2. P P

4. Rheology is derived from the Greek words  flow) –  s  science) 

5. Rheology is defined as the Science concerned with the laws of deformation and flow of materials under the influence of stresses

6. 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 materials, processing conditions and final products It clarifies the interaction between different ingredients From the economic point of view, It helps in selection of the proper mix design for the desired workability pumbability and placement pumbability and placement

8. Non-Newtonian flow - time dependent Non-Newtonian flow -time independent Newtonian flow

9. Newtonian Flow Newtonian Flow  : shear stress (Pa)  : shear rate (1/s)  : Newtonian viscosity (Pa.s)  = . 

10. Shear stress (Pa ) Flow behavior of Newtonian liquid Shear rate (s -1 ) Flow curve Viscosity curve Shear rate (s -1 ) Viscosity Pa.s

11. Non-Newtonian Flow, Time Independent S Shear thinning materials hear thickening materials M Materials with a yield value

12. Non-Newtonian Flow Shear Stress  =   n (Power law)  : Apparent viscosity (Pa.s),  : Shear rate (s -1 ),  : Apparent viscosity (Pa.s),  : Shear rate (s -1 ), n n < 1 Shear thinning liquids > 1 Shear thickening liquids = 1 Newtonian liquids

13. Shear stress (Pa ) Flow behavior of shear thinning liquids Shear rate (s -1 ) Flow curve Shear rate (s -1 ) Viscosity curve Viscosity Pa.s

14. Dispersion with shear thinning behaviour at rest and high shear rate Materials at high shear rate Materials at rest Orientation Stretching Deformation Dis-aggregation

15. Shear stress (Pa ) Flow behavior of shear thickening liquids Shear rate (s -1 ) Flow curve Shear rate (s -1 ) Viscosity curve Viscosity Pa.s

16. Materials having a yield value do not flow at rest 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. These materials tend to flow when the shear stress is exceeding a certain value, the so called yield point.

17. Shear rate (s -1 ) Shear Stress Pa Flow curves Casson Model Bingham Model Herschel-Bulkely Model

18. Bingham Flow Model  : Shear stress (Pa)  : Shear stress (Pa)  =  o +   o  =  o +   o.  o : Shear rate (s -1 )  o : Shear rate (s -1 )  : Plastic viscosity (Pa s)  : Plastic viscosity (Pa s)  o : Yield stress (Pa)  o : Yield stress (Pa)

19. Casson Flow Model  1/2 = K1 + K2  1/2  : Shear stress (Pa)  : Shear rate (s -1 ) K 1 and K 2 are functions of yield stress and viscosity

20.  =  y + K h  1/m  y, K h and m are equation Coefficients If m = 1 and  y = 0, the equation results in Newtonian model If m = 1 and  y = 0, the equation results in Newtonian model If m = 1, the equation results in Bingham model If m = 1, the equation results in Bingham model If  y = 0, and 1/m= n the equation results in Newtonian model If  y = 0, and 1/m= n the equation results in Newtonian model

21. Non-Newtonian Liquids,Time Dependent Thixotropic materialsThixotropic materials Anti-thixotropic materials Anti-thixotropic materials Rheopectic materials Rheopectic materials Shear Stress (Pa) Shear Rate (s -1 )

22. (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

23. Shear rate Time Time Shear Stress Continually Changed Rate

24. Shear rate Time Shear stress Time Break down Equilibrium Stepwise Changed Rate

25. Hattori-Izumi Theory B : Friction coefficient J : Number contact points between particles in suspension per volume unit Viscosity  = B. J 2/3 (1) Viscosity  = B. J 2/3 (1)

26.  ss = B ss. J t 2/3 (4)  ss = B ss. J t 2/3 (4)  =  ll  ll + ls ls ls ls +  ss  ss (2) H-I Theory In suspension  ll  ll ~ ls ls ls ls << <<  ss  ss   Susp  Susp   ss  ss (3)

27. H-I Theory Degree of Coagulation J=0 n t =16 n s =16 U=0 J=8 n t =8 n s =16 U=0.5 J=15 n t =1 n s =16 U=1

28. H-I Theory Primary Particles Number. ns From w/c, density of water (  1 )and the cement (  2 )From w/c, density of water (  1 )and the cement (  2 ) Volume concentration of particles Average particle radius From the fineness of the cementFrom the fineness of the cement Total number of particles (per unit volume)Total number of particles (per unit volume)

29. H-I Theory reported that shear rate is a function of energy and time Shear Rate in Relation to Energy H-I Theory t: time E m : mechanical energy K: Boltzman constant T: absolute temperature

30. 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 Theory Diffused double layer

31. DLVO Theory Perikinetic coagulation rate DLVO Theory Perikinetic coagulation rate Total Interaction energy VTVTVTVT+ - V max VRVRVRVR VAVAVAVA Schematic illustration of the total interation energy V T V T = V R +V A

32. DLVO Theory In the cement paste, the ions (electric charges) or dispersing agent adsorbed on the surface on the cement particles will creat repulsive forces (V R : 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 (V A : Attractive potential energy

33. DLVO Theory How the number of agglomerates of particles changes versus time n t : 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 V max : maximum potential interaction energy.

