Viscosity Factor (VF) Complementary to the Statistical Indicators Associated with the Rheological Behavior of Aqueous Solutions of Polyvinyl Alcohol
Abstract
:1. Introduction
1.1. Properties and Applications of PVA
1.2. Viscoelasticity
1.3. Shear and Extensional Flows
1.4. Yielding Effort
2. Materials and Methods
2.1. Rheological Methods Evaluated
2.1.1. Nonlinear Least Squares Regression
2.1.2. Rheological Models
2.2. Evaluation of the Regression and Sensitivity of the VF Criterion
2.3. Procedure for the Preparation of Experimental Solutions
2.4. Computing Environment: Polymath® v6.2 Software
3. Results
4. Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Model | Ferrys | Robertson-Stiff | Ellis de Haven | Williamson | Sisko |
---|---|---|---|---|---|
Equation | |||||
Apparent viscosity | |||||
Differential viscosity |
T 20 °C | T 25 °C | T 30 °C | T 35 °C | |||||
---|---|---|---|---|---|---|---|---|
(1/s) | (Pa) | (1/s) | (Pa) | (1/s) | (Pa) | (1/s) | (Pa) | |
4% of PVA in water | 4.63 | 1 | 4.47 | 1 | 6.61 | 1 | 6.91 | 1 |
12.8 | 1.5 | 10.6 | 1.5 | 15.7 | 1.5 | 17.4 | 1.5 | |
23.3 | 1.99 | 21.4 | 1.99 | 28.8 | 1.99 | 30.8 | 1.99 | |
36.7 | 2.49 | 34.5 | 2.49 | 44.5 | 2.49 | 46.7 | 2.49 | |
52.6 | 2.99 | 50.5 | 2.99 | 62.8 | 2.99 | 65.5 | 2.99 | |
70.8 | 3.49 | 69.2 | 3.49 | 84.1 | 3.49 | 86.9 | 3.49 | |
91.4 | 3.98 | 91.2 | 3.98 | - | - | - | - | |
6% of PVA in water | 3.23 | 1 | 6.41 | 1 | 5.32 | 1 | 5.99 | 1 |
12.5 | 1.5 | 15.6 | 1.5 | 15.7 | 1.5 | 14.6 | 1.5 | |
22.5 | 1.99 | 27.1 | 1.99 | 28.4 | 1.99 | 25.1 | 1.99 | |
34.9 | 2.49 | 40.2 | 2.49 | 43 | 2.49 | 37.4 | 2.49 | |
48.8 | 2.99 | 54.5 | 2.99 | 58.8 | 2.99 | 52.2 | 2.99 | |
64.5 | 3.49 | 70.7 | 3.49 | 75.7 | 3.49 | 69 | 3.49 | |
81.3 | 3.98 | 87.8 | 3.98 | 93.5 | 3.98 | 88.1 | 3.98 | |
99.9 | 4.48 | - | - | - | - | - | - | |
8% of PVA in water | 2.78 | 1 | 3.88 | 1 | 3.75 | 1 | 3.48 | 1 |
6.45 | 1.745 | 6.49 | 1.5 | 7.51 | 1.5 | 9.45 | 1.5 | |
12.1 | 2.49 | 12.4 | 1.99 | 14.1 | 1.99 | 16.4 | 1.99 | |
16.7 | 2.99 | 17.8 | 2.49 | 20.2 | 2.49 | 23.8 | 2.49 | |
21.5 | 3.49 | 23.6 | 2.99 | 26.4 | 2.99 | 31.1 | 2.99 | |
26.5 | 3.98 | 29.5 | 3.49 | 33.1 | 3.49 | 38.6 | 3.49 | |
31.8 | 4.48 | 35.6 | 3.98 | 40.3 | 3.98 | 46.6 | 3.98 | |
37.0 | 4.98 | 41.9 | 4.48 | 47.1 | 4.48 | 54.7 | 4.48 | |
42.6 | 5.48 | 48.8 | 4.98 | 53.9 | 4.98 | 62.9 | 4.98 | |
48.3 | 5.97 | 55.6 | 5.48 | 61.2 | 5.48 | 71.0 | 5.48 | |
54.1 | 6.47 | 61.9 | 5.97 | 68.5 | 5.97 | 79.5 | 5.97 | |
60.3 | 6.97 | 68.4 | 6.47 | 76.0 | 6.47 | 87.7 | 6.47 | |
