viscometry of newtonian fluids - report sm 4_leandro_final

7/31/2019 VIscometry of Newtonian Fluids - Report SM 4_Leandro_final

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Technical University of Dortmund

Facultyof Biochemical and Chemical Engineering

Report Lab Experiment

SM 4 Viscometry Newtonian and Non-newtonian Fluids

Chair of Fluid mechanics

Group

Leandro Michieleto

Mei Hai Tao

May 2012


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1. ObjectivesObjective for this experiment is the introduction of the basics of measurements of

viscous properties of Newtonian and Non-newtonian fluids and indirectly the introduction of

the fluid mechanics theory approaching these topics, introducing and providing knowledge

and first-hand experience of a real lab Haake viscometer.

2. Introduction2.1 Viscosity

Viscosity is the measure of the internal friction of a fluid. This friction becomes

apparent when a layer of fluid is made to move in relation to another layer. The greater the

friction, the greater the amount of force required to cause this movement, which is calledshear. Shearing occurs whenever the fluid is physically moved or distributed. Highly viscous

fluids, therefore, require more force to move than less viscous materials.

Isaac Newton defined viscosity by considering the model represented in the figure

above. Two parallel planes of fluid of equal area A are separated by a distance dxand are

moving in the same direction at different velocities V1 and V2. Newton assumed that the

force required to maintain this difference in speed was proportional to the difference in

speed through the liquid, or the velocity gradient. To express this, Newton wrote:

where h is a constant for a given material and is called its viscosity.

The velocity gradient, dv/dx, is a measure of the change in speed at which the

intermediate layers move with respect to each other. It describes the shearing the liquid

experiences and is thus called shear rate. This will be symbolized as S in subsequent

discussions. Its unit of measure is called the reciprocal second(sec-1

).

The term F/A indicates the force per unit area required to produce the shearing action. It is

referred to as shear stress and will be symbolized by F.

2.2.Types of Fluids and Viscosity BehaviorThe type of flow behavior Newton assumed for all fluids is called, not surprisingly,

Newtonian. It is, however, only one of several types of flow behavior you may encounter. A

Newtonian fluid is represented graphically in the figures below. Figure 1 shows that the

relationship between shear stress (F) and shear rate (S) is a straight line. Figure 2 shows thatthe fluid's viscosity remains constant as the shear rate is varied. Typical Newtonian fluids

include water and thin motor oils.


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What this means in practice is that at a given temperature the viscosity of a Newtonian fluid

will remain constant regardless of which Viscometer model, spindle or speed you use to

measure it.

A non-Newtonian fluid is broadly defined as one for which the relationship F/S is not

a constant. In other words, when the shear rate is varied, the shear stress doesn't vary in the

same proportion (or even necessarily in the same direction). The viscosity of such fluids will

therefore change as the shear rate is varied. This measured viscosity is called the apparent

viscosity of the fluid and is accurate only when explicit experimental parameters are

furnished and adhered to.

Non-Newtonian flow can be envisioned by thinking of any fluid as a mixture of

molecules with different shapes and sizes. As they pass by each other, as happens during

flow, their size, shape, and cohesiveness will determine how much force is required to move

them. At each specific rate of shear, the alignment may be different and more or less force

may be required to maintain motion.There are several types of non-Newtonian flow behavior, characterized by the way a

fluid's viscosity changes in response to variations in shear rate. The most common types of

non-Newtonian fluids it can be may encountered are:

Psuedoplastic

This type of fluid will display a decreasing viscosity with an increasing shear rate, as

shown in the figure below. Probably the most common of the non-Newtonian fluids, pseudo-

plastics include paints, emulsions, and dispersions of many types. This type of flow behavior

is sometimes called shear-thinning.

Dilatant

Increasing viscosity with an increase in shear rate characterizes the dilatant fluid; see

the figure below. Although rarer than pseudoplasticity, dilatancy is frequently observed in

fluids containing high levels of deflocculated solids, such as clay slurries, candy compounds,

corn starch in water, and sand/water mixtures. Dilatancy is also referred to as shear-

thickening flow behavior.

