viscosity experimental report

7/27/2019 Viscosity Experimental Report

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VISCOSITY MEASUREMENT LABORATORY 1

Q u e e n s l a n d U n i v e r s i t y o f T e c h n o l o g y

Viscosity Measurement Laboratory

ENB434 Tribology

Aaron Palm 07565887


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Table of Contents

INTRODUCTION 3

MATERIALS AND METHODS 3

RESULTS 4

DISCUSSION 7

CONCLUSION 8

LIST OF REFERENCES 9

APPENDICES 10

Figure 1 Section view of cone-plate viscometer ____________________________________________________________________ 3Figure 2 Working plane of cone, from cone-plate viscometer _____________________________________________________ 5Figure 3 Experimental Shear Stress vs. Shear Rate curves @ 25C _______________________________________________ 6Figure 4 Experimental Viscosity vs. Shear Rate curves @ 25C ___________________________________________________ 6Figure 5 Viscosity vs. Shear Rate curves of Newtonian and Non-Newtonian fluids (Stachowiak & Batchelor,

1993) ________________________________________________________________________________________________________________ 7Figure 6 Shear Stress vs. Shear Rate curves of Newtonian and Pseudoplastic fluids (Stachowiak &Batchelor, 1993) ____________________________________________________________________________________________________ 7

Table 1 Results from experiment ....................................................................................................................................................... 4


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Introduction

Viscosity is commonly regarded as the most important rheological property of a fluid

lubricant. Furthermore, the two parameters that have a dramatic effect on the viscosity of

a fluid are the temperature and pressure of the fluid and the velocity gradient between the

two wetted, working surfaces.

Initially it may seem appropriate to increase the viscosity of the fluid lubricant to separate

the two surfaces indefinitely however, this is not the case. As this requires larger forces to

shear the fluid the heat of the fluid increases, leading to premature component failure. The

lubricant viscosity may also be affected by the shearing rate of the fluid, depending on

whether the fluid obeys Newtonian theory or not. A fluid is regarded as Newtonian when

the shear rate of the fluid is proportional to the shear stress within the fluid (Stachowiak &

Batchelor, 1993). A Non-Newtonian fluid does not conform to this relationship and can

either be dilatant, where the fluid thickens with an increase in shear rate or pseudo-plastic,

where the fluid thins with an increase in shear rate. Additionally, to measure the viscosityof the fluid lubricant at several operating conditions, a viscometer is used. In this case a

cone and plate viscometer was employed, where the angular velocity of the cone is known

and remains constant. Due to the shallow geometry of the cone, the shear rate also

remains relatively constant, with a resistance torque placed on the cone as a result of the

shearing stress governed by the fluids viscosity. This experiment will take two fluid

lubricants, one being a Newtonian, thin mineral oil and the other a solution of

Carboxymethyl Cellulose. Furthermore, their behaviour over a range of shear rates at three

different temperatures using a cone plate viscometer will be examined, to determine

whether each fluid is Newtonian or Non-Newtonian.

Materials and Methods

A fluids viscosity can be determined by the use of the cone-plate viscometer. Furthermore

the cones have set dimensions and are classed accordingly. In this experiment a CP41 cone

is used, illustrated in the following figure.

Figure 1 Section view of cone-plate viscometer

The shear stress developed within the fluid as a result of the fluids resistance to movement

(viscosity) induces a torque on the shaft. This torque is transferred through a highly

sensitive spring that is connected to a piezo circuit, in result returning the said torque as a

percentage within a range set by the size of the spring in this case; the maximum torque is

673 Nm. The experiment will measure the shear stress over a series of shear rates within

R

h

CP41 cone

=3R=2.4 cm


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the set torque range. This process will be repeated over three temperatures to determine

whether the fluid is Newtonian or not.

Results

Table 1 illustrates the relationship between the shear stress and shear rate for fluid A and B.In conjunction with the governing parameters of speed in RPM and the resulting torque

percentage recorded at a moderately constant temperature.Table 1 Results from experiment

Fluid Viscosity Speed Torque Shear Stress

Shear

Rate Temp.