66.9 | 7.47 | 75.4 | 6.97 | 83.6 | 6.97 | 96.0 | 6.97 | |
73.4 | 7.96 | 82.1 | 7.47 | 91.4 | 7.47 | - | - | |
80.1 | 8.46 | 88.8 | 7.96 | 99.1 | 7.96 | - | - | |
86.9 | 8.96 | 95.9 | 8.46 | - | - | - | - | |
93.7 | 9.46 | - | - | - | - | - | - | |
10% of PVA in water | 2.7 | 1 | 1.94 | 1 | 2.07 | 1 | 4.5 | 1 |
7.1 | 1.745 | 4.78 | 1.5 | 5.43 | 1.5 | 7.01 | 1.5 | |
10.9 | 2.49 | 8.2 | 1.99 | 9.13 | 1.99 | 10.4 | 1.99 | |
13.3 | 2.99 | 10.4 | 2.49 | 12 | 2.49 | 13.0 | 2.49 | |
15.7 | 3.49 | 12.3 | 2.99 | 14.5 | 2.99 | 16.7 | 2.99 | |
18.1 | 3.98 | 15.1 | 3.49 | 17.2 | 3.49 | 19.9 | 3.49 | |
20.9 | 4.48 | 18.1 | 3.98 | 20.2 | 3.98 | 23.3 | 3.98 | |
23.7 | 4.98 | 20.7 | 4.48 | 23.4 | 4.48 | 26.9 | 4.48 | |
26.4 | 5.48 | 23.4 | 4.98 | 26.2 | 4.98 | 30.7 | 4.98 | |
29 | 5.97 | 26.0 | 5.48 | 29.3 | 5.48 | 34.3 | 5.48 | |
31.7 | 6.47 | 28.6 | 5.97 | 32.6 | 5.97 | 37.3 | 5.97 | |
34.4 | 6.97 | 31.2 | 6.47 | 35.9 | 6.47 | 40.8 | 6.47 | |
37.1 | 7.47 | 34.0 | 6.97 | 39.2 | 6.97 | 44.9 | 6.97 | |
39.7 | 7.96 | 36.8 | 7.47 | 42.3 | 7.47 | 48.6 | 7.47 | |
42.3 | 8.46 | 39.5 | 7.96 | 45.7 | 7.96 | 52.7 | 7.96 | |
45.0 | 8.96 | 42.7 | 8.46 | 49 | 8.46 | 55.8 | 8.46 | |
47.7 | 9.46 | 45.5 | 8.96 | 52.4 | 8.96 | 59.8 | 8.96 | |
50.1 | 9.95 | 48.1 | 9.46 | 55.6 | 9.46 | 64.3 | 9.46 | |
52.8 | 10.5 | 51.1 | 9.95 | 58.9 | 9.95 | 67.7 | 9.95 | |
55.5 | 10.9 | 53.7 | 10.5 | 62.2 | 10.5 | 71.5 | 10.5 | |
58.3 | 11.4 | 56.9 | 10.9 | 65.4 | 10.9 | 76.1 | 10.9 | |
60.9 | 11.9 | 59.5 | 11.4 | 68.7 | 11.4 | 79.4 | 11.4 | |
63.7 | 12.4 | 62.5 | 11.9 | 72.1 | 11.9 | 83.3 | 11.9 | |
66.4 | 12.9 | 65.6 | 12.4 | 75.5 | 12.4 | 87.6 | 12.4 | |
69.1 | 13.4 | 68.4 | 12.9 | 78.9 | 12.9 | 90.8 | 12.9 | |
71.8 | 13.9 | 71.2 | 13.4 | 82.4 | 13.4 | 95.2 | 13.4 | |
74.8 | 14.4 | 74.4 | 13.9 | 85.8 | 13.9 | 98.9 | 13.9 | |
77.5 | 14.9 | 77.1 | 14.4 | 89.2 | 14.4 | - | - | |
80.4 | 15.4 | 79.9 | 14.9 | 92.5 | 14.9 | - | - | |
83.3 | 15.9 | 82.9 | 15.4 | 95.8 | 15.4 | - | - | |
86.0 | 16.4 | 85.7 | 15.9 | 99.3 | 15.9 | - | - | |
88.9 | 16.9 | 88.8 | 16.4 | - | - | - | - | |
91.7 | 17.4 | 91.9 | 16.9 | - | - | - | - | |
94.5 | 17.9 | 94.9 | 17.4 | - | - | - | - | |
97.3 | 18.4 | 98 | 17.9 | - | - | - | - |
4% of PVA in Water | 6% of PVA in Water | 8% of PVA in Water | 10% of PVA in Water | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
T 20 °C | T 25 °C | T 30 °C | T 35 °C | T 20 °C | T 25 °C | T 30 °C | T 35 °C | T 20 °C | T 25 °C | T 30 °C | T 35 °C | T 20 °C | T 25 °C | T 30 °C | T 35 °C | ||
