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流 變 學 之 簡 介 與 應 用 An Introduction to Rheology and Its Applications

流 變 學 之 簡 介 與 應 用 An Introduction to Rheology and Its Applications. Complex Fluids & Molecular Rheology Lab., Department of Chemical Engineering. 課程大綱. I. 流變現象與無因次群分析 II. 基礎量測系統與功能 III. 影響流變行為的主要因素 IV. 實驗分析原理與技術.

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流 變 學 之 簡 介 與 應 用 An Introduction to Rheology and Its Applications

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  1. 流 變 學 之 簡 介 與 應 用An Introduction to Rheology and Its Applications Complex Fluids & Molecular Rheology Lab., Department of Chemical Engineering

  2. 課程大綱 I. 流變現象與無因次群分析 II. 基礎量測系統與功能 III. 影響流變行為的主要因素 IV. 實驗分析原理與技術 Principal References: “Dynamics of Polymeric Liquids: Volume 1 Fluid Mechanics” by R.B. Bird et al., 2nd Ed., Wiley-Interscience (1987)

  3. Scope of Rheology • 計算流變 • 流體的不穩性 • 泡沫、乳液、界面活性劑 • 食品、生物材料 • 材料加工 • 微結構模擬 • 奈料科技、微流體 • 非牛頓流體力學 • 融熔高分子 • 高分子溶液 • 流變量測、實驗方法 • 固體、複合物 • 懸浮物、膠體 • 應用流變、一般論文 • Mini-symposia organized in the 「2004 世界流變會議」 • A rheologist should be familiar with the following subjects • 輸送現象 • 統計力學 • 高分子物理 • 膠體科學 • 分子動態理論

  4. 什 麼 是 流 變(Rheology)? • Rheology is the science of fluids. More specifically, the study of Non-Newtonian Fluids • 流體 • 為何需要流變學家? • Macromolecules are easily deformable • Chain interactions are complicated • Processings typically involve flows • Try to make Rheology not an issue Newton’s law of viscosity 牛頓流體 - 水、有機小分子溶劑等 非牛頓流體 - 高分子溶液、膠體等 黏度η為定值 黏度不為定值 (尤其在快速流場下)

  5. I.流 變 現 象 與 無 因 次 群 分 析 • 非牛頓流體的三大特徵 • 二次流與不穩定現象 • 特徵時間與無因次群分析

  6. 非 牛 頓 流 體 的 特 徵 • 非牛頓黏度(Non-Newtonian Viscosity) - Shear Thinning Flow curve for non-Newtonian Fluids 牛頓流體 (甘油加水) 非牛頓流體 (高分子溶液)

  7. 正向力差的效應(Normal Stress Differences) - Rod-Climbing 牛頓流體 (水) 非牛頓流體 (稀薄高分子溶液)

  8. 記憶效應(Memory effects) -Elastic Recoil - Open Syphon Flow

  9. 牛 頓 流 體 的 不 穩 定 性: 慣 性 效 應 Concentric Cylinders Onset of Secondary Flow Ta (or Re) plays the central role! Laminar Secondary Turbulent Taylor vortices Turbulent

  10. 非 牛 頓 流 體 的 不 穏 定 性: 黏 彈 性 效 應 “The mountains flowed before the Lord” [From Deborah’s Song, Biblical Book of Judges, verse 5:5], quoted by Markus Reiner at the Fourth International Congress on Rheology in 1963 • 收縮流道 - 描述非牛頓流體行為之程度 流體的特徵或 “鬆弛”時間 流動系統的特徵時間 剪切速率 非牛頓流體 (0.057%聚丙烯醯胺/葡萄糖 溶液) 牛頓流體 (葡萄糖漿)

  11. 流 變 性 質 的 微 觀 (分 子) 成 因 • 微觀的角度 • 流變的性質主要決定於 ● ● Deformable Small molecule Macromolecule Dilute/Entangled Polydispersity Flexibility Linear/Branched Chain interactions 流體組成性質 流場因素 Competition between relaxation & deformation rates Flow strength Flow kinematics

  12. Lubrication High-speed coating Rolling Spraying • 典型製程之流場強度範圍 Injection molding Pipe flow Chewing Extrusion Sedimentation Typical viscosity curve of a polyolefin- PP homopolymer, melt flow rate (230 C/2.16 Kg) of 8 g/10 min- at 230 C with indication of the shear rate regions of different conversion techniques. [Reproduced from M. Gahleitner, “Melt rheology of polyolefins”, Prog. Polym. Sci., 26, 895 (2001).]

