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
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
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