Rheology Seminar Barcelona 2000
Contents
Introduction
Definition of Viscosity, Shear Stress, Shear Rate
Measuring Viscosity
Definitions Flow Behaviour
Determination of Thixotropy
Determination of Yield Stress
Flow Behaviour and Application
Shear rate calculations of real applications
Errors
Calibration of instruments
How is rheology defined?
Rheology – the “science of flow”
Rheometry – the experimental determination of flow behaviour
today too: of visco-elastic material properties
What´s rheology useful for?
Flow behaviour and material properties influence:
Processing
Product Stability
Customers Acceptance
Rheology delivers characteristics for
Processing, Product Stability and Customers Acceptance!
How is viscosity defined?
Viscosity can be determined indirectly by:
Shear Stress Shear Rate
F, v
A
x
y
Calculation of the Shear Rate ( )
Storage
Pumping (tubes)
Spraying (nozzles)
Spreading
Bleeding, Running
Typical shear rates
Application Shear rate (s-1)
Sedimentation 10-6 – 10-4
Phase separation 10-6 – 10-4
Leveling, running 10-1 – 101
Extrusion 100 – 102
Dip Coatings 101 – 102
Chewing 101 – 102
Pumping, stirring 101 – 103
Brushing 101 – 104
Spraying 103 – 104
Definition
Viscosity of fluids at 20°C
What is the effect of shearing?
Orientation Extension Deformation Destr. of Aggregates
Measuring Viscosity
Instrument Measured Unit Advantage
Finger Resistance, Friction Price
Ford Cup Time Price
Falling Ball Viscometer Time Precision
Capillary Viscometer Time Precision
Torsion Viscometer Damping Cleaning
Pressure Viscometer Force, Distance high Viscosity
Rotational Viscometer Torque, Deformation Flexibility
Rotational Rheometers
Method The torque is measured at a certain preset speed (controlled rate method, CR) or the speed is measured at a certain preset torque (controlled stress method, CS). The sensor system is designed to allow calculation of the rheologically relevant quantities
Advantage Flexibility in measuring methods and ranges
Drawback Expensive
Application For visco-elastic substances and conditions different from ambient
Design Measuring Unit
Motor with speed or torque control
Measurement of speed or deformation
Bearing (frictionless air bearing) with high axial and radial stiffness
Sensor system (cylinder, parallel plates or plate-cone) with temperature control (liquid, electrical, Peltier)
Basic equation:
M-Factor (Shear factor), [s/ rad/s]:
A-Factor (torque factor), [Pa/ Nm]
Calculation of viscosity
Design of Sensors
Cylindrical Sensors
– thin liquids
(large rotor surface)
– filled systems
(wide gaps)
Plate-Plate
– dynamic measurements
(oscillation)
– inhomogeneous materials
(particles, fibres)
Plate-Cone
– thick substances
– easy to clean
– no particles
– high shear rates
Cylinder sensors
Cone/ Plate sensors
HAAKE RotoVisco® 1
Specifications 0.0125 to 1000 rpm
0.1 to 5 Ncm
Sensor Systems cylinders, plate-cone, parallel plates, special rotors
Temperature range up to 350°C
Options remote control per display control unit or computer control, QC features
HAAKE Viscotester® VT550
Specifications 0.5 to 800 rpm 0.01 to 3 Ncm
Sensor Systems cylinders, plate-cone, parallel plates, special rotors
Temperature range up to 150°C
Options manual or computer control, implemented and free programmable speed rows and procedures
HAAKE RheoStress®
Specifications 0.01 to 1200 rpm (CR); 0.2 Nm to 15 Ncm
Sensor Systems cylinders, plate-cone, parallel plates, special rotors
Temperature range -100°C to 200°C (liquid)
Special Applications High pressure cell (up to 100 bar/200°C),
high temperature (up to 500°C),
normal force sensor
Measuring Flow Behaviour
Flow Curve:
time
— Ramp
_| Steps
can be given by:
– rpm
– linear speed
– flow rate
Viscosity = f (Temperature, Pressure)
Viscosity = f (T) Viscosity = f (p)
Temperature
Pressure
Viscosity
Viscosity
Viscosity – pressure dependency (crude oil)
Viscosity – temperature dependency
Definitions Flow Behaviour
Flow Curve: Viscosity Curve:
t
h
Newtonian Flow Behaviour
viscosity
shear stress
Flow- and viscosity curve
Bingham Flow behavior
Viscosity
Shear stress
Shear Thinning Flow Behaviour
viscosity
shear stress
Plastic flow behavior
Shear stress
Viscosity
Shear Thicking (Dilatant) Flow Behaviour
PVC plastisol (low shear rates)
viscosity
shear stress
Bingham/Plastic Flow Behaviour
shear stress
viscosity
Plastic flow behavior
with emulsifier
no emulsifier
Flow curve
Different flow behaviors
Thixotropic Flow Behaviour
shear stress
viscosity
Measuring program for thixotropic fluids
Determination of thixotropy: Time curve
Preset: Shear rate (const.),
Time (variabel)
Measurent: Shear stress
Result: Viscosity = f(t)
Application: Determination of the thixotropy factor (eta (t1)/eta(t2))
Rheopectic flow behavior
Flow Behaviour and Application
Behaviour during application (high shear rates) Painting, Spraying, Rubbing
Transport properties (medium to high shear rates) Pumping, Stirring Bottling
Behaviour after application (small shear rates) Spreading, Levelling
Storage properties (very small shear rates) Sedimentation Phase Separation
Spreadability, Pourability
Rheologically relevant quantities:
Viscosity as a function of shear rate =f()
Viscosity as a function of time =f(t) ( thixotropy)
Result: Parameters
for customer friendly handling!