A

22.79 cP 5 RPM 0.524 rad/s 9.9 % 66.627 Dyne-cm 2.28 Dyne/cm^2 10 24.9 C21.87 cP 10 RPM 1.047 rad/s 19 % 127.87 Dyne-cm 4.37 Dyne/cm^2 20 25.1 C

21.87 cP 15 RPM 1.571 rad/s 28.4 % 191.132 Dyne-cm 6.54 Dyne/cm^2 30 25.1 C




B


32.42 cP 6 RPM 0.628 rad/s 17 % 114.41 Dyne-cm 3.89 Dyne/cm^2 12 25.5 C






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By looking at an infinitely small area on the cone surface at an arbitrary radius a relationship

between the shear stress, shear rate and dynamic viscosity may be drawn,

Figure 2 Working plane of cone, from cone-plate viscometer

This relationship is quantified by the following expression,

Equation 1

By selecting an infinitely small area on the disc where the height is negligible the shear rate

is expressed as,

Equation 2

And the shear stress is defined as,

Equation 3

Substituting the two later equations into equation 1,

Equation 4

By integrating across the entire working area of the cone,

Equation 5

Equation 6

rR


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Rearranging for dynamic viscosity,

Equation 7

By taking the results for Fluid A at a speed of 50 RPM the dynamic viscosity is,

Comparing this value to the given viscosity values from Table 1 a 0.21 difference is evident.

Furthermore the assumption can be made that the error is a result of the difference in the

amount of significant figures used in each calculation and can be considered negligible.

Furthermore, by plotting the results from the experiment (Appendices) the relationship

between the shear stress and shear rate of Fluid A and B at 25C were drawn,

Figure 3 Experimental Shear Stress vs. Shear Rate curves @ 25C

The following plot show the relationship between the dynamic viscosity and the shear rate

of both Fluids A and B at 25C,

Figure 4 Experimental Viscosity vs. Shear Rate curves @ 25C

0.00 Dyne/cm^2

5.00 Dyne/cm^2

10.00 Dyne/cm^2

15.00 Dyne/cm^2

20.00 Dyne/cm^2

25.00 Dyne/cm^2

0 20 40 60 80 100 120

FLUID A

FLUID B

0 cP

5 cP

10 cP

15 cP

20 cP

25 cP30 cP

35 cP

40 cP

0 20 40 60 80 100 120

FLUID A

FLUID B


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Discussion

The results from the experiment relay certain rheological features that portray the

characteristics of Newtonian and Non-Newtonian fluids. To determine which is the former

and later, the relationship between the fluids viscosity over a series of shear rates at a set

temperature is employed.

Figure 5 Viscosity vs. Shear Rate curves of Newtonian and Non-Newtonian fluids (Stachowiak & Batchelor, 1993)

Although Figure 5 employs kinematic viscosity, dynamic viscosity may also be applied since

the nature of each curve will follow the same, general form. The relationship between the

viscosity and shear rate of Fluid A rendered results that emulated the characteristics of a

Newtonian fluid. In contrast, the results for Fluid B follow pseudoplastic behaviour, where

the viscosity decreases exponentially with an increase in shear rate. This phenomenon

occurs when the initially, tightly bound molecular chains with no connecting structurebetween each strand, unravel and align, giving a reduction in apparent viscosity (Stachowiak

& Batchelor, 1993).

By considering the relationship between the shear stress and the shear rate of Fluids A and

B, supporting conclusions were made.

Figure 6 Shear Stress vs. Shear Rate curves of Newtonian and Pseudoplastic fluids (Stachowiak & Batchelor, 1993)

Additionally, the relationship between the shear stress and shear rate of Fluid B, matches

pseudoplastic behaviour as represented in Figure 6 thus, complimenting the former

conclusion that Fluid B is pseudoplastic. Through further study of the rheological properties

Pseudoplastic Newtonian


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of Carboxymethyl Cellulose (CMC), it was found that CMC also follows pseudoplastic

behaviour and therefore, it can be concluded that Fluid B is the Carboxymethyl Cellulose

solution. Furthermore, the relationship between the shear stress and shear rate of Fluid A

does not take consistent form in respect to the predefined Newtonian and Non-Newtonian

relationships between shear stress and shear rate. However, based on the former

conclusions demonstrating that Fluid A follows the Newtonian form, it can be settled that

the results for Fluid A in Figure 3 retain significant error. Experimental error may be a result

of environmental effects, such as heat fluctuations due to the circulating heating system.

