1. Che5700 陶瓷粉末處理
Rheology of Slurries
Review briefly interactions between polymer stabilized colloid systems:

2. Schematic Interaction Energy
Schematic calculation, taken from J. Colloid Interface Sci., 6:492, 1951.
Small size polymer, less effective; rigid better than flexible polymer

3. Batch Consistency Chapter 14 in JS Reed book 5 consistency state:
Che5700 陶瓷粉末處理
Batch Consistency
Chapter 14 in JS Reed book
5 consistency state:
Bulk powder (no liquid)
Agglomerates (granules)
Plastic body
Paste
Slurry (dilute solution called suspension; slip: slurry containing clay)
Factors:
Amount, distribution and properties of liquid
Amount, size and packing of particles
Types, amount and distribution of additives
Interparticles forces: attractive or repulsive

4. DPS = degree of pore saturation = volume of liquid / volume of pore
Plastic body
paste
slurry
granule

5. Che5700 陶瓷粉末處理
More Comments
Plastic state : often during extrusion, plastic pressing etc.
Granule & plastic body may rearrange due to applied force, to become more dense
Paste : often used in printing (thick films in electronic ceramics)
Slip or slurry: for casting

6. Che5700 陶瓷粉末處理
Springback
For plastic material, DPS = 1, on decompression, due to small compressibi-lity of liquid, volume expansion accom-panying slight particle rearrange-ment occur  springback SB

7. Batch Calculation Mostly by weight%; sometimes by vol%
Che5700 陶瓷粉末處理
Batch Calculation
Mostly by weight%; sometimes by vol%
Mostly based on total weight, sometimes based on weight of major ceramic powders

8. Some properties of suspension
Che5700 陶瓷粉末處理
Some properties of suspension
Some related to solute conc. only, unrelated to its chemistry: vapor pressure lowering, freezing point depression, boiling point elevation
a1 = activity; TBP = normal boiling point

9. Che5700 陶瓷粉末處理
Osmotic Pressure
Solute conc. produce chemical potential difference: 1o (T,P) = 1o (T, P+) + Rg T ln(a1); : osmotic pressure (membrane is capable to separate solvent and solute)
thermodynamics:  = c2 Rg T (similar to ideal gas law; osmotic pressure exerted by solute concentration c2)
Since c2 = w2/M2  can be used to determine MW
For non-ideal solutions, expressions for  can be complex
A simplified equation for polymer solution:1=1/2 makes second virial coefficient zero; called Flory point, or theta point  theta temperature

10. Osmotic Pressure in Colloidal Suspension
Che5700 陶瓷粉末處理
Osmotic Pressure in Colloidal Suspension
One of source: electrical double layer of colloids; many complex equations, results as the right figure (TA Ring, 1996);
Affected by zeta potential, double layer thickness, solid volume fraction etc.
a,b,.. Different particle packing models

11. Rheology basically: Newtonian fluid and non-Newtonian fluid
Che5700 陶瓷粉末處理
Rheology
basically: Newtonian fluid and non-Newtonian fluid
Viscosity = constant for Newtonian fluid; for non-Newtonian power law fluid model, shown as follows
Necessary to know rheology to predict flow of suspension into mold;  predict velocity distribution, shear stress on wall, pressure distribution in mold, etc
Rheology important to – transport, mixing, forming etc.
Apparent viscosity

12. Shear thinning
Shear thickening
取自TA Ring, 1996;

13. Comparsion of Instruments
Che5700 陶瓷粉末處理
Comparsion of Instruments
Capillary viscometer: simple to use, easy to change temp. and shear rate, similar to real fluid condition, can study extrudate behavior at the same time; drawback: rate of shear is not constant across capillary
Coaxial cylinder viscometer: all region under constant shear rate, easy to calibrate; drawback: high viscous material difficult to fill in, polymer may creep up along shaft
Cone and plate viscometer: also constant shear rate in all region, small sample, less heat build up; easy to fill in, easy to clean up; drawback: rate of shear limited to low rates

14. Che5700 陶瓷粉末處理
Measurements
Double cylinder or cone-and-plate or capillary tube are three common methods; Eq. derived to calculate viscosity from data; T = torque;
Measuring shear rate should be close to shear rate in use; left figure: shear rate varies with position, hence often use narrow annulus

15. Che5700 陶瓷粉末處理
Relative Indices
Some simple relative index for viscosity: e.g. time of fluid to pass a small hole
Gel strength – related to history of sample, need to stir with high shear for some time, settled, then measurement
Index of structural buildup – B gel = (Y2 - Y1)/ln(t2/t1) t2, t1 = time to wait
Index of structural breakdown B thix = (Y2 - Y1)/ ln(t2/t1); or (p1 - p2)/ln(t1/t2) [after constant shear rate different time; or different shear rate, same time]
Elastic nature: memory effect, not ideal

