Rheology Notes Introduction to rheology

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Rheology Notes introduction to rheology. Dr. Morgan lecture

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  • Dr. Sarah E. Morgan, Rheology Class Notes, 2013

    Introduction to Rheology

    Sarah E. Morgan, Ph.D.

    School of Polymers and

    High Performance Materials

    University of Southern Mississippi

  • Dr. Sarah E. Morgan, Rheology Class Notes, 2013

    Rheology is defined as:

    The science of the flow and

    deformation of matter

    Small molecule fluids follow classical

    Newtonian fluid mechanics

    Polymers exhibit complex non-Newtonian

    flow behavior

  • Dr. Sarah E. Morgan, Rheology Class Notes, 2013

    Fluid

    A substance that continually deforms under an

    applied shear stress; includes gases, liquids and

    solids like polymers (under certain conditions)

    Shear stress:

    Stress: F/A

    Axial stress = F perpendicular to

    (normal) an area divided by area

    Shear stress = F parallel to an area

    divided by area

  • Dr. Sarah E. Morgan, Rheology Class Notes, 2013

    VISOCITY

    Resistance to deformation

    or flow

    Internal resistance to flow

    or fluid friction

  • Dr. Sarah E. Morgan, Rheology Class Notes, 2013

    Solid responds to shear stress with elastic deformation when the stress is removed, it returns to its original shape

    Fluid responds to shear stress with continuous deformation or flow when the stressis removed, flow stops

    Polymer exhibits a viscoelastic response, withbehavior of both a solid and a liquid

    Viscoelastic Behavior

  • Dr. Sarah E. Morgan, Rheology Class Notes, 2013

    tyx (shear stress)

    y

    x

    g

    g = magnitude of strain or angle of deformation

    dg/dt = g = rate of deformation = rate of increase of

    angle = strain rate = shear rate

    Simple Shear of a Fluid

  • Dr. Sarah E. Morgan, Rheology Class Notes, 2013

    Fluid Flow Between Parallel Plates

  • Dr. Sarah E. Morgan, Rheology Class Notes, 2013

    Newtonian Fluids, Laminar Flow

    F = hA(dV/dy) Newtons Law of Viscous Flow

    F = frictional force that resists flow of layers past one another

    h = viscosity

    A = area of contact of layers

    dV/dy = velocity gradient = shear rate = (dx/dt)/dy

    t = F/A = shear stress

    g = dV/dy = shear rate

    h = t/g.

    .

    Newtonian Fluid: plot of shear stress vs shear

    rate yields a straight line with slope = viscosity

  • Dr. Sarah E. Morgan, Rheology Class Notes, 2013

    Sh

    ea

    r S

    tre

    ss

    , t

    Shear Rate, g

    Newtonian Fluid

    Slope = h

  • Dr. Sarah E. Morgan, Rheology Class Notes, 2013

    Shear Rate, g

    Newtonian Fluid

    Vis

    co

    sit

    y

  • Dr. Sarah E. Morgan, Rheology Class Notes, 2013

    Examples of Newtonian Fluids

    Water

    Acetone

    Glycerol

    Mercury

    Honey

    Viscosity varies with temperature

  • Dr. Sarah E. Morgan, Rheology Class Notes, 2013

    h = t/g

    Typical Viscosity Units

    = (F/A)/(dV/dy) =((kg m/s2)/m2)/

    ((m/s)/m) =

    kg/m sSI UNITS

    Length m

    Mass kg

    Time s

    Temp. K

    Plane Angle rad

    Acceleration m/s2

    Angular Velocity rad/s

    Density kg/m3

    Energy J (joule) kg m2/s2

    Force N (newton) kg m/s2

    Power W (watt) kg m2/s3 (J/s)

    Pressure P (pascal) kg/ m s2 (N/m2)

    Velocity m/s

    Viscosity kg/ m s

    Kinematic Viscosity (viscosity/density) m2 /s

  • Dr. Sarah E. Morgan, Rheology Class Notes, 2013

    Typical Viscosity Units

    m often used for Newtonian viscosityh often used for non-Newtonian viscosity; more

    correct to say apparent viscosity must identify shear rate at which measured

    Dynamic Viscosity (often just called Viscosity)

    1 Pa s = 1000 mPa s (millipascal seconds)

    1000 cP (centipoise)

    10 P (poise)

    10 dyne sec/ cm2

    1 kg/m s

    1.45 x 10-4 psi sec

    For more units see: http://www.onlineconversion.com/viscosity.htm

  • Dr. Sarah E. Morgan, Rheology Class Notes, 2013

    Typical Viscosity Units

    Kinematic Viscosity = u = m/r

    = dynamic viscosity/ density

    Kinematic Viscosity

    1 m2/sec = 1 x 106 centistokes

    10,000 stokes

    1 x 106 mm2/sec

    10.76 ft2/sec

    For more units see: http://www.onlineconversion.com/viscosity.htm

    Kinematic Viscosity has same units as diffusion coefficient in mass

    transfer and thermal diffusivity in heat transfer.

