DOCSLIB.ORG

Using Rheology to Characterize Flow and Viscoelastic Properties of Hydrogels, Adhesives and Biopolymers

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Using Rheology to Characterize Flow and Viscoelastic Properties of Hydrogels, Adhesives and Biopolymers Using Rheology to Characterize Flow and Viscoelastic Properties of Hydrogels, Adhesives and Biopolymers Tianhong Terri Chen PhD Senior Applications Scientist TA Instruments – Waters LLC TAINSTRUMENTS.COM Outline Basics in Rheology Theory TA Instruments Rheometers and DMAs Instrumentation Test methodologies Rheological Applications in Biopolymer and Biomedical Materials Hydrogels and creams Adhesives Drug capsules Polymers for medical devices TAINSTRUMENTS.COM Rheology: An Introduction TAINSTRUMENTS.COM Rheology: An Introduction Rheology: The study of the relationship between a stress and deformation Deformation Solid F = F(x); F ≠ F(v) Purely Elastic Most material Deformation + Flow Viscoelastic Flow Liquid F = F(v); F ≠ F(x) Purely Viscous Stress Stress = Modulus = Viscosity Strain Shear rate TAINSTRUMENTS.COM What does a Rheometer do? Rheometer – an instrument that measures both viscosity and viscoelasticity of fluids, semi-solids and solids It can provide information about the material’s: Viscosity - defined as a material’s resistance to flow deformation and is a function of shear rate or stress, with time and temperature dependence Viscoelasticity – is a property of a material that exhibits both viscous and elastic character. Measurements of G’, G”, tan δ with respect to time, temperature, frequency and stress/strain are important for characterization. TAINSTRUMENTS.COM Who Will Need Help with Rheology Analysis? Food Personal Care Pharmaceutical Polymers Adhesives & coating Automotive Aerospace Bio-medical devices Asphalt TAINSTRUMENTS.COM TA Instruments Rheometers and DMAs TA Rotational Rheometers ARES-G2 and ARES (Strain Control – SMT) DHR or AR (Stress Control – CMT) TA DMAs RSA-G2 and RSA (Strain Control – SMT) DMA Q800 (Stress Control – CMT) TAINSTRUMENTS.COM Rotational Rheometers at TA ARES G2 DHR Controlled Strain Controlled Stress Dual Head Single Head SMT CMT TAINSTRUMENTS.COM Geometry Options Concentric Cone and Parallel Torsion Cylinders Plate Plate Rectangular Very Low Very Low Very Low Solids to Medium to High Viscosity Viscosity Viscosity to Soft Solids Water to Steel TAINSTRUMENTS.COM DMAs from TA Instruments RSA G2 Q800 ARES G2 and DHR Controlled Strain Controlled Stress DMA mode SMT CMT (oscillation) TAINSTRUMENTS.COM DMA Clamps Submersible Submersible S/D Cantilever Tension-Film Shear-Sandwich Compression 3 Pt Bend Submersible 3-Point Bending Tension-Fiber Compression Tension TAINSTRUMENTS.COM ElectroForce Load Frames ElectroForce 3300 ElectroForce 3510 ElectroForce 3500 Floor Standing (7500 N) (15000 N) ElectroForce 3300 (3000 N) (3000 N) ElectroForce 3200 (450 N) ElectroForce 5500 ElectroForce 3100 (200 N) (22 N) Frequency Forces to Interchangeable to 300 Hz 15kN Fixtures TAINSTRUMENTS.COM Common Rheological Experimental Methods TAINSTRUMENTS.COM Flow Experiments What flow measures o Viscosity “lack of slipperiness,” resistance to flow The viscosity of water at room temperature is 1cP Type of flow measurements on rheometer o Viscosity vs. time Viscosity at single shear rate/stress Time dependence (Thixotropy or Rheopexy) o Viscosity vs. shear stress or rate Newtonian Shear thinning, shear thickening, Yield stress o Viscosity vs. temperature TAINSTRUMENTS.COM Flow Behaviors TAINSTRUMENTS.COM Information from a Flow Curve What shear rate? 4) Chewing, swallowing 5) Dip coating 1) Sedimentation 6) Mixing, stirring 2) Leveling, Sagging 7) Pipe flow 3) Draining under gravity η log 8) Spraying and brushing 9) Rubbing 10) Milling pigments 11) High Speed coating 4 5 6 8 9 1 2 3 7 10 11 1.00E-5 1.00E-4 1.00E-3 