Another being discrepancies between theory and reality, where in this case the peak of the

cone theoretically comes to a point however, is slightly flat in reality to reduce wear. An

additional source of error affecting the results of Fluid A, may be the volume of fluid

lubricant used in the experiment. In this case a highly specific volume of 2 millilitres must

be used to wet the entire working face of the cone. Thus deducing that without such error

the curve for Fluid A in figure 3 would take a linear form.

To determine the effects of temperature on the viscosity for each fluid, the experiment wasrepeated at 35C and 45C (Appendices). The results illustrate a decrease in viscosity with

an increase in temperature in result, decreasing the amount of force required to shear the

fluid. This was complimented by the shear stress vs. shear rate curves, which demonstrate a

decrease shear stress in respect to shear rate with an increase in temperature.

Furthermore, the viscosity vs. shear rate results for Fluids A and B diverge with an increase

in temperature, suggesting that the cohesive forces between the molecules that surpass the

molecular momentum transfer in Fluid B are greater than Fluid A.

Conclusion

The objective of this experiment was to determine which of the two arbitrary fluids are

either the Newtonian, thin mineral oil or the Carboxymethyl cellulose solution. Through an

involved discussion of the relationship between the shear stress and shear rates of the fluid

and the relationship between the dynamic viscosity and shear rate of the fluid, particular

conclusions were drawn. Furthermore, it was determined that Fluid B portrayed the same

characteristics as a pseudoplastic fluid and in conjunction with further study, Fluid B was

determined to be the Carboxymethyl Cellulose solution. Additionally the results for Fluid A

rendered the same features as a Newtonian fluid, and was therefore deemed the

Newtonian, thin mineral oil.


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List of References

Ghannam, M. T., & Esmail, M. N. (1997). Rheological properties of carboxymethyl cellulose.

Applied Polymer Science, 64 (2), 289-301.

Stachowiak, G. W., & Batchelor, A. W. (1993). Viscosity-Shear Rate Relationship. In G. W.

Stachowiak, & A. W. Batchelor, Engineering Tribology. Amsterdam, The Netherlands:

Elsevier.


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Appendices

Fluid Viscosity Speed Torque Shear Stress

Shear

Rate Temp.

A

22.79 cP 5 RPM 0.524 9.9 % 66.627 Dyne-cm 2.28 Dyne/cm^2 10 24.9 C21.87 cP 10 RPM 1.047 rad/s 19 % 127.87 Dyne-cm 4.37 Dyne/cm^2 20 25.1 C





B







A







B

25.78 cP 5 RPM 0.524 rad/s 11.1 % 74.703 Dyne-cm 2.56 Dyne/cm^2 10 35 C

24.52 cP 10 RPM 1.047 rad/s 21.3 % 143.349 Dyne-cm 4.90 Dyne/cm^2 20 35 C22.73 cP 20 RPM 2.094 rad/s 39.5 % 265.835 Dyne-cm 9.09 Dyne/cm^2 40 34.9 C




A








B

19.57 cP 5 RPM 0.524 rad/s 8.6 % 57.878 Dyne-cm 2.00 Dyne/cm^2 10 44 C








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0.00 Dyne/cm^2

5.00 Dyne/cm^2

10.00 Dyne/cm^2

15.00 Dyne/cm^2

20.00 Dyne/cm^2

25.00 Dyne/cm^2

0 20 40 60 80 100 120

Shear Stress vs Shear Rate @ 25C

FLUID A

FLUID B

0.00 Dyne/cm^2

5.00 Dyne/cm^2

10.00 Dyne/cm^2

15.00 Dyne/cm^2

20.00 Dyne/cm^2

25.00 Dyne/cm^2

0 20 40 60 80 100 120 140


FLUID A

FLUID B

0.00 Dyne/cm^2

5.00 Dyne/cm^2

10.00 Dyne/cm^2

15.00 Dyne/cm^2

20.00 Dyne/cm^2

25.00 Dyne/cm^2

0 20 40 60 80 100 120 140 160


FLUID A

FLUID B


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0 cP

5 cP

10 cP

15 cP

20 cP

25 cP

30 cP

35 cP

40 cP

0 20 40 60 80 100 120

Viscosity vs Shear Rate @ 25C

FLUID A

FLUID B

0 cP

5 cP

10 cP

15 cP

20 cP

25 cP

30 cP

0 20 40 60 80 100 120 140 160


FLUID A

FLUID B

0 cP

5 cP

10 cP

15 cP

20 cP

25 cP

0 50 100 150 200 250


FLUID A

FLUID B

viscosity experimental report

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