# Methods for Determining Mold Development and Condensation on the Surface of Building Barriers

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emissions to the atmosphere, require newly designed buildings to be more airtight and have better thermal insulation. At the same time, there are still older facilities that do not meet the requirements for new facilities. That is why (with a similar method of use) older buildings function differently due to the lower insulation of external barriers and windows which are not well sealed, as opposed to new buildings with high insulation of external barriers and very well-sealed windows.

_{Rsi}resulting from the insulation of the barrier (its construction), and the factor f

_{Rsi,max}resulting from the humidity conditions prevailing in the room in the so-called critical month. In order to meet the design condition (to eliminate the risk of mold growth), the minimum thermal insulation of the barrier R

_{T,min}or the maximum value of the heat transfer coefficient U

_{max}need to be calculated. In practice, this involves the need to modernize the barrier, which in turn leads to the generation of costs for the task.

_{Rsi}parameter, the calculation of internal humidity φ

_{i}, humidity of the beginning of condensation φ

_{i,con}, the permissible humidity in the room φ

_{i,max}, with observance of the standard condition to avoid mold growth, the external temperature eliminating condensation Θ

_{e}

_{,con}, and the minimum thermal insulation of the barrier eliminating condensation U

_{con}.

## 2. Materials and Methods

#### 2.1. Methods for Preventing Mold Growth on Building Barriers

- the first method (M1) involves the procedure for determining the temperature factors f
_{Rsi}and f_{Rsi,max}; - the second method (M2) consists of comparing the relative humidity of air φ
_{i,max}and φ_{i}; - the third method (M3) uses the comparison of barrier temperatures Θ
_{si}and Θ_{si},_{min}; - the fourth method (M4) consists of comparing the air vapor pressures p
_{i,max}and p_{i}.

#### 2.1.1. M1—Avoiding Mold Growth on the Basis of Determining the Minimum Allowable Temperature Factor f_{Rsi,min}-Procedure According to PN-EN ISO 13788 [24]

- Define the average monthly value of the outside air temperature Θ
_{e}. - Define the outside air humidity: the average monthly water vapor pressure can be calculated using the equations:$${p}_{e}={\phi}_{e}\cdot {p}_{sat}\left({\Theta}_{e}\right)$$
- p
_{e}—average monthly water vapor pressure; - φ
_{e}—average monthly relative humidity of air; - p
_{sat}—pressure of water vapor at saturation; - Θ
_{e}—average monthly value of the outside air temperature

- Determine the indoor air temperature Θ
_{i}(according to the purpose of the room according to national standards) - Calculate the partial pressure of water vapor in the room p
_{i}on the basis of Δp or take the relative humidity in the air-conditioned room as constant, taking into account the correction for the safety margin:Based on the internal humidity class (from 1 to 5):$${p}_{i,ISO}={p}_{e}+\mathsf{\Delta}p\cdot 1.1$$Based on relative humidity in the room (φ_{i}):$${p}_{i,ISO}=\left({\phi}_{i}+0.05\right)\cdot {p}_{sat}\left({\Theta}_{i}\right)$$_{i}-assumed average monthly value of relative humidity of the indoor air - Calculate the minimum permissible pressure of saturated water vapor on the barrier surface p
_{sat}(Θ_{si}) (corresponding to the surface temperature, Θ_{si}). The maximum permissible relative humidity on the surface is assumed φ_{si}= 0.8:$${p}_{sat}\left({\Theta}_{si}\right)=\frac{{p}_{i,ISO}}{0.8}$$ - Determination of the minimum permissible barrier surface temperature Θ
_{si}, min (based on psat Θ_{si}):$${p}_{sat}\left({\Theta}_{si}\right)\to \left(ISO\left[24\right]-AnnexE\right)\to {\Theta}_{si,min}$$ - Calculation of the minimum allowable temperature factor f
_{Rsi,min}:$${f}_{Rsi,min}=\frac{{\Theta}_{si,min}-{\Theta}_{e}}{{\Theta}_{i}-{\Theta}_{e}}$$ - Determination of the critical month and f
_{Rsi,max}(f_{Rsi,max}is the highest value of f_{Rsi,min}from 12 months). - Design condition:$${f}_{Rsi}>{f}_{Rsi,max}$$$${f}_{Rsi}=\frac{{U}^{-1}-{R}_{si}}{{U}^{-1}}=\frac{\frac{1}{U}-{R}_{si}}{\frac{1}{U}}=\frac{{R}_{T}-{R}_{si}}{{R}_{T}}$$
- R
_{T}—thermal resistance of barrier; - R
_{i}—heat transfer resistance on the internal surface.

