# Correlation of Air Permeability to Other Breathability Parameters of Textiles

^{*}

## Abstract

**:**

## 1. Introduction

^{3}/kg) and its density ρ (kg/m

^{3}) depend on its pressure p (Pa) and temperature T (K), with so-called gas constant r (J/(kg·K)) being the constant of proportionality. As for small deviations of the state variables, their influence on the result is negligible, but in general, these influences must be taken into account. It is true that in the laboratory measurements of porous materials the pressure gradient is small, which means the effect of pressure variation on the volumetric flow rate is negligible. Conversely, when measuring dense and poorly permeable materials, the pressure gradient is larger and the measured volumetric flow rate should be converted into a selected standard state. The ideal approach is to express the gas/vapour flow rate as a mass flow rate (kg/s), since this, unlike the volumetric flow rate (m

^{3}/s), does not depend on the state variables of the medium being measured. In addition, variations in the ambient state (barometric pressure, temperature, humidity) objectively affect the actual volumetric flow rate, as discussed below.

#### 1.1. Air Humidity Effect

_{2}+ 21% O

_{2}) and water vapour (only a few grams of dry air), and its density is therefore determined by the formula according to [3] and others as

- ρ (kg/m
^{3}): Calculated density - B (kPa): Barometric pressure
- T (K): Temperature
- φ = pp/pp″ (-): Relative air humidity (its saturation with vapour) [3 and others]
- pp″ (Pa) = f(T): Vapour pressure [6]
- pp (Pa) = f(T,φ): Partial vapour pressure in unsaturated air
- rv (J/(kg·K)): Air gas constant = 287.1
- rp (J/(kg·K)): Water vapour gas constant = 461.8

^{3}, i.e., by 1.6%.

#### 1.2. Air Flow Rate Measurement

- p (Pa): Pressure
- T (K): Absolute temperature
- V (m
^{3}/s): Volumetric flow rate - ρ (kg/m
^{3}): Density - r (J/(kg·K)): Gas constant
- index c: Calibration condition
- index m: Measurement condition

#### 1.3. Viscosity Effect

#### 1.4. Breathability/Permeability Parameters

^{3}/s) through the sample area (m

^{2}). In physics, or rather thermodynamics [7], this quantity is called the volumetric flow rate density:

^{3}/(m

^{2}·s) = m/s.

^{2}·s).

#### 1.5. Air Permeability

^{3}/s) per area unit (m

^{2}), i.e., as the velocity of flow through a surface (m/s) according to (4). In order to compare different results obtained under different conditions, it is necessary to convert the observed data to a suitable standard value.

^{3}/s) = f(Δp(Pa)),

#### 1.6. Water Vapour Permeability

#### 1.6.1. Theory

- m (kg): Diffused vapour
- δ (s): Water vapour diffusion coefficient (building materials in the order of magnitude of 10
^{−10}) - S (m
^{2}): Area of flow - t (s): Time
- d (m): Thickness
- Δp (Pa): Pressure gradient

^{2}·s)

^{2}·day)

#### 1.6.2. Water Vapour Resistance—SGHP Method

^{2}·Pa/W] in accordance with ISO 11092 [8]. The skin model is thermally insulated so that the heat required to make distilled water evaporate passes only towards the material being tested. The entire instrument must be housed in an air-conditioned chamber to achieve steady-state thermal and humidity conditions. The velocity of flow over the sample is constant, but it must be noted that the rate of removal of the passing vapour is largely dependent on the velocity of the ambient air. This method is definitely one of the basic standard methods for determining the thermal and evaporative resistance of fabrics.

- p″ (Pa): Partial (saturated) water vapour pressure upstream of the test sample
- pa (Pa): Partial water vapour pressure downstream of the test sample
- S(m
^{2}): Measurement surface - H (W/m
^{2}): Heat flow rate - ΔHe (W/m
^{2}): Heat flow adjustment due to loss - Ret (Pa·m
^{2}/W): Water vapour resistance of the sample - $\mathrm{Ret}0$ (Pa·m
^{2}/W): Adjustment − resistance of flow through cellophane = instrument constant

^{2}·Pa/W = m

^{2}·N/m

^{2/}(N·m/s) = s/m

^{3}/s) = f(Δp (Pa)).

- (1)
- Setting the partial pressure of saturated air vapour downstream of the sample (φ = 1) is pointless since the driving pressure gradient Δp is zero in that case.
- (2)
- Setting the partial pressure downstream of the sample to zero, i.e., absolutely dry air (φ = 0), is technically challenging; in practice, drying the air to the dew point of +3 °C—i.e., pp = 758 Pa, is commonly used. Thus, the maximum pressure gradient for a temperature of +35 °C is in fact 4866 Pa.

## 2. Hypothesis

## 3. Measurements

_{et}= 35–36 m

^{2}·Pa/W = 35–36 s/m or to a multilayer sample

_{et}= 35–45 m

^{2}·Pa/W = 35–45 s/m.

^{3}/(m

^{2}·s) and, when converted to mass units is (for a saturated vapour density of ρ = 30.35 g/m

^{3}at 30 °C)

^{2}·s) = 3.059 kg/(m

^{2}·h).

^{2}·Pa/W = 4.5 s/m.

^{2}·s), i.e., 0.38 m/s, which is about 13.5 times more than in the case of vapour. Vapour viscosity is 7–35 times greater than that of air; subsequently, a flow rate lower by this ratio can be expected in the same sample and under the same ambient conditions. The result for vapour therefore corresponds to the result for air to a large extent.

