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Rheology Fundamentals

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In rheology, we are interested in the description of the change in shape. ... Rheology Study of Flow by George Smoluk, SPE Journal, Vol 27, 1971. ... – PowerPoint PPT presentation

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Title: Rheology Fundamentals


1
Rheology Fundamentals
  • Lecture Notes 2

2
Outline
  • Continuum
  • Stress
  • Strain
  • Ideal Solids
  • Ideal Liquids
  • Non-Newtonian Fluids
  • Visco-elastic Behavior

3
Continuum Approach
  • What is a continuum?
  • What is continuum approach?
  • Eulerian method of description
  • Lagrangian method of description

4
Stress
  • Stressforce/unit area
  • Tensile
  • Compressive
  • Shear

5
Stress
  • Body and surface forces
  • Simple and isolated stresses
  • Tensile
  • Compression
  • Shear
  • Stress vector
  • Shear and normal components

Fluid element
The stress vector at the point on the surface is
given by
6
Stress Tensor
  • Stress tensor
  • Numbers of unknowns
  • Sign convention
  • Stress in static fluids
  • Hydrostatic pressure
  • Stress in dynamic fluids
  • Pressure and viscous stresses
  • Invariant of stress tensor
  • Principal stresses

Total stress tensor
Extra stress tensor or Viscous stress tensor
or Dissipative stress tensor
7
Viscous Stress Tensor for a Newtonian
Incompressible Fluid
Viscosity
8
Deformation
  • When you apply an external force to a body,
    you either cause a rigid body movement and/or you
    cause a change in shape. In rheology, we are
    interested in the description of the change in
    shape.
  • Change in shape is the change of distances
    between points within a continuum and is a
    geometrical concept.

9
Concepts used to Describe Deformation
  • Compressible and Incompressible materials
  • Lagrange and Euclidian Approaches
  • Translation
  • Rotation
  • Linear and angular deformation
  • Rate of deformation
  • Velocity
  • Acceleration
  • Velocity gradient
  • Vorticity
  • Strain
  • Average strain
  • Strain tensor
  • Rate of change of strain tensor
  • Principal strain

10
Strain
  • Strain is the absolute amount of distortion which
    occurs, expressed as a fraction of an original
    dimension of the unstressed sample. Strain is
    dimensionless.
  • Tensile strain
  • Compressive strain
  • Shear strain
  • Rate of strain

11
Relation Between Force and Deformation
  • Relation for ideal solids
  • Relation for ideal fluids
  • Relation for viscoelastic materials
  • Constitutive equations or rheological equations
    of state

12
Important Deformations in Rheology
  • Shear
  • Elongation

13
Ideal SolidsHooks Law 1676
http//www.upscale.utoronto.ca/GeneralInterest/Har
rison/Flash/ClassMechanics/HookesLaw/HookesLaw.htm
l
14
Ideal LiquidsNewtons Law
The resistance of which arises from the lack of
slipperiness originating In a fluid, other things
being equal, is proportional to the velocity by
which the parts o f the fluid are being separated
from each other. Isaac N. Newton (1687) From
Rheology Principles, Measurements, and
Applications By C. W. Macosko, 1994, VCH
Publishers, page 65
15
Visco-elastic Behavior
  • Elasticoviscous fluids
  • Viscoelastic solids
  • Creep
  • Relaxation
  • Material models

Ludwig Boltzmann
16
Voigt (Kelvin-Voigt) Model for Viscoelastic
Behavior
Spring Elastic Modulus Force) ? (Position)
Dashpot Viscosity Force ? (Speed)
17
Maxwell Model forViscoelastic Behavior
James Clerk Maxwell 1831-1879
18
Non-Newtonian Behavior
  • Bingham body
  • Yield stress
  • Psudoplastic behavior
  • Dilatancy
  • St. Venant body
  • Apparent viscosity
  • The power law or Ostwald model (Ostwald de Walle)
  • Time-dependent behavior
  • Thixotropic
  • Rheotropic or anti-thixotropic

19
References
  • Chapter 1 of your text book
  • Rheology Study of Flow by George Smoluk, SPE
    Journal, Vol 27, 1971.
  • Chapter 5 of Introduction to Fluid Mechanics by
    Fox, McDonald, and Pritchard, 6th edition, Wiley
  • Rheology Study of Flow, G.R. Smoluk, SPE Journal,
    Vol. 27, December 1971, pages 19-30
  • http//www.rheologyschool.com/rheology_glossary.ht
    ml
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