- If the design condition is not met, we calculate the minimum thermal insulation of the barrier R
_{T,min}, or maximum value of the heat transfer coefficient U_{max}:$${f}_{Rsi,max}=\frac{{R}_{T,min}-{R}_{si}}{{R}_{T,min}}\text{\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}}\to \text{\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}}{R}_{T,min}=\frac{{R}_{si}}{1\text{\hspace{0.17em}}-{f}_{Rsi,max}}$$$${f}_{Rsi,max}=\frac{\frac{1}{{U}_{max}}-{R}_{si}}{\frac{1}{{U}_{max}}}\text{\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}}\to \text{\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}}{U}_{max}=\frac{1-{f}_{Rsi,max}}{{R}_{si}}$$

_{R}= f

_{Rsi}−f

_{Rsi,min}. A positive value (Δf

_{R}> 0) means no risk of mold growth but also shows a reserve of safe barrier function. However, a negative value (Δf

_{R}< 0) means a threat of mold growth and shows the depth of this phenomenon in the critical month and other months.

#### 2.1.2. M2—Avoiding Mold Growth on the Basis of Determining the Permissible Humidity in the Room φ_{i,max}

_{i,max}, so that there is no mold growth on the wall surface and that the standard condition is observed”. According to the standard procedure, if the design condition is not met, the minimum thermal insulation of the barrier or the maximum value of the heat transfer coefficient (Equations (8) and (9)) needs to be calculated. This is a one-way procedure because it gives the user no alternative. It boils down to increasing the thermal insulation of the barrier, that is, carrying out retrofitting. This means that mold development will be eliminated only after these construction works have been carried out. This treatment requires time, an appropriate period of the year to carry it out, permission to perform (historic buildings) and considerable funding. However, the user expects to eliminate this phenomenon as soon as possible, recommendations for use and financial estimates. The following method gives this possibility.

_{con}occurs, the surface temperature of barrier Θ

_{si}and the air dew point temperature Θ

_{dp},

_{con}are equal. Of these three quantities, the easiest way is to determine the surface temperature of barrier Θ

_{si}. It is calculated using the temperature factor f

_{Rsi}or the heat transfer coefficient U. The temperature factor of the barrier f

_{Rsi}is given by the formula:

_{si}, we determine the condensation pressure p

_{i,con}(equal to the saturated water vapor pressure related to the septum surface temperature) [2]:

_{i,ISO}can be 80% of the pressure specified in the formula (14):

_{i}or 10% moisture increase Δp. The permissible relative humidity of the air in the room φ

_{i,max}, for a case of 5% moisture, we will determine from the relationship analogous to that in Equation (3):

_{i,ISO}, comparing Equations (15) and (16) we get:

_{i,max}, for a case of 10% moisture increase, we determine from the equation:

_{max}, we determine as in Equation (2):

_{i,ISO}, we get:

_{i,max}is obtained after inserting Δp

_{max}(Equation (22)) in Equation (19):

#### 2.1.3. M3—Avoiding Mold Growth on the Basis of Characteristic Temperatures

_{si}and the minimum permissible barrier surface temperature Θ

_{si,min}, it is possible to formulate a design condition to avoid mold growth:

_{si}) is calculated from Equation (13):

_{si,min}will be determined on the basis of the standard procedure given in points 1–6 (Equations (1)–(4b)). If the design condition is not met, we calculate the maximum value of the heat transfer coefficient U

_{max}. This factor is derived from the minimum surface temperature of the barrier and results from the conversion of the modified Equation (29):

_{i}(m) > 0) means no risk of mold growth (meeting the design condition) and informs about the value of a safe surface temperature reserve. However, a negative value (ΔΘ

_{i}(m < 0) means a threat of mold growth and informs how many degrees the temperature of the barrier is lower in the critical month and in other months in which this threat occurs.

_{e,min}at which mold growth will begin on the barrier surface. To determine it, Equation (29) needs to be modified and then converted.

#### 2.1.4. M4—Avoiding Mold Growth on the Basis of Determining the Characteristic Water Vapor Pressure

_{i}and the maximum allowable water vapor pressure p

_{i,max}, it is possible to formulate a design condition to avoid mold growth:

_{i,max}is calculated from the equation below, in which the maximum moisture increase Δp

_{max}was determined in Equation (22):

_{i}then the maximum permissible vapor pressure p

_{i,max}is calculated from the equation:

_{i}will be determined from Equation (24).

#### 2.2. Methods for Checking the Presence of Water Vapor Condensation on Building Barriers

- method 1 (M1
_{con}) based on a comparison of temperature factors f_{Rsi}and f_{Rdp}; - method 2 (M2
_{con}) based on comparison of relative humidity φ_{i,con}and φ_{i}; - method 3 (M3
_{con}) involving the comparison of the barrier temperature Θ_{si}and the air dew point temperature Θ_{dp}and - method 4 (M4
_{con}) based on comparing the water vapor pressure of p_{i,con}and p_{i}.

#### 2.2.1. M1_{con}—Avoiding Condensation on the Basis of Determining the Air Dew Point Temperature Factor f_{Rdp}

_{Rsi}resulting from the insulation (construction) of the barrier and the factor f

_{Rdp}resulting from humidity conditions in the room. To avoid condensation, the air dew point temperature should not exceed the room surface temperature. On this basis, it is possible to formulate a design condition to avoid surface condensation:

_{Rsi}can be determined on the basis of the known value of the heat transfer coefficient (U) according to formula (7) or the known value of the barrier surface temperature Θ

_{si}according to formula (11). The barrier surface temperature is calculated according to formula (13). The temperature factor f

_{Rdp}is calculated on the basis of the dew point temperature Θ

_{dp}according to the formula:

_{dp}is determined on the basis of the actual water vapor pressure in the room p

_{i}:

_{i}shall be determined on the basis of pressure increase Δp according to formula (24) or on the basis of relative humidity in room φ

_{i}according to the following formula:

#### 2.2.2. M2_{con}—Avoiding Condensation on the Basis of Determining Condensation Humidity φ_{i,con}

_{i,con}understood as relative humidity of the surface should not exceed the actual pressure of the water vapor in the room. The design condition to avoid surface condensation can be formulated as follows:

_{si}:

_{i}in this formula is determined on the basis of the pressure increase Δp according to formula (24) or on the basis of relative humidity in the room φ

_{i}according to formula (40).

#### 2.2.3. M3_{con}—Avoiding Condensation on the Basis of Characteristic Temperatures

_{si}and the air dew point temperature in the room Θ

_{dp}, it is possible to formulate a design condition to avoid surface condensation:

_{si}in the following months will be calculated from Equation (29). However, the air dew point temperature in the room Θ

_{dp}in subsequent months will be determined according to the relationship (39) on the basis of the actual water vapor pressure in the room p

_{i}determined according to formulas (24 or 40). Based on this design condition, it is possible to determine the difference between the temperature at the barrier surface and the air dew point temperature in the following months of the year:

