This document summarizes the results of experiments measuring the rheological properties of rayon and nylon fibers in water using a torque rheometer and Parr reactor. Both rayon and nylon exhibited negative plastic viscosity and high yield stress. Rayon showed high temperature dependence of plastic viscosity, while nylon's plastic viscosity was independent of temperature. Fiber length was found to not impact rayon's viscosity, yield stress, or plastic viscosity at 10wt% solid level. Results from the two rheometers deviated from each other.
1. A Rheological Property Study of Rayon and Nylon fiber
in both a Torque Rheometer and the Parr Reactor
CBE 562 Complex Fluid, Spring 2014
Prepared for
Daniel Klingenberg
Professor-Department of Chemical and Biological Engineering
University of Wisconsin-Madison
Timothy Scott
Forest Product Laboratory
USDA Forest Service
By
Liyang Gan
Geyunjian Zhu
Students-Department of Chemical and Biological Engineering
University of Wisconsin-Madison
2. Abstract
The rheological properties of rayon and nylon fiber were studied in this project. The
experiments were conducted in both a torque rheometer and the Parr Reactor. It is found that
both Rayon and Nylon fiber, when mixed with water, exhibit negative plastic viscosity and high
yield stress. These two characteristics also show high temperature dependence for rayon, but the
plastic viscosity of nylon is independent of temperature. At 10wt% solid level, the fiber length
of Rayon was found to exert no obvious effect on viscosity, yield stress, and plastic viscosity.
Because nylon was available in only one fiber length, the influence of fiber length on its
rheological properties was not examined. It is also found that the result from the torque
rheometer and the Parr Reactor deviates from each other.
Methods
Calibration
The inside and outside temperature data acquired by Labview of the torque rheometer has
been calibrated. Three sets of inside/outside temperatures have been recorded and then plotted
against the data from Labview, respectively. According to the trendline equation, the correlation
between inside temperature and Labview data can be expressed as:
𝑇𝑖𝑛𝑠𝑖𝑑𝑒 = 11.826𝑥1 − 1.4434 (1)
where 𝑥1, the output data for inside temperature, is from “Untitled 1” column in the Excel
worksheet and 𝑇𝑖𝑛𝑠𝑖𝑑𝑒 is the temperature measured at degrees Celsius (ºC). While for outside
(water) temperature, the correlation can be written as:
𝑇𝑜𝑢𝑡𝑠𝑖𝑑𝑒 = 555𝑥2 − 10.194 (2)
3. where 𝑥2 the output data for inside temperature, is from “Untitled 2” column in the Excel
worksheet and 𝑇𝑜𝑢𝑡𝑠𝑖𝑑𝑒 is the temperature measured at degrees Celsius (ºC) as well.
The interior and exterior temperature for Parr Reactor are recorded by Specview during
the experiment and are ready to use (do not need to be calibrated).
Experiments
A torque rheometer is used to measure the torque for 20wt% Corn Stover without kernel,
10wt% 3mm Nylon, 10wt% 1mm Rayon, 10wt% and 15wt% 3mm Rayon. For the first trial
(20wt% Corn Stover without kernel), 21.5gram total Corn Stover is weighed since it already
contains 7% moisture content. The solids is then poured into the rheometer and the rheometer
starts to run at 60 RPM. After this step, 80mL water is added into the rheometer in 20mL
aliquots. Rheometer is stopped when water is added in each time. Temperature of the experiment
remains high during the water addition process and drops afterwards. Several speed cycles are
carried out at low temperature to obtain torque profile. For the rest of the materials tested, the
solid/water mixtures are prepared in the same way and within each experiment; also, within each
experiment, several speed cycles are tested to obtain the torque profile.
Parr Reactor is used to measure torque for 10wt% 1mm Rayon, 10wt% 3mm Nylon and
10wt% 3mm Rayon. The mixture for 10wt% 1mm Rayon is prepared by mixing 100gram of
Rayon fiber with 900mL of water prior to adding the mixture into the reaction column. Same
method is used for making the other two mixtures. For 1mm Rayon test, the material is first
heated up to around 160ºC, which is sufficiently higher than 𝑇𝑔 of Rayon (around 150ºC), then
cooled down to 50ºC at the end. Several speed cycles are carried out during the run. For the other
two, similar temperature set up is used in order to obtain the torque profile.
4. Data Analysis
Torque, as well as inside and outside temperature data for torque rheometer are all
recorded by Labview at the rate of 5Hz. The moving average of torque, which is obtained by
taking average over thirty consecutive points (6 seconds), is then plotted together with inside
temperature against time.
