The effect of the transfer abilities of single layers on the heat and mass transport through multilayered outerwear clothing for cold protection

Abstract

This paper deals with performance properties related to human thermo-physiological comfort of three-layer textile systems used for the production of outerwear for cold protection. The transfer of heat and fluids through the compound single layers (woven and non-woven) is investigated and compared to the heat and mass transfer of the systems for clothing. Six characteristics are measured for both single layers and systems of layers: thermal resistance, air permeability, water vapor resistance, relative water vapor permeability, the accumulative one-way transport index and overall moisture management capacity. For each of the characteristics, regression analysis is applied to prove or reject the proposed mathematical dependencies between the transfer abilities of the single layers and the respective systems. The results obtained showed that the fluid transfer abilities of the single layers applied in clothing for cold protection strongly affect the fluid transfer ability of the system of layers, while the heat transfer of the system is dominated by the heat transfer ability of the thermo-insulating layer. The proposed approach for assessment of the transfer processes through a system of layers for the production of outerwear for cold protection could be successfully applied in the design of other textile and clothing items, produced by using systems of different textile layers.

Keywords

systems of textiles multilayer heat transfer air permeability moisture transfer cold protection outerwear clothing

Clothing ensembles for cold protection consist, as a rule, of three or four layers of different type of garments. The underwear has to guarantee pleasant contact with the skin, the middle layer of clothing is used for insulation and the outerwear protects the whole ensemble and the human body from the effects of the environment (wind, precipitation).

Outerwear clothing for cold protection itself is organized in a similar way: it often involves three layers, having a different purpose and organized in a system of layers. The inner layer (lining) contacts with the surface of the inner clothing garments and partly with the skin (around the wrists, neck and face); the middle layer (hidden insulating layer) is used to increase the thermal resistance of the system; and the outer layer has to stop the penetration of wind flow and liquids from the environment to the inner layers of the system.

The thermo-physiological comfort of the clothed human body strongly depends on the heat and mass transfer processes through the clothing. This means that every textile layer and the air layer between the textiles influence the transfer of air, liquids, water vapor and heat from the surface of the skin to the environment and vice versa.¹ When designing outerwear for cold protection it is necessary to assess the influence of every single layer used in the construction of the garment (jacket, overall) on the transfer ability of the whole system (the outerwear garment itself).

Several studies on the transport abilities of ensembles of textiles have been performed. The heat transfer through a system of textiles was studied in the works of Matusiak² and Das et al.³ Yoo et al.⁴ investigated the mechanical properties of thermal protective clothing for firefighters together with their thermal insulation, moisture evaporation and air permeability. They established the positive influence of both the thickness and weight of the single layers on thermal insulation properties of the systems. Recently, Matusiak and Kowalczyk⁵ investigated the thermal insulation properties of multilayer textile systems, combining two woven, two knitted and two non-woven macrostructures to create two-, three- and four-layer systems. They analyzed the effect of the number of layers and thermal resistance of the single layer on the thermal resistance of the system. However, none of these studies dealt with a system of three layers, specially combined to protect the body from low temperatures and precipitations. The topic of thermal resistance of multilayer textile systems is still open and needs further investigation.

The transfer of water vapor through three-layer systems of waterproof breathable fabrics was studied by Ren and Ruckman.⁶ The study showed how the condensation problem could be overcome via changing the properties of the system. Similar were the studies of Rossi et al.⁷ and Oh.⁸ Yoo and Kim⁹ investigated the water vapor transfer through a system of five layers of fabric ensembles, finding the influence of the design effect and the method of layering on the performance of the system. They also discussed the lack of experiments on heat and moisture transfer in systems for clothing for cold protection, which coincide with the starting point of the present investigation: to study the moisture transfer abilities of the single layer in the content of the system of layers they form in the clothing for cold protection.

Epps¹⁰ studied the air permeability and thermal conductivity of 10 samples of woven, knitted and non-woven macrostructures, but systems of different macrostructures were not investigated. Mohammadi et al.¹¹ investigated the air permeability of a system of non-woven macrostructures using statistical analysis and developing a regression model of the relationship between the type of the non-woven, thickness and density on one side and the air permeability of the system, on the other. Previous research of the authors was dedicated to thermal conductivity and radiative heat transfer of multilayered systems of non-wovens.^12,13 However, there is a lack of reports dealing with the influence of the air permeability of single layers on the permeability of a system of heterogeneous layers (woven and non-woven) for protection from cold.

