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Theoretical and Experimental Evaluation of Thermal Resistance for Compression Bandages

Online veröffentlicht: 20 Nov 2020
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Format
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Introduction
Overview of thermal resistance testing on thermal manikins

Thermal manikins are devices by means of which it is possible to simulate heat exchange between humans and the environment [1, 2]. Human thermal comfort is defined as a condition of mind, which expresses satisfaction with the surrounding environment. High temperatures and humidity provide discomforting sensations and sometimes heat stress, which leads to reduce the body's ability to cool itself. Moreover, this discomfort reduces the productivity of workers and may lead to more serious health problems, especially for aged people [3].

Clothing comfort is an important factor in the stage at which people make their clothing selections [3]. The thermal resistance (Rct) of fabrics is a primary determinant of body heat loss in cold environments. Generally, high Rct values of clothing are required to maintain the body under thermal equilibrium conditions. In hot environments or at high activity levels, evaporation of sweat becomes an important avenue for body heat loss, and fabrics must allow water vapor to escape in time to maintain the relative humidity between the skin and the first layer of clothing to about 50% [3, 4, 5, 6]. Perspiration is the process of losing body heat due to the evaporation of moisture from the skin to the environment [7]. The warm–cool feeling is another parameter showing thermal comfort. When a human touches a garment that has a temperature that is different than that of the skin, heat exchange occurs between the hand and the fabric, so the warm–cool feeling is the first sensation. Which feeling is better depends on the customer – a cooler feeling is demanded in hot summer, while a warmer feeling is preferred in winter [8].

Factors affecting testing of thermal resistance on thermal foot manikin (TFM) and ALAMBETA

The measurement of clothing insulation with a thermal manikin is a dynamically balanced adjustment process, which initially depends on the central temperature inside the manikin. It means that continuous adjustment of heat flux makes the manikin skin temperature approach a constant temperature gradually under the heat diffusion. These adjustments limit the change in the manikin skin temperature of all parts to a range of ±0.5°C around the required temperature. The final state is that the manikin skin temperature is steady and very close to the constant temperature [9].

The main factors affecting testing of Rct are the temperature difference between ambient conditions and skin, yarn structure and material, fabric structure (fibrous assembly), thickness, porosity, areal density, and number of fabric layers which increase the static air [10]. Porosity can be defined as the fraction of void space in the total material volume [11]. It has a vital role in evaluating the thermal performance of any fibrous material. The Rct increases proportionally when the porosity increases by 70–90% [12].

Effect of air convection on thermal resistance of multilayer fabrics

Convection is a process in which heat is transferred by a moving fluid (liquid or gas). For example, air in contact with the body is heated by conduction, and then carried away from the body by convection [13].

A common method for removing water from textiles is convective drying. When the fluid starts at a constant temperature and the surface temperature is suddenly increased above that of the fluid, there will be convective heat transfer from the surface to the fluid as a result of the temperature difference (ΔT). The rate of heat transfer (Q) due to convection can be calculated by Newton's law of cooling, as follows [14]: Q=αAΔT{\rm{Q}} = \alpha \,{\rm{A}}\,\Delta \,{\rm{T}} where A is the heat transfer surface area and α is the coefficient of heat transfer by convection.

When people wear multilayer clothing ensembles in cold weather conditions or in hot environments, air spaces are present between the skin and the inner layer or between two adjacent layers. The Rct of multilayer fabrics with air spaces increases generally as the thickness of the air spaces increases up to a critical point. When the thickness of the air space increases further above this point, the rate of increase in Rct is found to be slow owing to disturbance in the convection and turbulence. This critical thickness was observed to be variable in different studies. Thus, including air spaces that are close to real life is an effective way to enhance the Rct of multilayer fabrics [15].

Thermal resistance models and their applications

The thermal resistance of fabrics can be calculated by means of experimental, analytical, and numerical methods [16, 17]. There are many models to be found within the textile engineering and heat transfer fields for the thermal resistance prediction. The preference of selection depends on the requisite precision and nature of the solution. Conductive heat transfer is the simplest way to illustrate mathematically and is often the key way of heat transfer [18].