0.0100 0.100 1.00 10.00 100.00 1000.00 1.00E4 1.00E5 1.00E6 shear rate (1/s) TAINSTRUMENTS.COM Dynamic Oscillatory Tests Phase angle δ Strain, ε Stress, σ* Dynamic stress applied sinusoidally User-defined Stress or Strain amplitude and frequency TAINSTRUMENTS.COM Viscoelastic Parameters The Modulus: Measure of materials overall ̍∗ = ̴̙̲̥̳̳ ∗ resistance to deformation. ̴̡̙̲̩̮ The Elastic (Storage) Modulus: Measure of ɑ ·΢ΠΓΡΡ ∗ elasticity of material. The ability of the G = ·΢ΠΏΗΜ cos δ material to store energy. The Viscous (loss) Modulus: ∗ G" = ·΢ΠΓΡΡ sin δ The ability of the material to dissipate ·΢ΠΏΗΜ energy. Energy lost as heat. Tan delta (phase angle): ͻ" tan δ = ͻɑ Measure of material damping - such as vibration or sound damping. G* The triangle relationship G" Phase angle δ G' TAINSTRUMENTS.COM Understanding Oscillation Experiments What oscillation measures? oViscoelastic properties (G’/E’, G”/E”, tan δ) Approach to Oscillation Experimentation oStress and Strain Sweep • Measure linear viscoelastic region • Yield stress, stability oTime Sweep • Stability and structure recovery • Curing o Frequency Sweep • Measure polymer relaxation • Compare viscoelasticity of different formulations oTemperature Ramp • Measure glass transition, • Temperature operation range of a material TAINSTRUMENTS.COM Rheology Applications in Biopolymers & Biomedical Materials TAINSTRUMENTS.COM Purpose of a Rheological Measurement Three main reasons for rheological testing: • Characterization Structure-property relationship. MW, MWD, branching, state of flocculation, etc. • Process performance Formulation stability, processing temperatures, extrusion, blow molding, pumping, leveling, etc. • End product properties Mechanical strength, glass transition and sub-ambient transition temperatures, dimensional stability, settling stability, etc. TAINSTRUMENTS.COM Hydrogels and Creams • Hydrogels and creams are soft matters that contain high level of liquids such as water or oil • Hydrogels and creams are used in a wide variety of applications including tissue engineering, wound patch, drug delivery, contact lenses and superabsorbent materials • Rheology can provide key information on gel formation and gel strength on different formulations TAINSTRUMENTS.COM Natural Polymer: Hyaluronic Acid • Hyaluronic acid is a natural polysaccharide, which is commonly used in pharmaceutical, biomedical and personal care • Rheology can evaluate the visco-elastic properties as function of concentration, ionic strength, Mw, degree of crosslinking, formulations etc. TAINSTRUMENTS.COM Hyaluronic Acid Gels: • Hyaluronic acid gels are used as lubricating agent during abdominal surgeries to prevent adhesion and also for join lubrication, wound healing etc. • Rheology can monitor HA gelation and evaluate the gel strength TAINSTRUMENTS.COM Gels: Gelatin Gelation vs. Temperature Thermal reversible gelatin gels: o Measure gelation and gel melt TAINSTRUMENTS.COM Gelatin Gel Strength at Different Concentration • A dynamic frequency sweep test can be used to compare gel strength at applications temperature TAINSTRUMENTS.COM Gelatin/Chitosan Conjugation • Use enzymatic approach to covalently graft gelatin to chitosan • The conjugate exhibits interesting Tyrosine mechanical properties • Applications as biomedical adhesives Chen et al. Biopolymers, Vol. 64, 292-302 (2002) TAINSTRUMENTS.COM Vesicle-Biopolymer Gels • Attach n-dodecyl tails to Chitosan backbone to obtain an associating biopolymer (HM-Chitosan) • HM-Chitosan mixed with surfactant vesicle solution leads to a gel formation • This hydrogel showed strong elasticity HM-Chitosan behavior and has potential applications in biomedical control release Chen T; Raghavan SR et al, Langmuir, 21, 26-33 (2005) TAINSTRUMENTS.COM Contact Lens Visco-elasticity • Compare frequency dependency of contact lens elasticity 