Our previous work investigated the influence of basic structural, geometric and mass characteristics of single textile layers and systems of three layers on the heat and mass transfer processes in the through-thickness direction of single textiles and the systems.¹⁴ The novelty of the present study lies in the assessment of the effect of the transfer abilities of single layers on the transfer abilities of a system of three different (heterogeneous) layers used for the production of clothing for cold protection (jackets and coveralls). The study aimed to assess the effect of the single layer transfer abilities on the performance of the resulting system of layers in terms of transfer processes that precondition the thermo-physiological comfort of the wearer. All basic characteristics of the textiles related to thermo-physiological comfort, namely thermal resistance, air permeability, water vapor resistance, relative water vapor permeability, the accumulative one-way transport index and overall moisture management capacity (OMMC), were measured for both single layers and systems of layers. Regression analysis was applied to prove or reject the proposed mathematical dependences between the transfer abilities of the single layers and the respective systems.

Materials and methods

Materials

A total of 16 single textile samples of woven and non-woven types were selected. They were used to constitute 14 systems of fabrics used for the production of outerwear clothing for protection from the cold. Seven woven macrostructures formed the outer layer (Samples А) and seven formed the inner layer or the lining (Samples B). The middle layer (Samples N) was formed by two non-woven webs with different thicknesses.

Table 1 summarizes the coding and data of the single layers. The measurements were performed after conditioning of the samples for 24 h (22℃, 65% relative humidity (RH)). The mass per unit area was determined following ISO 3801:1977¹⁵ and the average of 10 readings per a sample was calculated. The thickness was measured in accordance with EN ISO 5084:2002¹⁶ and an average of 10 readings per a sample was calculated.
Table 1.
Characteristics of the heat and mass transfer in the through-thickness direction of the single layers

Sample code Composition Thickness, mm Fabric weight, g/m² Thermal resistance, m²mK/W Water vapor resistance, m²Pa/W Relative water-vapor permeability, % Air permeability, m/s Accumulative one-way transport index, mm²/s Overall moisture management capacity, -

A1 PES 100% 0.56 170.8 1.9 4.4 53.4 0.056 112.63 0.29

A2 PA 90%. PU 10% 0.18 85.5 <1 19.8 22.6 0.012 496.53 0.71

A3 CO 100% 0.95 289.4 3.8 5.2 48.5 0.118 1174.07 0.61

A4 PA 100% 0.16 76.2 <1 28.9 15.1 0.013 655.24 0.71

A5 PA 100% 0.23 128.6 <1 43.4 12.8 0.012 1119.06 0.6

A6 PES 100% 0.25 180.7 <1 7.4 43.2 0.011 13.03 0.04

A7 PES 100% 0.23 148.7 <1 3.7 58.5 0.011 1148.46 0.05

N1 PES 100% 12.81 200.83 225.2 39.2 12.1 3.036 1380.79 0.53

N2 PES 100% 9.56 105.40 145.3 17.5 23.5 3.623 1327.87 0.53

B1 PES 100% 0.10 63.2 <1 4.0 53.3 0.342 672.16 0.74

B2 PES 100% 0.13 64.1 <1 4.6 54.6 0.253 950.72 0.74

B3 CO 100% 0.65 118.4 10.2 3.1 61.8 0.481 1092.18 0.62

B4 PES 100% 0.09 58.6 4.9 2.3 69.7 0.500 1209.31 0.67

B5 PES 100% 0.16 68.3 2.6 3.3 62.3 0.027 972.46 0.7

B6 PES 100% 0.12 62.1 4.7 5.2 56.6 0.158 493.66 0.71

B7 PES 100% 0.09 58.6 4.9 2.3 69.7 0.500 1209.31 0.67

PES: polyester: PA: polyamide; PU: polyurethane; CO: cotton.

Methods

A Permetest instrument that simulates human skin was used to determine thermal resistance, water vapor resistance and relative water vapor permeability following ISO 11092:2014 standard.¹⁷

The air permeability was measured on a Metrimpex apparatus in accordance with EN ISO 9237:1999,¹⁸ applying 100 Pa pressure difference between both sides of each sample. Ten measurements were performed for each sample.

Water transfer was measured using a Moisture Management Tester (MMT), following the AATCC 195:2012 standard.^19,20 The average values of the accumulative one-way transport index (R_index) and the OMMC were calculated on the basis of five readings per sample.

All samples were conditioned for 24 h (22℃, 65% RH) before measurements.

The systems of layers were tested having in mind the direction of the main processes of heat and mass exchange between the human body and the cold environment. The following directions were used.
For heat and water vapor transfer: from the inner layer to the outer, as the skin temperature or the temperature of the clothing is higher than the temperature of the environment.

For air transfer: from the outer layer to the inner, assuming the presence of forced convection in outdoor conditions.

For moisture transfer: from the outer layer to the inner, simulating the effect of precipitation.

