Suspensions Particles and Polymers Polymer Rheology trees and plants-gum-arabic,cellulose ·seeds Guar gum,locust bean gum seaweed carageenan,alginates,agar .fruit ·pectins grains -starches microbial xanthan gum ◆animal -gelatin,keratin and petroleum -acrylic acid,polyacrylamide,and many plastics. Kinds of Polymer Chains Long Rods Coils/Strings Branching Polymer melts and solutions Viscosity of Polymer melts -molecular weight distribution -degree of branching shear rate -Temperature and Pressure Polymer solutions -all of the above -concentration -solvent interactions 1
1 Suspensions Particles and Polymers Polymer Rheology Kinds of Polymer Chains Long Rods Coils/Strings Branching Polymer melts and solutions Viscosity of Polymer melts -molecular weight distribution - degree of branching - shear rate - Temperature and Pressure Polymer solutions - all of the above -concentration -solvent interactions
Polymer melts Critical Molecular weight Mw.of a polymer Mw Mw;no of molten polymer is almost directly proportional to the weight average molecular weight Mw Mw>Mwe no is 。=K[MJ户4 Mw is the point where at which entanglemments become important.Below this value the chains may be considered as non-penetration spheres. Mw.depends on chain configuration and is usually on the order of tens of thousands. At higher shear complete entanglement rates chain entanglements begin to decrease and shear thinning complete alignment- occurs. Shear rate.(log scale) All the individual curves for a series of Mw's, temperatures,and shear rates can be incorprated into a master curve by plotting n versus。dhpe n。 PT where a is a constant near unity 2
2 Polymer melts Critical Molecular weight Mwe of a polymer Mw Mwe ; ηο is ηo = K Mw [ ]w 3.4 Mwe is the point where at which entanglemments become important. Below this value the chains may be considered as non-penetration spheres. Mwe depends on chain configuration and is usually on the order of tens of thousands. At higher shear rates chain entanglements begin to decrease and shear thinning occurs. where is a constant near unity versus into a master curve by plotting temperatures, and shear rates can be incorprated All the individual curvesfor a series of Mw's, α ρ η γ η η α T o Mw o &
All else being equal,broadening the molecular-weight distribution generally results in a polymer melt becoming non-Newtonian at lower values of shear rate,so by the time we come to those shear rates relevant to extruding etc.,the polymer is easier to handle with a lower viscosity. A small degree of branching of the polymer chains generally decreases the viscosity of a melt with the same average molecular weight since the branched chain is more compact.However,if the branching is extensive,for a reasonably high molecular weight (-10)the viscosity at low shear rates may be much higher,giv the difficulties for these cor 之netran rtheless,in almost all cases esults in a lower viscosity at h igh shear r rates. Polymer Solutions Solution Viscosity depends on same factors as polymer melts Viscosity also effect by concentration and solvent interaction effects ox 20 10 3.5 10 2 1 0.35 10) 103 10 103103 10 Shear rate,/s The flow curve for 3%w/w polystyrene in toluene, for different molecular weights(shown in millions) 3
3 Polymer Solutions Viscosity also effect by concentration and solvent interaction effects Solution Viscosity depends on same factors as polymer melts
10 10' 10 -0.5 103 103 10' 10 103 Shear rate,/s The flow curve for polystyrene in toluene, Mw-20M,for different concentrations of polymer (shown as wt.%) 参 哥 G位 good solvent bad solvent The effect of solvent quality on polymer coil dimensions. 丽 low electrolyte level high electrolyte level The effect of electrolyte on the coil dimensions of a polyelectrolyte
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Critical Concentration c* log7。 NB.235>10 so doubling concentration increases viscosity by ove an order of magnitude! slope =1.5 log c The zero-shear-rate viscosity of a polymer solution versus polymer concentration,showing the critical overlap concentration c. Intrinsic viscosity [n]=KM K and a are constants a varies from 0.5 for a random coil to 2 for a rigid rod Highly branched polymers When highly branched polymers are sheared. they too unwind,but they cannot form very long strings because of branching.Thus they do not give 'stringy liquids.' 5
5 Critical Concentration c* logηo log c Intrinsic viscosity [ ] η = KMα K and α are constants α varies from 0.5 for a random coil to 2 for a rigid rod Highly branched polymers When highly branched polymers are sheared, they too unwind, but they cannot form very long strings because of branching. Thus they do not give ‘stringy liquids.’
