Capillary and Cone & Plate Viscometers Viscosity Capillary and Cone & Plate Viscometers Brydger Cauch November 27, 2006

Importance Classifies fluid flow Motor Oil: 5W30 Newtonian or non-Newtonian Motor Oil: 5W30 Higher Number=Thicker

What is viscosity? Rheology Viscosity 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 Operation of capillary and cone & plate viscometers 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 Newtonian Fluid 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 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 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± (1) Standard deviation (2) Propagated error

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

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

Viscosity Reading (cP) Unknown Fluid Brookfield Cone and Plate Viscometer Average viscosity=95.5±1.5 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

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?