ViscosityCapillary 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 non-Newtonian

Characterization of Fluids

dy

dV

(de Nevers 2005)

• Non-Newtonian Fluids are usually complex mixtures

• Newtonian Fluid

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

– Second term neglected for sufficiently long times (>60 sec)

– Fluid of known viscosity used to determine parameter B

2

'

t

BtB

Calibration

Brookfield Standard

Density

(g/mL)

Viscosity (cP @ 25°C)

Average time (sec)

Parameter B (cP*mL/g*sec)

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)

Cannon-Fenske Routine Capillary Viscometer: Size 400 with T=25°C

(1) Standard deviation (2) Propagated error

Calibration

• Brookfield cone and plate viscometer with cone size CP-41 and T=28.5°C

y = 1.1221x - 1.8099

y = 1.1405x - 1.4843

0

20

40

60

80

100

120

30 40 50 60 70 80 90 100

Measured Viscosity (cP)

Act

ual

Vis

cosi

ty (

cP)

6 RPM 12 RPM Linear (6 RPM) Linear (12 RPM)

Viscosity of an Unknown Fluid

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)

89.89±0.17 (1) 0.974±0.005 (2) 96.7±0.7 (2)

(1) Standard deviation (2) Propagated error

Unknown Fluid

Motor speed (RPM)

Viscosity Reading (cP)

Viscosity (cP)

6 85.8 94.5

12 86.0 96.6

• Brookfield Cone and Plate Viscometer

• 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%201.22%20%20%206-21-05.PRC.doc>

Questions?