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