Results and discussion

Theoretical considerations

The results from the measurement of the heat and mass transfer processes in the through-thickness direction of the single layers are summarized in Table 1. Table 2 presents the results from the measurement of the heat and mass transfer through the system of layers and the coding of the systems and Table 3 presents the standard deviation of the average values from Table 2.
Table 2.
Characteristics of the heat and mass transfer in the through-thickness direction of the three-layer systems

System code Combination of layers Thermal resistance, m²mK/W Water vapor resistance, m²Pa/W Relative water-vapor permeability, % Air permeability, m/s Accumulative one-way transport index, mm²/s Overall moisture management capacity, -

AN1B1 A1-N1-B1 214.0 45.3 11.4 0.114 589.9 0.53

AN1B2 A2-N1-B2 134.4 44.5 10.6 0.062 545.5 0.55

AN1B3 A3-N1-B3 154.1 37.4 11.5 0.146 579.5 0.51

AN1B4 A4-N1-B4 158.3 42.6 10.2 0.065 293.0 0.38

AN1B5 A5-N1-B5 145.4 42.6 11.6 0.022 289.6 0.38

AN1B6 A6-N1-B6 162.8 44.1 10.3 0.042 0.0 0.00

AN1B7 A7-N1-B7 165.8 40.1 11.5 0.062 0.0 0.00

AN2B1 A1-N2-B1 142.7 29.6 15.5 0.078 331.0 0.44

AN2B2 A2-N2-B2 98.2 36.8 12.0 0.028 150.2 0.22

AN2B3 A3-N2-B3 112.7 23.0 16.7 0.108 252.7 0.36

AN2B4 A4-N2-B4 100.4 36.2 11.6 0.026 28.5 0.09

AN2B5 A5-N2-B5 115.3 38.3 13.3 0.018 65.2 0.13

AN2B6 A6-N2-B6 114.1 33.5 12.9 0.026 0.0 0.00

AN2B7 A7-N2-B7 117.6 29.1 15.2 0.027 0.0 0.00

Table 3.
Standard deviations of the results for the heat and mass transfer of the three-layer systems

System code Standard deviation of

Thermal resistance, m²mK/W Water vapor resistance, m²Pa/W Relative water-vapor permeability, % Air permeability, m/s Accumulative one-way transport index, mm²/s Overall moisture management capacity, -

AN1B1 2.14 1.70 0.33 0.012 2.76 0.003

AN1B2 1.19 0.14 0.05 0.006 3.49 0.005

AN1B3 13.92 0.41 0.29 0.011 1.45 0.001

AN1B4 0.48 2.74 1.08 0.065 3.48 0.006

AN1B5 3.55 1.74 0.37 0.007 1.41 0.004

AN1B6 2.44 2.16 0.22 0.001 2.10 N/A

AN1B7 0.65 2.37 0.61 0.001 4.02 N/A

AN2B1 3.88 0.73 1.16 0.004 2.13 0.001

AN2B2 2.14 1.18 0.54 0.002 3.31 0.002

AN2B3 5.20 1.02 0.59 0.005 2.70 0.003

AN2B4 12.01 2.18 0.62 0.003 3.02 0.001

AN2B5 9.01 3.84 1.11 0.001 2.05 0.001

AN2B6 3.37 0.08 0.05 0.002 N/A N/A

AN2B7 1.79 2.21 0.71 0.003 N/A N/A

To investigate the influence of the transfer processes through each of the three single layers on the transfer abilities of the system of the same three layers, a regression analysis was applied. The method is frequently applied, but in this case the heat or mass transfer property of the system of layers Y_system is presented as a function of a mathematical dependence between the respective properties of each layer
$Y_{system} = f (Y_{A}, Y_{N}, Y_{B})$
(1)
where Y_A, Y_N and Y_B are the measured value of the same property of the outer, middle and inner layers, respectively.

The basic question is to find out a mathematical dependence between Y_A, Y_N and Y_B_. Regression analysis is further applied to assess the strength of the proposed mathematical relationship.

The thermal resistance of the system Rct_system in this study was presented as a function of the thermal resistance of the outer Rct_A, middle Rct_N and the inner layer Rct_B, using an additive low,²¹ namely
${Rct}_{system} = f ({Rct}_{A} + {Rct}_{N} + {Rct}_{B})$
(2)

The same additive relationship²¹ was applied for the water vapor resistance of the system Ret_system
${Ret}_{system} = f ({Ret}_{A} + {Ret}_{N} + {Ret}_{B})$
(3)
where Ret_A, Ret_N and Ret_B are the respective values of the water vapor resistance of the outer, middle and the inner layers of the system.

An additive function was used to present the joint effect of the single layers on the accumulative one-way transport index of the overall system R_index,system
$R_{index, system} = f (R_{index, A} + R_{index, N} + R_{index, B})$
(4)
where R_index, _A is the accumulative one-way transport index of the outer layer A, mm²/s; R_index, _N is the accumulative one-way transport index of the middle layer N, mm²/s; and R_index, _B is the accumulative one-way transport index of the inner layer B, mm²/s.