In order to obtain viscosity profile for each material along time scale, Shear Stress and
Shear Strain Rate need to be calculated first. Shear Stress can be calculated by equation (3) and
(4):
τ = 𝐾𝜏𝑏𝑜𝑤𝑙 ∗ 𝛤 (3)
𝐾𝜏𝑏𝑜𝑤𝑙 = 757
𝑃𝑎
𝑖𝑛∗𝑙𝑏
(4)
where Shear Stress (τ) is in 𝑃𝑎, averaged torque (𝛤) is in 𝑖𝑛 ∗ 𝑙𝑏 and the conversion factor
(𝐾𝜏𝑏𝑜𝑤𝑙) converts torque into Shear Stress. Similarly, Shear Strain Rate can be calculated by
equation (5) and (6):
γ = 𝐾𝛾𝑏𝑜𝑤𝑙 ∗ 𝛺 (5)
𝐾𝛾𝑏𝑜𝑤𝑙 = 1.1763
1
𝑅𝑃𝑀∗𝑠
(6)
where Shear Strain Rate (γ) is in 𝑠−1
, rotation speed (𝛺) is in 𝑅𝑃𝑀 and conversion factor
(𝐾𝛾𝑏𝑜𝑤𝑙) converts rotation speed into Shear Strain Rate.
For Parr Reactor, the viscosity for each material is obtained in the similar way with only
two conversion factor changed. In this case, the values for two parameters become:
𝐾𝜏𝑃𝑎𝑟𝑟 = 84.7
𝑃𝑎
𝑖𝑛∗𝑙𝑏
(7)
5. 𝐾𝛾𝑃𝑎𝑟𝑟 = 0.453
1
𝑅𝑃𝑀∗𝑠
(8)
Once the torque and rotational speed are converted to Shear Stress and Shear Strain Rate,
viscosity can be calculated by equation:
𝜇 =
𝜏
𝛾
(9)
where viscosity 𝜇 is in 𝑃𝑎 ∗ 𝑠.
The calculated viscosity is then plotted against time. Also, Shear Stress is plotted against
Shear Stress under constant temperature for each speed cycle to obtain the plastic viscosity
profile. Yield stress of the material equals to the intercept of the linear fit for the data points. Size
reduction effect for 1mm Rayon is also studied by plotting viscosity versus time under constant
temperature but different rotational speed. For Parr Reactor, temperature effect on viscosity is
also studied by plotting these two against each other.
Result Analysis
Torque Rheometer
Corn Stover (20wt% solid without kernel)
Our test run is conducted on corn stover without kernel at 20wt% solid in water. The
calculated viscosity as well as rotational speed and inside temperature are plotted against time for
Corn Stover test. According to Figure 1, water is added into the rheometer to mix with the solids
from 𝑡 = 0 till 𝑡 = 930𝑠 (200s, 350s, 500s and 600s). The viscosity drops as the solid
concentration decreases during this water addition period. Then, from 𝑡 = 930𝑠 to 𝑡 = 1130𝑠,
inside temperature of torque rheometer drops while the solid concentration remains the same.
The figure shows that viscosity of this material increases as temperature decreases. Then
6. from 𝑡 = 1130𝑠 to the end of the experiment, two sets of speed cycles are carried out. The inside
temperature of torque rheometer is treated as constant throughout the whole speed cycle process.
The figure indicates that viscosity of Corn Stover increases as rotational speed drops, which
indicates that the material has a negative plastic viscosity.
Figure 1. 10wt% Corn Stover without Kernel in Torque Rheometer
Rayon fiber (1mm, 10wt% solid)
For 1mm Rayon, solid/water mixture has been prepared before added into torque
rheometer. Figure 2 presents data that has already been modified (stop time that is used to get
sample for Kajaani test has been removed). The length of error bars on the viscosity curve
represents the standard deviation of data over the averaging blocks.
7. Figure 2. 10wt% 1mm Rayon fiber in Torque Rheometer
Figure 3 presents two speed cycles at different temperatures. The blue (low temperature)
cycle is at 20ºC, while the red (high temperature) cycle is at 80ºC. At 20ºC, the material shows
negative plastic viscosity; however, at 80ºC, the effect is not obvious. The slope for the plastic
viscosity trendline is only 2.5157 (very close to 0) at 80ºC, which indicates that the plastic
viscosity effect barely exists. The intercepts of the trendlines represent the yield stress of the
material in 𝑃𝑎. The arrows on the curves indicate that in which way the speed cycle goes; and
according to the process, the viscosity is reversible with change of temperature since the starting
viscosity point and the end viscosity point are close to each other. The small difference in
viscosities between these two points may be caused by size reduction of the fibers.
