Rheology. the science of flow and deformation of matter. ij ij. Material Element (m) {Force} {Deformation}

Size: px

Start display at page:

Download "Rheology. the science of flow and deformation of matter. ij ij. Material Element (m) {Force} {Deformation}"

Daniella Golden
5 years ago
Views:

1 Rheology the science of flow and deformation of matter {Force} Material Element (m) {Deformation} Stress ij Material Fnction or Rheological Eqation of state f (,, t ij ij ij ) Strain, ij ij,

2 Difference bt. Rheology and Flid Mechanics Rheology Eqation of motion for the system + Measred pressre drop and flow rate for the flid in the system Rheological properties of the flid Eqation of motion for the system Flid Mechanics + Rheological properties of the flid Measred pressre drop and flow rate for the flid in the system

3 Applied Fields of Rheology Polymer Rheology (Soltion, Melt, Solid) Sspension and Emlsion Rheology Electro- and Magneto- Rheology Food Rheology Bio-rheology, Hemo-rheology, Psyco-rheology Chemorheology Lbricant Rheology Srface Rheology

4 Why Rheology? Rheology is sensitive to material strctre => characterization Rheology describes the flow behavior => processing behavior Rheology correlates with end se performance => material performance

5 Interrelationship bt. Strctre- Property and Processing Moleclar Strctre MW & MWD Chain Branching and Cross-linking Interaction of Fillers with Matri Polymer Single or Mlti-Phase Strctre Viscoelastic Properties As a fnction of : Strain Rate(freqency) Strain Amplitde Temperatre Processability & Prodct Performance

6 Viscoelastic Behaviors. 시간의존성을갖는완화탄성율 G(t) : 점탄성. 전단담화점도거동 η( ) 3. 정상상태의단순전단장하에서의수직응력 τ -τ > 0 4. 연신심화점도거동 η E ( )

7 Rod Climbing (Weissenberg) Effect Newtonian Viscoelastic Free srface shape for a rotating rod in a reservior

8 Viscoelastic Flid Flow in a Sdden Contraction Tbe Streakline photographs illstrating the changing vorte growth as a fnction of λ for a viscoelastic liqid flowing in a 4.08 to circlar contraction (from Mackay and Boger, 988).

9 Die Swell

10 Rheological Eplanation on Die swell Die swell is related to the elastic properties of materials : reslt of a disorientation of macromolecles which have been oriented within the die by the high shear field. : reslt of the recovery of the elastic deformation imposed in the die. Die swell ratio depends on moleclar parameters : increase with MW and MWD : increase with long chain branching Die swell ratio depends on process parameters Die swell f L D, T, t

11 Die Design

$Melt Fractre Gloss Melt fractre slip Slip-stick sharkskin smooth Fig.$

12 Melt Fractre Gloss Melt fractre slip Slip-stick sharkskin smooth Fig. Apparent wall shear stress vs. apparent shear rate of the metallocene based LLPDE resin at T=0 o C. ( L/D=30, D=mm )

$Inflence of Long Chain Branching on Melt Fractre Resin A Resin B Resin C 0 0 0 3 Apparent shear rate (s - ) smooth sharkskin srface melt fractre gross melt fractre Fig.$

13 Inflence of Long Chain Branching on Melt Fractre Resin A Resin B Resin C Apparent shear rate (s - ) smooth sharkskin srface melt fractre gross melt fractre Fig. Photographs of the etrded strands for three resins at for apparent shear rates. (50 o C, Tngsten carbide die, D=mm, L/D =30; (a) 40.3 s -, (b) 5.4 s -, (c) s -, (d) 46.4 s - )

14 Die Srface Effect on Melt Fractre Diameter : mm L/D : 30 Entry angle : 80 o Hot-pressed Boron Nitride die Temperatre : 000 o C Pressre : 4 MPa Binder : B O 3 (boric acid ;-5 wt%) Fig. Photographs of the etrded strands for Resin A at varios processing conditions. ( Powder A; (a) 5.4 s -, (b) 4. s -, (c) 85.3 s -, (d) s - )

15 Ultrasonic Improvement of the Prodctivity of Etrsion Effect of ltrasonic vibrations on the pressre drop PS etrdates at 00 o C

16 Polymer Migration: The lower viscosity component tends to migrate to the region of higher shear rate 0 o C 40 o C Fig. Stained etrdate cross sections of Nylon6,/HDPE blends from the.5 etrder (Nylon appears black)

17 PS/PMMA Blend G ; G (Pa E+07 E+06 E+05 E+04 E+03 E+0 E+0 G B0 G B0 G B0 G B0 G B0 G B0 E+00 E-03 E-0 E+0 E+03 E-0 E+00 E+0 E+04 Freqency (rad/s) Additional relaation at low freqency is a reslt of the spherical domain relaation

18 LDPE/SEBS/PS Blend

19 Rbber Modls E [Pa] E+0 E+09 E+08 E+07 E tan SBR has a Tg at 44 o C. Adding carbon black increases the modls. If the SBR is replaced with polyisoprene (natral rbber*, the transition shifts to lower temperatre (56 o C). E Temperatre E (SBR E (SBR +CB E (NR tan delta (SBR tan delta (SBR+CB tan delta (NR