Similarly, the OMMC of the system was presented as the sum of the OMMC values of the compound layers, namely
${OMMC}_{system} = f ({OMMC}_{A} + {OMMC}_{N} + {OMMC}_{B})$
(5)
where OMMC_A, OMMC_N and OMMC_B are the OMMC of the outer, middle and inner layers, respectively.

The air permeability, however, required a different method of approach. The reason for not using an additive dependence, like in the case of thermal resistance, is that the air permeability of the system is preconditioned by the air permeability of the most impermeable layer, but it is always lower.²² Therefore we suggest the air permeability of the system AP_system to be presented as a dependent from the product of the air permeability of the single layers. The product of the values for the single layers is much closer to the reality than the sum of them. Clayton²³ realized the same problem and proposed a model to calculate the air permeability of the system with an additive function, but of the reciprocal values of the air permeability of the single layers
${AP}_{N} = (\frac{1}{{AP}_{11}} + \frac{1}{{AP}_{12}} + \dots + \frac{1}{{AP}_{1 N}})^{- 1}$
(6)
where AP_N is the air permeability coefficient of a system of N layers, and AP₁₁–AP₁ _N are the air permeability coefficients of the single layers.

It has to be mentioned that the model of Clayton²³ did not differentiate between the types of layers (woven, non-woven, knitted).

The following function was applied for the air permeability of the system AP_system
${AP}_{system} = f ({AP}_{A} . {AP}_{N} . {AP}_{B})$
(7)
where AP_A is the air permeability of the outer layer A, m/s; AP_N is the air permeability of the middle layer N, m/s; and AP_B is the air permeability of the inner layer B, m/s.

By analogy, the same approach was applied for the relative water vapor permeability of the system: it was presented as a fraction, which is a product of the fractions of the relative water vapor permeability of the single layers, namely
$\frac{1}{100} P_{system} = f (\frac{1}{100} P_{A} \frac{1}{100} P_{N} \frac{1}{100} P_{B})$
(8)
where P_A, P_N and P_B are the relative water vapor permeability of the outer, middle and inner layers, respectively, %.

Thermal resistance

The thermal resistance Rct_system is plotted in Figure 1 as a dependent variable from the sum $({Rct}_{A} + {Rct}_{N} + {Rct}_{B})$ . Then a regression analysis was applied to find a statistical equation that described best the function. In this case, a regression equation of linear type was found with a determination coefficient R² = 0.58.
Figure 1.
Thermal resistance of the system as a function of the sum of the single layers’ thermal resistance.

However, the grouping of the readings into two “clouds” does not allow one to prove the trend in the data. An important result here is that the thermal resistance of the system is strongly dependent on the middle, insulation layer N: each of the “clouds” consists of the systems with N1 or N2 non-woven web only.

This is demonstrated well by Figures 2 and 3, where the non-woven web, having a large amount of air entrapped between the fibers, has the determining role in the thermal resistance.
Figure 2.
Measured thermal resistance of the system of layers with middle layer N1 and calculated sum of the resistances, compared to the resistance of the middle layer.

Figure 3.
Measured thermal resistance of the system of layers with middle layer N2 and calculated sum of the resistances, compared to the resistance of the middle layer.

Figure 4.
Air permeability of the system as a function of the product of the single layers’ air permeability.

The results in Figure 1 clearly suggest that during the design stage for cold protection outerwear clothing, only the insulating abilities of the insulating layer have to be taken into account to assure the proper performance of the system. ISO 9920:2007²¹ suggests that the thermal insulation of a clothing system (many textile layers) is a sum of the thermal insulation of the compound layers. Our study has found, however, that the resulting thermal resistance of the system was lower than the sum of the readings for each layer. Only in the case of A1N1B1 (Figure 2) and A1N2B1 (Figure 3) systems did the sum of the thermal resistance of the single layers reach 94% and 97% of the thermal resistance of the system, respectively. In all other cases the thermal resistance, calculated as a sum of the single layer’s reading, was between 60% and 72% for the systems with N1 insulating layer and between 64% and 78% for the systems with N2 insulating layer. These results are in a good correlation with other findings in the literature.^2,5,22 Yoo et al.² explained the lower values of the thermal resistance of the system with the occurrence of forced convection between the layers during their testing. However, that explanation could not be attributed to the current study, as one and the same conditions were applied for testing of the single layers and the system.

Actually, it was expected that the thermal resistance of the system would be higher than the sum of the readings for the single layers, due to the presence of air gaps between the layers. The results changed in the opposite direction, however. A reasonable explanation of the phenomenon could be found in the air entrapped within the non-woven layer. It has been already mentioned that the thermal resistance of the system is mainly affected by the thermal resistance of the middle layer, the non-woven web. The much greater volume of the web entraps a lot of air between the fibers, thus increasing the insulation ability of web: it is around 10 times higher than the insulation ability of the woven macrostructures and even more (see Table 1). However, when the two “active” surfaces of the web are covered between the other woven layers (Samples A and B), some of the surface pores “lose” the air inside them as the fibers on the boundary layers becomes bent and pressed. In addition, during the testing of the thermal conductivity with the Permetest instrument, the testing sample is fixed and respectively pressed from the upper side using one ring. The middle area of the non-woven web remains free and the fibers there can still keep some of the air layer and act as additional resistance. In the multilayer construction the upper fabric presses these fibers and reduces the actual volume and thickness of the non-woven layers and, in this way, influences the thermal resistance of the multilayer set.

