# The Correlation between Air and Water Vapour Permeability of Textiles

^{*}

## Abstract

**:**

## 1. Introduction

#### Air Permeability

^{3}/s)/m

^{2}= m/s

- p (Pa) = absolute pressure;
- v (m
^{3}/kg) = specific volume; - T (K) = absolute temperature;
- r (J/(kg · K)) = gas constant;
- m (kg) = mass;
- V (m
^{3}) = volume.

^{2}. It is independent of state quantities; thus, the conversion is simple:

- B (Pa) = barometric pressure;
- ±Δp (Pa) = variance in barometric pressure.

- M = measured value;
- C = calibration value (or any standard value).

- r (m) = the radius of the relevant sphere;
- v (m) = the height of the relevant segment.

^{2}+ v

^{2})/(2 · v).

^{2}; moreover, for example, when v/a = 0.01, the increase in the flow area of the spherical segment compared to the initial flat circle is 0.01%, which can also be neglected. For v/a = 0.1, the increase in the segment area is 1%, which is also in the range of the usual measurement error.

- (1)
- The diffusion flow J is proportional to the gradient of concentration ∂c/∂x, with proportionality constant D (m
^{2}/s) as the so-called diffusion coefficient:J = D · ∂c/∂x

- (2)
- The characteristics of the concentration change over time. Some argue that in the used device, both of the concentrations, before and after sampling, remain constant (at least theoretically; however, this has not been verified).

^{2}). As for the airflow above the sample, when measuring the air permeability of gases, it is better to use mass flow instead of volume flow. For values in g/(m

^{2}· day), as measured by the device, it is necessary to recalculate them into legitimate SI measuring units as kg/(m

^{2}· s). This is the same for air permeability. The relation between mass and volume flow is given by (3). Instead of such a simple quantity, the standard [8] contains a complicated quantity for “evaporating resistance” Ret (m

^{2}· Pa/W), and probably more precisely, “the resistance of the vapour flow through the sample”. Using basic SI units, the resistance Ret is in (s/m), which is the reciprocal value of the vapour flow through the sample. This is the vapour permeability for the sample. This result is logical since flow and flow resistance are reciprocal values.

^{2}· h · Pa). It is the reciprocal value of the evaporating resistance above and divided by the so-called latent heat; this heat is the evaporative heat q (J/kg), generally used in thermo-mechanics. It is the heat that is necessary for the evaporation of water at the saturation limit (boiling) into the saturated vapour. So, suddenly, here is the heat (enthalpy) mentioned, contained in the passing vapour, which can be understood as the heat passed through the sample, as well as some cooling. Introducing legal SI measuring units, the result is simple (s/m); in addition, the dimensions of such vapour permeability Wd are the same as for the evaporating resistance Ret, more precisely, the flow resistance. However, according to the standard, the two reciprocal values have the same dimensions.

^{2}are fixed above the water’s surface at the upper edge of the cups. The carousel is turning so that every 5 min, one cup is weighed to determine the mass (water) in order to determine the water vapour permeability. In the beginning, the samples are initially conditioned for the time of half an hour. The unit is permanently shut air-tight and isothermally, which means that no condensation of the diffused vapour can take place. In the inner volume, the adjusted and required air temperature and relative humidity are kept, i.e., the lower pressure of unsaturated air behind the sample and higher pressure of saturated vapour over the water level in the cup before the sample. The penetrated vapour is led away by airflow, the velocity of which is also reputedly defined. However, the air velocity is controlled by a simple flap, only in the range of one order.

## 2. Materials and Methods

#### 2.1. Air Permeability of Sample No. 1

^{2}, w), see, e.g., [9]. At low velocities, the linear term is prevailing (Darcy’s law for slow flow in porous structures). On the contrary, at higher velocities, the influence of the quadratic term is increasing (Nikuradse’s or Moody’s law for flows through orifices, flows around bodies, etc.). The real flow through the textile sample is a combination of both terms.

#### 2.2. Water Vapour Permeability for Sample No. 1

^{2}· day) are recalculated into the volume flow (m

^{3}/(m

^{2}· s) = m/s) using the specific volume of the saturated vapour v″ = 19.55 m

^{3}/kg (for 40 °C).

