Viscosity

1
Viscosity

• Capillary and Cone Plate Viscometers

Brydger Cauch November 27, 2006
2
Importance

• Classifies fluid flow
• Newtonian or non-Newtonian
• Motor Oil 5W30
• Higher NumberThicker

3
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

4
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

5
Theory
6
Shear Stress Experiment

• Internal friction between layers of flow

(Wikipedia 2006)
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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 non-Newtonian

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Characterization of Fluids

• Newtonian Fluid

• Non-Newtonian Fluids are usually complex mixtures

(de Nevers 2005)
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Operation of Capillary and Cone Plate
Viscometers
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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

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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

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Calibrations
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Calibration

• Capillary Viscometer
• Second term neglected for sufficiently long times
  (gt60 sec)
• Fluid of known viscosity used to determine
  parameter B

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Calibration
Cannon-Fenske Routine Capillary Viscometer Size
400 with T25C
Brookfield Standard Density (g/mL) Viscosity (cP _at_ 25C) Average time (sec) Parameter B (cPmL/gsec)
Fluid 100 0.974 0.005 (2) 96.6 89.84 0.22 (1) 1.104 0.006 (2)
Fluid 50 0.971 0.005 (2) 47.9 44.74 0.14 (1) 1.102 0.006 (2)
(1) Standard deviation (2) Propagated error
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Calibration

• Brookfield cone and plate viscometer with cone
  size CP-41 and T28.5C

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Viscosity of an Unknown Fluid
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Unknown Fluid

• Capillary Viscometer
• Accuracy 0.7 vs 0.2 reported
• Reproducibility 0.19 vs 0.1

Average Time (sec) Density (g/mL) Viscosity (cP)
89.890.17 (1) 0.9740.005 (2) 96.70.7 (2)
(1) Standard deviation (2) Propagated error
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Unknown Fluid

• Brookfield Cone and Plate Viscometer
• Average viscosity95.51.5 cP (st dev)
• Accuracy 1.6 vs 1

Motor speed (RPM) Viscosity Reading (cP) Viscosity (cP)
6 85.8 94.5
12 86.0 96.6
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Results

• Unknown fluid determined to be Brookfield Fluid
  100 (µ96.6 cP)
• Capillary Viscometer (25C)
• 96.70.7 cP
• Error of 0.10
• Cone and Plate Viscometer (28.5C)
• 95.51.5 cP
• Error of 1.1
• Students T Test
• 84.4 Probability they are the same

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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

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Review

• Theory
• Operation of capillary and cone plate
  viscometers
• Calibrations
• Determining the viscosity of an unknown fluid
• Results
• Conclusions

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References

• Viscosity. Wikipedia. 2006. 24 August 2006.
• lt http//en.wikipedia.org/wiki/Viscositygt
• 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.
• lthttp//www.che.utah.edu/ring/Instrumental20Ana
  lysis20CHE5503/SOP's/DigitalViscosity20SOP20Ver
  201.222020206-21-05.PRC.docgt

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Questions?