Numerical solutions deal with materials of irregular shapes and properties, different types of heat transfer, and boundary conditions. Numerical methods also have the capability to achieve the maximum precision [19]. There are many commercially available softwares that allow users to solve their problems through numerical solutions. However, these methods are inherently more difficult and complicated, and in some conditions, simple methods prove to be more accurate at much less effort [20]. Thermal resistance is also predicted by using artificial neural networks and statistical models. Some researchers have predicted the thermal resistance of fabrics using mathematical approaches.

Schuhmeister suggested a relationship for the thermal conductivity prediction of fabrics by assuming one-third of fibers to be parallel and two-third in series with a homogeneous distribution in all directions [21]. Later, many researchers used Schuhmeister's model by assuming different ratios of series and parallel components [22, 23, 24]. Presently, Mansoor et al. [25, 26] have modified Schuhmeister and Militky models by combining the water and fiber filling coefficients for the prediction of thermal resistance of wet socks.

Das et al. [27] calculated the heat transfer through the fabric assemblies with the electric resistance and Fricke's law analogy by assuming them as cuboids packed with randomly oriented infinite fibers. Wie et al. [28] suggested a model for fabric thermal resistance prediction by assuming that heat passes through the fabric as a combination of fiber and air in series plus the air in parallel.

Most studies on Rct of textiles were performed either on knitted fabrics or nonwoven, with only a few on woven fabrics [29, 30, 31, 32, 33]. Hence it was necessary to evaluate and distinguish the Rct of woven compression bandage (WCB), dealing with different yarn materials, fabric structures, and number of bandage layers as a function of the applied extension and packing density during testing. Then the experimental results of Rct were validated using the following three theoretical models.

Maxwell–Eucken2 model

The Maxwell–Eucken (ME) model (Eq. (2)) can be used to describe the effective thermal conductivity of a two-component material with simple physical structures. In Eq. (2), λa, λpolymer, Fa, Fpolymer are the thermal conductivities and volume fractions, respectively, and the subscripts represent the two components of the system. The effective thermal conductivity of the two-component material is λfab [34]. An emulsion is a dispersion of one liquid in another immiscible liquid. The phase that is present in the form of droplets is the dispersed phase and the phase in which the droplets are suspended is called the continuous phase. A number of effective thermal conductivity models require the naming of a continuous and a dispersed phase. In materials with exterior porosity, individual solid particles are surrounded by a gaseous matrix, and hence the gaseous component forms the continuous phase while the solid component forms the dispersed phase. For external porosity, and λa and λpolymer are considered as the continuous and dispersed phases, respectively [35, 36].

λfab=λaFa+λpolymerFpolymer3λa2λa+λpolymerFa+Fpolymer3λa2λa+λpolymer{\lambda _{fab}} = {{{\lambda _a}{F_a} + {\lambda _{polymer}}\,{F_{polymer}}{{3{\lambda _a}} \over {2{\lambda _a} + {\lambda _{polymer}}}}} \over {{F_a} + {F_{polymer}}{{3{\lambda _a}} \over {2{\lambda _a} + {\lambda _{polymer}}}}}}

Fpolymer and λpolymer are calculated based on Eqs (7) and (8).

Schuhmeister's model

Schuhmeister summarized the relationship between the thermal conductivity and structural parameters of a fabric using Eq. (3): λfab=0.67×λs+0.33×λp{\lambda _{fab}} = 0.67 \times {\lambda _s} + 0.33 \times {\lambda _p}λs=λpolymer×λaλpolymerFa+λaFpolymer{\lambda _s} = {{{\lambda _{polymer}}\, \times {\lambda _a}} \over {{\lambda _{polymer}}{F_a} + {\lambda _a}{F_{polymer}}}}λp=Fpolymerλpolymer×Faλa{\lambda _p} = {F_{polymer}}{\lambda _{polymer}}\, \times {F_a}{\lambda _a} where λfab is the thermal conductivity of a fabric, λpolymer is the conductivity of fibers, λa is the conductivity of air, Fpolymer is the filling coefficient of the solid fiber, and Fa is the filling coefficient of air in the insulation [ 37].

