p p rheology is derived from the greek words flow) – s science)
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PP
Rheology
is derived from the Greek words
( rew flow) – logos (science)
Rheology
is derived from the Greek words
( rew flow) – logos (science)
Rheology is defined as
Rheology is defined as
the Science concerned with the laws of deformation and flow of materials under the influence of
stresses
the Science concerned with the laws of deformation and flow of materials under the influence of
stresses
It gives a comprehensive characterization of cement
What is the purpose of performing rheological measurement ?
What is the purpose of performing rheological measurement ?
Rheological tests are used for quality control of raw materials, processing conditions and final products
It clarifies the interactionbetween different ingredients
From the economic point of view, It helps in selection of the proper mix design for the desired workability pumbability and placement
Non-Newtonian flow - time dependent
Non-Newtonian flow -time independent
Newtonian flow
Newtonian FlowNewtonian Flow
: shear stress (Pa)
: shear rate (1/s)
: Newtonian viscosity (Pa.s)
= .
Sh
ear
str
ess
(P
a )
Flow behavior of Newtonian liquid
Shear rate (s-1)
Flow curve
Viscosity curve
Shear rate (s-1)V
isco
sit
y P
a.s
Non-Newtonian Flow, Time Independent
Non-Newtonian Flow, Time Independent
• Shear thinning materials
• Shear thickening materials
• Materials with a yield value
Non-Newtonian FlowNon-Newtonian Flow
Shear Stress = n (Power law)
: Apparent viscosity (Pa.s), : Shear rate (s-1),
• n < 1 Shear thinning liquids
• n > 1 Shear thickening liquids
• n = 1 Newtonian liquids
Sh
ear
str
ess
(P
a )
Flow behavior of shear thinning liquids
Shear rate (s-1)
Flow curve
Shear rate (s-1)
Viscosity curve
Vis
cos
ity
Pa
.s
Dispersion with shear thinning behaviour at rest and high shear rate
Materials at high shear rate
Materials at rest
Orientation
Stretching
Deformation
Dis-aggregation
Sh
ear
str
ess
(P
a )
Flow behavior of shear thickening liquids
Shear rate (s-1)
Flow curve
Shear rate (s-1)
Viscosity curve
Vis
cos
ity
Pa.
s
• Materials having a yield value do not flow at rest
• These materials tend to flow when the shear stress is exceeding a certain value, the so called yield point.
Shear rate (s-1)
Sh
ear
Str
ess
Pa
Flow curves
Casson Model
Bingham Model
Hersc
hel-Bulk
ely
Mod
el
Bingham Flow ModelBingham Flow Model
: Shear stress (Pa)
= o + o
.
o : Shear rate (s -1)
: Plastic viscosity (Pa s)
o : Yield stress (Pa)
Casson Flow ModelCasson Flow Model
1/2 = K1 + K2 1/2
: Shear stress (Pa)
: Shear rate (s-1)
K1 and K2 are functions of yield stress and viscosity
= y + Kh 1/m
y , Kh and m are equation Coefficients
• If m = 1 and y = 0, the equation results in Newtonian model
• If m = 1, the equation results in Bingham model
• If y = 0, and 1/m= n the equation results in Newtonian model
Non-Newtonian Liquids,Time Dependent
• Thixotropic materials
• Anti-thixotropic materials
• Rheopectic materials
Sh
ear
Str
ess
(Pa)
Shear Rate (s-1)
(Pa)
(S-1)
Area of hystresis (A)
A= . [Pa . S-1]
A = Nm-2.S-1 = N.m.s-1.m-3
A = (work/shear time)/ volume
A = energy/volume
She
ar r
ate
Time
Time
She
ar S
tres
s
Continually Changed Rate
She
ar r
ate
Time
She
ar s
tres
sTime
Break downEquilibrium
Stepwise Changed Rate
Hattori-Izumi TheoryHattori-Izumi Theory
B : Friction coefficient
J : Number contact points between particles in suspension per volume unit
Viscosity = B . J2/3 (1)
ss = Bss . Jt 2/3 (4)
= ll + ls + ss (2)
H-I TheoryIn suspension
ll ~ ls << ss Susp ss (3)
H-I TheoryDegree of Coagulation
J=0
nt=16
ns =16
U=0
J=8
nt=8
ns =16
U=0.5
J=15
nt=1
ns =16
U=1
H-I TheoryPrimary Particles Number. ns
•From w/c, density of water (1)and the cement (2)
w/c.C
1
1
SV ρρ
ρ
Volume concentration of particles
σρ S .
3r Average particle radius
•From the fineness of the cement
3..4
.3n
r
CVs
•Total number of particles (per unit volume)
H-I Theory reported that shear rate is a function of energy and time
kTE.
mtγ
Shear Rate in Relation to EnergyShear Rate in Relation to Energy
H-I Theory
t: timeEm : mechanical energyK: Boltzman constant T: absolute temperature
The inverse of 1/k, the thickness of the diffused double is the estimated size of how far electrostatic stabilization reaches from the surface of the particles
H - I TheoryDiffused double layer
.kT1000.
.N.I8.E.k
DLVO TheoryPerikinetic coagulation
rate
DLVO TheoryPerikinetic coagulation
rate
Tot
al I
nte
ract
ion
en
ergy
VT
+
-
Vmax
VR
VA
Schematic illustration of the total interation energy VT
VT = VR +VA
DLVO TheoryDLVO TheoryIn the cement paste, the ions (electric charges) or dispersing agent adsorbed on the surface on the cement particles will creat repulsive forces (VR: Repulsive potential energy). Opposite of this, there are some attractive force, like Van der Vaal forces which try to pull the particles togather if they are close enough to each other (VA: Attractive potential energy
DLVO TheoryHow the number of agglomerates of particles
changes versus time
]kt
V[
t
max
e
.r.t.K.2
t
dn k
nt: Number of agglomerate at the time t.
k: Debye Huckel parameter.
k: Boltzman constant.