Air permeability

Forced convection due to the wind and human activity can affect significantly the thermo-physiological comfort of the body in a cold environment. The wind-chill index and Required Clothing Insulation are two indexes used for assessment of the cold stress in outdoor conditions at low temperatures.²⁴ The wind can penetrate the clothing ensemble through the outerwear or at least break up the boundary layer between the outerwear and the environment.

Regression dependence was searched for between the air permeability of the system and the product of the air permeability of the single layers. The results are plotted in Figure 4. Two types of trendlines were used to derive the regression equation of the supposed dependence: linear (equation (9)) and second-order polynomial (equation (10))
${AP}_{system} = 0.507 {AP}_{A} . {AP}_{N} . {AP}_{B} + 0.0364$
(9)

${AP}_{system} = - 4.87 ({AP}_{A} . {AP}_{N} . {AP}_{B})^{2} + 1.46 {AP}_{A} . {AP}_{N} . {AP}_{B} + 0.023$
(10)

Figure 5.
Air permeability of system N1, measured and calculated according to equation (6) and the minimal value of all layers.

The coefficient of determination of the polynomial regression equation (R² = 0.8) is higher than that of the linear equation (R² = 0.67), which means that the second-order equation describes best the dependence between the air permeability of the system and the product of the air permeability of the single layers. However, the second-order curve has reached a maximum within the investigated range and starts decreasing: the presence of an extremum can be hardly physically explained.

For the linear regression equation, an additional proof is required for the reliability of the linear dependence. The calculation showed that the p-value (0.0003) is less than the significance level (α = 0.05), which is evidence that a statistically significant linear relationship exists between the air permeability of the system and the product of the air permeability of its compound layers.

In order a suitable way for evaluation of the air permeability of the system to be found, the model of Clayton²³ (equation (6)) was applied as well. The comparisons between the measured data for the complete system and the calculated values are presented in Figures 5 and 6. There is well recognizable correlation between the measured air permeability and the calculated air permeability according to Clayton’s equation value, where the calculated value always underestimates the real one. Applying a pure engineering approach, very similar results can be achieved. For a system of three layers, the air permeability of the system cannot be higher than the permeability of the layer with the minimal one. As both systems with N1 and N2 in the middle show, the calculated value according to Clayton’s equation is very close to the minimal air permeability of the layers in the system and can be used as its calculation is simpler than the addition of the reciprocal values.
Figure 6.
Air permeability of the system N2, measured and calculated according to equation (6) and the minimal value of all layers.

Water vapor resistance

Water vapor resistance is particularly important for garments that are to be used in a cold environment. The high water vapor resistance of the outerwear clothing works against the evaporation of sweat, which may provoke condensation between the layers of the system or between the individual garments in the clothing ensemble. The condensation leads to very fast cooling of the body, which can cause cold injuries in low temperature environments.²⁵

The water vapor resistance of the system was plotted against the sum $({Ret}_{A} + {Ret}_{N} + {Ret}_{B})$ of the water vapor resistance of the compound layers and the graph is presented in Figure 7.
Figure 7.
Water vapor resistance of the system as a function of the sum of the single layers’ water vapor resistance.

Three types of trendlines were derived: linear (equation (11)), second-order polynomial (equation (12)) and exponential (equation (13))
${Ret}_{system} = 0.273 ({Ret}_{A} + {Ret}_{N} + {Ret}_{B}) + 24.18$
(11)

${Ret}_{system} = - 0.0075 ({Ret}_{A} + {Ret}_{N} + {Ret}_{B}) 2 + 1.0487 ({Ret}_{A} + {Ret}_{N} + {Ret}_{B}) + 6.632$
(12)

${Ret}_{system} = 8.0365 ({Ret}_{A} + {Ret}_{N} + {Ret}_{B}) 0.4$
(13)

The highest coefficient of determination has the second-order polynomial relationship (R² = 0.76), but again because of the maximum within the investigated area it shows currently no really natural behavior and should be investigated in more detail before being used for further predictions.

The linear correlation coefficient of the linear dependence is r = 0.76, which is proof of a strong linear dependence between the studied variables.²⁶ The calculation of the p-value (0.009), which is less than the significance level (α = 0.05), is sufficient evidence that the linear relationship between the water vapor resistance of the system and the sum of the water vapor resistance of the involved layers is significant.

