Viscosities Of Newtonian (autosaved).docx

VISCOSITIES OF NEWTONIAN & NON-NEWTONIAN LIQUIDS

Abstract This experiment aims to determine the viscosities of two fluids, Glycerol and gelatinized starch and investigate the effect of different shear rates on viscosity of fluids in different temperatures. The experiment also provided the model parameters of Newtonian and non-Newtonian liquids. HAAKE rotational viscometer model VT550 was used to determine viscosity of both fluids. In a desired temperature, the spindle was rotated by the motor at a given speed and torque to rotate the fluid. Shear rate was calculated from speed of rotation and shear stress was calculated from torque. With these, viscosity was computed for the fluid. The results obtained were as expected in that gelatinized starch had higher viscosity than glycerol. Gelatinized starch showed the characteristics of non-Newtonian liquid while glycerol showed the characteristics of Newtonian liquid. The viscosity of gelatinized starch decreased with increasing shear rate but decreased with increasing temperature and the viscosity of glycerol remained constant with increasing shear rate but decreased with increasing temperature. Gelatinized starch is a thixotropic fluid based on the results obtained.

1.0 Introduction 1.1 Newtonian Fluid A Newtonian fluid is the fluid in which the shear stress, created by the flow, is linearly proportional to shear rate. That means that the viscosity of the fluid remains constant as the shear rate changes.

Fig.1

1.

𝛕 = 𝛍𝛄 Where, 𝝉 is shear stress, μ is viscosity and 𝜸 is shear rate. No real fluid perfectly fits the definition of Newtonian fluid. However, many common fluids such as air and water can be assumed to be Newtonian fluid. Newtonian fluids are the basic mathematical model for fluids that account for viscosity. Air, water and thin motor oil are some examples of Newtonian fluid which have different densities and account for different shear stress and shear rate.

1.2 Non Newtonian Fluid Non Newtonian fluids are fluids which have different properties than Newtonian fluids. Unlike Newtonian fluids, viscosity depends on shear rate. In a non-Newtonian fluid, the shear stress is not linearly proportional to shear strain, the relation can be different and time dependant. Therefore, a constant viscosity coefficient cannot be achieved. There are different types of nonNewtonian fluids depending on how viscosity changes with shear rate. 

Shear thickening fluid

The viscosity of shear thickening fluid, also known as dilatant fluid, increases with increase in shear rate. The more the fluid is stirred, the more it feels thick. μ = m 𝜸 n-1 where n is more than 1.



Shear thinning fluid

The viscosity of shear thinning fluid, also known as thixotropic fluid, decreases with increase in shear rate. That means, the more the fluid is stirred, the more it feels thin. Paint is one of the example of thixotropic fluid. μ = m 𝜸 n-1 where n is less than 1.



Bingham plastic

Some fluids have linear shear stress and shear strain graph but requires a finite yield stress before they can flow. That means the line does not pass through origin. Such fluids are known as Bingham fluids. Some examples are mustard sauce and mayonnaise. μ=

𝜏𝑜 𝛾

+m

where 𝝉o is yield stress

2.

There are also some fluids whose strain rate is a function of time. These fluids are known as anti-thixotropic fluid. Such fluids require an increasing shear stress to maintain a constant shear rate.

Fig 2. Relation of shear stress and shear rate of different non Newtonian fluids.

2.0 Methodology HAAKE rotational viscometer model VT550 was used for the experiment.

Figure 3. Experimental setup

3.

APPENDIX. Results in Tabulated Form.

Temperature Speed

Temperature Rpm(1/min) (unit)

Viscosity (mPa.s)

Shear Stress(Pa)

Shear Rate(1/s)

30

1

5

31.4

282.7

1.204

4.5

2

8.3

31.6

219.0

1.636

7.47

3

13.9

31.7

154.7

2.048

12.51

4

23.2

32.0

139.3

2.046

20.88

5

45.3

32.1

115.0

2.766

40.76

Speed

Temperature Rpm(1/min) (unit)

Viscosity (mPa.s)

Shear Stress(Pa)

Shear Rate(1/s)

1

5

45.0

280.0

1.204

4.5

2

8.3

45.0

201.0

1.486

7.47

3

13.9

45.0

141.7

1.998

12.51

4

23.2

45.0

121.7

2.480

20.88

5

45.3

45.0

92.5

3.763

40.76

Speed

Temperature Rpm(1/min) (unit)

Viscosity (mPa.s)

Shear Stress(Pa)

Shear Rate(1/s)

1

5

60.0

244.3

1.074

4.5

2

8.3

60.0

177.7

1.382

7.47

3

13.9

60.0

155.7

1.561

12.51

4

23.2

60.0

103.5

2.099

20.88

5

45.3

60.0

79.1

3.225

40.76

45

60

Table 1. Results showing data obtained from experiment for 10% Gelatinized Starch