.
How can spreadability be quantified?
Input:
varying
shear rate
Measurement:
shear stress
Result:
viscosity
Pumping, Mixing and Embottling
Rheologically relevant quantities:
Viscosity as function of shear rate =f()
Viscosity as function of time =f(t) ( Thixotropy)
Result: Parameters
for pump design, possible flow rates, thickening!
.
How can =f() be determined?
.
Input:
varying
shear rate
Measurement:
shear stress
Result:
viscosity
viscosity
shear stress
Chocolate Coating
How can =f(t) be determined?
Input:
constant
shear rate
Measurement:
shear stress
Result:
viscosity
Viscosity – time – curve of a thixotropic paint
Discharging, Pump Initializing
Rheologically relevant quantity:
Yield stress 0
Result: Parameters for
pump design, optimization of discharging, thickening!
What is the yield Stress? – a model
Yield stress is the shear stress necessary to initialize stationary flow
How can yield stress be determined?
CD-mode: maximum of -time-curve
Flow curve: -intercept at small in the flow curve
CS- ramp: change of slope of the curve log versus log
Creep: slope of the curve d /d t >0
.
Yield Stress Determination in CD-Mode
Input:
increasing
deformation
Measurement:
shear stress
Evaluation:
maximum
Result:
yield stress
Yield Stress from Flow Curve Extrapolation
Input:
varying
shear rate
Measurement:
shear stress
Evaluation:
extrapolation
Result:
yield stress
Yield Stress from Controlled Stress Ramps
Input:
varying
shear stress
Measurement:
deformation
Evaluation:
transition
Result:
yield stress
Printing Ink
Yield point – an example
Yield point – an example
Yield point – an example
Yield point – an example
What is the relevant information from Tau(o)
Shear stress necessary for initalizing stationary flow
= information about behaviour at the beginning of pumping
shear stress
viscosity
Two different Cremes
Sedimentation, Phase Separation
Rheologically relevant quantities:
Deformation upon small stresses =f(t)
(viscous and elastic parts)
Yield stress 0
Result:
tendency to sedimentation, measure for product stability!
Sedimentation accord. to Stokes
density solvent dL
density particle dP
Stoke's law describes the sedimentation
Speed:
Shear rate max.:
Stress max.:
Running paint
Stress (wall) = force of the paint per area
Tau (w)=(h-y)*g*density
Tau (wall)= F/A with
F=m.g=density*h*A*g
Leveling
x
z
lambda
Stress required for leveling
= surface tension
Brushability
Shear rate Gp
Gp = v/y (1/s)
Errors
Sources of error
Machine
(uncertainty of torque, sensors etc.)
Sample
(slippage, particles etc.)
User
(parameters, filling etc.)
Machine errors
According to DIN 53018: Viscosity = Geometry * Md/ n
Geometry: +/- 0,5% abs.
(uncertainty of diameter, radius, cone angle, gap, shaft alignment etc.)
Angular speed n: +/- 0,5% abs.
(measuring with stepper motors or digital encoders)
Torque M: +/- 0,5% FSD
(full scale deflection of measuring range)
Errors caused by the sample
Particles
Air bubbles
Chemical reaction
Elasticity
Swelling
Sedimentation
… … …
Errors caused by the user
Wrong geometry or parameters
Measuring range
Gap setting
Filling
Sample preparation
Temperature
Shear heating