Figures 8 and 9 show graphically both the calculated and measured values of the systems of layers if (equation (11)) is applied. The two figures show large variations between the measured and calculated water vapor resistance of the systems. For most samples, the calculated value is higher than the measured one, but for some of the samples it is lower (A1N2B1, A6N2B6, A7N2B7). For the first system, the maximal resistance within one sample is very close to the measured value for the complete system (Figure 8), but for the second system (with N2 as a middle layer) this is not always the case. The reason for this is that in the second system the resistances of each layer are comparable, so there is no determining layer as in the case of system N1, where one layer in most cases has a significantly higher resistance than the others.
Figure 8.
Water vapor resistance of the system as a function of the sum of the single layers’ water vapor resistance.

Figure 9.
Water vapor resistance of the system as a function of the sum of the single layers’ water vapor resistance.

Relative water vapor permeability

The relative water vapor permeability is a practical characteristic that allows faster arrangement of the system between the limits “non-permeable “and “100% permeable”. One-hundred percent is the permeability of the free surface of the measuring apparatus.²⁷

The relative water vapor permeability of the systems was quite a lot lower compared to that of the single layers. The highest values were obtained for the AN2B3 system (16.7%) and the lowest for the AN1B4 system (10.2%). For comparison, the highest average reading of the relative water vapor permeability was obtained for B4 and B7 single layers (69.4%) and the lowest for the non-woven web N1 (12.1%).

The relative water vapor permeability of the system P_system was presented as a function of the product of the fractions of the relative water vapor permeability of the single layers (equation (8)). The results are plotted in Figure 10 and a regression equation of linear type was derived
$\frac{1}{100} P_{system} = 0.62 \frac{1}{100} P_{A} \frac{1}{100} P_{N} \frac{1}{100} P_{B} + 0.1$
(14)

Figure 10.
Relative water vapor permeability of the system as a function of the product of the single layers’ relative water vapor permeability.

The testing of other regression equations showed that the coefficient of determination of the linear dependence (equation (14)) and a second-order polynomial relationship was one and the same (R² = 0.62).

The linear correlation coefficient of the dependence in Figure 10 is r = 0.79, which shows a strong positive correspondence between the relative water vapor permeability of the system and the product of the relative water vapor permeability of the single layers. The calculation of the p-value (0.0008 < α = 0.05) is sufficient evidence to conclude that the linear relationship between the studied values is significant. However, using this equation for prediction is not really helpful as the single values, presented in Figures 11 and 12, demonstrate. The calculated value is, for some samples, significantly higher than the measured one. In this case, the checking of the minimal value of the permeability layers of each sample shows again significantly closer values to the reality than the calculated ones and can be used for simple evaluation of the behavior of the complete system of layers.
Figure 11.
Relative water vapor permeability of the system N1 as a function of the product of the single layers’ relative water vapor permeability and the minimal value per sample for comparison.

Figure 12.
Relative water vapor permeability of the system N2 as a function of the product of the single layers’ relative water vapor permeability and the minimal value per sample for comparison.

Moisture transport

The accumulative one-way transport index and the OMMC are used as characteristics of the moisture transport through and within the single layers and the system of layers. The two characteristics are incorporated in the MMT apparatus.²⁰

The accumulative one-way transport index (R_index) reflects the difference in the cumulative moisture transport between the two surfaces of the specimen, in the case of the single layer testing, and between the top and bottom surface of the system. R_index helps to evaluate the risk for moisture penetration through the outer layer of the clothing system towards the inner layers, which decreases the thermal resistance of the system. The results from the measurements of the system of layers are presented as a function of the sum of the results for each of the compound layers, and scatter plot is presented in Figure 13.
Figure 13.
Accumulative one-way transport index of the system as a function of the sum of the single layers’ accumulative one-way transport index.

The OMMC characterizes the overall ability of the samples to transport liquids. The calculation of the dimensionless OMMC involves data for the rate of moisture absorption by the bottom side and its drying speed, together with the R_index. Similar to the R_index, the OMMC of the system was plotted as a function of the sum of the results for the OMMC for each of the single layers. The graph is presented in Figure 14.
Figure 14.
Overall moisture management transfer of the system as a function of the sum of the single layers’ overall moisture management transfer.

The derived linear regression equations for Figures 13 and 14 have very low determination coefficients. This result corresponds to the conclusions of Angelova,¹ where the same “chaotic” distribution of the results for R_index and the OMMC of the systems of two cotton layers was established. The testing of other types of relationship between these characteristics of the systems and the single layers did not give better results.

Conclusions

A comprehensive experimental assessment of the effect of the transfer processes of heat, water vapor, air and liquids through single layers on the transfer processes through three-layer systems of textiles, used for the production of outwear clothing for cold protection, was performed.