Militky's model

Militky summarized the relationship between the thermal conductivity and structural parameters of a fabric using empirical Eq. (6) and used the same steps for calculating λs and λp using Eq. (4) and (5), respectively [23, 38], as follows: λfab=(λs+λp2){\lambda _{fab}} = \left({{{{\lambda _s} + {\lambda _p}} \over 2}} \right)

Average thermal conductivity and filling coefficient calculations

It is assumed that fabric density changes with wetting, which causes a change in the filling coefficient, porosity, and thermal conductivity of the fabrics. Based on these assumptions the following three equations were developed that will be used to find the fabric density, filling coefficient, and thermal conductivity for different moisture levels. The average thermal conductivity for different fibers (within socks) at different moisture levels are calculated based on Eq. (7) as follows: Averagethermalconductivity(λpolymer)=(Ffib1λfib1+Ffib2λfib2+Ffib3λfib3Ffib1+Ffib2+Ffib3){\rm{Average}}\,{\rm{thermal}}\,{\rm{conductivity}}({\lambda _{polymer}}) = \left({{{{F_{fib1}} \cdot {\lambda _{fib1}} + {F_{fib2}} \cdot {\lambda _{fib2}} + {F_{fib3}} \cdot {\lambda _{fib3}}} \over {{F_{fib1}} + {F_{fib2}} + {F_{fib3}}}}} \right)

Ffib1 = First fiber filling coefficient

Ffib2 = Second fiber filling coefficient

Ffib3 = Third fiber filling coefficient

λfib1 = First fiber thermal conductivity

λfib2 = Second fiber thermal conductivity

λfib3 = Third fiber thermal conductivity

Filling coefficients for fiber and air are calculated as listed in Table 1, according to the following steps.

Filling coefficients calculation

MeasurementFfib =Fiber filling coefficient
Content%
WeightG
Aream2
Areal densityg/m
Volumetric densityFabricarealdensityFabricthickness[Kg/m3]{{{\rm{Fabric}}\,{\rm{areal}}\,{\rm{density}}} \over {{\rm{Fabric}}\,{\rm{thickness}}}}[{\rm{Kg}}/{{\rm{m}}^3}]
Filling coefficientVolumetricdensityFiberdensity{{{\rm{Volumetric}}\,{\rm{density}}} \over {{\rm{Fiber}}\,{\rm{density}}}}

Air filling coefficient (Fa) is calculated as follows: AirFillingcoefficient(Fa)=1Ffib{\rm{Air}}\,{\rm{Filling}}\,{\rm{coefficient}}\,({F_a}) = 1 - {F_{fib}}

The outputs of Eqs (7) and (8) are used as input for all the above models. Thermal conductivity of water and air is taken as 0.6 and 0.026 W/m/K while density of water is 1,000 Kg/m3. The values of the different input parameters used in this study are listed in Table 2 [UllmannF.2008Ullmann's fibers1Wiley-VCH VerlagWeinheim' href="#j_aut-2020-0052_ref_039_w2aab3b7c27b1b6b1ab2b1c39Aa">39].

Different fiber properties

Fiber nameDensity (Kg/m3)Thermal conductivity (W/m/K)
Cotton1,5400.5
Viscose1,5300.5
Polyester1,3600.4
Nylon 661,1400.3
Polypropylene9000.2
Wool1,3100.5
Acrylic1,1500.3
Experimental work
Materials

Experimental samples are 100% bleached cotton (BL-CO), cotton–polyamide–polyurethane (CO-PA-PU), and viscose–polyurethane (VI–PU) bandages. All Rct tests and measurements of the areal density of samples (g/m2) and total thickness are performed on the extended state as illustrated in Table 3.

Specifications of woven bandage samples on thermal foot manikin

Sample codeFiber compositionSample typeWeight (g/m2)Thickness (mm)
BL-CO-2Bleached cotton 100%100% cotton, two layers, 50% extension, 50% overlapTwo layers = 212.3One layer = 0.76Two layers = 1.39
CO-PA-PU-2Cotton 78%, polyamide 16%, polyurethane 6%CO-PA-PU, two layers, 50% extension, 50% overlapTwo layers = 238.1One layer = 0.84Two layers = 1.53
VI-PU-2Viscose 94%, polyurethane 6%VI-PU, two layers, 50% extension, 50% overlapTwo layers = 220.7One layer = 0.79Two layers = 1.43
BL-CO-3Bleached cotton 100%100% cotton, three layers, 50% extension, 66% overlapThree layers = 317.5One layer = 0.76Three layers = 2.01
CO-PA-PU-3Cotton 78%, polyamide 16%, polyurethane 6%CO-PA-PU, three layers, 50% extension, 66% overlap356.3One layer = 0.84Three layers = 2.17
VI-PU-3Viscose 94%, polyurethane 6%VI-PU, three layers, 50% extension, 66% overlap329.4One layer = 0.79Three layers = 2.05
Testing procedure
Adjusting the testing procedure of Rct on TFM and ALAMBETA