20 Reactive Systems Modli G, G" [Pa] E+05 E+04 E+03 E+0 E+0 E+00 E 0 E Time t [min] E+0 E+0 E+00 tan The time dependence of the modli allows to follow the cre. The crossover point of G and G can be correlated with the gel point

21 Storage Stability of Comple Flids The freqency dependence of the modls below the yield characterizes the internal strctre: G',G'' [Pa]; Viscosity [Pas] E+04 E+03 E+0 E+0 * G'' G' tan = G''/G' > to.5 good stability E freqency [rad/s] tan mst be between -.5 for best stability tan <: elasticity too high, interparticle forces case aggregation tan >.5: prely viscos behavior, no interparticle forces prevent coaglation

24 Rheometer An instrment that measres both stress and deformation history on a material to determine material fnctions Category of Rheometer what material fnctions they can measre Kinematics Type of straining Type of geometry shear rheometer etension rheometer small strain large strain steady straining homogeneos non-homogeneos indeer

25 Type of Rheometer EXTENSION SHEAR Nonhomogeneos Homogeneos RHEOMETERS Bbble collapse Rotating clamps, inflation methods Simple etension, lbricated compression Sliding plates Concentric cylinders Cone and plate Eccentric rotating disks Shear srface Parallel disks Capillary Slit Annls small strain (t ) G (t ) (, t ) E ( t, ) large strain G ( t, ) ( t, ) Etension Shear Steady straining INDEXERS Entrance flows Fiber spinning Stagnation flows ), ( ) ( ( ), ( ) ( ) Falling ball Rotating disk Etrdate swell Pressre hole Sqeezing flows

26 Spectrm of Material Classification in simple shear deformation Rigid Solid(Eclidean) 0 Linear Elastic Solid(Hookean) Nonlinear Elastic Solid G G ( ) Solid Viscoelastic F (,, t ) Nonlinear Viscos Flid(Non-Newtonian) Linear Viscos Flid(Newtonian) ( ) Flid Inviscid Flid(Pascalian) 0

27 Stress X F F ~ 3 F X 3 3 F X 3 33 F F F 3 etc. A A A 3 33 ij

28 Classical Strain Strain : a qantitative measre of the deformation of a material element Deformation occrs whenever any two points in a material are displaced from their initial position sch that a change in the separation between them reslts X s s s The magnitde of the deformation is determined by the relative displacements of the points. X X 3 Displacement gradient lim lim d s s 0 at point s s s s ds

29 ds d j i ~ T T i j j i i j j i j i ~ ~ ~ ~ Pre deformation Pre rotation Deformation Tensor

30 ji T i j j i j i i j i j j i ij ij v v v v t t t t e ~ ~ T i j j i ij e ~ ~ Strain Tensor Rate of Strain Tensor Strain and Rate of Strain Tensor

31 Isotropic and Anisotropic Stress and Strain Isotropic (volmetric) stress and strain -p Anisotropic (shear) stress and strain

32 Total Stress and Strain ij 3 ij ( e ij, ( 33 3 e ij e 33 ) ij 3 ) tr( ) ij ij v ( v v 3 3 ) 3 e v For an incompressible (isochoric) material ij p o ij, at eqilibrim p, ij ij o ij ij 0 3 tr( e ij ) 0, ij ij v ( i j v j i )

33 Constittive Eqation Prely Viscos Flid ij f ij Elastic Solid ij f ij Viscoelastic Flid ij f ij, ij, t

34 Criterion of Viscoelasticity Pipkin-Diagram - flow instabilities - slip-stick - etrdate roghness Deborah No. De t flid flow relaation time flow time G G the inverse of the typical deformation rate flid Fig. Schematic diagram showing the behavior of viscoelastic flids. The inverse of the amplitde of the oscillatory strain times its freqency 0

35 Maimm relaation time G 0 What is a maimm relaation time? in transient: G 0 e -t/ for t= = ma = t(0.367g 0) t G c in dynamic: G' = G'' = G c => ma =/

36 Simple Shear Flow V v y, v 0, v 0 y z v v 3 Viscosity Coefficient First Normal Stress Difference Coefficient Second Normal Stress Difference Coefficient 33

37 Viscosity and st normal stress difference coefficient as a fnction of shear rate Fig. Master crves for the viscosity and first normal stress difference coefficient as fnctions of shear rate for the LDPE melt. Reference temperatre = 43 K.