#### 2.2.4. M4_{con}—Avoiding Condensation on the Basis of Determining the Characteristic Water Vapor Pressure

_{i}and the water vapor condensation pressure on the surface of the barrier p

_{i,con}, it is possible to formulate a design condition to avoid condensation:

_{i,con}in the following months will be calculated from Equation (43) on the basis of the barrier surface temperature Θ

_{si}calculated according to formula (29). However, the actual water vapor pressure in the room (p

_{i}) in the following months will be determined according to the formula (24 or 40). Based on this design condition, it is possible to determine the difference between the water vapor condensation pressure on the barrier surface and the air vapor pressure in the following months of the year:

## 3. Results and Discussion

_{e}, and relative humidity of the outdoor air φ

_{e}, according to the Rzeszów-Jasionka meteorological station [25], indoor air temperature Θ

_{i}= 20 °C, moisture increase in a room for the 4th class of internal humidity Δp = 10.8 hPa [24], external wall (50 cm thick made of solid brick) with a heat transfer coefficient U = 1.20 W/(m

^{2}

^{.}K); heat transfer resistance on the internal surface of the barrier R

_{si}= 0.25 (m

^{2}K)/W [24]. Data for calculations are presented in Table 5.

_{Rsi}; barrier temperature Θ

_{si}; maximum water vapor pressure in the room p

_{i,max}; maximum relative air humidity in the room φ

_{i,max}, while for the indoor microclimate it is: minimum permissible barrier temperature factor, f

_{Rsi,min}; minimum permissible barrier temperature Θ

_{si,min}; water vapor pressure in the p

_{i}room; relative air humidity in the room φ

_{i}, (Table 6).

_{Rsi}; barrier temperature, Θ

_{si}; condensation pressure of water vapor p

_{i,con}; condensation humidity in the room, φ

_{i,con}, while for the internal microclimate it is: barrier temperature factor f

_{Rdp}; dew point temperature Θ

_{dp}; water vapor pressure in the p

_{i}room; relative air humidity in the room φ

_{i}, (Table 7).

#### 3.1. Mold Growth on the Surface of the Barrier

#### 3.2. Condensation on the Surface of the Barrier

## 4. Conclusions

_{R}; Δφ; ΔΘ; Δp) having negative values show how much the given quantity has been exceeded, which is associated with the phenomenon of mold or condensation. However, in the case of positive values obtained, they show what given value a supply has in relation to the boundary value. The calculation methods presented allow for a comprehensive assessment of the risk of mold and condensation on the surface of building barriers. Methods not described in the standard (ISO [24]) are of particular importance here. The result of the standard method (in the case of a negative value of the Δf

_{R}coefficient) is the answer in the form of information about the need to retrofit the analyzed building barrier. In contrast, "non-standard" methods allow for a quantitative indication of the cause of the phenomenon (in the form of, for example, too high relative humidity in the room) and protection against the risk of mold and condensation by reducing this humidity in a specific period of time (in months in which the values Δφ are negative). This approach to the problem may be of particular importance in buildings where, for various reasons, the retrofitting of barriers is not possible (e.g., in some historic buildings under conservation protection).

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Graphs of characteristic parameters in the phenomenon of mold development; (

**a**) method M1; (

**b**) method M2; (

**c**) method M3; (

**d**) method M4.

No. | Mold Growth | Beginning (End) of Mold Growth | Design Condition (No Mold Development) |
---|---|---|---|

1. | f_{Rsi} < f_{Rsi,min} | f_{Rsi} = f_{Rsi,min} | f_{Rsi} > f_{Rsi,min} |

2. | φ_{i,max} < φ_{i} | φ_{i,max} = φ_{i} | φ_{i,max} > φ_{i} |

3. | Θ_{si} < Θ_{si,min} | Θ_{si} = Θ_{si,min} | Θ_{si} > Θ_{si,min} |

4. | p_{i,max} < p_{i} | p_{i,max} = p_{i} | p_{i,max} > p_{i} |

**Table 2.**Conditions for mold growth on the surface of a building barrier in the form of a parameter difference (Δ).

No. | Mold Growth | Beginning (End) of Mold Growth | Design Condition (No Mold Development) |
---|---|---|---|