Thermal manikins are designed to simulate the human body's heat exchange and its interaction with the surrounding environment. There are two types of testing on thermal manikin, practically called “nude and clothed Manikin” [2]. Experimental samples consist of three types of WCBs, which as porous materials should provide thermal comfort to enable air permeability, heat transfer, and liquid perspiration out of the human body. Mercerized cotton socks were used to cover TFM as underwear to measure Rct0 for all measured samples to ensure more stabilization and steady conditions before measuring Rct. The testing method in this case is called “clothed Manikin.” The three types of WCBs were wrapped on TFM at 50% extension using both 50% and 66% overlap to achieve two- and three-layer bandaging, respectively (see Figure 1). Thermal resistance was evaluated for all samples at the standard ambient conditions (T: 20 ± 2°C, RH: 65 ± 5%) using TFM at air convection speed 0–0.25 m/s for all types of WCBs, as shown in Figures 1 and 2 [40]. Then the Rct results by TFM and ALAMBETA were validated using the three theoretical models, such as ME-2, Schuhmeister, and Militky.

Figure 1

Rheological curves of the stirring doped STG with different amounts of doped flocks.

Figure 1

Adjusting the bandage extensions and number of layers on the thermal foot manikin (TFM).

Figure 2

Measuring the total bandage thickness on thermal foot manikin. (A) clothed TFM with socks without bandage, (B) TFM with socks and CO-PA-PU-2 bandage, and (C) TFM with socks and VI-PU-2 bandage.

However, the same tests were confirmed on ALAMBETA at the same extension and number of layers using special tensioning frame, as shown in Figure 3, but using the free air convection system [41].

Figure 3

Thermal resistance of two bandage layers on the ALAMBETA testing device.

Calculating and measuring Rct on TFM and ALAMBETA respectively

The stabilization process of the TFM could be achieved after 20 min – at least – then the final testing step takes place [10]. Finally, Rct values can be measured using the measured Rct0 as a reference value, as illustrated in Figure 4, and it can be calculated using Eq. (9) as follows: Rct=A(TsTa)HRct0{R_{ct}} = {{A \cdot ({T_s} - {T_a})} \over H} - {R_{ct0}} where Rct is the dry resistance of sample only (m2.°C/W), or (m2.°C.W−1)Ts is the hot plate surface temperature (°C), Ta is ambient temperature (°C), H/A is the zone heat flux (W/m2), and Rct0 is the clothed TFM dry resistance (m2/°C/W).

Figure 4

Measuring Rct while wrapping the compression bandage over socks.

Results and discussion
Thermal resistance measured by TFM compared with ALAMBETA

For comparison, all bandage types were wrapped on TFM and ALAMBETA at the same extension level ranging from 10% to 100% using both two and three layers of bandages [10]. Figure 5 illustrates that Rct values slightly improve when the applied extension increases on ALAMBETA; on the contrary, it is significantly decreasing for TFM. The main effective factors on ALAMBETA are the bandage volumetric porosity and the applied tension as a function of the total bandage thickness and fiber density, as illustrated in Figures 7 and 8.

Figure 5

Effect of applied extension on thermal resistance of two layers of bandage on ALAMBETA and TFM. *Note that all the sample codes with the abbreviation TFM, such as CO-2-TFM, indicates testing results on the TFM for Figures 58, whereas the other codes like BL-CO-2 refer to the ALAMBETA tester.

The same analysis is proved for the three layers of bandages as demonstrated in Figures 6 and 8. Moreover, the effect of higher applied tension by three-layer bandaging appeared as the third main factor that decreases the volume of the air layers between the adjacent bandage layers.

Figure 6

Effect of applied extension on thermal resistance of three-layer bandage on ALAMBETA and TFM.

Figure 7

Effect of total bandage thickness on thermal resistance of two-layer bandage on ALAMBETA and TFM.

Figure 8

Effect of total bandage thickness on thermal resistance of three-layer bandage on ALAMBETA and TFM.