0.3500 " t͕͢ = ɒ 0.3000 Vendor A 0.2500 0.2000 Vendor B tan(delta) 0.1500 0.1000 0.05000 0 1.000 10.00 100.0 ang. frequency (rad/s) TAINSTRUMENTS.COM Creams/Lotions: Stability Testing Stability, phase separation of a cosmetic cream 1E+06 l G' emulsion Ap G'' emulsion A l G' emulsion Bp G'' emulsion B 1E+05 l l l l l l l l l l l l l 1E+04 l p p p lp p ' ' ' ' l' 'p 'p 'p 'p 'p 'p l l Moduli [Pa] G'' G' & l l l l 1E+03 0 1 2 3 4 5 6 7 8 910 strain [%] TAINSTRUMENTS.COM High Temperature Performance of Lotions A: Hydrating Lotion B: UV Protection C: Generic Brand o 10 3 G‘ for A decreases at 37 C G‘ for B withstands higher temperature =>used at 10 2 2 higher temperature hydrating beauty lotion δ same lotion with UV protection conditions (beach) generic hydrating lotion 1 10 G‘ for lotion C increases Loss tan before dropping; tan δ decreases => phase ModulusG' [Pa] 0 10 0 separation for lotion C Tan δ for A & B increases above 37 oC=> wax crystals 0 10 20 30 40 50 60 melt and lower the modulus Temperature T [°C] Ming L. Yao; Jayesh C. Patel Appl. Rheol. 11 ,2,83 (2001) TAINSTRUMENTS.COM Low Temperature Performance of Lotions 0.8 7 6 10 w/o emulsion 10 o/w emulsion: G' G' 10 6 G" 0.6 G" 5 tand δ 10 10 5 0.4 δ 10 4 tan 10 4 3 Modulus G' [Pa] 10 0.2 Modulus G', G" [Pa] Modulus G" G', Modulus G’, G” [Pa] G” G’, Modulus 2 10 3 10 -8 oC 0.0 -30 -20 -10 0 10 20 30 -100 -80 -60 -40 -20 0 20 40 60 80 100 Temperature T [ oC] Temperature T [ oC] In an o/w emulsion the freezing point of water is depressed due to the dispersed oil phase. Cooling below the freezing point has a major effect on temperature stability In an w/o emulsion, the dispersed water droplets freeze, but not the matrix. These emulsions do not have a sharp freezing point R.Brummer Rheology essentials of Cosmetics Springer ISBN: 3-540-25553-2 TAINSTRUMENTS.COM Emulsion Temperature Stability • Cycle temperature to evaluate temperature stability of emulsions V. André, N. Willenbacher, H. Debus, L. Börger, P. Fernandez, T. Frechen, J. Rieger. Prediction of Emulsion Stability: Facts and Myth . Cosmetics and Toiletries Manufacture
Load more

Recommended publications
  • On Nonlinear Strain Theory for a Viscoelastic Material Model and Its Implications for Calving of Ice Shelves
    Journal of Glaciology (2019), 65(250) 212–224 doi: 10.1017/jog.2018.107 © The Author(s) 2019. This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives licence (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is unaltered and is properly cited. The written permission of Cambridge University Press must be obtained for commercial re- use or in order to create a derivative work. On nonlinear strain theory for a viscoelastic material model and its implications for calving of ice shelves JULIA CHRISTMANN,1,2 RALF MÜLLER,2 ANGELIKA HUMBERT1,3 1Division of Geosciences/Glaciology, Alfred Wegener Institute Helmholtz Centre for Polar and Marine Research, Bremerhaven, Germany 2Institute of Applied Mechanics, University of Kaiserslautern, Kaiserslautern, Germany 3Division of Geosciences, University of Bremen, Bremen, Germany Correspondence: Julia Christmann <[email protected]> ABSTRACT. In the current ice-sheet models calving of ice shelves is based on phenomenological approaches. To obtain physics-based calving criteria, a viscoelastic Maxwell model is required account- ing for short-term elastic and long-term viscous deformation. On timescales of months to years between calving events, as well as on long timescales with several subsequent iceberg break-offs, deformations are no longer small and linearized strain measures cannot be used. We present a finite deformation framework of viscoelasticity and extend this model by a nonlinear Glen-type viscosity. A finite element implementation is used to compute stress and strain states in the vicinity of the ice-shelf calving front.