Temperature

Speed

30

45

60

1

Rpm(1/min) Temperature (unit) 5 31.3

Viscosity (mPa.s) 557.3

Shear Stress(Pa) 2.585

Shear Rate(1/s) 4.50

2

8.3

32.0

414.3

3.199

7.47

3

13.9

32.0

452.0

5.836

12.51

4

23.2

32.2

470.3

9.804

20.88

5

45.3

32.3

480.0

19.710

40.76

Speed 1

Rpm(1/min) Temperature (unit) 5 45.0

Viscosity (mPa.s) 238.3

Shear Stress(Pa) 1.152

Shear Rate(1/s) 4.50

2

8.3

45.1

226.0

1.767

7.47

3

13.9

45.0

237.0

2.841

12.51

4

23.2

45.1

220.3

4.633

20.88

5

45.3

45.1

220.0

8.985

40.76

Speed 1

Rpm(1/min) Temperature (unit) 5 60

Viscosity (mPa.s) 85.1

Shear Stress(Pa) 0.486

Shear Rate(1/s) 4.50

2

8.3

60

109.3

0.793

7.47

3

13.9

60

92.0

1.331

12.51

4

23.2

60

89.4

1.945

20.88

5

45.3

60

92.3

3.737

40.76

Table 2. Results showing data obtained from experiment for Glycerine

Temperature

Shear Rate(1/s)

Shear Stress(Pa)

log shear rate

log shear stress

30

4.5

1.203

0.653

0.080

7.47

1.638

0.873

0.214

12.51

2.048

1.097

0.311

20.88

2.048

1.320

0.311

40.76

2.764

1.610

0.442

Shear Rate(1/s)

Shear Stress(Pa)

log shear rate

log shear stress

4.5

1.203

0.653

0.080

7.47

1.485

0.873

0.172

12.51

1.996

1.097

0.300

20.88

2.483

1.320

0.395

40.76

3.763

1.610

0.576

Shear Rate(1/s)

Shear Stress(Pa)

log shear rate

log shear stress

4.5

1.075

0.653

0.031

7.47

1.305

0.873

0.116

12.51

1.561

1.097

0.193

20.88

2.099

1.320

0.322

40.76

3.199

1.610

0.505

45

60

Table 3. Relation between log shear stress and log shear rate for gelatinized starch

Temperatur e 30

45

60

Shear Rate(1/s)

Shear Stress(Pa)

log shear rate

log shear stress

4.5

1.740

0.653

0.241

7.47

3.199

0.873

0.505

12.51

5.836

1.097

0.766

20.88

9.804

1.320

0.991

40.76

19.710

1.610

1.295

Shear Rate(1/s)

Shear Stress(Pa)

log shear rate

log shear stress

4.5

0.563

0.653

-0.250

7.47

1.024

0.873

0.010

12.51

2.253

1.097

0.353

20.88

3.840

1.320

0.584

40.76

7.910

1.610

0.898

Shear Rate(1/s)

Shear Stress(Pa)

log shear rate

log shear stress

4.5

-0.204

0.653

#NUM!

7.47

0.127

0.873

-0.895

12.51

0.384

1.097

-0.416

20.88

1.126

1.320

0.052

40.76

2.790

1.610

0.446

Table 4. Relation between log shear stress and log shear rate for Glycerine

Starch speed 1

Temperature (K) Viscosity (mPa.s) 1/T 304.8 284.3 0.00328 318.0 278.7 0.00314 333.0 244.0 0.00300 speed 2 305.4 219.0 0.00327 318.1 201.7 0.00314 333.0 177.7 0.00300 speed 3 305.9 155.0 0.00327 318.1 141.0 0.00314 333.0 157.0 0.00300 speed 4 306.1 140.7 0.00327 318.1 121.0 0.00314 333.0 102.5 0.00300 speed 5 306.2 112.3 0.00327 318.1 92.9 0.00314 333.0 79.1 0.00300 Table 5. Relation between ln viscosity and 1/T for gelatinized starch

Glycerin

Temperature (K)

Viscosity (mPa.s) speed 1 304.5 375.0 318.0 119.0 333.0 0.0 speed 2 305.0 414.3 318.0 150.3 333.0 13.6 speed 3 305.0 452.0 318.0 153.0 333.0 20.4 speed 4 305.2 470.3 318.0 177.3 333.0 47.8 speed 5 305.3 480.0 318.0 192.0 333.0 67.2 Table 6. Relation between ln viscosity and 1/T for Glycerine

ln viscosity 5.650 5.630 5.497 5.389 5.307 5.180 5.043 4.949 5.056 4.946 4.796 4.630 4.721 4.532 4.371

1/T

ln viscosity

0.003284 0.003145 0.003003 0.003279 0.003145 0.003003 0.003278 0.003145 0.003003 0.003277 0.003145 0.003003 0.003276 0.003145 0.003003

5.927 4.779 #NUM! 6.027 5.013 2.613 6.114 5.030 3.016 6.153 5.178 3.866 6.174 5.257 4.207