## 3. Results

#### 3.1. Correlation of Air–Vapour

#### 3.2. Permeability Measurement at Higher Pressure Gradients

#### 3.3. Checking Measurement of Water Vapour Permeability

- y = −7168.7x
^{2}− 19,091x + 28,129R^{2}= 0.9782; - y = −26,926x + 29,841R
^{2}= 0.9755.

#### 3.4. Vapour Diffusion

- m (kg) diffused vapour;
- S (m
^{2}) sample area; - D (m) sample thickness;
- t (s) time of diffusion;
- Δp (Pa) pressure gradient;
- δ (s) diffusion coefficient.

^{−9}in the air at 0 °C or 0.125–0.179 × 10

^{−9}in rock wool. Another source presents a value of 0.1 × 10

^{−9}for glass wool. Therefore, all available values are in the range of one order, but the relative differences are quite high, within 25–78%. The vapour diffusion directly in the air also corresponds to the upper limit of the range, presented for fibrous insulating materials. At a temperature of 0 °C, as was used in [3], the pressure of saturated water vapour is 611 Pa. This is more than of one order less than the temperature of 40 °C (7375 Pa) used in isothermal clothing tests.

- -
- Slightly increases with the increase in φ for low-pressure gradients (low φ);
- -
- Is practically constant for medium-pressure gradients;
- -
- Increases by a jump for φ = 90%.

## 4. Conclusions

^{2}· s) or density of volume flow (m

^{3}/(m

^{2}· s), modified as (m/s), should be used.

^{2}· s/kg) and (s/m), respectively.

- -
- Setting, reading, and evaluation of measurement;
- -
- From the measured values, variable values of the diffusion coefficient for different pressure gradients were found.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Sample | No. 1 | No. 2 |
---|---|---|

description | grey strip | green check |

material | 100% wool | 45% wool, 55% PES |

warp sett | 29 threads/cm | 27 threads/cm |

weft sett | 20 threads/cm | 24 threads/cm |

warp threads | 31.2 tex | 38.1 tex |

weft threads | 29.6 tex | 34.5 tex |

density | 580 threads/cm^{2} | 648 threads/cm^{2} |

areal weight | 173 g/m^{2} | 204 g/m^{2} |

thickness | 0.265 mm | 0.47 mm |

porosity | 36.59% | 43.43% |

Sample | Cubical Correlation | R^{2} |
---|---|---|

Water | y = 111.452x^{3} − 191.791x^{2} + 71.810x + 15,456 | 0.9996 |

Sieve | y = 48.574x^{3} − 84.066x^{2} + 34.385x + 4162.1 | 0.9998 |

Sample 1 | y = 45.198x^{3} − 81.925x^{2} + 38.545x + 549.91 | 0.9955 |

Sample 2 | y = 26.395x^{3} − 46.249x^{2} + 17.492x + 4263.3 | 0.9989 |

Rel. Humid. behind Sample | 20% | 90% |
---|---|---|

pressure gradient (40 °C) | 5900 Pa | 740 Pa |

water | 5.33 × 10^{−10} | 1.39 × 10^{−10} |

metallic sieve | 1.95 × 10^{−10} | 0.56 × 10^{−10} |

sample 1 | 1.43 × 10^{−10} | 0.42 × 10^{−10} |

sample 2 | 1.38 × 10^{−10} | 0.42 × 10^{−10} |

water vapour | 1.78 × 10^{−10} |

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## Share and Cite

**MDPI and ACS Style**

Adámek, K.; Havelka, A.; Kůs, Z.; Mazari, A.
The Correlation between Air and Water Vapour Permeability of Textiles. *Coatings* **2023**, *13*, 163.
https://doi.org/10.3390/coatings13010163

**AMA Style**

Adámek K, Havelka A, Kůs Z, Mazari A.
The Correlation between Air and Water Vapour Permeability of Textiles. *Coatings*. 2023; 13(1):163.
https://doi.org/10.3390/coatings13010163

**Chicago/Turabian Style**

Adámek, Karel, Antonin Havelka, Zdenek Kůs, and Adnan Mazari.
2023. "The Correlation between Air and Water Vapour Permeability of Textiles" *Coatings* 13, no. 1: 163.
https://doi.org/10.3390/coatings13010163