    [Show full text]
  • 1 Fluid Flow Outline Fundamentals of Rheology
    Fluid Flow Outline • Fundamentals and applications of rheology • Shear stress and shear rate • Viscosity and types of viscometers • Rheological classification of fluids • Apparent viscosity • Effect of temperature on viscosity • Reynolds number and types of flow • Flow in a pipe • Volumetric and mass flow rate • Friction factor (in straight pipe), friction coefficient (for fittings, expansion, contraction), pressure drop, energy loss • Pumping requirements (overcoming friction, potential energy, kinetic energy, pressure energy differences) 2 Fundamentals of Rheology • Rheology is the science of deformation and flow – The forces involved could be tensile, compressive, shear or bulk (uniform external pressure) • Food rheology is the material science of food – This can involve fluid or semi-solid foods • A rheometer is used to determine rheological properties (how a material flows under different conditions) – Viscometers are a sub-set of rheometers 3 1 Applications of Rheology • Process engineering calculations – Pumping requirements, extrusion, mixing, heat transfer, homogenization, spray coating • Determination of ingredient functionality – Consistency, stickiness etc. • Quality control of ingredients or final product – By measurement of viscosity, compressive strength etc. • Determination of shelf life – By determining changes in texture • Correlations to sensory tests – Mouthfeel 4 Stress and Strain • Stress: Force per unit area (Units: N/m2 or Pa) • Strain: (Change in dimension)/(Original dimension) (Units: None) • Strain rate: Rate
    [Show full text]
  • Computational Rheology (4K430)
    Computational Rheology (4K430) dr.ir. M.A. Hulsen [email protected] Website: http://www.mate.tue.nl/~hulsen under link ‘Computational Rheology’. – Section Polymer Technology (PT) / Materials Technology (MaTe) – Introduction Computational Rheology important for: B Polymer processing B Rheology & Material science B Turbulent flow (drag reduction phenomena) B Food processing B Biological flows B ... Introduction (Polymer Processing) Analysis of viscoelastic phenomena essential for predicting B Flow induced crystallization kinetics B Flow instabilities during processing B Free surface flows (e.g.extrudate swell) B Secondary flows B Dimensional stability of injection moulded products B Prediction of mechanical and optical properties Introduction (Surface Defects on Injection Molded Parts) Alternating dull bands perpendicular to flow direction with high surface roughness (M. Bulters & A. Schepens, DSM-Research). Introduction (Flow Marks, Two Color Polypropylene) Flow Mark Side view Top view Bottom view M. Bulters & A. Schepens, DSM-Research Introduction (Simulation flow front) 1 0.5 Steady Perturbed H 2y 0 ___ −0.5 −1 0 0.5 1 ___2x H Introduction (Rheology & Material Science) Simulation essential for understanding and predicting material properties: B Polymer blends (morphology, viscosity, normal stresses) B Particle filled viscoelastic fluids (suspensions) B Polymer architecture macroscopic properties (Brownian dynamics (BD), molecular dynamics (MD),⇒ Monte Carlo, . ) Multi-scale. ⇒ Introduction (Solid particles in a viscoelastic fluid) B Microstructure (polymer, particles) B Bulk rheology B Flow induced crystallization Introduction (Multiple particles in a viscoelastic fluid) Introduction (Flow induced crystallization) Introduction (Multi-phase flows) Goal and contents of the course Goal: Introduction of the basic numerical techniques used in Computational Rheology using the Finite Element Method (FEM).