1. | Δf_{R} = (f_{R i} − f_{Rsi,min}) < 0 | Δf_{R} = 0 | Δf_{R} = (f_{Rsi} − f_{Rsi,min}) > 0 |

2. | Δφ = (φ_{i,max} − φ_{i}) < 0 | Δφ = 0 | Δφ = (φ_{i,max} − φ_{i}) > 0 |

3. | ΔΘ = (Θ_{si} − Θ_{si,min}) < 0 | ΔΘ = 0 | ΔΘ = (Θ_{si} − Θ_{si,min}) > 0 |

4. | Δp = (p_{i,max} − p_{i}) < 0 | Δp = 0 | Δp = (p_{i,max} − p_{i}) > 0 |

No. | A Condition of Occurrence of Condensation | Beginning (End) of Condensation | Design Condition (No Condensation) |
---|---|---|---|

1. | f_{Rsi} < f_{Rdp} | f_{Rsi} = f_{Rdp} | f_{Rsi} > f_{Rdp} |

2. | φ_{i,con} <φ_{i} | φ_{i,con} =φ_{i} | φ_{i,con} >φ_{i} |

3. | Θ_{si} < Θ_{dp} | Θ_{si} = Θ_{dp} | Θ_{si} > Θ_{dp} |

4. | p_{i,con} < p_{i} | p_{i,con} = p_{i} | p_{i,con} > p_{i} |

**Table 4.**Conditions for the occurrence of surface condensation on a building barrier in the form of a difference of parameters (Δ).

No. | A Condition of Occurrence of Condensation | Beginning (End) of Condensation | Design Condition (No Condensation) |
---|---|---|---|

1. | Δf_{Rcon} = (f_{Rsi} − f_{Rdp}) < 0 | Δf_{Rcon} = 0 | Δf_{Rcon} = (f_{Rsi} − f_{Rdp}) > 0 |

2. | Δφ_{con} = (φ_{i,con} − φ_{i}) < 0 | Δφ_{con} = 0 | Δφ_{con} = (φ_{i,con} − φ_{i}) > 0 |

3. | ΔΘ_{con} = (Θ_{si} − Θ_{dp}) < 0 | ΔΘ_{con} = 0 | ΔΘ_{con} = (Θ_{si} − Θ_{dp}) > 0 |

4. | Δp_{con} = (p_{i,con} − p_{i}) < 0 | Δp_{con} = 0 | Δp_{con} = (p_{i,con} − p_{i}) > 0 |

Month | Θ_{e} | p_{sat.e} | φ_{e} | p_{e} | Δp | Θ_{i} | p_{sat.i} | U | R_{si} |
---|---|---|---|---|---|---|---|---|---|