38 st and nd normal stress difference coefficient as a fnction of shear rate % PIB in Primol 3% PEO in a 57/38/5 Waterglycerinisopropyl alcohol mitre 7% alminim larate in decalin and m-cresol.5% PAA in a waterglycerin mitre.5% PAA in a 50/50 waterglycerin mitre Fig. Dependence of the first and second normal stress coefficients on shear rate for two polymer soltions and a soap soltion

39 Varios Types of Simple Shear Flow A. steady shear flow y v y B. smallampitde oscillatory shear y v ( cos( t)) y o C. stress growth pon inception of steady shear flow y Flid at rest v 0 v Steady shear flow t < 0 t > 0 o y Stress growth

40 Varios Types of Simple Shear Flow (contined) Steady shear flow Motion sddenly stopped D. Stress relaation after cessation y v of steady shear o y v 0 flow t < 0 t > 0 E. Stress relaation after a sdden shearing displacement F. Creep G. Constrained recoil after steady shear flow y y y Flid is rest t < 0 v Flid is rest t < 0 Steady shear flow v v t < 0 o 0 0 y v o Flid is rest y t > 0 Stress relaation Stress relaation Constant shear stress applied v ( t) y v ( t) Creep t > 0 Shear stress sddenly removed y recoil t > 0

41 Material Fnctions in Simple Shear Flows Steady shear flow Small-amplitde oscillatory shear Flow y constant o cost Material Fnction,,, G, G stress growth pon inception of steady shear flow Stress relaation after cessation of steady shear flow Stress relaation after a sdden shearing displacement Creep Constrained recoil after steady shear flow 0 t 0, t 0 y o t 0, o y 0 t 0 o ( t 0 t 0, t 0 y ) y y o y y t 0, 0 t 0 o G t,, t,, t, t,, t,, t, 0 0 t,, G t, J t, r , t,, J 0, e

42 Etentional (Shearfree ) Flow Deformation that involves stretching along streamlines. Simple etension: (same streamlines) Simple shear: (same streamlines) (different streamlines)

43 Characteristics of Etensional Flow Strong Flow: (Weak flow in shear flow: Irrotational flow - deformation by stretching & aligning (rotational flow in shear flow - deformation by tmbling & stretching) Not a viscometric flow The nonvanishing third invariant of deformation rate tensor Three major different types of etensional flows; niaial, biaial, planar etensional flows L(t) L0 ep t (eponential fnction) (t) (0) t (linear fnction)

44 Three Major Types of Etensional Flow niaial etension biaial etension planar etension

45 Three Major Types of Etensional Flow (contined) Unification of shearfree flows V b V y by V z z niaial: b=0, 0 biaial: b=0, 0 planar: b=, 0 Rate of deformation (Strain) tensor: 0 0 m m niaial: m = -/ biaial: m = planar: m = 0

46 Etensional Material Fnctions E(t, ) E for linear viscoelastic region: lim (t, ) (t) 3 (t) Uniaial etension: t, Biaial etension: t, B E 33 for linear viscoelastic region: 0 (t, ) E B B B B B lim B(t, B) B(t) 6 (t) 0 Planar etension: 33 t t E P, P, for linear viscoelastic region: 4 (t) (t) B P 33 P

47 Etensional Viscosity of LDPE

48 Comparison of Shear Rheometers Method Advantages Disadvantages Cone and plate Parallel disks (Torsional flow) Concentric cylinders (Coette flow) Capillary (Poiseille flow) Homogeneos 0. rad Best for N Best for G(t, ) Easy to load viscos samples Best for G and G for melt, cring Vary by h and (N-N)( ) Low, high Homogeneos if Ri/Ro0.95 Good for sspension settling High Sealed Process simlation et from P ent Wide range with L High : low, edge failre, loading difficlt Low : inertia Evaporation Need good alignment Nonhomogeneos:not good for G(t,) Ok for G(t) and ( ) Edge failre Evaporation End correction N impractical High flids are difficlt to clean Corrections for Pent time-consming Nonhomogeneos: no G(t,) Bad for time dependence Etrdate swell only qalitative for N

49 Comparison of Shear Rheometers (contined) Method Advantages Disadvantages Sliding plates Slit flow Aial annlar Flow Falling ball Sqeeze flow Contained bobs Simple design Homogeneos Linear motion High, G(t, ) t 0-3 s No Pent with wall-monted pressre transients (p) P e, P h give N Slit with no edges P can give N Very simple Neddle better Sealed rheometer High T, p Simple Process simlation ( ) at long times Sealed Process simlator Edges limit <0 Gap control Loading Edge effects with W/B>5 Similar to capillary Difficlt to clean Difficlt constrction and clean Not sefl for viscoelastic flids Nonhomogeneos Transparent flid Need Indeer flow: mied shear rates and shear transients Indeers Friction limits range

50 Viscosity measred by several Rheometers Adapted from Lan (988)

51 Late Sspensions with Yield Stress Adapted from Lan et. al. (99) The yield stress is best measred with a stress controlled rotational rheometer

52 The Co-Merz Relation 3.5% PAA in water

53 Comparison of Viscosity and First Normal Stress Coefficient PDMS melt Closed symbols: cone and plate Open symbols: birefringence

RHEOLOGY Principles, Measurements, and Applications. Christopher W. Macosko

RHEOLOGY Principles, Measurements, and Applications I -56081-5'79~5 1994 VCH Publishers. Inc. New York Part I. CONSTITUTIVE RELATIONS 1 1 l Elastic Solid 5 1.1 Introduction 5 1.2 The Stress Tensor 8 1.2.1