#### 3.1. Definition of Air Permeability for Various Pressure Gradients

- (1)
- As this is a quadratic function, to capture its character it is necessary to measure at least 3 points. As a matter of course, the more points are measured, the more accurate the quadratic regression.
- (2)
- The absolute element C in the quadratic regression should be zero since at zero velocity (w) there is zero resistance (Δp)—this is also another point of the quadratic relationship being searched for. A nonzero value of C indicates some error in the measurement or evaluation and should be detected and corrected. If, for example, the value of C is nonzero, but it is small compared to the other coefficients A, B, it can be neglected as a result.
- (3)
- In another substitution of the relationship between flow rate and pressure gradient, the power function Δp = f(w · n) was used in [22], where n = 1.45—i.e., 1 < n < 2. It can be concluded that such a pressure resistance function also contains a combination of the first and second powers of the velocity.
- (4)
- For geometrically simple shapes (for example, perforated sheet metal), this relationship can be obtained by numerical simulation; for complicated structures (fabrics, knitted fabrics, filter layer, etc.), it must be determined experimentally. However, specialized programs are already available for the direct simulation of the flow through even such complicated real-life layers. A wealth of useful information regarding this can be found for example in [23].

#### 3.2. Measurement Results

## 4. Summary

- (a)
- For correct physical measurements of volumetric flow, all parameters that may affect the measurement results should be reported. In particular, barometric pressure, temperature and relative humidity in the laboratory should be precisely defined.
- (b)
- Use the correct naming convention for air permeability measurements, volumetric flow rate density (m/s) or mass flow rate density (kg/(m
^{2}·s)), see (6) and (7). To assess water vapour resistance (evaporative resistance), Ret simpler expression (11): m^{2}·Pa/W = m^{2}·N/m^{2}/(N·m/s) = s/m should be used, which is the inverse value of the volumetric flow rate density m/s. The result of gravimetric measurement (12) in g/(m^{2}·24 h) can easily be converted to the mass flow rate density kg/(m^{2}·s) and, if necessary, subsequently to mass flow rate density (11). - (c)
- For the evaluation of water permeability measurements, choose the method that best simulates the actual rain resistance. Thus, the measured parameters for determining the resistance of a sample against defined rain should be the period of time until the first drop appears on the reverse of the sample and the amount of water soaked into the sample during the test. Measuring pressure in metres is nonsense; the correct statement should be “hydrostatic pressure of a column of water of height”.
- (d)
- The determination of permeability should be based on the measured flow characteristics of permeability m (kg/s) = f (Δp (Pa)) for both air and water vapour, which provide a better indication of the nature of permeability than single-point measurements. From such more comprehensive data, an attempt is made to verify or refute the hypothesis of a correlation of flow characteristics for air and water vapour. The procedure is given for a single test sample as an example.

- -
- low air permeability from the outside (wind),
- -
- high water vapour permeability from the inside (perspiration) and
- -
- low water permeability from the outside (rain).

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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Air [3] | Water Vapour [6] | ||||
---|---|---|---|---|---|

Temperature | 10^{6}·Dyn·Visc. | Density | 10^{6}·Dyn·Visc. | Density | Vapour Pressure |

°C | kg/(ms) | kg/m^{3} | kg/(ms) | kg/m^{3} | Pa |

0 | 17.168 | 1.252 | 9.216 | 0.0048 | 619 |

10 | 17.756 | 1.206 | 9.461 | 0.0094 | 1244 |

20 | 18.404 | 1.164 | 9.727 | 0.0173 | 2370 |

30 | 18.816 | 1.128 | 10.01 | 0.0304 | 4303 |

40 | 19.228 | 1.092 | 10.31 | 0.0512 | 7482 |

50 | 19.669 | 1.058 | 10.62 | 0.0831 | 12,515 |

60 | 20.111 | 1025 |

φ (−) | 1.0 | 0.8 | 0.6 | 0.4 | 0.2 | 0.0 | |
---|---|---|---|---|---|---|---|

t (°C) | |||||||

10 | 1228 | 982 | 736 | 491 | 245 | 0 | |

15 | 1708 | 1366 | 1025 | 683 | 342 | 0 | |

20 | 2337 | 1870 | 1402 | 935 | 467 | 0 | |

25 | 3168 | 2534 | 1901 | 1267 | 634 | 0 | |

30 | 4238 | 3390 | 2543 | 1695 | 848 | 0 | |

35 | 5624 | 4499 | 3374 | 2250 | 1125 | 0 | |

40 | 8342 | 6672 | 5004 | 3336 | 1668 | 0 |

φ | % | 20 | 30 | 60 | 90 | 100 |
---|---|---|---|---|---|---|

pp | Pa | 1668 | 2503 | 5005 | 7508 | 8342 |

Δp | Pa | 6674 | 5839 | 3337 | 834 | 0 |

m | g/(m^{2}·d) | 6646 | 6415 | 3630 | 1599 | 0 |

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**MDPI and ACS Style**

Adámek, K.; Havelka, A.; Kůs, Z.; Mazari, A. Correlation of Air Permeability to Other Breathability Parameters of Textiles. *Polymers* **2022**, *14*, 140.
https://doi.org/10.3390/polym14010140

**AMA Style**

Adámek K, Havelka A, Kůs Z, Mazari A. Correlation of Air Permeability to Other Breathability Parameters of Textiles. *Polymers*. 2022; 14(1):140.
https://doi.org/10.3390/polym14010140

**Chicago/Turabian Style**

Adámek, Karel, Antonin Havelka, Zdenek Kůs, and Adnan Mazari. 2022. "Correlation of Air Permeability to Other Breathability Parameters of Textiles" *Polymers* 14, no. 1: 140.
https://doi.org/10.3390/polym14010140