長興化工 講稿 3/22/2013 An Introduction to Rheology: Phenomenon, Concept, Measuring, and Case Study Complex Fluids & Molecular Rheology Lab., Department of Chemical Engineering The XVIth International Congress on Rheology Non-Newtonian Fluid Mechanics Colloids and Suspensions Advanced Experimental Methods Emulsions and Foams Materials Processing Solids and Granular Materials Polymer Solutions, Melts and Blends Industrial Rheology Biopolymers, Biofluids and Foods Complex Flows Constitutive and Computational Modeling General Rheology Rheology of Bio-Pharmaceutical Systems Rheology of Nano- and Natural Composites Interfacial Rheology, Micro-rheology & Microfluidics Associative Polymers, Surfactants and Liquid Crystals Professor Ken Walters Commemorative Symposium Frequent Q & A Q: Rheometer = Rheology? A: Unfortunately, the answer is negative! Q: How to judge the correctness of rheological data and know the physical meanings? A: Mostly, it’s all about the theories or the predictions Q: A practical processing issue can be well characterized by a set of rheological parameters? A: Well,…………………………………………..let’s see! Rheology is the science of fluids or—more precisely— deformable materials Y 牛頓流體 - 水、有機小分子溶劑等 V Newton’s law of viscosity V yx V Y 黏度η為定值 非牛頓流體 - 高分子溶液、膠體等 Small molecule Macromolecule V ● Deformable 黏度不為定值 (尤其在快速流場下) 非牛頓流體的三大特徵 特徵時間與無因次群分析 非牛頓流體的特徵 非牛頓黏度 (Non-Newtonian Viscosity) - Shear Thinning p Flow curve for non-Newtonian Fluids 牛頓流體 (甘油加水) 非牛頓流體 (高分子溶液) 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) 記憶效應 (Memory effects) - Elastic Recoil - Open Syphon Flow Time-dependent effects (搖變性) Thixotropy behavior Anti-thixotropy behavior A decrease (thixotropy) and increase (anti-thixotropy) of the apparent viscosity with time at a constant rate of shear, followed by a gradual recovery when the motion is stopped The distinction between a thixotropic fluid and a shear thinning fluid: A thixotropic fluid displays a decrease in viscosity over time at a constant shear rate. A shear thinning fluid displays decreasing viscosity with increasing shear rate. 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 De Elastic force tflow Viscous force or We = (Re 103 in all cases) - 描述非牛頓流體行為之程度 : 流體的特徵或 “鬆弛” 時間 tflow : 流動系統的特徵時間 : 剪切速率 De 0 0.2 牛頓流體 (葡萄糖漿) 3 1 收 縮 流 道 非牛頓流體 (0.057% 聚丙烯醯胺/葡萄糖 溶液) 8 典型製程之流場強度範圍 Lubrication High-speed coating Rolling Spraying Injection molding Pipe flow Chewing Extrusion Sedimentation 105 103 101 101 (s-1 ) 103 105 107 Typical viscosity curve of a polyolefin- PP homopolymer, melt flow rate (230 C/2.16 Kg) of 8 g/10 minat 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).] 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)] Instability for dilute solutions Taylor vortex R1 R2 [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).] Flow visualization of the elastic Taylor-Couette instability in Boger fluids. [http://www.cchem.berkeley.edu/sjmgrp/] 剪切流與非剪切流 基礎流變量測模式與功能 典型均勻流場 Two standard types of flows, shear and shearfree, are frequently used to characterize polymeric liquids (b) Shearfree (a) Shear vx y Steady simple shear flow vx yx y; vy 0; vz 0 Shear rate Streamlines for elongational flow (b=0) Elongation rate x 2 vy y 2 vz z vx The Stress Tensor y x z Shear Flow Elongational Flow Total stress tensor* Stress tensor yx p xx p yx p yy 0 0 0 p zz 0 p xx p 0 0 0 p yy 0 Hydrostatic pressure forces Shear Stress : yx First Normal Stress Difference : xx yy Second Normal Stress Difference : yy zz Tensile Stress : zz xx 0 p zz 0 流變夾具種類與適用範圍 (a) Shear Concentrated Regime Homogeneous deformation:* Cone-andPlate Nonhomogeneous deformation: (b) Elongation Dilute Regime 103 Concentric Cylinder Parallel Plates Capillary 102 101 100 Moving clamps 101 102 103 104 γ (s-1 ) 105 (s-1 ) For Melts & High-Viscosity Solutions *Stress and strain are independent of position throughout the sample 基礎流變量測之物理解析與應用 According to the Reptation Theory: 0 GN(0) d , where GN(0) the "plateau modulus" is temperature insensitive Newtonian