Validation of the experimental Rct results on TFM and ALAMBETA with three theoretical models

The experimental results of Rct match with the three mathematical models that the increase in total fabric (WCB layers) thickness is associated with an enhancement in the Rct values, as displayed in Figure 9. Moreover, there are significant similarities between the ALAMBETA results and both Schuhmeister and Militky models, at approximately 92% and 93% respectively (see Figure 11); whereas the correspondence values for the TFM are approximately 82% and 83% respectively, as shown in Figure 12. This may be because the ALAMBETA testing corresponded well to the use of socks inside a shoe (boundary conditions of first order). The ALAMBETA enables fast measurement of both steady-state and transient-state thermal properties, as shown in Figure 10. This diagram clearly demonstrated the maximum qmax, dynamic (transient) qdyn, and steady-state qsteady heat flow [ 42].

Figure 9

Experimental thermal resistance results for bandages by thermal foot manikin and ALAMBETA versus theoretical calculations by the Maxwell–Eucken2, Schuhmeister, and Militky models.

Figure 10

Time-dependence heat flow after contact [42].

Figure 11

Experimental thermal resistance for bandages by ALAMBETA versus theoretical calculations by the Maxwell–Eucken2, Schuhmeister, and Militky models.

Figure 12

Experimental thermal resistance for bandages by thermal foot manikin versus theoretical calculations by the Maxwell–Eucken2, Schuhmeister, and Militky models.

The transient heat flow is shown in Eq. (10), whereas the steady-state heat flow is shown in Eq. (11) as follows: qdym=b(T1T2)πτ{q_{dym}} = {{b \cdot ({T_1} - {T_2})} \over {\surd \pi \tau}}qsteady=T1T2Rct{q_{steady}} = {{{T_1} - {T_2}} \over {{R_{ct}}}} where b is the thermal absorptivity (W s0.5/m2/K1), Δ T = T1T2 is the temperature difference between the two convection surfaces, and τ is the tortuosity [–] [43]. The first mathematical model (ME-2) has significant deviations at approximately 15% and 25% with the recorded experimental Rct values on both ALAMBETA and TFM, respectively. These results confirm that the Schuhmeister and Militky models enhanced the prediction of Rct values for WCBs.

Conclusion

The experimental evaluation of Rct for the three main types of WCBs was performed on TFM and ALAMBETA testers and validated using three theoretical models. The Rct values improved when the bandage volumetric porosity increased as the static air existed between each two adjacent fabric layers and between fibers inside the yarn (the intra-yarn porosity). There is a strong correlation between the Schuhmeister and Militky models with the ALAMBETA results; the maximum deviation was only 8% and 7%, respectively, whereas the deviations with the TFM were 18% and 17%, respectively.

The obtained results of Rct in the case of WCB confirmed that clothed TFM is more accurate for measuring Rct0 and the corresponding values of Rct due to more stabilization and less effect of air convection. There were significant deviations in the experimental results between ALAMBETA and TFM. Hence, the TFM might be technically recommended for testing the Rct of WCB because the high levels of applied tension during the bandage application were more effective on the TFM results.

Figure 1

Rheological curves of the stirring doped STG with different amounts of doped flocks.
Rheological curves of the stirring doped STG with different amounts of doped flocks.

Figure 1

Adjusting the bandage extensions and number of layers on the thermal foot manikin (TFM).
Adjusting the bandage extensions and number of layers on the thermal foot manikin (TFM).

Figure 2

Measuring the total bandage thickness on thermal foot manikin. (A) clothed TFM with socks without bandage, (B) TFM with socks and CO-PA-PU-2 bandage, and (C) TFM with socks and VI-PU-2 bandage.
Measuring the total bandage thickness on thermal foot manikin. (A) clothed TFM with socks without bandage, (B) TFM with socks and CO-PA-PU-2 bandage, and (C) TFM with socks and VI-PU-2 bandage.

Figure 3

Thermal resistance of two bandage layers on the ALAMBETA testing device.
Thermal resistance of two bandage layers on the ALAMBETA testing device.

Figure 4

Measuring Rct while wrapping the compression bandage over socks.
Measuring Rct while wrapping the compression bandage over socks.