8. Figure 3. 10wt% 1mm Rayon fiber Shear Stress vs. Shear Strain Rate
Figure 4 shows the viscosity profile for Rayon at similar temperature, however, different
rotational speed. Both the blue (55RPM) curve and the red (110RPM) curve have negative slopes
according to the figure. The reduction in viscosity is very likely caused by size reduction in
Rayon fiber lengths. Kajaani data is needed to determine the further correlation between size
reduction and viscosity.
9. Figure 4. 10wt% 1mm Rayon fiber viscosity vs. time
3mm Nylon fiber and 3mm Rayon fiber (failed trials in torque rheometer)
Before testing 1mm Rayon fiber, a run was conducted on 3mm Nylon fiber at 10wt%
solid level. The experiment ceded quickly because torque exceeded the limit of the system. The
motor kept slipping and no useful data was collected. It was also observed that the fibers did not
dissipate well, but rather segregated as they were stirred by the impellers.
The 1mm Rayon fiber was stirred well in the torque rheometer, but the resulting torque is
fairly low. We then turned to 3mm rayon, hoping to see a higher level of torque. The fiber,
however, segregated instead of getting well mixed. The motor not only slipped this time but also
stopped rotating several times. Both 15wt% and 10wt% solid were tested, but neither were able
to provide useful result.
10. Parr Reactor
Rayon Fiber (1mm, 10wt% solid in water)
After examining the rheological properties of 1mm rayon in torque rheometer, the similar
experiment was repeated in the Parr Reactor. First the moving averages of torque and speed
were obtained over 6s intervals. Then averaged torque and speed were converted to Shear Stress
and Shear Strain Rate. The viscosity of the material was then calculated as the ratio of the Shear
Stress and Shear Strain Rate. The result is summarized in Figure 5.
It can be seen from the plot that the viscosity of 1mm rayon highly depends on the
temperature. It is obvious that the viscosity increases from 38 Pa*s to 60 Pa*s as the temperature
decreases form 160 ºC to 40 º over 2100s to 4400s. It was expected that the mixture will show
dramatic change at Tg of rayon, which is around 150ºC. However, it is not observed in the
graph. Thus we are able to conclude that the rheological properties of rayon-water mixture do
not change dramatically across Tg of rayon. Viscosity is also observed to change inversely with
Shear Strain Rate, indicating negative plastic viscosity of the material. The result also shows
obvious deviation from the result obtained from torque rheometer. It is expected as rheometers
with different geometries usually give out different result.
12. At each speed cycle, it is obvious that the viscosity of rayon displays negative
relationship with the speed of rotation, indicating the material having negative plastic viscosity.
It is also noticeable that the extent of changes in viscosity at speed cycles gets larger as the
system cools down. To quantify the negative plastic viscosity and yield stress of the mixture, a
plot of Shear Stress versus Shear Strain Rate is made under different temperatures. Linear fit is
conducted on each series of data. The equations of fitted straight lines are obtained with the
slopes equal to the negative plastic viscosity, and the y-intercept being the yield stress of the
material. The magnitude of yield stress is much less than what is found from torque rheometer.
Figure 6. Shear Stress vs Shear Strain Rate for 10wt% 1mm Rayon in Parr Reactor
From Figure 6, it can be concluded that both the plastic and yield stress of the mixture
highly depend on the temperature and they change inversely with temperature. It is important to
notice that at high temperature, the slope becomes very flat, which means the plastic viscosity of
1mm rayon approaches zero as the temperature increases.
13. Figure 7. Viscosity vs Temperature for 10wt% 1mm Rayon in Parr Reactor
Finally, a plot of viscosity against temperature is made under the most common rotating
speed. Due to the inappropriate temperature range selection, the reversibility of viscosity with
temperature cannot be fully studied for this run. It is advised in future experiment that the
experiment be conducted under full temperature cycles. Despite that, the decreasing trend of
viscosity versus temperature can is clearly shown in the graph.
Nylon Fiber (3mm, 10wt% in water)
Nylon fiber is expected to have higher viscosity than rayon fiber under same solid
concentration. Its torque exceeds the upper limit in the torque rheometer, so it can only be tested
in the Parr Reactor. The experiment is conducted in a same manner. The temperature ranges
from 100ºC to 30ºC, which covers the Tg of nylon at 47ºC. The change viscosity of nylon
during experiment course is summarized in Figure 8.
15. The nylon shows similar rheological behavior as rayon in response to change of
temperature and Shear Strain Rate, namely viscosity changing inversely against temperature and
having negative plastic viscosity. However, from Figure 9, it can be seen that the trendlines are
much flatter than those of 1mm rayon and the slopes do not change much under different
temperatures. The yield stress of nylon is found be close to but slightly smaller than the yield
stress of rayon.