Plastic

This type of fluid will behave as a solid under static conditions. A certain amount of

force must be applied to the fluid before any flow is induced; this force is called the yield

value. Tomato catsup is a good example of this type fluid; its yield value will often make it

refuse to pour from the bottle until the bottle is shaken or struck, allowing the catsup to gush

freely. Once the yield value is exceeded and flow begins, plastic fluids may display

Newtonian, pseudoplastic, or dilatant flow characteristics. See the figure below.


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2.3.Laminar and Turbulent FlowThe very definition of viscosity implies the existence of what is called laminar flow: the

movement of one layer of fluid past another with no transfer of matter from one to the

other. Viscosity is the friction between these layers.

Depending on a number of factors, there is a certain maximum speed at which one layer

of fluid can move with relation to another, beyond which an actual transfer of mass occurs.

This is called turbulence. Molecules or larger particles jump from one layer to another and

dissipate a substantial amount of energy in the process. The net result is that a larger energy

input is required to maintain this turbulent flow than a laminar flow at the same velocity.

The increased energy input is manifested as an apparently greater shear stress than would

be observed under laminar flow conditions at the same shear rate. This results in an

erroneously high viscosity reading.

The point at which laminar flow evolves into turbulent flow depends on other factors

besides the velocity at which the layers move. A material's viscosity and specific gravity as

well as the geometry of the Viscometer spindle and sample container all influence the point

at which this transition occurs.

Care should be taken to distinguish between turbulent flow conditions and dilatant

flow behavior. In general, dilatant materials will show a steadily increasing viscosity with

increasing shear rate; turbulent flow is characterized by a relatively sudden and substantial

increase in viscosity above a certain shear rate. The material's flow behavior may be

Newtonian or non-Newtonian below this point.

2.4.Factors that affect Rheological PropertiesTemperature - one of the most obvious factors that can have an effect on the rheological

behavior of a material is temperature. Some materials are quite sensitive to temperature,

and a relatively small variation will result in a significant change in viscosity. Others are

relatively insensitive. Consideration of the effect of temperature on viscosity is essential in

the evaluation of materials that will be subjected to temperature variations in use or

processing.

Shear Rate - non-Newtonian fluids tend to be the rule rather than the exception in thereal world, making an appreciation of the effects of shear rate a necessity for anyone

engaged in the practical application of rheological data. When a material is to be subjected


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to a variety of shear rates in processing or use, viscosity measurements should then be made

at shear rates as close as possible to the estimated values.

2.5.Experimental ApparatusViscosity is measured with various types of viscometers and rheometers. A

viscometer is used for those fluids which cannot be defined by a single value of viscosity and

therefore require more parameters to be set and measured.

A rotational speed is preset and the flow resistance of the sample is measured in

other words, the torque maintaining the set speed is proportional to the viscosity. All final

information on the viscosity, shear stress and the shear rate is calculated from the torque

required, the set speed and the geometry factors of the applied sensor.

They measure the torque required to rotate a disk or bob in a fluid at a known speed.

'Cup and bob' viscometers work by defining the exact volume of a sample which is to be

sheared within a test cell. The torque required to achieve a certain rotational speed ismeasured and plotted. There are two classical geometries in "cup and bob" viscometers,

known as the Couette systems - distinguished by whether the cup or bob rotates. In this

apparatus, one of the cylinders is rotating at a fixed angular velocity.

Figure 3 Example of Rotational Viscometer and its chamber

3. Results and Discussion3.1. Experiment 1: Choice of the most appropriate head

In order to achieve good and trustworthy data from the equipment for the upcoming

measurements, an experiment was carried to choose the best and most appropriate head of

measurement for the applied conditions.

Three heads were used, MVI, MVII, MVIII, for both liquids. A compete flow curve

shear stress vs. Shear rate, achieved by the equipment by varying rotation speed, for each

liquid was recorded and is presented below. The experiments were conducted at room


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temperature according to the conditions described in the provided script, and also by varying

the damping factor. The results presented are already with the damping factor set to zero.

Figure 4 Shear stress vs. Shear Rate for the different equipment heads liquid: Glycerol-

Water

From the graph, we can conclude that, the head MVIII is more adequate for the

upcoming measurements. As it can be seen in the picture, the values provided by the MVIII

are smoother, and have a linear behaviour with the variation of shear stress. For the other 2

heads, there it is possible to visualize a region where the behaviour is not linear, or present

some strong oscillations, what could cause errors and provide bad reproducibility of the data

if those were used.