Power law Zero-shear viscosity, 0 0 Relaxationtime, 1/ critical Relative Viscosity: rel s : Solution viscosity s : Solvent 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: s [ ] lim c0 c s c: Mass concentration Intrinsic viscosity of dilute polystyrene Solutions, With various solvents, as a function of reduced shear rate β 小振幅反覆式剪切流: 黏性與彈性檢定 Exp b: Small-Amplitude Oscillatory Shear Flow The shear stress oscillates with frequency , but is not in phase with either the shear strain or shear rate Shear Stress : yx A() 0 sin(t ) strain rate: yx (t ) 0 cos t strain: yx (t ) 0 sin t Oscillatory shear strain, shear rate, shear stress, and first normal stress difference in small-amplitude oscillatory shear flow It is customary to rewrite the above equations to display the in-phase and out-of-phase parts of the shear stress Storage modulus yx G() 0 sin t G() 0 cos t 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 Molecular Architecture—The Fingerprints Linear Polymer Star Polymer Pom-Pom Polymer polybutadiene Polyisoprene Polyisoprene C. C. Hua, H. Y. Kuo, J Polym Sci Part B: Polym Phys 38, 248-261 (2000) S. C. Shie, C. T. Wu, C. C. Hua, Macromolecules 36, 2141-2148 (2003) 拉伸流黏度量測與特徵 Shearfree Flow Material Functions For Uniaxial Elongational Flow (b 0, 0): Zero - elongation- rate elongational viscosity 0 zz xx ( ) : Elongational viscosity : Elongation rate Elongation viscosity and viscosity for a polystyrene melt as functions of elongation rate and shear rate, respectively Zero - shear - rate viscosity 0 Elongational Stress Growth Function H. Munstedt, J. Rheol. 24, 847-867 (1980) Hua and Yang , J Polym Res 9, 79-90 (2002) The Rheology of Colloidal Dispersions Onset of shear thickening : the Péclet number Fluid drag on the particle leads to the Stokes-Einstein relationship: D kBT 6 a a: particle's hydrodynamic radius 2 x Dt The mean square of the particle’s displacement is Accordingly, the diffusivity sets the characteristic time scale for the particle’s Brownian motion. a2 t particle D A dimensionless number known as Péclet number, Pe Pe a2 D a 3 kBT Lubrication hydrodynamics and hydroclusters Pe~1 Pe<<1 The flow-induced density fluctuations are known as hydroclusters which lead to an increase in viscosity. The formation of hydroclusters is reversible, so reducing the shear rate returns the suspensions to a stable fluid Pe>>1 At (Pe<<1) regime, random collisions among particles make them naturally resistant to flow. As the shear rate increase (Pe~1), particles become organized in the flow, which lowers their viscosity. At (Pe>>1) regime, the strong hydrodynamic coupling between particles leads to the formation of hydroclusters (red particles) which cause an increase in viscosity. Controlling shear thickening fluids: to modify colloidal surface The addition of a polymer “brush” grafted or absorbed onto the particles’ surface can prevent particles from getting close together. The figure shows that shear thickening is suppressed by imposing a purely repulsive force field. With the right selection of grafted density, molecular weight, and solvent , the onset of shear thickening moves out of the desired processing regime Case Study I: 導電金屬漿流變性質的鑑定 1. Steady-state Viscosity 2. First normal stress difference 3. Linear viscoelasticity The Viscosity Curves of Steady Shear Flow 1e+6 1e+6 1e+5 1e+5 1e+4 1e+4 Viscosity ( Pa s ) Viscosity ( Pa s ) A 1e+3 1e+2 1e+1 1e+3 1e+2 1e+1 PP 25(TEK) 1e+0 0.0001 0.001 0.01 PP 25(TEK) 0.1 1 10 100 1e+0 0.0001 1000 0.001 0.01 Shear Rate ( 1/s ) 0.1 10 100 1000 10 100 1000 D 1e+6 1e+6 1e+5 1e+5 1e+4 1e+4 Viscosity ( Pa s ) Viscosity ( Pa s ) 1 Shear Rate ( 1/s ) C 1e+3 1e+2 1e+1 1e+3 1e+2 1e+1 PP 25(TEK) PP 25(TEK) 1e+0 0.0001 B 0.001 0.01 0.1 1 Shear Rate ( 1/s ) 10 100 1000 1e+0 0.0001 0.001 0.01 0.1 1 Shear Rate ( 1/s ) A A The 1st Normal Stress Curves of Steady Shear Flow 6000 3000 6000 PP 25 PP CP 25(TEK) 25-4 4000 2000 1000 Normal Stress ( Pa ) Normal Normal Stress Stress (( Pa Pa )) 4000 2000 0 