    [Show full text]
  • Cohesive Crack with Rate-Dependent Opening and Viscoelasticity: I
    International Journal of Fracture 86: 247±265, 1997. c 1997 Kluwer Academic Publishers. Printed in the Netherlands. Cohesive crack with rate-dependent opening and viscoelasticity: I. mathematical model and scaling ZDENEKÏ P. BAZANTÏ and YUAN-NENG LI Department of Civil Engineering, Northwestern University, Evanston, Illinois 60208, USA Received 14 October 1996; accepted in revised form 18 August 1997 Abstract. The time dependence of fracture has two sources: (1) the viscoelasticity of material behavior in the bulk of the structure, and (2) the rate process of the breakage of bonds in the fracture process zone which causes the softening law for the crack opening to be rate-dependent. The objective of this study is to clarify the differences between these two in¯uences and their role in the size effect on the nominal strength of stucture. Previously developed theories of time-dependent cohesive crack growth in a viscoelastic material with or without aging are extended to a general compliance formulation of the cohesive crack model applicable to structures such as concrete structures, in which the fracture process zone (cohesive zone) is large, i.e., cannot be neglected in comparison to the structure dimensions. To deal with a large process zone interacting with the structure boundaries, a boundary integral formulation of the cohesive crack model in terms of the compliance functions for loads applied anywhere on the crack surfaces is introduced. Since an unopened cohesive crack (crack of zero width) transmits stresses and is equivalent to no crack at all, it is assumed that at the outset there exists such a crack, extending along the entire future crack path (which must be known).
    [Show full text]
  • An Investigation Into the Effects of Viscoelasticity on Cavitation Bubble Dynamics with Applications to Biomedicine
    An Investigation into the Effects of Viscoelasticity on Cavitation Bubble Dynamics with Applications to Biomedicine Michael Jason Walters School of Mathematics Cardiff University A thesis submitted for the degree of Doctor of Philosophy 9th April 2015 Summary In this thesis, the dynamics of microbubbles in viscoelastic fluids are investigated nu- merically. By neglecting the bulk viscosity of the fluid, the viscoelastic effects can be introduced through a boundary condition at the bubble surface thus alleviating the need to calculate stresses within the fluid. Assuming the surrounding fluid is incompressible and irrotational, the Rayleigh-Plesset equation is solved to give the motion of a spherically symmetric bubble. For a freely oscillating spherical bubble, the fluid viscosity is shown to dampen oscillations for both a linear Jeffreys and an Oldroyd-B fluid. This model is also modified to consider a spherical encapsulated microbubble (EMB). The fluid rheology affects an EMB in a similar manner to a cavitation bubble, albeit on a smaller scale. To model a cavity near a rigid wall, a new, non-singular formulation of the boundary element method is presented. The non-singular formulation is shown to be significantly more stable than the standard formulation. It is found that the fluid rheology often inhibits the formation of a liquid jet but that the dynamics are governed by a compe- tition between viscous, elastic and inertial forces as well as surface tension. Interesting behaviour such as cusping is observed in some cases. The non-singular boundary element method is also extended to model the bubble tran- sitioning to a toroidal form.