As described, the same experiment was conducted for CMC-Solution and the data are

presented in the graph below.

Figure 5 Shear stress vs. Shear Rate for the different equipment heads liquid: CMC-

Solution

0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1

MV1

MV2

MV3

ShearStress(N/m2)

Shear Rate (1/s)

0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1

MV1

MV2

MV3ShearStress(N/m2)

Shear Rate (1/s)


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Similar as for water-glycerol, we can conclude that, the head MVI is more adequate

for the upcoming measurements. As it can be seen in the picture, the values provided by the

MVIII are smoother, and have a linear behaviour with the variation of shear stress. For the

other 2 heads, there it is possible to visualize a region where the behaviour is not linear, or

present some strong oscillations, what could cause errors and provide bad reproducibility of

the data if those were used.

3.2.Experiment 2 Dependence of Shear Stress and Shear Rate for different TemperaturesThe best suitable measurement head is used to measure the stress in dependence of

the time which shall be plotted for the temperatures T = 30 C / 40 C / 50 C /60 C. TO this

purpose, a curve shear stress vs. time (-t) was recorded for rotational frequencies 10, 20,

30, 40, 50, 60, 70, 80, 90 and 100% (Dmax=500 s-1

), for each liquid and for the temperatures

30, 40, 50 and 60 C, in order to obtain data for the viscosity of each liquid with relation totemperature and shear stress, according to the settings described in the lab script provided.

The results apre presented in the graphs and tables below.

3.2.1. Shear Rate and Shear Stress DependencyFor the described experiment, the values of viscosity vs time for all temperatures and

times were measured and the results are presented below.

3.2.1.1.CMC SolutionCarboxymethylcellulose is a modified polymer derived from cellulose; which has a

complex tridimensional polymeric structure. For such substances, a non-Newtonian behavior

could be expected due to the complex intermolecular interactions in the bulk phase solute-

solute and solute-solvent. As can be seen through the graph, the CMC-solution does not

present a curvature in the relation shear rate vs. shear stress, neither shear-thickening nor

shear-thinning behavior of non-Newtonian fluids, as it could be expected for this kind of

solution. In contrast, it is possible so see n coefficients near to 1, as listed in the table below,

what describe a linear behavior of the function and a constant viscosity.


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linear behavior for the relation shear stress/shear rate. The trend lines for linear regression

were added for comparison, but the oscillations of the points of each series make the analyse

and interpretation of the fluid flow profile difficult. No assumption can be made with relation

to characteristics of the fluid.

Figure 7 Shear stress over shear rate, for different temperatures Water-glycerol solution

Table2: Values for k and coefficient n for CMC solution

T K n

30 21.769 0.576

40 6.6606 1.0279

50 0.9297 1.463

60 1.3218 1.3934

3.2.2. Viscosity and Shear Rate Dependency3.2.2.1.CMC SolutionThe values of viscosity with relation to the variation of shear rate for CMC-Solution

are presented in the graph below.

y = 5.9795x + 23.576

y = 8.131x - 5.0367

y = 5.2872x - 11.333

y = 4.3641x - 9.7761

0

10

20

30

40

50

60

70

80

90

shearstress[N/m^2]

shear rate[1/s]

T30

T40

T50

T60


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Figure 8 Values of viscosity in dependence of Shear rate applied for different temperatures

CMC-solution.

In contrast to the behavior presented in the last graph for this solution, it is clear to

see that the carboymethylcellulose solution, as expected, shows a non-linear behavior of

shear stress and shear rate, clearly seen though the non-constant behavior of the viscosity,

as shown here. Although as well with high deviation from ideal, or expected, behavior, it is

possible to identify a 2nd

.order polynomial profile, characteristic of a shear-thinning fluid with

n


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Figure 10 Values of viscosity in dependence of Shear rate applied for differenttemperatures Water glycerol solution.

