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