  • Dr. Sarah E. Morgan, Rheology Class Notes, 2013

    Sh

    ea

    r S

    tre

    ss

    , t

    Shear Rate, g

    Bingham Fluid

    (yield stress fluid)

    Pseudoplastic Fluid

    High Viscosity Newtonian

    Dilatant Fluid

    Low Viscosity Newtonian

    Flow Curves for Newtonian and Simple Non-Newtonian

    Fluids with Increasing and Decreasing Shear Rate

  • Dr. Sarah E. Morgan, Rheology Class Notes, 2013

    Sh

    ear

    Str

    ess

  • Dr. Sarah E. Morgan, Rheology Class Notes, 2013

    xBingham Fluids

  • Dr. Sarah E. Morgan, Rheology Class Notes, 2013

    Shear Rate, g

    Vis

    co

    sit

    y

    Newtonian

    Dilatant

    Pseudoplastic

    Flow curves, Newtonian and simple non-Newtonian

  • Dr. Sarah E. Morgan, Rheology Class Notes, 2013

  • Dr. Sarah E. Morgan, Rheology Class Notes, 2013

  • Dr. Sarah E. Morgan, Rheology Class Notes, 2013

    Examples of Non-Newtonian Fluids

    Pseudoplastic (shear thinning) most polymer solutions and melts

    Dilatant (shear thickening) sand in water, cornstarch in water

    Thixotropic viscosity decreases with time at constant shear rate:some suspensions with particulates and polymer molecules, such

    as paint, cosmetic formulations

    Rheopectic viscosity increases with time at constant shear rate: some lubricants

  • Dr. Sarah E. Morgan, Rheology Class Notes, 2013

    Viscoelastic Behavior

    Viscous

    Fluid

    Viscoelastic

    Fluid

    Elastic

    Solid

    Deforms

    continuously

    Returns to original shape

    when stress removed

  • Dr. Sarah E. Morgan, Rheology Class Notes, 2013

    http://web.mit.edu/nnf/research/phenomena/Demos.pdf

    Die Swell

  • Dr. Sarah E. Morgan, Rheology Class Notes, 2013

    Polyacrylamide Solution Climbing Stir Bar

    http://www.chaosscience.org.uk/dem/public_html//article.php?story=20050307145058285

    Weissenberg Effect

  • Dr. Sarah E. Morgan, Rheology Class Notes, 2013

    Silly Putty

    chemistry.about.com

    blog.modernmechanix.com

  • Dr. Sarah E. Morgan, Rheology Class Notes, 2013

    Fluid Dynamics: Reynolds Number

    NReD Vav r

    m

    4 r Q

    m D

    NRe = dimensionless Reynolds number

    D = diameter of circular pipe

    Vav = average velocity of fluid

    r = density of fluid

    m = viscosity of fluid

    Q = volumetric flow rate

  • Dr. Sarah E. Morgan, Rheology Class Notes, 2013

    Fluid Dynamics: Reynolds Number

    NReD Vav r

    m

    4 r Q

    m D

    NRe = dimensionless Reynolds number S = cross sectional area

    D = diameter of circular pipe r = radius

    Vav = average velocity of fluid

    r = density of fluid

    m = viscosity of fluid

    Q = volumetric flow rate

    S r2

    D

    2

    2

    Q Vav S

  • Dr. Sarah E. Morgan, Rheology Class Notes, 2013

    Fluid Dynamics: Reynolds Number

    NReD Vav r

    m

    4 r Q

    m D

    NRe < 2100, flow is laminar

    NRe > 4000, flow is turbulent

    NRe = 2100 4000, transition region

    Fluid Inertial Forces

    NRe = Fluid Cohesive Forces

  • Dr. Sarah E. Morgan, Rheology Class Notes, 2013

    Understanding of rheology is important for:

    Polymer melt and solution processing

    Polymer reaction processes

    Polymer formulation

    Polymer fabrication

  • Dr. Sarah E. Morgan, Rheology Class Notes, 2013

    Homework:

    Read Chapter 1 Gupta

    Install Mathcad, begin working

    tutorials