0 -2000 -1000 -4000 -2000 -6000 -3000 -8000 -4000 0.001 0.0001 PP PP25(TEK) 25 2000 0 -2000 -4000 -6000 0.01 0.001 0.010.1 0.1 1 1 10 10 100 100 -8000 0.0001 1000 1000 0.001 0.01 Shear Rate Shear Rate (( 1/s 1/s )) 0.1 100 1000 1000 PP 25 PP 25(TEK) 800 PP 25 25(TEK) PP 600 2000 Normal Stress ( Pa ) Normal Stress ( Pa ) 10 D 6000 0 -2000 -4000 400 200 0 -200 -6000 -8000 0.0001 1 Shear Rate ( 1/s ) C 4000 B -400 0.001 0.01 0.1 1 Shear Rate ( 1/s ) 10 100 1000 -600 0.0001 0.001 0.01 0.1 1 Shear Rate ( 1/s ) 10 100 1000 A B PP 25(TEK) PP 25(TEK) 1e+6 10000 1e+5 10000 1e+3 1e+4 1000 G' ; G'' ( Pa ) 1000 Complex Viscosity Pa s ) 1e+4 G' ; G'' ( Pa ) Complex Viscosity Pa s ) 1e+5 1e+3 100 1e+2 1e+2 1e+1 0.01 100 0.1 1 10 1e+1 0.01 100 10 0.1 Angular Frequency ( 1/s ) 1 100 Angular Frequency ( 1/s ) C D 10000 1e+5 1e+3 100 Complex Viscosity 1e+2 Storage Modulus G' 1e+4 1000 G' ; G'' ( Pa ) G' ; G'' ( Pa ) 1000 10000 1e+4 Complex Viscosity Pa s ) 1e+5 Complex Viscosity Pa s ) 10 1e+3 100 1e+2 Loss Modulus G'' 1e+1 0.01 10 0.1 1 Angular Frequency ( 1/s ) 10 100 1e+1 0.01 10 0.1 1 Angular Frequency ( 1/s ) 10 100 Screen Printing Technique Starting position for a screen printer squeegee gauze medium frame gap (‘snap-off’) board holder emulsion mask board 1. The screen is fixed just above the board, and the medium lies in front of the flexible squeegee. 2. The mesh of the screen is pushed down into contact with the board by the squeegee as it moves across the screen, rolling the medium in front of it. The screen printing process medium medium drawn from open mesh snap-off 3. The squeegee blade first presses the medium into the open apertures of the image, and then removes the excess as it passes across each aperture. 4. The screen then peels away from the printed surface behind the squeegee, leaving the medium that was previously in the mesh aperture deposited on the board beneath http://www.ami.ac.uk/courses/topics/0222_print/index.html#1 流變-光學 (Rheo-Optical) 整合量測系統: 結構 vs. 應力 Versatile Optical Rheometry Lens Iris PEM Iris Objective lens Polarier Pinhole Spatial filter & Beam expander Flow-LS (large-angle detection) Couette cell Rheology CCD Analyzer Rheo-SALS Lens Screen with aperture (from PEM) 1f 2f Photodiode Rheo-Birefringence Lock-in amplifiers CASE STUDY II : Combined Rheo-Optical Measurements Rheo-Optical Studies of Shear-Induced Structures in Semidilute Polystyrene Solutions [Kume et al. (1997)] 1. Shear-induced structure formation in semidilute solutions of high molecular weight polystyrene was investigated using a wide range of rheo-optical techniques 2. The effects of shear on the semidilute polymer solutions could be classified into some regimes w.r.t. shear rate c : Onset of the shear - enhanced concentration fluctuations a : Onset of the anomalies in the rheological and scattering behaviors FIG. A complete picture of the shear-induced phase separation and structure formation from a wide range of techniques on the same polymer solutions Continued Comparisons with Mechanical Characterizations: 6.0 wt% PS/DOP solution (c c 30) Mechanical M w 3.84 106 ; M w M n 1.06 FIG The plots of shear viscosity ( ), birefringence (n), and dichroism (n) of the solution as a function of shear rate ( ) Notice that the behavior of the shear viscosity is also classified into three regimes Physics governing the fluid behavior The Smoluchowski equation: (r1 , r2 ,..., t ) U H nm kBT t R m R m n , m R n subject to appropriate boundary and initial conditions U sum of deterministic forces= Fmh Fmintra Fminter Fmex R m Tips and Recommendations of problem solving Identify an analogous model system that had been studied earlier Go through literature survey and read carefully and apprehensively Design tactics for collecting preliminary data—experimental or computational Discuss with your supervisor or counselor for the significance of the current data and appropriate next steps. Repeat this procedure until the problem has been resolved to a satisfactory extent.