elsevier,Amsterdam(1948)

[47] H.

[48] T. Ree, H. Eyring, J. Appl. Phys. 26, pp.793(1955)

[49] S.H. Maron, P.E. Pierce, J. Colloid Sci. 11, pp.80 (1956)

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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)

[53] R. Buscall, J.Chem.Soc.Faraday Trans., 87, pp.1365(1991)

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[55] D. Quemada, C. Berli, Advances in Colloid and Interface Science, 98, pp51-85

(2002)

[56] R.H. Ottewill, N.St.J. Williams, Nature, 325, pp.232 (1987)

[57] W.G. Hoover, F.H. Ree, J. Chem. Phys. 49, pp.3609 (1968)

[58] P.N. Pusey, W. van Megen, Nature, 320, pp.340 (1986)

[59] A. Coniglio, L. de Arcangeilos, E.del Gado, A. Foerro and N. Sator, Journal of

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.

NIHON REOROJIGAKKISHI, Vol.28, No.3, 143-144 (2000)

[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)


1297-1301 (2008)

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97, 26-34, (1998)



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4772-4779 (1990)

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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)


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

)


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

)


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)


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

)


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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[4]

Vol.16No.1pp.335-340 (1994)

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155

(AFM)

Mills

2.2 3.0

156

D=2.88

2.99 0.40

PC

PC PC

PC

nm

AFM

PC

PC

157

:

No.64pp.545-551(2010)

No.65, pp.544-551 (2011)

No.66, pp.167-174(2012)

No.672014

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159

10

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