It was found that the thermal resistance of the systems is strongly influenced by the thermal resistance of the insulating (non-woven) layer. It was also found that the resulting thermal resistance of the system was lower than the sum of the readings for each layer, due to the decrement of the influence of the air entrapped within the insulating layer.

It was also found that the transport processes of fluids in the through-thickness direction of the system of layers strongly depend on the transfer abilities of the single layers. Regression analysis was used to prove that the information about the transfer of air and water vapor through the single layers can be used for preliminary assessment of the transfer abilities of the system involving these layers.

The results obtained can be used in the design stage of outerwear clothing for cold protection. The method for analysis of the influence of the single layers can be applied to other clothing and textile items produced by using systems of different textile layers.

Sample code	Composition	Thickness, mm	Fabric weight, g/m²	Thermal resistance, m²mK/W	Water vapor resistance, m²Pa/W	Relative water-vapor permeability, %	Air permeability, m/s	Accumulative one-way transport index, mm²/s	Overall moisture management capacity, -
A1	PES 100%	0.56	170.8	1.9	4.4	53.4	0.056	112.63	0.29
A2	PA 90%. PU 10%	0.18	85.5	<1	19.8	22.6	0.012	496.53	0.71
A3	CO 100%	0.95	289.4	3.8	5.2	48.5	0.118	1174.07	0.61
A4	PA 100%	0.16	76.2	<1	28.9	15.1	0.013	655.24	0.71
A5	PA 100%	0.23	128.6	<1	43.4	12.8	0.012	1119.06	0.6
A6	PES 100%	0.25	180.7	<1	7.4	43.2	0.011	13.03	0.04
A7	PES 100%	0.23	148.7	<1	3.7	58.5	0.011	1148.46	0.05
N1	PES 100%	12.81	200.83	225.2	39.2	12.1	3.036	1380.79	0.53
N2	PES 100%	9.56	105.40	145.3	17.5	23.5	3.623	1327.87	0.53
B1	PES 100%	0.10	63.2	<1	4.0	53.3	0.342	672.16	0.74
B2	PES 100%	0.13	64.1	<1	4.6	54.6	0.253	950.72	0.74
B3	CO 100%	0.65	118.4	10.2	3.1	61.8	0.481	1092.18	0.62
B4	PES 100%	0.09	58.6	4.9	2.3	69.7	0.500	1209.31	0.67
B5	PES 100%	0.16	68.3	2.6	3.3	62.3	0.027	972.46	0.7
B6	PES 100%	0.12	62.1	4.7	5.2	56.6	0.158	493.66	0.71
B7	PES 100%	0.09	58.6	4.9	2.3	69.7	0.500	1209.31	0.67

System code	Combination of layers	Thermal resistance, m²mK/W	Water vapor resistance, m²Pa/W	Relative water-vapor permeability, %	Air permeability, m/s	Accumulative one-way transport index, mm²/s	Overall moisture management capacity, -
AN1B1	A1-N1-B1	214.0	45.3	11.4	0.114	589.9	0.53
AN1B2	A2-N1-B2	134.4	44.5	10.6	0.062	545.5	0.55
AN1B3	A3-N1-B3	154.1	37.4	11.5	0.146	579.5	0.51
AN1B4	A4-N1-B4	158.3	42.6	10.2	0.065	293.0	0.38
AN1B5	A5-N1-B5	145.4	42.6	11.6	0.022	289.6	0.38
AN1B6	A6-N1-B6	162.8	44.1	10.3	0.042	0.0	0.00
AN1B7	A7-N1-B7	165.8	40.1	11.5	0.062	0.0	0.00
AN2B1	A1-N2-B1	142.7	29.6	15.5	0.078	331.0	0.44
AN2B2	A2-N2-B2	98.2	36.8	12.0	0.028	150.2	0.22
AN2B3	A3-N2-B3	112.7	23.0	16.7	0.108	252.7	0.36
AN2B4	A4-N2-B4	100.4	36.2	11.6	0.026	28.5	0.09
AN2B5	A5-N2-B5	115.3	38.3	13.3	0.018	65.2	0.13
AN2B6	A6-N2-B6	114.1	33.5	12.9	0.026	0.0	0.00
AN2B7	A7-N2-B7	117.6	29.1	15.2	0.027	0.0	0.00

System code	Standard deviation of
AN1B1	2.14	1.70	0.33	0.012	2.76	0.003
AN1B2	1.19	0.14	0.05	0.006	3.49	0.005
AN1B3	13.92	0.41	0.29	0.011	1.45	0.001
AN1B4	0.48	2.74	1.08	0.065	3.48	0.006
AN1B5	3.55	1.74	0.37	0.007	1.41	0.004
AN1B6	2.44	2.16	0.22	0.001	2.10	N/A
AN1B7	0.65	2.37	0.61	0.001	4.02	N/A
AN2B1	3.88	0.73	1.16	0.004	2.13	0.001
AN2B2	2.14	1.18	0.54	0.002	3.31	0.002
AN2B3	5.20	1.02	0.59	0.005	2.70	0.003
AN2B4	12.01	2.18	0.62	0.003	3.02	0.001
AN2B5	9.01	3.84	1.11	0.001	2.05	0.001
AN2B6	3.37	0.08	0.05	0.002	N/A	N/A
AN2B7	1.79	2.21	0.71	0.003	N/A	N/A

Footnotes

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The authors received no financial support for the research, authorship and/or publication of this article.