    [Show full text]
  • Fluid Inertia and End Effects in Rheometer Flows
    FLUID INERTIA AND END EFFECTS IN RHEOMETER FLOWS by JASON PETER HUGHES B.Sc. (Hons) A thesis submitted to the University of Plymouth in partial fulfilment for the degree of DOCTOR OF PHILOSOPHY School of Mathematics and Statistics Faculty of Technology University of Plymouth April 1998 REFERENCE ONLY ItorriNe. 9oo365d39i Data 2 h SEP 1998 Class No.- Corrtl.No. 90 0365439 1 ACKNOWLEDGEMENTS I would like to thank my supervisors Dr. J.M. Davies, Prof. T.E.R. Jones and Dr. K. Golden for their continued support and guidance throughout the course of my studies. I also gratefully acknowledge the receipt of a H.E.F.C.E research studentship during the period of my research. AUTHORS DECLARATION At no time during the registration for the degree of Doctor of Philosophy has the author been registered for any other University award. This study was financed with the aid of a H.E.F.C.E studentship and carried out in collaboration with T.A. Instruments Ltd. Publications: 1. J.P. Hughes, T.E.R Jones, J.M. Davies, *End effects in concentric cylinder rheometry', Proc. 12"^ Int. Congress on Rheology, (1996) 391. 2. J.P. Hughes, J.M. Davies, T.E.R. Jones, ^Concentric cylinder end effects and fluid inertia effects in controlled stress rheometry, Part I: Numerical simulation', accepted for publication in J.N.N.F.M. Signed ...^.^Ms>3.\^^. Date Ik.lp.^.m FLUH) INERTIA AND END EFFECTS IN RHEOMETER FLOWS Jason Peter Hughes Abstract This thesis is concerned with the characterisation of the flow behaviour of inelastic and viscoelastic fluids in steady shear and oscillatory shear flows on commercially available rheometers.
    [Show full text]
  • Analysis of Viscoelastic Flexible Pavements
    Analysis of Viscoelastic Flexible Pavements KARL S. PISTER and CARL L. MONISMITH, Associate Professor and Assistant Professor of Civil Engineering, University of California, Berkeley To develop a better understandii^ of flexible pavement behavior it is believed that components of the pavement structure should be considered to be viscoelastic rather than elastic materials. In this paper, a step in this direction is taken by considering the asphalt concrete surface course as a viscoelastic plate on an elastic foundation. Assumptions underlying existing stress and de• formation analyses of pavements are examined. Rep• resentations of the flexible pavement structure, im• pressed wheel loads, and mechanical properties of as• phalt concrete and base materials are discussed. Re• cent results pointing toward the viscoelastic behavior of asphaltic mixtures are presented, including effects of strain rate and temperature. IJsii^ a simplified viscoelastic model for the asphalt concrete surface course, solutions for typical loading problems are given. • THE THEORY of viscoelasticity is concerned with the behavior of materials which exhibit time-dependent stress-strain characteristics. The principles of viscoelasticity have been successfully used to explain the mechanical behavior of high polymers and much basic work U) lias been developed in this area. In recent years the theory of viscoelasticity has been employed to explain the mechanical behavior of asphalts (2, 3, 4) and to a very limited degree the behavior of asphaltic mixtures (5, 6, 7) and soils (8). Because these materials have time-dependent stress-strain characteristics and because they comprise the flexible pavement section, it seems reasonable to analyze the flexible pavement structure using viscoelastic principles.
    [Show full text]
  • On Exact Solution of Unsteady MHD Flow of a Viscous Fluid in An
    Rana et al. Boundary Value Problems 2014, 2014:146 http://www.boundaryvalueproblems.com/content/2014/1/146 R E S E A R C H Open Access On exact solution of unsteady MHD flow of a viscous fluid in an orthogonal rheometer Muhammad Afzal Rana1, Sadia Siddiqa2* and Saima Noor3 *Correspondence: [email protected] Abstract 2Department of Mathematics, COMSATS Institute of Information This paper studies the unsteady MHD flow of a viscous fluid in which each point of Technology, Attock, Pakistan the parallel planes are subject to the non-torsional oscillations in their own planes. Full list of author information is The streamlines at any given time are concentric circles. Exact solutions are obtained available at the end of the article and the loci of the centres of these concentric circles are discussed. It is shown that the motion so obtained gives three infinite sets of exact solutions in the geometry of an orthogonal rheometer in which the above non-torsional oscillations are superposed on the disks. These solutions reduce to a single unique solution when symmetric solutions are looked for. Some interesting special cases are also obtained from these solutions. Keywords: viscous fluid; MHD flow; orthogonal rheometer; eccentric rotation; exact solutions 1 Introduction Berker [] has defined the ‘pseudo plane motions’ of the first kind that: if the streamlines in a plane flow are contained in parallel planes but the velocity components are dependent on the coordinate normal to the planes. Berker [] has obtained a class of exact solutions to the Navier-Stokes equations belonging to the above type of flows.