°C | hPa | % | hPa | hPa | °C | hPa | W/m^{2}K | m^{2}K/W | |

I | −4.57 | 4.16 | 83.0 | 3.45 | 10.80 | 20 | 23.35 | 1.2 | 0.25 |

II | 0.33 | 6.25 | 82.8 | 5.18 | 10.62 | 20 | 23.35 | 1.2 | 0.25 |

III | 0.95 | 6.54 | 77.9 | 5.09 | 10.29 | 20 | 23.35 | 1.2 | 0.25 |

IV | 8.00 | 10.72 | 74.6 | 7.99 | 6.48 | 20 | 23.35 | 1.2 | 0.25 |

V | 12.51 | 14.49 | 74.4 | 10.78 | 4.04 | 20 | 23.35 | 1.2 | 0.25 |

VI | 16.83 | 19.14 | 76.8 | 14.70 | 1.71 | 20 | 23.35 | 1.2 | 0.25 |

VII | 16.87 | 19.19 | 78.0 | 14.97 | 1.69 | 20 | 23.35 | 1.2 | 0.25 |

VIII | 17.65 | 20.16 | 79.0 | 15.93 | 1.27 | 20 | 23.35 | 1.2 | 0.25 |

IX | 14.32 | 16.30 | 82.1 | 13.38 | 3.07 | 20 | 23.35 | 1.2 | 0.25 |

X | 6.80 | 9.87 | 83.4 | 8.23 | 7.13 | 20 | 23.35 | 1.2 | 0.25 |

XI | 2.03 | 7.07 | 86.2 | 6.09 | 9.70 | 20 | 23.35 | 1.2 | 0.25 |

XII | −1.23 | 5.51 | 85.6 | 4.72 | 10.80 | 20 | 23.35 | 1.2 | 0.25 |

Month | p_{i.ISO} | p_{sat}(Θ_{si.min}) | Θ_{si.min} | f_{Rsi.min} | f_{Rsi} | Θ_{si} | p_{i} | φ_{i} | p_{i.max} | φ_{i.max} |
---|---|---|---|---|---|---|---|---|---|---|

hPa | hPa | °C | − | − | °C | hPa | % | hPa | % | |

I | 15.33 | 19.17 | 16.8 | 0.871 | 0.70 | 12.6 | 14.25 | 61.1 | 10.93 | 46.8 |

II | 16.86 | 21.08 | 18.3 | 0.916 | 0.70 | 14.1 | 15.80 | 67.7 | 12.16 | 52.1 |

III | 16.41 | 20.51 | 17.9 | 0.890 | 0.70 | 14.3 | 15.38 | 65.9 | 12.29 | 52.6 |

IV | 15.12 | 18.90 | 16.6 | 0.718 | 0.70 | 16.4 | 14.47 | 62.0 | 14.27 | 61.1 |

V | 15.23 | 19.03 | 16.7 | 0.563 | 0.70 | 17.8 | 14.82 | 63.5 | 15.74 | 67.4 |

VI | 16.58 | 20.73 | 18.1 | 0.394 | 0.70 | 19.0 | 16.41 | 70.3 | 17.34 | 74.3 |

VII | 16.83 | 21.03 | 18.3 | 0.460 | 0.70 | 19.1 | 16.66 | 71.4 | 17.38 | 74.4 |

VIII | 17.32 | 21.65 | 18.8 | 0.478 | 0.70 | 19.3 | 17.20 | 73.7 | 17.70 | 75.8 |

IX | 16.76 | 20.94 | 18.2 | 0.691 | 0.70 | 18.3 | 16.45 | 70.5 | 16.49 | 70.6 |

X | 16.07 | 20.09 | 17.6 | 0.817 | 0.70 | 16.0 | 15.36 | 65.8 | 13.99 | 59.9 |

XI | 16.77 | 20.96 | 18.3 | 0.903 | 0.70 | 14.6 | 15.80 | 67.7 | 12.63 | 54.1 |

XII | 16.60 | 20.75 | 18.1 | 0.910 | 0.70 | 13.6 | 15.52 | 66.5 | 11.77 | 50.4 |

Month | Θ_{dp} | f_{Rdp} | f_{Rsi} | Θ_{si} | p_{i.con} | p_{i} | φ_{i} | φ_{i.con} |
---|---|---|---|---|---|---|---|---|