References

Angelova

. Textiles and human thermophysiological comfort in the indoor environment, Boca Raton: CRC Press, 2016.

Matusiak

. Thermal insulation properties of single and multilayer textiles. Fibres Text East Eur 2006; 14: 98–112.

Das

Shabaridharan

Biswas

. Study on heat and moisture vapor transmission characteristics through multilayered fabric ensembles. Ind J Fibre Text Res 2011; 36: 410–414.

Yoo HS, Sun G and Pan N. Thermal, protective performance and comfort of wildland firefighter clothing: the transport properties of multilayer fabric systems, performance of protective clothing: issues and priorities for the 21st century: seventh volume. In: Nelson CN and Henry NW (eds), ASTM STP 1386. Society for Testing and Materials, West Conshohocken, PA, 2000, pp.504–518.

Matusiak

Kowalczyk

. Thermal-insulation properties of multilayer textile packages. AUTEX Res J 2014; 14: 299–307.

Ren

Ruckman

. Condensation in three-layer waterproof breathable fabrics for clothing. Int J Cloth Sci Technol 2004; 16: 335–347.

Rossi

Gross

May

. Water vapor transfer and condensation effects in multilayer textile combinations. Text Res J 2004; 74: 1–6.

. The measurement of water vapour transfer rate through clothing system with air gap between layers. Int J Heat Mass Transfer 2008; 44: 375–379.

Yoo

Kim

. Effects of multilayer clothing system array on water vapor transfer and condensation in cold weather clothing ensemble. Text Res J 2008; 78: 189–197.

10.

Epps

. Prediction of single-layer fabric air permeability by statistics modeling. J Test Evaluat 1996; 24: 26–31.

11.

Mohammadi

Banks-Lee

Ghadimi

. Air permeability of multilayer needle punched nonwoven fabrics: experimental method. J Ind Text 2002; 32: 139–150.

12.

Mohammadi

Banks-Lee

Ghadimi

. Determining effective thermal conductivity of multilayered nonwoven fabrics. Text Res J 2003; 73: 802–808.

13.

Mohammadi

Banks-Lee

Ghadimi

. Determining radiative heat transfer through heterogeneous multilayer nonwoven materials. Text Res J 2003; 73: 896–900.

14.

Angelova RA, Reiners P, Georgieva E, et al. Heat and mass transfer through outerwear clothing for protection from cold: influence of geometrical, structural and mass characteristics of the textile layers. Text Res J 2016; 0040517516648507.

15.

ISO 3801:1977. Textiles – woven fabrics – determination of mass per unit length and mass per unit area.

16.

EN ISO 5084:2002. Textiles - determination of thickness of textiles and textile products.

17.

EN ISO 11092:2014. Textiles – physiological effects – Measurement of thermal and water-vapour resistance under steady-state conditions (sweating guarded-hotplate test).

18.

EN ISO 9237:1999. Textiles - determination of permeability of fabrics to air.

19.

AATCC 195:2012. Liquid moisture management properties of textile fabrics.

20.

SDL Atlas. M290 Moisture Management Tester, Instruction Manual. SDL Atlas Inc., 2010.

21.

ISO 9920:2007. Ergonomics of the thermal environment — estimation of thermal insulation and water vapour resistance of a clothing ensemble.

22.

Kyosov

Angelova

Stankov

. Numerical modeling of the air permeability of two-layer woven structure ensembles. Text Res J, 2016; 86: 2067–2079.

23.

Clayton

. The measurement of the air permeability of fabrics. J Text Inst Trans 1935; 26: T171–T186.

24.

Angelova

Maintaining the workers comfort and safety in extreme temperatures industrial environment. In: Stankov

Fracastoro

(eds). Proceedings of EuroAcademy on ventilation and indoor climate “industrial ventilation”, Pamporovo, Bulgaria, 18–25 October 2007, pp. 197–205. Avangard Prima, Sofia, Bulgaria.

25.

Holmér

. Evaluation of cold workplaces: an overview of standards for assessment of cold stress. Ind Health 2009; 47: 228–234.

26.

Rumsey

. Statistics for dummies, Hoboken, NJ: John Wiley & Sons, 2011.

27.

Hes

. Non-destructive determination of comfort parameters during marketing of functional garments and clothing. Indian J Fiber Textile Res 2008; 33: 239–245.