Ferrys parameters | A | 1.664 | 1.948 | 1.254 | 1.318 | 0.460 | 0.371 | 0.255 | 0.410 | 0.242 | 0.159 | 0.148 | 0.135 | 0.247 | 0.240 | 0.205 | 0.180 |
B | 0.107 | 0.093 | 0.119 | 0.108 | 0.475 | 0.536 | 0.776 | 0.491 | 6.560 | 9.963 | 9.042 | 7.636 | 51.500 | 51.500 | 51.500 | 46.505 | |
0.999 | 0.998 | 0.999 | 0.999 | 0.997 | 0.996 | 0.996 | 0.999 | 0.998 | 0.995 | 0.996 | 0.994 | 0.996 | 0.998 | 0.999 | 0.999 | ||
0.711 | 3.081 | 0.668 | 1.674 | 3.486 | 3.862 | 5.631 | 0.597 | 1.834 | 4.443 | 4.582 | 6.035 | 3.493 | 1.702 | 1.207 | 0.738 | ||
Robertson-Stiff parameters | A | 0.3457 | 0.441 | 0.309 | 0.260 | 0.248 | 0.217 | 0.175 | 0.3005 | 0.384 | 0.186 | 0.168 | 0.128 | 0.228 | 0.246 | 0.224 | 0.241 |
B | 2.5550 | 1.103 | 2.150 | 3.402 | 6.036 | 4.389 | 7.989 | 2.0124 | 1.621 | 4.940 | 5.565 | 7.674 | 1.535 | 2.025 | 2.339 | 0.795 | |
n | 0.5380 | 0.485 | 0.543 | 0.576 | 0.620 | 0.642 | 0.676 | 0.5746 | 0.702 | 0.826 | 0.829 | 0.859 | 0.955 | 0.930 | 0.921 | 0.879 | |
1.0000 | 0.999 | 0.999 | 1.000 | 0.999 | 1.000 | 1.000 | 0.9999 | 0.999 | 0.999 | 0.999 | 0.999 | 1.000 | 0.999 | 0.999 | 0.999 | ||
- | 0.0006 | 0.0002 | - | 0.0001 | 0.0001 | 0.0001 | 0.0002 | 0.001 | 0.002 | 0.001 | 0.0002 | 0.001 | 0.002 | 0.002 | 0.002 | ||
Williamson parameters | A | 1.687 | 1.897 | 1.590 | 1.473 | 1.445 | 1.412 | 1.273 | 1.684 | 2.562 | 1.485 | 1.371 | 1.136 | 0.873 | 1.275 | 1.266 | 1.930 |
B | 4.774 | 5.378 | 6.131 | 5.667 | 2.271 | 5.181 | 2.890 | 6.807 | 7.278 | 3.864 | 3.304 | 1.750 | 4.973 | 5.350 | 5.073 | 16.85 | |
C | 0.027 | 0.024 | 0.024 | 0.025 | 0.032 | 0.031 | 0.030 | 0.028 | 0.076 | 0.074 | 0.068 | 0.061 | 0.181 | 0.171 | 0.149 | 0.124 | |
0.998 | 0.999 | 0.999 | 0.999 | 0.997 | 0.999 | 0.999 | 0.998 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | ||
0.003 | 0.002 | 0.001 | 0.001 | 0.007 | 0.001 | 0.001 | 0.003 | 0.004 | 0.001 | 0.002 | 0.001 | 0.004 | 0.008 | 0.008 | 0.002 | ||
Sisko parameters | A | 0.012 | 0.007 | 0.010 | 0.013 | 0.023 | 0.020 | 0.023 | 0.010 | 0.044 | 0.064 | 0.059 | 0.057 | 0.174 | 0.161 | 0.138 | 0.087 |
B | 0.515 | 0.533 | 0.431 | 0.429 | 0.642 | 0.436 | 0.564 | 0.409 | 0.553 | 0.539 | 0.541 | 0.613 | 0.260 | 0.372 | 0.383 | 0.226 | |
n | 0.384 | 0.408 | 0.412 | 0.387 | 0.274 | 0.369 | 0.258 | 0.451 | 0.500 | 0.321 | 0.297 | 0.203 | 0.390 | 0.390 | 0.379 | 0.683 | |
1.000 | 1.000 | 1.000 | 1.000 | 0.999 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | ||
0.000 | 0.000 | 0.000 | 0.000 | 0.002 | 0.000 | 0.000 | 0.001 | 0.001 | 0.002 | 0.001 | 0.000 | 0.002 | 0.004 | 0.004 | 0.002 | ||