34. H - I Theory H-I Theory is partly based on the last equation. [P= 2. K.k.r.n 3 & x = V max /Kt] Number of particles at time (t) Number of junction at time (t) J t = n s - n t Degree of coagulation at time t

35. H: Coagulation rate constant

36.  = const. high shear rate  = 0 at rest Shear stress

37. Mathematical Explaination of Thixotrpy General viscosity in the H-I Theory Viscosity at equilibriun The increase in Viscosity at rest

38. H CH 2 C O C C O C H 2 O H SO 3 H O

39. SO 3 H 2 C Na n

40. HN NHCH 2 N N N NHCH 2 HNH 2 C SO 3 Na O

41. C CH 2 C CH 2 R 1 R 1 COONa COOR 2 n

42. CH2 CH CH2 CH CO CH2CH2 O ( ) H ( ) x O Polymer Backbone Side chain

43. Individual Cement Compounds The Frrite phase C 4 AF C 3 S andC 2 S together make up 75-80 % of OPC. Dicalcium silicate C 2 S Tricalclum silicate C 3 S Tricalcium aluminate C 3 A 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.

44. Tricalcium Silicate C 3 S Tricalcium Silicate C 3 S 3CaO*2SiO 2 *4H 2 O +3Ca(OH) 2 2 [3CaO*SiO 2 ]+7 H 2 O

45. Dicalcium Silicate C 2 S 3CaO*2SiO 2 *4H 2 0+Ca(OH) 2 2[3CaO*SiO 2l ]+ 5 H 2 O

46. Tricalcium Aluminate C 2 A C 3 A*3CSH 32 C 3 A + 3CSH 2 + 26H 3[C 3 A*CSH 12 ] C 3 A*3CSH 32 + C 3 A + 4H

47. Tetracalcium Aluminoferate C 2 S C 4 (A,F)Hl3 +(AF)H3 C 4 AF+ 3CSH 2 + 16H 4[C6(A,F)SH32]+2(AF)H3 C3AF+ 12CSH2+110H

55. w/c Dose % Neat (B) 0.25 0.30 0.35 0.40 Na-MFS 0.25 0.30 0.35 0.40 0.25 Na-PhFS 0.25 0.30 0.35 0.40 0.25 Na-MFS 0.25 0.50 0.75 1.0 Na-PhFS 0.25 0.50 0.75 1.0 pp  R 24.889 15.474 5.0181 2.4086 376.68 310.49 308.11 233.37 0.999 0.990 0.904 0.816 18.177 7.8362 3.0269 1.05 315.72 307.11 241.99 159.73 0.998 0.945 0.859 0.814 17.638 5.8862 1.8217 0.8677 290.6 267.57 163.55 115.84 0.998 0.954 0.939 0.924 7.8401 3.5018 3.063 3.1816 307.26 219.97 141.11 84.164 0.946 0.938 0.990 0.993 Bingham parameters 5.8843 4.2855 2.9971 2.7883 267.79 91.92 126.23 75.597 0.954 0.976 0.982 0.984 K1K1 K2K2 R 4.0857 3.2812 1.6191 1.0218 12.456 10.76 13.081 12.228 0.996 0.997 0.960 0.910 3.7139 2.2007 1.2211 0.5807 11.523 11.872 11.924 10.888 0.992 0.979 0.921 0.883 3.4894 1.834 0.8406 0.5089 10.558 11.643 10.563 9.3924 0.998 0.982 0.974 0.963 2.2008 1.3055 1.2244 1.387 11.88 11.389 9.1136 6.3113 0.979 0.973 0.996 0.995 Casson parameters 1.8331 1.5186 1.2701 1.3246 11.654 10.173 8.2471 5.8018 0.982 0.991 0.994 Table 1 : Effect of admixtures on rheological parameters of Bingham and Casson equations for neat and superplasticizers cement pastes

56. Shearrate s -1 Shear rate s -1 Neat Na-MFS W/C= 0.25 Na-PhFS W/C=0.25 Shear stress 10 -1 Pa

57. Shear rate s -1 Na-MFSNa-PhFSNeat