  13. Secondary flow Secondary Flows and Instabilities Secondary flow around a rotating sphere in a polyacrylamide solution. [Reporduce from H. Giesekus in E. H. Lee, ed., Proceedings of the Fourth International Congress on Rheology, Wiley-Interscience, New York (1965), Part 1, pp. 249-266]

  14. Melt instability Sharkskin Melt fracture Photographs of LLDPE melt pass through a capillary tube under various shear rates. The shear rates are 37, 112, 750 and 2250 s-1, respectively. [Reproduced from R. H. Moynihan, “The Flow at Polymer and Metal Interfaces”, Ph.D. Thesis, Department of Chemical Engineering, Virginia Tech., Blackburg, VA, 1990.] [Retrieved from the video of Non-Newtonian Fluid Mechanics (University of Wales Institute of Non-Newtonian Fluid Mechanics, 2000)]

  15. Taylor-Couette flow for dilute solutions Taylor vortex R2 R1 Flow visualization of the elastic Taylor-Couette instability in Boger fluids. [http://www.cchem.berkeley.edu/sjmgrp/] [S. J. Muller, E. S. G. Shaqfeh and R. G. Larson, “Experimental studies of the onset of oscillatory instability in viscoelastic Taylor-Couette flow”, J. Non-Newtonian Fluid Mech., 46, 315 (1993).]

  16. II.基 礎 量 測 系 統 與 功 能 • 剪切流與非剪切流 • 流變儀夾具選擇與應用 • 基礎流變量測模式與功能

  17. Two standard typesof flows, shear and shearfree, are frequently used to characterize polymeric liquids 典 型 均 勻 流 場 (b) Shearfree (a) Shear Elongation rate Steady simple shear flow Shear rate Streamlines for elongational flow (b=0)

  18. The Stress Tensor y x z Elongational Flow Shear Flow Total stress tensor* Stress tensor Hydrostatic pressure forces

  19. 流 變 儀 夾 具 與 流 場 特 性 (a) Shear Pressure Flow: Capillary Drag Flows: Concentric Cylinder Cone-and-Plate Parallel Plates (b) Elongation Moving Clamps

  20. 適 用 流 場 強 度 與 濃 度 範 圍 (a) Shear Concentrated Regime Dilute Regime Homogeneous deformation:* Cone-and-Plate Concentric Cylinder Nonhomogeneous deformation: Parallel Plates Capillary (b) Elongation Moving clamps For Melts & High-Viscosity Solutions *Stress and strain are independent of position throughout the sample

  21. 基 礎 黏 度 量 測 Concentric Cylinder FIG. Concentric cylinder viscometer (homogeneous)

  22. Cone-and-Plate Instrument (From p.205 of ref 3) FIG. 1.3-4. Cone-and-plate geometry (homogeneous)

  23. Uniaxial Elongational Flow Device used to generate uniaxial elongational flows by separating Clamped ends of the sample

  24. 典 型 剪 切 流 量 測 模 式

  25. 穩 態 剪 切 流 Exp a: Steady Shear Flow Non-Newtonian viscosity η of a low-density polyethylene at several Different temperatures The first and second normal stress coefficients are defined as follows: The shear-rate dependent viscosity η is defined as:

  26. Relative Viscosity: Master curves for the viscosity and first normal stress difference coefficient as functions of shear rate for the low-density polyethylene melt shown in previous figure Intrinsic Viscosity: Intrinsic viscosity of dilute polystyrene Solutions, With various solvents, as a function of reduced shear rate β

  27. 小振幅反覆式剪切流: 黏性與彈性檢定 Exp b: Small-Amplitude Oscillatory Shear Flow Oscillatory shear strain, shear rate, shear stress, and first normal stress difference in small-amplitude oscillatory shear flow

  28. It is customary to rewrite the above equations to display the in-phase and out-of-phase parts of the shear stress Storage modulus Loss modulus Storage and loss moduli, G’ and G”, as functions of frequency ω at a reference temperature of T0=423 K for the low-density polyethylene melt shown in Fig. 3.3-1. The solid curves are calculated from the generalized Maxwell model, Eqs. 5.2-13 through 15

  29. III. 拉 伸 流 黏 度 量 測 與 特 徵 Shearfree Flow Material Functions

  30. The number average and weight average molecular weights of the samples: Monodisperse, but with a tail in high M.W. (GPC results)

  31. III. 影 響 流 變 行 為 的 主 要 因 素 • 時間－溫度疊合原理 • 分子量及其分佈的效應 • 高分子結構的影響 • 溶劑品質及其效應

  32. 時間－溫度 疊合原理(Time-Temperature Superposition) Master curves for the viscosity and first normal Stress coefficient as functions of shear rate for a low-density polyethylene melt Non-Newtonian viscosity of a low-density polyethylene melt at several different temperatures.