    [Show full text]
  • Engineering Viscoelasticity
    ENGINEERING VISCOELASTICITY David Roylance Department of Materials Science and Engineering Massachusetts Institute of Technology Cambridge, MA 02139 October 24, 2001 1 Introduction This document is intended to outline an important aspect of the mechanical response of polymers and polymer-matrix composites: the field of linear viscoelasticity. The topics included here are aimed at providing an instructional introduction to this large and elegant subject, and should not be taken as a thorough or comprehensive treatment. The references appearing either as footnotes to the text or listed separately at the end of the notes should be consulted for more thorough coverage. Viscoelastic response is often used as a probe in polymer science, since it is sensitive to the material’s chemistry and microstructure. The concepts and techniques presented here are important for this purpose, but the principal objective of this document is to demonstrate how linear viscoelasticity can be incorporated into the general theory of mechanics of materials, so that structures containing viscoelastic components can be designed and analyzed. While not all polymers are viscoelastic to any important practical extent, and even fewer are linearly viscoelastic1, this theory provides a usable engineering approximation for many applications in polymer and composites engineering. Even in instances requiring more elaborate treatments, the linear viscoelastic theory is a useful starting point. 2 Molecular Mechanisms When subjected to an applied stress, polymers may deform by either or both of two fundamen- tally different atomistic mechanisms. The lengths and angles of the chemical bonds connecting the atoms may distort, moving the atoms to new positions of greater internal energy.
    [Show full text]
  • Lecture 1: Introduction
    Lecture 1: Introduction E. J. Hinch Non-Newtonian fluids occur commonly in our world. These fluids, such as toothpaste, saliva, oils, mud and lava, exhibit a number of behaviors that are different from Newtonian fluids and have a number of additional material properties. In general, these differences arise because the fluid has a microstructure that influences the flow. In section 2, we will present a collection of some of the interesting phenomena arising from flow nonlinearities, the inhibition of stretching, elastic effects and normal stresses. In section 3 we will discuss a variety of devices for measuring material properties, a process known as rheometry. 1 Fluid Mechanical Preliminaries The equations of motion for an incompressible fluid of unit density are (for details and derivation see any text on fluid mechanics, e.g. [1]) @u + (u · r) u = r · S + F (1) @t r · u = 0 (2) where u is the velocity, S is the total stress tensor and F are the body forces. It is customary to divide the total stress into an isotropic part and a deviatoric part as in S = −pI + σ (3) where tr σ = 0. These equations are closed only if we can relate the deviatoric stress to the velocity field (the pressure field satisfies the incompressibility condition). It is common to look for local models where the stress depends only on the local gradients of the flow: σ = σ (E) where E is the rate of strain tensor 1 E = ru + ruT ; (4) 2 the symmetric part of the the velocity gradient tensor. The trace-free requirement on σ and the physical requirement of symmetry σ = σT means that there are only 5 independent components of the deviatoric stress: 3 shear stresses (the off-diagonal elements) and 2 normal stress differences (the diagonal elements constrained to sum to 0).