°C | − | − | °C | hPa | hPa | % | % | |

I | 12.25 | 0.685 | 0.70 | 12.6 | 14.60 | 14.25 | 61.1 | 62.5 |

II | 13.83 | 0.686 | 0.70 | 14.1 | 16.07 | 15.80 | 67.7 | 68.8 |

III | 13.42 | 0.654 | 0.70 | 14.3 | 16.26 | 15.38 | 65.9 | 69.7 |

IV | 12.49 | 0.374 | 0.70 | 16.4 | 18.63 | 14.47 | 62.0 | 79.8 |

V | 12.85 | 0.045 | 0.70 | 17.8 | 20.29 | 14.82 | 63.5 | 86.9 |

VI | 14.41 | −0.762 | 0.70 | 19.0 | 22.01 | 16.41 | 70.3 | 94.3 |

VII | 14.65 | −0.711 | 0.70 | 19.1 | 22.02 | 16.66 | 71.4 | 94.3 |

VIII | 15.14 | −1.069 | 0.70 | 19.3 | 22.35 | 17.20 | 73.7 | 95.7 |

IX | 14.45 | 0.023 | 0.70 | 18.3 | 21.00 | 16.45 | 70.5 | 89.9 |

X | 13.40 | 0.500 | 0.70 | 16.0 | 18.20 | 15.36 | 65.8 | 78.0 |

XI | 13.82 | 0.656 | 0.70 | 14.6 | 16.61 | 15.80 | 67.7 | 71.1 |

XII | 13.55 | 0.696 | 0.70 | 13.6 | 15.59 | 15.52 | 66.5 | 66.8 |

**Table 8.**Parameters for determining the conditions of surface condensation and the state of the phenomenon for four methods.

M1_{con} | M2_{con} | M3_{con} | M4_{con} | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Month | f_{Rsi} | f_{Rdp} |
Δf_{Rcon} | φ_{i.con} | φ_{i} |
Δφ_{con} | Θ_{si} | Θ_{dp} |
ΔΘ_{con} | p_{i.con} | p_{i} | Δp | Phenomenon |

− | − | − | % | % | % | °C | °C | °C | hPa | hPa | hPa | ||

I | 0.70 | 0.685 | 0.015 | 62.5 | 61.1 | 1.5 | 12.6 | 12.25 | 0.38 | 14.60 | 14.25 | 0.35 | lack |

II | 0.70 | 0.686 | 0.014 | 68.8 | 67.7 | 1.2 | 14.1 | 13.83 | 0.27 | 16.07 | 15.80 | 0.27 | lack |

III | 0.70 | 0.654 | 0.046 | 69.7 | 65.9 | 3.8 | 14.3 | 13.42 | 0.87 | 16.26 | 15.38 | 0.88 | lack |

IV | 0.70 | 0.374 | 0.326 | 79.8 | 62.0 | 17.8 | 16.4 | 12.49 | 3.91 | 18.63 | 14.47 | 4.15 | lack |

V | 0.70 | 0.045 | 0.655 | 86.9 | 63.5 | 23.4 | 17.8 | 12.85 | 4.90 | 20.29 | 14.82 | 5.47 | lack |

VI | 0.70 | −0.762 | 1.462 | 94.3 | 70.3 | 24.0 | 19.0 | 14.41 | 4.63 | 22.01 | 16.41 | 5.59 | lack |

VII | 0.70 | −0.711 | 1.411 | 94.3 | 71.4 | 23.0 | 19.1 | 14.65 | 4.42 | 22.02 | 16.66 | 5.36 | lack |

VIII | 0.70 | −1.069 | 1.769 | 95.7 | 73.7 | 22.1 | 19.3 | 15.14 | 4.16 | 22.35 | 17.20 | 5.15 | lack |

IX | 0.70 | 0.023 | 0.677 | 89.9 | 70.5 | 19.5 | 18.3 | 14.45 | 3.85 | 21.00 | 16.45 | 4.55 | lack |

X | 0.70 | 0.500 | 0.200 | 78.0 | 65.8 | 12.2 | 16.0 | 13.40 | 2.64 | 18.20 | 15.36 | 2.84 | lack |

XI | 0.70 | 0.656 | 0.044 | 71.1 | 67.7 | 3.5 | 14.6 | 13.82 | 0.79 | 16.61 | 15.80 | 0.81 | lack |

XII | 0.70 | 0.696 | 0.004 | 66.8 | 66.5 | 0.3 | 13.6 | 13.55 | 0.08 | 15.59 | 15.52 | 0.07 | lack |

**Table 9.**Parameters for determining the boundary conditions for mold development and the state of the phenomenon for four methods - the bold font indicates negative values of the analyzed parameters at which the mold phenomenon occurs.

