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Complex Fluids & Molecular Rheology Lab., Department of Chemical Engineering An Introduction to Rheology: Phenomenon, Concept, Measuring, and Case Study TA 4/16/2013

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Non-Newtonian Fluid Mechanics Advanced Experimental Methods Materials Processing Polymer Solutions, Melts and Blends Biopolymers, Biofluids and Foods Constitutive and Computational Modeling 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 The XVIth International Congress on Rheology Colloids and Suspensions Emulsions and Foams Solids and Granular Materials Industrial Rheology Complex Flows General Rheology

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Frequent Q & A Q: Rheometer = Rheology? A: Unfortunately, the answer is, to a large extent, negative! Q: How to judge the correctness of rheological data and know the physical meanings? A: Mostly, its all about the theories Q: A practical processing issue can be well characterized by a set of rheological parameters? A: Well,..lets see!

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Rheology is the science of fluids ormore precisely deformable materials - - Newtons law of viscosity ( ) Small molecule Macromolecule Deformable

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(Non-Newtonian Viscosity) - Shear Thinning ( ) ( ) Flow curve for non-Newtonian Fluids

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(Normal Stress Differences) - Rod-Climbing ( ) ( )

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( Memory effects ) - Elastic Recoil - Open Syphon Flow

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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 Thixotropy behaviorAnti-thixotropy behavior 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. Time-dependent effects ( )

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: ( ) (0.057% / ) - The mountains flowed before the Lord [From Deborahs Song, Biblical Book of Judges, verse 5:5], quoted by Markus Reiner at the Fourth International Congress on Rheology in 1963

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High-speed coating Injection molding Lubrication Sedimentation Rolling Pipe flow Extrusion Spraying Chewing 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).]

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Melt instability 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)] Sharkskin Melt fracture

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Instability for dilute solutions Flow visualization of the elastic Taylor-Couette instability in Boger fluids. [http://www.cchem.berkeley.edu/sjmgrp/] Taylor vortex R1R1 R2R2 [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).]

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Two standard types of flows, shear and shearfree, are frequently used to characterize polymeric liquids Steady simple shear flow Streamlines for elongational flow ( b =0) (a) Shear (b) Shearfree Shear rate Elongation rate

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

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Homogeneous deformation:* Nonhomogeneous deformation: Parallel Plates (a) Shear (b) Elongation Capillary Cone-and- Plate Concentric Cylinder Concentrated RegimeDilute Regime For Melts & High-Viscosity Solutions Moving clamps *Stress and strain are independent of position throughout the sample

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According to the Reptation Theory: NewtonianPower law Zero-shear viscosity, 0

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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 of dilute polystyrene Solutions, With various solvents, as a function of reduced shear rate Intrinsic Viscosity: Relative Viscosity:

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: 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

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Storage and loss moduli, G and G, as functions of frequency at a reference temperature of T 0 =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 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

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Linear Polymer Star Polymer Pom-Pom Polymer Molecular ArchitectureThe Fingerprints polybutadiene Polyisoprene Polyisoprene S. C. Shie, C. T. Wu, C. C. Hua, Macromolecules 36, 2141-2148 (2003) C. C. Hua, H. Y. Kuo, J Polym Sci Part B: Polym Phys 38, 248-261 (2000)

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Shearfree Flow Material Functions

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H. Munstedt, J. Rheol. 24, 847-867 (1980) Hua and Yang, J Polym Res 9, 79-90 (2002)

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The Rheology of Colloidal Dispersions

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Onset of shear thickening : the Pclet number Fluid drag on the particle leads to the Stokes-Einstein relationship: The mean square of the particles displacement is Accordingly, the diffusivity sets the characteristic time scale for the particles Brownian motion. A dimensionless number known as Pclet number, Pe

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Lubrication hydrodynamics and hydroclusters 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 Pe1 At (Pe1) regime, the strong hydrodynamic coupling between particles leads to the formation of hydroclusters (red particles) which cause an increase in viscosity.

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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

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1.Steady-state Viscosity 2.First normal stress difference 3.Linear viscoelasticity Case Study I:

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A D B C The Viscosity Curves of Steady Shear Flow

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A D B C The 1 st Normal Stress Curves of Steady Shear Flow

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A D B C

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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. Starting position for a screen printer The screen printing process http://www.ami.ac.uk/courses/topics/0222_print/index.html#1 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 gauze gap (snap-off) board holder board emulsion mask frame medium squeegee medium snap-off medium drawn from open mesh Screen Printing Technique

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Silver paste CM-ASilver paste CM-B Powders sample Binders sample

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Silver pastePowders sampleBinders sample

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- ( Rheo-Optical ) : vs.

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Versatile Optical Rheometry Couette cell Laser CCD Iris Spatial filter & Beam expander Screen with aperture Lens Objective lens Pinhole Lens Analyzer PolarierPEM Photodiode 1f 2f Lock-in amplifiers (from PEM) Rheo-SALS Rheo-Birefringence Rheology Flow-LS (large-angle detection)

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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 FIG. A complete picture of the shear-induced phase separation and structure formation from a wide range of techniques on the same polymer solutions

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Continued Notice that the behavior of the shear viscosity is also classified into three regimes Comparisons with Mechanical Characterizations: Mechanical

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Physics governing the fluid behavior

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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 dataexperimental 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.

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People used to tell me, The problems encountered in industry are typically too complex to be studied in a (academic) lab (like yours)

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My response was, Just because the problems are so complex that they must eventually be resolved in a (academic) lab (like mine)!

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Complex Fluids & Molecular Rheology Lab., Department of Chemical Engineering An Introduction to Rheology: Phenomenon, Concept, Measuring, and Case Study TA 4/16/2013