K: Smoluchowski rapid coagulation constant.
k: Boltzman constant.
T: Absolute temperature
Vmax: maximum potential interaction energy.
H - I Theory
H-I Theory is partly based on the last equation.
]/[V
3t
maxe
K.k.r.t2
n
1
n
1kT
[P= 2. K.k.r.n3 & x = Vmax/Kt]
x
T
x
s
t eP
e.nn
Number of particles at time (t)
Number of junction at time (t) Jt = ns - nt
x
s
t
S ePt
Pt
n
JU
Degree of coagulation at time t
1Ht
HtU
S
Degree of coagulation at time t
H: Coagulation rate constant
T
V
s
x
max
e
2.K.k.r.nH
e
PH
k
= const. high shear rate
= 0 at rest
She
ar s
tres
s
32
)1)1)(γ)(H
γt1.(n.Bη
t333
Mathematical Explaination of Thixotrpy
32
1)1)(γ(HHt1γHtU
.n.Bηtt
2
o333
32
333 1Ht
Ht.n.Bη
General viscosity in the H-I Theory
Viscosity at equilibriun
The increase in Viscosity at rest
H
CH2 C
O
C C
O
C H2O H
SO3H
O
SO3
H2C
Na
n
HN
NHCH2
N
NN
NHCH2 HNH2C
SO3Na
O
C CH2 C CH2
R1R1
COONa COOR2n
CH2 CH CH2 CH
C O
CH2 CH2O( ) H
( )x
O
Polymer Backbone
Side chain
Individual Cement Compounds
The Frrite phase C4AF The Frrite phase C4AF
C3S andC2S together make up 75-80 % of OPC.C3S andC2S together make up 75-80 % of OPC.
Dicalcium silicate C2SDicalcium silicate C2STricalclum silicate C3STricalclum silicate C3S
Tricalcium aluminate C3ATricalcium aluminate C3A
Ettrengite and monosulphate are deposited on the surface of the gel-like CSH. Calcium ion, which rapidly adsorb on the hydrates cement grains giving a net positive charge.
Ettrengite and monosulphate are deposited on the surface of the gel-like CSH. Calcium ion, which rapidly adsorb on the hydrates cement grains giving a net positive charge.
Tricalcium Silicate C3S
3CaO*2SiO2*4H2O +3Ca(OH)2
2 [3CaO*SiO2]+7 H2O
Dicalcium Silicate C2S
3CaO*2SiO2*4H20+Ca(OH)2
2[3CaO*SiO2l]+ 5 H2O
Tricalcium Aluminate C2A
C3A*3CSH32
C3A + 3CSH2 + 26H
3[C3A*CSH12]
C3A*3CSH32 + C3A + 4H
Tetracalcium Aluminoferate C2S
C4(A,F)Hl3 +(AF)H3
C4AF+ 3CSH2 + 16H
4[C6(A,F)SH32]+2(AF)H3
C3AF+ 12CSH2+110H
w/cDose
%
Neat(B)
0.250.300.350.40
Na-MFS
0.250.300.350.40
0.25
Na-PhFS
0.250.300.350.40
0.25
Na-MFS0.25
0.250.500.751.0
Na-PhFS0.25
0.250.500.751.0
p R
24.88915.4745.01812.4086
376.68310.49308.11233.37
0.9990.9900.9040.816
18.1777.83623.0269
1.05
315.72307.11241.99159.73
0.9980.9450.8590.814
17.6385.88621.82170.8677
290.6267.57163.55115.84
0.9980.9540.9390.924
7.84013.50183.063
3.1816
307.26219.97141.1184.164
0.9460.9380.9900.993
Bingham parameters
5.88434.28552.99712.7883
267.7991.92
126.2375.597
0.9540.9760.9820.984
K1 K2 R
4.08573.28121.61911.0218
12.45610.76
13.08112.228
0.9960.9970.9600.910
3.71392.20071.22110.5807
11.52311.87211.92410.888
0.9920.9790.9210.883
3.48941.834
0.84060.5089
10.55811.64310.5639.3924
0.9980.9820.9740.963
2.20081.30551.22441.387
11.8811.3899.11366.3113
0.9790.9730.9960.995
Casson parameters
1.83311.51861.27011.3246
11.65410.1738.24715.8018
0.9820.9910.9910.994
Table 1 : Effect of admixtures on rheological parameters of Bingham and Casson equations for neat and superplasticizers cement pastes
Shear rate s-1Shear rate s-1
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0 50 100 150
w/c = 0.25
w/c = 0.30
w/c = 0.35
w/c = 0.40
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0 50 100 150
Dose = 0.25%
Dose = 0.50%
Dose = 0.75%
Dose = 1.0%
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0 50 100 150
Dose = 0.25%
Dose = 0.50%
Dose = 0.75%
Dose = 1.0%
Neat Na-MFSW/C= 0.25
Na-PhFSW/C=0.25
Sh
ear
stre
ss 1
0-1 P
aS
hea
r st
ress
10-1
Pa
Sh
ear
stre
ss 1
0-1 P
a
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0 50 100 150
w/c = 0.25
w/c = 0.30
w/c = 0.35
w/c = 0.40
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0 50 100 150
Dose = 0.25%
Dose = 0.50%
Dose = 0.75%
Dose = 1.0%
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0 50 100 150
Dose = 0.25%
Dose = 0.50%
Dose = 0.75%
Dose = 1.0%
Shear rate s -1
Na-MFS Na-PhFSNeat