M1 | M2 | M3 | M4 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Month | f_{Rsi} | f_{Rsi.min} |
Δf_{R} | φ_{i.max} | φ_{i} | Δφ | Θ_{si} | Θ_{si.min} | ΔΘ | p_{i.max} | p_{i} | Δp | Pheno-menon |

− | − | − | % | % | % | °C | °C | °C | hPa | hPa | hPa | ||

I | 0.70 | 0.871 | −0.171 | 46.8 | 61.1 | −14.2 | 12.6 | 16.8 | −4.21 | 10.93 | 14.25 | −3.32 | mold |

II | 0.70 | 0.916 | −0.216 | 52.1 | 67.7 | −15.6 | 14.1 | 18.3 | −4.24 | 12.16 | 15.80 | −3.64 | mold |

III | 0.70 | 0.890 | −0.190 | 52.6 | 65.9 | −13.2 | 14.3 | 17.9 | −3.63 | 12.29 | 15.38 | −3.09 | mold |

IV | 0.70 | 0.718 | −0.018 | 61.1 | 62.0 | −0.9 | 16.4 | 16.6 | −0.22 | 14.27 | 14.47 | −0.20 | mold |

V | 0.70 | 0.563 | 0.137 | 67.4 | 63.5 | 3.9 | 17.8 | 16.7 | 1.03 | 15.74 | 14.82 | 0.91 | lack |

VI | 0.70 | 0.394 | 0.306 | 74.3 | 70.3 | 4.0 | 19.0 | 18.1 | 0.97 | 17.34 | 16.41 | 0.93 | lack |

VII | 0.70 | 0.460 | 0.240 | 74.4 | 71.4 | 3.1 | 19.1 | 18.3 | 0.75 | 17.38 | 16.66 | 0.72 | lack |

VIII | 0.70 | 0.478 | 0.222 | 75.8 | 73.7 | 2.2 | 19.3 | 18.8 | 0.52 | 17.70 | 17.20 | 0.50 | lack |

IX | 0.70 | 0.691 | 0.009 | 70.6 | 70.5 | 0.2 | 18.3 | 18.2 | 0.05 | 16.49 | 16.45 | 0.04 | lack |

X | 0.70 | 0.817 | −0.117 | 59.9 | 65.8 | −5.9 | 16.0 | 17.6 | −1.54 | 13.99 | 15.36 | −1.37 | mold |

XI | 0.70 | 0.903 | −0.203 | 54.1 | 67.7 | −13.6 | 14.6 | 18.3 | −3.64 | 12.63 | 15.80 | −3.16 | mold |

XII | 0.70 | 0.910 | −0.210 | 50.4 | 66.5 | −16.1 | 13.6 | 18.1 | −4.46 | 11.77 | 15.52 | −3.75 | mold |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Starakiewicz, A.; Miąsik, P.; Krasoń, J.; Lichołai, L.
Methods for Determining Mold Development and Condensation on the Surface of Building Barriers. *Buildings* **2020**, *10*, 4.
https://doi.org/10.3390/buildings10010004

**AMA Style**

Starakiewicz A, Miąsik P, Krasoń J, Lichołai L.
Methods for Determining Mold Development and Condensation on the Surface of Building Barriers. *Buildings*. 2020; 10(1):4.
https://doi.org/10.3390/buildings10010004

**Chicago/Turabian Style**

Starakiewicz, Aleksander, Przemysław Miąsik, Joanna Krasoń, and Lech Lichołai.
2020. "Methods for Determining Mold Development and Condensation on the Surface of Building Barriers" *Buildings* 10, no. 1: 4.
https://doi.org/10.3390/buildings10010004