Use of Extended Cover Factor Theory in UV Protection of Woven Fabric
Abstract
:1. Introduction
2. Theoretical Part
2.1. Extended Woven Fabric Cover Factor Theory
2.2. Introduction of Simplified Mathematical Model for Predicting UV Properties of Woven Fabrics
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- Optically: from the single-layer samples, we can get linear curve of Cwa,we. At the point where the linear curve becomes 1, we can get the maximum density and also the proper diameter of yarn (Equation (18)). This is also possible following the double-layer curve (Equation (19)) [25]:
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- Determining the maximum of reflection curve from the double-layer systems of yarns—R2, that way, calculating the maximal density, diameter of yarns, and value of KR. (R2 = −0.00008x2 + 0.008x, from the first derivation of the equation of the function curve R2′ = −0.00016x + 0.008 = 0, we calculate x (maximal density of yarns) x = 50 and KR = 0.2).
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- Supposing the reflection from single-layer and double-layer fabrics at cover factor 1 will be equal, we can verify the previous mentioned findings using the same values when curves for R1 and R2 cross each other (−0.00008x2 + 0.008x = 0.004x, where we get x = 50 in KR = 0.2).
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- If we determine T1m by subtraction T1me for OA of single-layer samples, we can see that the linear curves for T1me and T1m cross each other in the point that corresponds to maximal density and to the value of KR at the same time (−0.14x + 1 = 0.006x, follows x = 50 and KT1 = 0.3).
2.3. Development of Method for Creating Samples Proper for Processing
3. Materials and Methods
3.1. Materials
3.2. Methods
4. Results and Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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d [µm] | D [yarns/cm] | Cfwa,we | Cf | Cf1 | Cf2 | OA |
---|---|---|---|---|---|---|
200 | 10 | 0.20 | 0.36 | 0.32 | 0.04 | 0.64 |
15 | 0.30 | 0.51 | 0.42 | 0.09 | 0.49 | |
20 | 0.40 | 0.64 | 0.48 | 0.16 | 0.30 | |
25 | 0.50 | 0.75 | 0.50 | 0.25 | 0.25 | |
30 | 0.60 | 0.84 | 0.48 | 0.30 | 0.16 | |
35 | 0.70 | 0.91 | 0.42 | 0.49 | 0.09 | |
40 | 0.80 | 0.96 | 0.32 | 0.64 | 0.25 |
Dwa,we [yarns/cm] | T1me | T2me | T1m | T2m | A1 | A2 | R1 | R2 |
---|---|---|---|---|---|---|---|---|
20 | 0.72 | 0.5184 | 0.12 | 0.1584 | 0.2 | 0.3531 | 0.08 | 0.128 |
25 | 0.65 | 0.4225 | 0.15 | 0.1725 | 0.25 | 0.4268 | 0.1 | 0.15 |
30 | 0.58 | 0.3364 | 0.18 | 0.1764 | 0.3 | 0.4946 | 0.12 | 0.168 |
35 | 0.51 | 0.2601 | 0.21 | 0.1701 | 0.35 | 0.5565 | 0.14 | 0.182 |
40 | 0.44 | 0.1936 | 0.24 | 0.1536 | 0.4 | 0.6126 | 0.16 | 0.192 |
45 | 0.37 | 0.1369 | 0.27 | 0.1269 | 0.45 | 0.6628 | 0.18 | 0.198 |
50 | 0.30 | 0.09 | 0.30 | 0.09 | 0.50 | 0.7071 | 0.20 | 0.200 |
Dd [yarns/cm] | Dme [yarns/cm] | T1 [%] | T2 [%] | R1 [%] | R2 [%] |