Figure 5

Effect of applied extension on thermal resistance of two layers of bandage on ALAMBETA and TFM. *Note that all the sample codes with the abbreviation TFM, such as CO-2-TFM, indicates testing results on the TFM for Figures 5–8, whereas the other codes like BL-CO-2 refer to the ALAMBETA tester.
Effect of applied extension on thermal resistance of two layers of bandage on ALAMBETA and TFM. *Note that all the sample codes with the abbreviation TFM, such as CO-2-TFM, indicates testing results on the TFM for Figures 5–8, whereas the other codes like BL-CO-2 refer to the ALAMBETA tester.

Figure 6

Effect of applied extension on thermal resistance of three-layer bandage on ALAMBETA and TFM.
Effect of applied extension on thermal resistance of three-layer bandage on ALAMBETA and TFM.

Figure 7

Effect of total bandage thickness on thermal resistance of two-layer bandage on ALAMBETA and TFM.
Effect of total bandage thickness on thermal resistance of two-layer bandage on ALAMBETA and TFM.

Figure 8

Effect of total bandage thickness on thermal resistance of three-layer bandage on ALAMBETA and TFM.
Effect of total bandage thickness on thermal resistance of three-layer bandage on ALAMBETA and TFM.

Figure 9

Experimental thermal resistance results for bandages by thermal foot manikin and ALAMBETA versus theoretical calculations by the Maxwell–Eucken2, Schuhmeister, and Militky models.
Experimental thermal resistance results for bandages by thermal foot manikin and ALAMBETA versus theoretical calculations by the Maxwell–Eucken2, Schuhmeister, and Militky models.

Figure 10

Time-dependence heat flow after contact [42].
Time-dependence heat flow after contact [42].

Figure 11

Experimental thermal resistance for bandages by ALAMBETA versus theoretical calculations by the Maxwell–Eucken2, Schuhmeister, and Militky models.
Experimental thermal resistance for bandages by ALAMBETA versus theoretical calculations by the Maxwell–Eucken2, Schuhmeister, and Militky models.

Figure 12

Experimental thermal resistance for bandages by thermal foot manikin versus theoretical calculations by the Maxwell–Eucken2, Schuhmeister, and Militky models.
Experimental thermal resistance for bandages by thermal foot manikin versus theoretical calculations by the Maxwell–Eucken2, Schuhmeister, and Militky models.

Different fiber properties

Fiber nameDensity (Kg/m3)Thermal conductivity (W/m/K)
Cotton1,5400.5
Viscose1,5300.5
Polyester1,3600.4
Nylon 661,1400.3
Polypropylene9000.2
Wool1,3100.5
Acrylic1,1500.3

Filling coefficients calculation

MeasurementFfib =Fiber filling coefficient
Content%
WeightG
Aream2
Areal densityg/m
Volumetric densityFabricarealdensityFabricthickness[Kg/m3]{{{\rm{Fabric}}\,{\rm{areal}}\,{\rm{density}}} \over {{\rm{Fabric}}\,{\rm{thickness}}}}[{\rm{Kg}}/{{\rm{m}}^3}]
Filling coefficientVolumetricdensityFiberdensity{{{\rm{Volumetric}}\,{\rm{density}}} \over {{\rm{Fiber}}\,{\rm{density}}}}

Specifications of woven bandage samples on thermal foot manikin

Sample codeFiber compositionSample typeWeight (g/m2)Thickness (mm)
BL-CO-2Bleached cotton 100%100% cotton, two layers, 50% extension, 50% overlapTwo layers = 212.3One layer = 0.76Two layers = 1.39
CO-PA-PU-2Cotton 78%, polyamide 16%, polyurethane 6%CO-PA-PU, two layers, 50% extension, 50% overlapTwo layers = 238.1One layer = 0.84Two layers = 1.53
VI-PU-2Viscose 94%, polyurethane 6%VI-PU, two layers, 50% extension, 50% overlapTwo layers = 220.7One layer = 0.79Two layers = 1.43
BL-CO-3Bleached cotton 100%100% cotton, three layers, 50% extension, 66% overlapThree layers = 317.5One layer = 0.76Three layers = 2.01
CO-PA-PU-3Cotton 78%, polyamide 16%, polyurethane 6%CO-PA-PU, three layers, 50% extension, 66% overlap356.3One layer = 0.84Three layers = 2.17
VI-PU-3Viscose 94%, polyurethane 6%VI-PU, three layers, 50% extension, 66% overlap329.4One layer = 0.79Three layers = 2.05

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