Figure 9. Shear Stress vs Shear Strain Rate for 10wt% 3mm Nylon in Parr Reactor
A plot of viscosity versus temperature, Figure 10, reveals that the viscosity decreases
relatively linearly with increasing temperature. There is also no obvious change in viscosity
around Tg of nylon, which is consistent with the observation from 1mm rayon test.
16. Figure 10. Viscosity vs Temperature for 10wt% 3mm Nylon in Parr Reactor
Rayon Fiber (3mm, 10wt% solid in water)
Last, the 3mm rayon is tested in Parr Reactor. It is hypothesized that the viscosity of
rayon-water mixture is positively related to the fiber length, as longer fiber will result in higher
level of fiber entanglement. However, based on our result, the 1mm rayon and 3mm rayon fibers
require almost same level of torque to retain at the same Shear Strain Rate. This leads to the
conclusion that at 10wt% solid, the fiber length does not have noticeable effects the rheological
properties of rayon. Figure 11 shows the viscosity change of 3mm rayon in water in response to
change in temperature and Shear Strain Rate.
18. Implementing the same linear fit method, the plastic viscosity and yield stress of 3mm
rayon is obtained and summarized in Figure 12. The negative viscosity of 3mm rayon is very
close to and slightly higher than that of 1mm rayon under similar temperature. The yield stress
for 3mm rayon is also slightly higher. This observation is expected, because the entanglement of
fiber should be positively related to the yield stress for a material. However, the differences in
negative plastic viscosity and yield stress is not very significant between 1mm and 3mm rayon.
Figure 12. Shear Stress vs Shear Strain Rate for 10wt% 3mm Rayon in Parr Reactor
The plot of viscosity versus temperature changes again confirms that the effect of fiber
length on viscosity of rayon fiber is negligible under 10wt% solid level. The full temperature
cycle of this run enables us to examine the reversibility of viscosity in response to temperature.
Based on Figure 13, the viscosity of 3mm rayon fiber first decreases as the mixture gets heated,
and then the viscosity climbs back to the initial value. The difference around 90ºC could be due
to dissipation effect or possible size reduction.
19. Figure 13. Viscosity vs Temperature for 10wt% 3mm Rayon in Parr Reactor
Conclusion and Recommendation
Rheological properties of commercial 1mm and 3mm rayon fiber and 3mm nylon fiber
are studied. All three material are found to have negative plastic viscosity and high yield stress
at the range of 1~2kPa. The viscosity of all three material show negative correlation with
temperature change. It is also find that the rheological properties of these two fibers do not
change dramatically at glass transition temperatures.
The yield stress of nylon highly depends on the temperature, whereas its plastic viscosity
is independent of temperature. Due to the unavailability of nylon fiber with different fiber length,
its fiber length effect is yet to be examined.
For rayon fiber, it is found that its plastic viscosity and yield stress are both highly
dependent on temperature as expected. However, its plastic viscosity and yield stress are almost
independent of fiber length, which contradicts our initial hypothesis. A possible explanation for
20. this observation is that the decrease in number of fibers compensates the increase in fiber length.
Although 3mm rayon fiber is longer than 1mm rayon fiber, there much less number of 3mm
rayon fiber in the mixture as the concentration is kept constant based on weight. The level of
entanglement should be on both the fiber length and number of fibers per unit volume. By
keeping the weight percent constant, we failed to control the number of fibers present. In the
future, it is suggested to test the fiber length effect at constant molar concentration.
It is recommended in the future to repeat some of the above experiments to confirm the
conclusion made from this study. The effect of concentration is another factor which did not get
tested, and can be studied in the future. If possible, the experiments should be done to other
yield stress material. One improvement is needed for data analysis. In this report, most data was
analyzed based on moving average of the raw data. This method fails to quantify the irregularity
of the raw data. It is advised to implement some method in data analysis, so that the irregularity
can be quantified.
22. Figure 14. Raw data and moving average of torque for Corn Stover in Torque Rheometer
Figure 15. Raw data and moving average of torque for 10wt% 1mm Rayon fiber in Torque Rheometer
23. Figure 16. Raw data and moving average of torque for 10wt% 1mm Rayon fiber in Parr Reactor
Figure 17. Raw data and moving average of torque for 10wt% 3mm Nylon fiber in Parr Reactor
24. Figure 18. Raw data and moving average of torque for 10wt% 3mm Rayon fiber in Parr Reactor
Figure 19. 10wt% 1mm Rayon fiber Yield Stress vs Temperature
25. Figure 20. 10wt% 3mm Nylon fiber Yield Stress vs Temperature
Figure21. 10wt% 3mm Rayon fiber Yield Stress vs Temperature
26. Figure 22. 1mm Rayon fiber in Torque Rheometer
Figure 23. Tim Scott assembling the Parr Reactor before experiment