3.2.3. Temperature Dependency of ViscosityThe temperature dependency of viscosity is shown the graphs below. It is possible to

see can see that for both Newtonian and Non-Newtonian fluids, the viscosity decreases with

temperature, but the difference should be higher for lower temperatures, as observed in the

graph viscosity vs. Shear rate.

3.2.3.1.CMC SolutionIt can be seen that the curves present the expected behavior, for which viscosity

decreases with temperature for a constant shear rate. Although not all the curves are

correctly related to each other in a decreasing order, as it should be expected, they do

present a decreasing profile, when the trend-line is analysed. It cannot be seen from this

picture the correct shear rate/viscosity behavior. It should be expected a decreasing viscosity

with increasing shear rate, but, since the values of viscosity vary smoothly with shear rate,small experimental deviation of the values can lead to an overlap of the next point.

0

20

40

60

80

100120

140

160

180

200

viscosity[m

pas/s]

shear rate[1/s]

T30

T40

T50


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Figure 11 Temperature dependency of viscosity for constant shear rates CMC solution

3.2.3.2.Water Glycerol SolutionSince all the values from this calculation sequence are linked, the values for

temperature dependency of water also show an inconsistency, with strong oscillations inside

each series and not following the normal pattern of decreasing viscosity with increasing

temperature. Again, no conclusion can be taken from these data.

Figure 12 Temperature dependency of viscosity for constant shear rates Water glycerol

solution

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0.13

0.14

viscosity[Pa/s]

Temperature[C]

117

234

351

468585

702

819

936

1053

1170

0

10

20

30

40

50

60

70

80

90

v

iscosity[mPa/s]

T[C]

117

234

351

468

585

702

819

936

1053


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3.2.4. Activation Energy CalculationThe activation energy is than calculated using the Arrhenius equation by a graphical

method. Plotting ln() vs 1/T, the slope of the curve is numerically equal to -Ea/R and thus

the activation energy can be calculated.

3.2.4.1.CMC SolutionThe values obtained for CMC Solution, for each shear rate are presented below, for

the slope and the calculated activation energy.

Figure 13 ln (viscosity) vs 1/T for different shear rates, for the determination of Ea CMC

solution.

Table 2 Values for the slope of the curves and calculated Activation energy for shear rate /

CMC Solution

Shear Rate Slope Ea/R Ea (J/mol)

117 3245.57 26983.669

234 3041.87 25290.1072

351 2790.88 23203.3763

468 2690.12 22365.6577

585 2542.1 21135.0194

702 2450.9 20376.7826

819 2305.6 19168.7584

936 2398.36 19939.965

1053 2008.53 16698.9184

1170 2200.85 18297.8669

4.2

4.3

4.4

4.5

4.6

4.7

4.8

4.9

0.0029 0.003 0.0031 0.0032 0.0033 0.0034

117

234351

468

585

702

819

936

1053

1170

ln(viscosity)[m

Pa/s]

1/T [1/K]


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3.2.4.2.Water Glycerol solutionThe values obtained for CMC Solution, for each shear rate are presented below, for

the slope and the calculated activation energy.

Figure 14 ln (viscosity) vs 1/T for different shear rates, for the determination of Ea Water

Glycerol Solution solution.

Since all the values obtained for water until now make no physical sense, it has no

physical fundament the calculation of the values of activation Energy for this system.

4. ConclusionUnfortunately, not all investigations proposed in the script could be investigated with

the data obtained from the actual experiment and expressive deviations from the reality

were observed.

Actually, we have not enough information to prove the origin of deviations between

experimental and theoretical data appeared along the experiment and further investigations

would be needed, in order to identify the real sources of error. Only new investigations could

lead to consistent results, and maybe the identification of possible mistake sources that

could be have been avoided.Though, it is expected in any case to lie basically on 3 factors: measurement errors of

conduction in the experiment, exactness of the analytical method chosen and/or equipment

errors. All the possible source of errors could normally be associated with didactical lab

experiments conducted by students.

Nevertheless, the experiment provides the students expressive didactical

fundaments and is able to pass concise knowledge in the field of fluid mechanics.

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

viscosity[Pa/s]

Temperature[C]

117

234

351

468

585

702

819

936

1053

1170

viscometry of newtonian fluids - report sm 4_leandro_final

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