    [Show full text]
  • Rheometry SLIT RHEOMETER
    Rheometry SLIT RHEOMETER Figure 1: The Slit Rheometer. L > W h. ∆P Shear Stress σ(y) = y (8-30) L −∆P h Wall Shear Stress σ = −σ(y = h/2) = (8-31) w L 2 NEWTONIAN CASE 6Q Wall Shear Rateγ ˙ = −γ˙ (y = h/2) = (8-32) w h2w σ −∆P h3w Viscosity η = w = (8-33) γ˙ w L 12Q 1 Rheometry SLIT RHEOMETER NON-NEWTONIAN CASE Correction for the real wall shear rate is analogous to the Rabinowitch correction. 6Q 2 + β Wall Shear Rateγ ˙ = (8-34a) w h2w 3 d [log(6Q/h2w)] β = (8-34b) d [log(σw)] σ −∆P h3w Apparent Viscosity η = w = γ˙ w L 4Q(2 + β) NORMAL STRESS DIFFERENCE The normal stress difference N1 can be determined from the exit pressure Pe. dPe N1(γ ˙ w) = Pe + σw (8-45) dσw d(log Pe) N1(γ ˙ w) = Pe 1 + (8-46) d(log σw) These relations were calculated assuming straight parallel streamlines right up to the exit of the die. This assumption is not found to be valid in either experiment or computer simulation. 2 Rheometry SLIT RHEOMETER NORMAL STRESS DIFFERENCE dPe N1(γ ˙ w) = Pe + σw (8-45) dσw d(log Pe) N1(γ ˙ w) = Pe 1 + (8-46) d(log σw) Figure 2: Determination of the Exit Pressure. 3 Rheometry SLIT RHEOMETER NORMAL STRESS DIFFERENCE Figure 3: Comparison of First Normal Stress Difference Values for LDPE from Slit Rheometer Exit Pressure (filled symbols) and Cone&Plate (open symbols). The poor agreement indicates that the more work is needed in order to use exit pressures to measure normal stress differences.
    [Show full text]
  • 20. Rheology & Linear Elasticity
    20. Rheology & Linear Elasticity I Main Topics A Rheology: Macroscopic deformation behavior B Linear elasticity for homogeneous isotropic materials 10/29/18 GG303 1 20. Rheology & Linear Elasticity Viscous (fluid) Behavior http://manoa.hawaii.edu/graduate/content/slide-lava 10/29/18 GG303 2 20. Rheology & Linear Elasticity Ductile (plastic) Behavior http://www.hilo.hawaii.edu/~csav/gallery/scientists/LavaHammerL.jpg http://hvo.wr.usgs.gov/kilauea/update/images.html 10/29/18 GG303 3 http://upload.wikimedia.org/wikipedia/commons/8/89/Ropy_pahoehoe.jpg 20. Rheology & Linear Elasticity Elastic Behavior https://thegeosphere.pbworks.com/w/page/24663884/Sumatra http://www.earth.ox.ac.uk/__Data/assets/image/0006/3021/seismic_hammer.jpg 10/29/18 GG303 4 20. Rheology & Linear Elasticity Brittle Behavior (fracture) 10/29/18 GG303 5 http://upload.wikimedia.org/wikipedia/commons/8/89/Ropy_pahoehoe.jpg 20. Rheology & Linear Elasticity II Rheology: Macroscopic deformation behavior A Elasticity 1 Deformation is reversible when load is removed 2 Stress (σ) is related to strain (ε) 3 Deformation is not time dependent if load is constant 4 Examples: Seismic (acoustic) waves, http://www.fordogtrainers.com rubber ball 10/29/18 GG303 6 20. Rheology & Linear Elasticity II Rheology: Macroscopic deformation behavior A Elasticity 1 Deformation is reversible when load is removed 2 Stress (σ) is related to strain (ε) 3 Deformation is not time dependent if load is constant 4 Examples: Seismic (acoustic) waves, rubber ball 10/29/18 GG303 7 20. Rheology & Linear Elasticity II Rheology: Macroscopic deformation behavior B Viscosity 1 Deformation is irreversible when load is removed 2 Stress (σ) is related to strain rate (ε ! ) 3 Deformation is time dependent if load is constant 4 Examples: Lava flows, corn syrup http://wholefoodrecipes.net 10/29/18 GG303 8 20.
    [Show full text]