---|---|---|---|---|---|
20 | 21.67 | 47.06 | 20.8 | 9.67 | 10.46 |
25 | 25.67 | 35.87 | 13.08 | 9.74 | 11.00 |
30 | 30.00 | 28.52 | 9.16 | 10.06 | 10.99 |
35 | 36.33 | 19.06 | 2.89 | 10.53 | 11.03 |
K1T | K2T | K1R = K2R | K1A | K2A |
---|---|---|---|---|
0.04329 | 0.00187 | 0.10931 | 0.84740 | 0.92054 |
Dmax [yarns/cm] | dmin [µm] (Equation (18)) | Cfwa,we [%] | Cf [%] | Cf1 [%] | Cf2 [%] | OA [%] | OA1 [%] |
---|---|---|---|---|---|---|---|
43.61 | 0.02293 | 49.69 | 74.69 | 50.00 | 24.69 | 25.31 | 50.31 |
58.86 | 83.08 | 48.43 | 34.65 | 16.92 | 41.14 | ||
68.79 | 90.26 | 42.94 | 47.32 | 9.74 | 31.21 | ||
83.30 | 97.21 | 27.82 | 69.40 | 2.79 | 16.70 |
Dd [yarns/cm] | T2 (Equation (11)) | R2 (Equation (17)) | A2 (Equation (15)) | Δ|T2c − T2me| | Δ|R2c − R2me| | Δ|A2c − A2me| |
---|---|---|---|---|---|---|
21.67 | 0.27522 | 0.08164 | 0.65097 | 0.06722 | 0.02296 | 0.03643 |
25.67 | 0.19085 | 0.09081 | 0.72933 | 0.06005 | 0.01919 | 0.02987 |
30.00 | 0.11688 | 0.09866 | 0.79947 | 0.02528 | 0.01124 | 0.00097 |
36.33 | 0.04121 | 0.10626 | 0.87454 | 0.01231 | 0.00404 | 0.01374 |
r (c:me) | 0.995 | 0.827 | 0.996 |
Dd [yarns/cm] | Dme [yarns/cm] | T1 [%] | T2 [%] | R1 [%] | R2 [%] |
---|---|---|---|---|---|
6 | 6.67 | 85.26 | 71.94 | 15.28 | 16.12 |
10 | 11.25 | 73.64 | 52.30 | 20.68 | 22.57 |
14 | 13.33 | 68.03 | 46.65 | 20.33 | 24.47 |
18 | 18.33 | 56.58 | 31.55 | 23.11 | 28.40 |
K1T | K2T | K1R = K2R | K1A | K2A |
---|---|---|---|---|
0.31564 | 0.09963 | 0.30056 | 0.38376 | 0.61948 |
Dmax [yarns/cm] | dmin [µm] (Equation (18)) | Cfwa,we [%] | Cf [%] | Cf1 [%] | Cf2 [%] | OA [%] | OA1 [%] |
---|---|---|---|---|---|---|---|
28.33 | 0.03530 | 23.28 | 41.14 | 35.72 | 5.42 | 58.45 | 76.45 |
39.26 | 63.11 | 47.69 | 15.42 | 36.34 | 60.28 | ||
46.52 | 71.40 | 49.76 | 21.64 | 28.03 | 52.94 | ||
63.97 | 87.02 | 46.10 | 40.92 | 12.45 | 35.29 |
Dd [yarns/cm] | T2 (Equation (11)) | R2 (Equation (17)) | A2 (Equation (15)) | Δ|T2c − T2me| | Δ|R2c − R2me| | Δ|A2c − A2me| |
---|---|---|---|---|---|---|
6.67 | 0.70367 | 0.12488 | 0.12472 | 0.01573 | 0.03632 | 0.05205 |
11.25 | 0.53027 | 0.19133 | 0.25014 | 0.00727 | 0.03437 | 0.02710 |
13.33 | 0.45960 | 0.21632 | 0.31779 | 0.00690 | 0.02838 | 0.03527 |
18.33 | 0.31040 | 0.26313 | 0.50776 | 0.01580 | 0.02087 | 0.03667 |
r (c:me) | 0.998 | 0.999 | 0.980 |
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Kostajnšek, K.; Dimitrovski, K. Use of Extended Cover Factor Theory in UV Protection of Woven Fabric. Polymers 2021, 13, 1188. https://doi.org/10.3390/polym13081188
Kostajnšek K, Dimitrovski K. Use of Extended Cover Factor Theory in UV Protection of Woven Fabric. Polymers. 2021; 13(8):1188. https://doi.org/10.3390/polym13081188
Chicago/Turabian StyleKostajnšek, Klara, and Krste Dimitrovski. 2021. "Use of Extended Cover Factor Theory in UV Protection of Woven Fabric" Polymers 13, no. 8: 1188. https://doi.org/10.3390/polym13081188