Viscosity
Capillary and Cone & Plate
Viscometers
Brydger Cauch
November 27, 2006
Importance
• Classifies fluid flow
– Newtonian or non-Newtonian
• Motor Oil: 5W30
– Higher Number=Thicker
What is viscosity?
• Rheology
– Deformation and flow of matter under the
influence of applied stress
– Viscosity, elasticity, and plasticity
• Viscosity
– Measure of the resistance to deformation
of a fluid under shear stress
Overview
• Theory
– Shear Stress
– Molecular Origins
– Newtonian and non-Newtonian fluids
• Operation of capillary and cone & plate
viscometers
• Calibrations
– Parameter for Capillary Viscometer
– Calibration Curve for Cone and Plate Viscometer
• Viscosity of an unknown fluid
• Conclusions
• Questions
Theory
Shear Stress Experiment
• Internal friction between layers of flow
(Wikipedia 2006)
Molecular Origins
• Gases
– Molecular diffusion
between layers of
flow
– Independent of
pressure
– Increases with
increasing
temperature
– Newtonian
• Liquids
– Additional forces
between molecules but
exact mechanics
unknown
– Independent of
pressure except at very
high pressure
– Decrease with
increasing temperature
– Newtonian and nonNewtonian
Characterization of Fluids
• Newtonian Fluid
dV
 
dy
• Non-Newtonian
Fluids are
usually complex
mixtures
(de Nevers 2005)
Operation of Capillary and
Cone & Plate Viscometers
Capillary Viscometer
• Select appropriate
capillary size to give
reasonable times
• Keep constant
temperature
• Time fluid falling
between two fiducial
marks (a) and (b)
• Avoid parallax
Brookfield Cone & Plate
Viscometer
• Shallow angled cone in very close proximity
with a flat plate
• Important features
–
–
–
–
–
Circulating bath to keep constant temperature
Different cone sizes
Level on the instrument
Adjusting ring
Motor speed in RPM
• Operation
– Adjust cup so pins barely not making contact
– Measure torque needed to overcome viscous
resistance
Calibrations
Calibration
• Capillary Viscometer
B'
  B   t  2
t
– Second term neglected for sufficiently long times
(>60 sec)
– Fluid of known viscosity used to determine
parameter B
Calibration
Cannon-Fenske Routine Capillary Viscometer:
Size 400 with T=25°C
Brookfield Density
Standard (g/mL)
Viscosity
(cP @
25°C)
Average
time (sec)
Parameter B
(cP*mL/g*sec)
89.84±
0.22 (1)
44.74±
0.14 (1)
1.104±
0.006 (2)
1.102±
0.006 (2)
Fluid 100
0.974±
0.005 (2)
96.6
Fluid 50
0.971±
0.005 (2)
47.9
(1) Standard deviation (2) Propagated error
Calibration
• Brookfield cone and plate viscometer with
cone size CP-41 and T=28.5°C
120
Actual Viscosity (cP)
100
y = 1.1405x - 1.4843
80
y = 1.1221x - 1.8099
60
40
20
0
30
40
50
60
70
80
90
Measured Viscosity (cP)
6 RPM
12 RPM
Linear (6 RPM)
Linear (12 RPM)
100
Viscosity of an
Unknown Fluid
Unknown Fluid
• Capillary Viscometer
Average Time
(sec)
Density
(g/mL)
Viscosity
(cP)
89.89±0.17 (1)
0.974±0.005 (2)
96.7±0.7 (2)
(1) Standard deviation (2) Propagated error
• Accuracy: 0.7% vs ±0.2% reported
• Reproducibility: 0.19% vs ±0.1%
Unknown Fluid
• Brookfield Cone and Plate Viscometer
Motor speed
(RPM)
6
Viscosity
Reading (cP)
85.8
Viscosity (cP)
12
86.0
96.6
94.5
• Average viscosity=95.5±1.5 cP (st dev)
• Accuracy: 1.6% vs ±1%
Results
• Unknown fluid determined to be Brookfield
Fluid 100 (μ=96.6 cP)
• Capillary Viscometer (25°C)
– 96.7±0.7 cP
– Error of 0.10%
• Cone and Plate Viscometer (28.5°C)
– 95.5±1.5 cP
– Error of 1.1%
• Student’s T Test
– 84.4% Probability they are the same
Conclusions
• Both viscometers straightforward once
set up
• Capillary viscometer simpler and more
accurate
• Cone and plate viscometer showed a
larger deviation from the known
viscosity
– Higher temperature creates error
– Lower viscosity at a higher temperature
follows the expected trend
Review
• Theory
• Operation of capillary and cone & plate
viscometers
• Calibrations
• Determining the viscosity of an
unknown fluid
• Results
• Conclusions
References
• “Viscosity.” Wikipedia. 2006. 24 August 2006.
< http://en.wikipedia.org/wiki/Viscosity>
• de Nevers, Noel. Fluid Mechanics. McGraw-Hill, New
York, 2005.
• Shoemaker, D.P., C.W. Garland, and J.W. Nibler.
Experiments in Physical Chemistry, 6th ed. Mc-Graw-Hill,
New York, 1996.
• “Measuring Viscosity with a Digital Viscometer.” 21 June
2005. University of Utah. 24 August 2006.
<http://www.che.utah.edu/~ring/Instrumental%20Analysis
%20CHE5503/SOP's/DigitalViscosity%20SOP%20Ver%2
01.22%20%20%206-21-05.PRC.doc>
Questions?