  33. Newtonian Power law Zero-shear viscosity, 0 According to the Reptation Theory:

  34. Time-temperature superposition holds for many polymer melts and solutions, as long as there are no phase transitions or other temperature-dependent structural changes in the liquid. Time-temperature shifting is extremely useful in practical applications, allowing one to makeprediction of time-dependent material response. WLF 溫度重整因子:

  35. WLF temperature shift parameters J. D. Ferry, Viscoelastic Properties of Polymers, 3rd ed., Wiley: New York (1980).

  36. II. 分子量的效應 (Molecular Weight Dependences) For linear polymer melts Mc (=2Me): critical molecular weight Me: entangled molecular weight Plot of constant + log 0 vs. constant + log M for nine different polymers. The two constants are different for each of the polymers, and the one appearing in the abscissa is proportional to concentration, which is constant for a given undiluted polymer. For each polymer the slopes of the left and right straight line regions are 1.0 and 3.4, respectively. [G. C. Berry and T. G. Fox, Adv. Polym. Sci. 5, 261-357 (1968).]

  37. A “Time-Temperature-Molecular Weight-Concentration” Superposition: A master curve of polystyrene-n-butyl benzene solutions. Molecular weights varied from 1.6x105 to 2.4x106 g/mol, concentration from 0.255 to 0.55 g/cm3, and temperature from 303 to 333 K.

  38. III. 分子量分佈的影響 H. Munstedt, J. Rheol. 24, 847-867 (1980)

  39. IV. 高分子結構的影響 (Molecular Architecture) Linear PolymerStar PolymerPom-Pom Polymer polybutadienePolyisoprenePolyisoprene S. C. Shie, C. T. Wu, C. C. Hua, Macromolecules36, 2141-2148 (2003) C. C. Hua, H. Y. Kuo, J Polym Sci Part B: Polym Phys38, 248-261 (2006)

  40. V. 溶劑品質及其對高分子溶液的影響 (Effects of Solvent Quality for Polymer Solutions) [cf. p109] An example of viscosity versus concentration plots for polystyrene (Mw=7.14106 g/mol) in benzene at 30 C. White circles: plot of sp / c vs. c; black circles: plot of (lnr)/c vs. c. (1) Zimm-Crothers viscometer (3.710-3 ~7.610-2 dyn/cm2); (2)Ubbelohde viscometer (8.67 dyn/cm2); (3)Ubbelohde viscometer (12.2 dyn/cm2). T. Kotaka et al., J. Chem. Phys. 45, 2770-2773 (1966).

  41. Superposition of Intrinsic Viscosity Data on Various Solvent Systems: • Magnitude of intrinsic viscosity • -temperature & Solvent • Flow curve T. Kotaka et al., J. Chem. Phys. 45, 2770-2773 (1966).

  42. The solvent quality is an index describing the strength of polymer-solvent interactions. This interaction strength is a function of chemical species of polymer & solvent molecules, temperature, and pressure. Essential Scaling Laws: Scaling law of polymer size and molecular weight (<R2>end-to-end 1/2 ~ Mw).

  43. Phase Separation by Temperature-Induced Solvent Quality Changes: The (temperature, weight fraction) phase diagram for the polystyrene-cyclohexane system for samples of Indicated molecular weight. S. Saeki et al, Macromolecules 6, 246-250(1973). TU: upper critical solution temperature TL: lower critical solution temperature

  44. coil globule Coil-Globule Transition due to Changes in Solvent Quality: Poly(N-isopropylacrylamide) in water Mw = 4.45x105 g/mol, c = 6.65x10-4 g/ml Mw = 1.00x107 g/mol, c = 2.50x10-5 g/ml coil globule X. Wang et al., Macromolecules 31, 2972-2976 (1998). H. Yang et al., Polymer 44, 7175-7180 (2003).

  45. IV. 實 驗 分 析 原 理 與 技 術 • 線性黏彈性與轉換關係 • 非線性應力鬆弛與分析

  46. The Maxwell model (for melts or concentrated solutions) I. 線性黏彈性分析 (Linear Viscoelasticity) The nature of flow Relaxation modulus, G(t): The nature of fluid

  47. Other Transformation Relationships s = t-t’ η0 is zero-shear viscosity η’ is dynamic viscosity Je0 is steady- state compliance

  48. G0 The single exponential mode, eq1, with relaxation time λ=0.1 s and G0=105 Pa. G(t) (Pa) The single mode dose not fit typical data well. A logical improvement on this model is to try several relaxation times , shown as eq2. G(t) (Pa) G1 G2 G3 t (s) A spectral decomposition of five-constant model combined with eq2. G4 G5 C. H. Macosko, Rheology Principles, Measurements, and Applications, Wiley-VCH: New York (1994).

  49. G”(Pa) ω(s-1) Relaxation times and moduli for LDPE at 150℃ G’(Pa) Dynamic shear moduli for LDPE at 423 K. Data were collected at different temperatures and shifted according to time-temperature superposition. The solid curves are calculated from G(t) using eq1-2. ω(s-1) Spectral decomposition of the storage and loss moduli for LDPE at 423 K. The moduli are calculated by eq1-2 with the Gk and λk given in left table.

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