o0 10 10 01.001.011110 1001000 EAR RATE( 01 Viscosity relationship to shear stress and shear rate for a o 33% xanthan gum (XG)solution in"Standardized Tap Water (STW). Xanthan Gum Suspensions 0.33% 100 Xanthan D Xanthan E 35 10 xanthan B 3.5 134 Xanthan C 3.2 130 1 .01 1 0 Shear Stress dynes/cm^2 Aqueous Suspensions of Xanthan Gum PGA 1000 (MD) 100 Xanthan 3.5 PGA 0.27 36 XG%·PG% .01 8:88 .001 :83 01 .1 1 10 SHEAR STRESS (Pa) 6
6 .0001.001 .01 .1 1 10 100 1000 .01 .11 10 100 SHEAR RATE (1/s) VISCOSITY (Pa s) .01 .1 1 10 100 .01 .11 10 100 SHEAR STRESS (Pa) VISCOSITY (Pa s) Viscosity relationship to shear stress and shear rate for a 0.33% xanthan gum (XG) solution in "Standardized Tap Water" (STW). Xanthan Gum Suspensions 0.33 % .01 .1 1 10 .01 .11 10 100 Xanthan E 3.5 133 Mw Rw (MD) (nm) Xanthan D 3.75 136 Xanthan C 3.2 130 Xanthan B 3.5 134 Shear Stress dynes/cm^2 Viscosity (P) Aqueous Suspensions of Xanthan Gum & PGA .01 .1 1 10 .001 .01 .11 10 100 1000 SHEAR STRESS (Pa) VISCOSITY (Pa s) 0.33 - 0.00 XG% - PG% 0.33 - 0.55 0.33 - 0.33 0.00 - 0.33 0.00 - 0.55 Mw rw (MD) (nm) Xanthan 3.5 134 PGA 0.27 36
The Effect of Stabilizer,Stabilizer Blend,and Concentration on the Viscosity of O/W Emulsions(40%Oil) 1000001 1000 XGX -PGA% 8 4033.0.55 +033-0.33 0-0.33-000 +-0.00.0.55 60.00-000 10 100 SHEAR STRESS(Pa) Low shear viscosity of solutions and emulsions.Particle size was calculated as mean volume diameter. Gum Aqueous Emulsion viscosity Emulsion particle viscosity (Pa-s) 胎 = 0.00+0.00 4±012 107±18 88 0.04±0.002 10.61±0.01 50±5 3.00±0.66 0.33+0.33 145±12 28,000±2800 2.93±0.12 0.33+055 250±36 48,100±7200 2.43±0.61 ain the aqueous phase. "Orbitz"Soft Drink Candy "Beads" Size of bead 3.5 mm diameter. mass~30 mg, volume =~0.02 cc density =1.34g/cc suspending phase=1.01g/cc Xanthan/Gellan High Fructose Corn Syrup
7 The Effect of Stabilizer, Stabilizer Blend, and Concentration on the Viscosity of O/W Emulsions (40% Oil) 1 10 100 .1 10 1000 100000 SHEAR STRESS (Pa) * Gum concentration in aqueous phase XG% - PGA% 0.00 - 0.00 0.00 - 0.55 0.33 - 0.33 0.33 - 0.00 0.33 - 0.55 Low shear viscosity of solutions and emulsions. Particle size was calculated as mean volume diameter. 0.00 + 0.00 - 1.4 ± 0.12 10.17 ± 1.8 0.00 + 0.55 0.04 ± 0.002 25 ± 7 10.61 ± 0.01 0.33 + 0.00 50 ± 5 10,000 ± 900 3.00 ± 0.66 0.33 + 0.33 145 ± 12 28,000 ± 2800 2.93 ± 0.12 0.33 + 0.55 250 ± 36 48,100 ± 7200 2.43 ± 0.61 Gum concentrationsa (XG% + PGA%) Aqueous viscosity (Pa. s) (n=4) Emulsion viscosity (Pa. s) (n=2) Emulsion particle size (μm) a in the aqueou s phase. "Orbitz" Soft Drink Xanthan/Gellan High Fructose Corn Syrup Candy "Beads" Size of bead 3.5 mm diameter, mass ~30 mg, volume = ~0.02 cc density = 1.34g/cc suspending phase =1.01g/cc
Suspending Phase 1033 n=500 mPa s 102 710 100 50s1 10-1 10-2 月卡6mP 104 10-2 10 102 10 Plastic liquids and Yield points O 60 slope plastic viscosity Bingham 60 Plastic models √G=6。+n Casson 0=0。+k" Herschel Bulkley P
8 Suspending Phase 102 103 101 100 10-1 10-2 10-4 10-2 100 102 104 γ& η 50 s-1 η = 6 mPa s η = 500 mPa s Plastic liquids and Yield points σ γ& Bingham σ o σ o slope = ηp plastic viscosity Plastic models = Herschel Bulkley Casson o n o p σ σ kγ σ σ η γ & & + = +
latex dispersion-vield point? 01 6 (b) .,50Pg 50 06 2 latex dispersion-yield point? 104 (e) 102 103010 103 Shear rate.i/s"1 eu.a/P 9
9 latex dispersion - yield point? latex dispersion - yield point?
ketchup and drilling muds ~15 Pa spaghetti sauce ~25Pa mustard,and apple sauce ~60Pa mayonnaise ~90Pa tomato paste ~125Pa Casson Equation and Chocolate Confectioner's handling of chocolate %Coverage Dipping Thickness uniformity Enrobing Side coating Molding Feet/tails Air bubbles Decoration Pumping Tank agitation Casson O 0。 Bingham 0 V 10
10 • Confectioner’s handling of chocolate %Coverage Dipping Thickness & uniformity Enrobing Side coating Molding Feet/tails Air bubbles Decoration Pumping Tank agitation Casson Equation and Chocolate σ γ& Bingham σ o Casson σ o