16. Four regimes of uniform rigid-sphere system: (I) Newtonian fluid; (II) shear thinning regime; (III) high shear Newtonian regime; (IV) shear thickening regime

17. Che5700 陶瓷粉末處理
Equations
Dilute suspension: Einstein equation – for spherical particles, =2.5; limited to <0.02 (volume fraction); s = solvent viscosity
Electro-viscous effect by Smouluchowski: zeta potential is included
Generalized Casson eq.

18. Effect of Polymers on Viscosity
Che5700 陶瓷粉末處理
Effect of Polymers on Viscosity
Polymer effect: (a) increase viscosity of solution; (b)adsorb on particle surface to increase its effective volume c [1 + (Ls/a)3]; Ls = span of polymer layer on particle surface
P = polymer volume fraction soluble in solvent (after deduction of adsorption; + dilation effect)

19. Dilute, Slightly Aggregated Suspension
Che5700 陶瓷粉末處理
Dilute, Slightly Aggregated Suspension
Colloidally unstable suspension; memory effect over long time scales  thixotropy
Cross equation: c and m are fitted parameters;o = low shear limit viscosity;  = high shear limit viscosity

20. Two limiting viscosities
Che5700 陶瓷粉末處理
Cross equation characteristics, and its corresponding particle structure (in suspension); shear rate stopped, Brownian motion will bring particle back to its network
取自TA Ring, 1996;
Two limiting viscosities

21. Percolation Threshold
Che5700 陶瓷粉末處理
Percolation Threshold
This concept occurs in many situations; here to unstable colloidal system, exist a minimum particle concentration, if higher than this value, particle form bridging network, showing yield strength; from Newtonian fluid to Cross equation or Bingham plastic fluid
percolation or bond percolation (後者數值較低) – because one bond involves two sites only; if site percolation, then each site can have z coordination
One can estimate percolation threshold for specific structures
Critical percolation volume fraction ~ 16%

22. Theoretical prediction of percolation threshold for various geometries: 取自TA Ring, 1996

23. For electro-statically stabilized suspensions: when close to PZC, viscosity of suspension increase quickly; away from pzc, like a Newtonian fluid; but for much higher or lower pH, due to ionic strength, double layer thickness decrease, system unstable again

24. Around PZC, high viscosity; after adding HEC, pzc shift  highest viscosity point also shift; due to HEC, value of viscosity also increase;
取自JS Reed, 1995

25. Concentrated Slurries
Che5700 陶瓷粉末處理
Concentrated Slurries
Can be sub-divided into different systems, e.g. stable or unstable; polymer or not; mono-modal particle size distribution
Polymer may entangle together  pseudo-plastic flow  Cross equation; some of parameters may be estimated from theory, e.g. m = (Mn/Mw) 1/5 [Mn = number averaged MW; Mw = weight averaged MW; ratio of these two values = width of MW distribution]
Concentrated suspension often time dependent rheology  thioxtropy  due to particle structure may change with shear stress  different stress lead to different steady state

26. Time Dependent Behavior
Che5700 陶瓷粉末處理
Time Dependent Behavior
After rest for a while, a gel strength developed due to particle structure formation;
With yield stress, coating can resist creep flow (gravitation)

27. Che5700 陶瓷粉末處理
Monodisperse System
Derivation rely on description of particle structure and their interaction
Still Cross equation, but for concentrated system, can be simplified to the following form: Pe = ratio between particle motion and diffusion; t for translational instead of rotational

28. Taken from TA Ring, 1996;

29. Shear thinning  3 body interaction

30. Che5700 陶瓷粉末處理
General Equation
Cross equation: both low shear or high shear viscosity can be represented by following equation: wherem =maximum volume fraction  often a fitted value from experimental data 0.5 – 0.74; n = 2 – 3; often 2
Doughtery-Krieger eq. similar; others include Mooney equation, Chong equation etc

31. Doughtery-Krieger equation: 取自JS Reed, 1995
cr & KH are two fiited parameters

32. Anisotropic Particles
Che5700 陶瓷粉末處理
Anisotropic Particles
E.g. rod, plate-like particles (clay) and its rheology; still use Cross equation to describe rheology; with one extra parameter r = b/a (aspect ratio)
For clay: different face, different charge, hence different behavior (structure) under different pH
For clay particles

33. 取自TA Ring, 1996

34. Different particle structure, different rheology