Ellis de Haven parameters | A | 0.631 | 0.744 | 0.511 | 0.463 | 0.592 | 0.473 | 0.456 | 0.548 | 0.946 | 0.712 | 0.648 | 0.567 | 0.437 | 0.461 | 0.452 | 0.351 |
B | 3.020 | 3.020 | 3.020 | 3.020 | 3.020 | 3.020 | 3.020 | 3.020 | 2.497 | 3.020 | 3.020 | 3.020 | 0.851 | 0.822 | 0.974 | 0.735 | |
n | 2.089 | 2.213 | 2.062 | 2.006 | 1.939 | 1.831 | 1.859 | 1.945 | 1.546 | 1.407 | 1.417 | 1.430 | 1.150 | 1.216 | 1.231 | 1.276 | |
0.999 | 0.999 | 0.999 | 0.999 | 0.998 | 0.999 | 0.997 | 1.000 | 0.999 | 0.998 | 0.998 | 0.997 | 1.000 | 1.000 | 1.000 | 1.000 | ||
1.198 | 0.935 | 1.239 | 1.590 | 3.681 | 1.910 | 5.494 | 0.581 | 0.645 | 1.981 | 2.057 | 3.183 | 0.142 | 0.321 | 0.405 | 0.215 |
Parameter | Source | DF | SS | MS | F | p-Value |
---|---|---|---|---|---|---|
ANOVA for | Models | 4 | 0.000067 | 0.000017 | 17.28 | 0.000 |
Error | 75 | 0.000073 | 0.000001 | |||
Total | 79 | 0.000139 | ||||
ANOVA for | Models | 4 | 100.26 | 25.066 | 22.75 | 0.000 |
Error | 75 | 82.65 | 1.102 | |||
Total | 79 | 182.91 |
Model | %CV Minimum | %CV Average | %CV Maximum | Stability | Order |
---|---|---|---|---|---|
Ferrys | 1.04 | 6.12 | 10.49 | NO | 2 |
Ellis | 0.47 | 2.26 | 3.65 | YES | 1 |
Robertson-Stiff | 3.90 | 15.26 | 31.82 | NO | 5 |
Sisko | 2.89 | 12.78 | 26.07 | NO | 3 |
Williamson | 3.25 | 14.95 | 27.57 | NO | 4 |
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Carrasco-Venegas, L.A.; González-Fernández, J.V.; Castañeda-Pérez, L.G.; Palomino-Hernández, G.; Dueñas-Dávila, F.A.; Trujillo-Pérez, S.A. Viscosity Factor (VF) Complementary to the Statistical Indicators Associated with the Rheological Behavior of Aqueous Solutions of Polyvinyl Alcohol. Polymers 2023, 15, 1743. https://doi.org/10.3390/polym15071743
Carrasco-Venegas LA, González-Fernández JV, Castañeda-Pérez LG, Palomino-Hernández G, Dueñas-Dávila FA, Trujillo-Pérez SA. Viscosity Factor (VF) Complementary to the Statistical Indicators Associated with the Rheological Behavior of Aqueous Solutions of Polyvinyl Alcohol. Polymers. 2023; 15(7):1743. https://doi.org/10.3390/polym15071743
Chicago/Turabian StyleCarrasco-Venegas, Luis Américo, José Vulfrano González-Fernández, Luz Genara Castañeda-Pérez, Guido Palomino-Hernández, Federico Alexis Dueñas-Dávila, and Salvador Apolinar Trujillo-Pérez. 2023. "Viscosity Factor (VF) Complementary to the Statistical Indicators Associated with the Rheological Behavior of Aqueous Solutions of Polyvinyl Alcohol" Polymers 15, no. 7: 1743. https://doi.org/10.3390/polym15071743