viscosity capillary and cone & plate viscometers brydger cauch november 27, 2006
TRANSCRIPT
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
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
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
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)
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>