Simplified Model of Humidity in the Space of a Protective Mask and Experimental Verification—A Pilot Study

Abstract

Air humidity is an important parameter of the microclimate in the mask space. The aim of the study is to assess the mask microclimate in terms of air humidity and to develop a simplified model of humidity distribution as a function of time, which can be used to estimate and predict humidity in the mask space. Humidity and temperature parameters were tested for five different types of protective masks. The protective masks used for the tests differed in their construction and material thickness of the mask walls. The microclimate in the mask space was assessed based on one-hour measurements of temperature and humidity during office work, based on publicly available guidelines and standards. Based on the moisture balance in the space between the face and the mask wall, a simplified one-dimensional model of absolute humidity in space was determined. The results of the study indicated that in all cases, regardless of the type of mask, the permissible values of temperature and relative humidity were exceeded. The average values of temperature and relative humidity in the mask space for all masks and people were 31.94 °C and 83.65%, respectively. The absolute humidity value is strongly dependent on the ambient air humidity. In months with higher absolute humidity values, such as September, a higher absolute humidity occurs in the mask space. One way to lower the humidity level in the mask is to dry the air in the room.

1. Introduction

Air humidity is a basic parameter related to air quality and microclimate [1,2,3]. Wearing masks undoubtedly changes the parameters of the air in the inhaled air compared to the parameters of the environment [4,5,6,7]. Masks are commonly used in healthcare settings to protect healthcare workers from respiratory infections [8,9,10]. Masks are also used to reduce the spread of bacteria from the mouth, nose and face to the outside air [11,12]. Since the COVID-19 pandemic, the wearing of masks has become recommended and even mandatory in public places in many countries [13]. Masks are also used to protect against dangerous substances contained in the air, such as pesticides [6].

During the frequent use of protective masks during the COVID-19 pandemic, masks caused problems most often related to the discomfort of wearing masks [8,14]. Commonly reported problems were pressure on the face, difficulty breathing, discomfort, communication difficulties and headache [8]. Wearing a mask can also cause “dry eye” [14], which is caused by the upward flow of air towards the surface of the eye during exhalation. The research results from the study [15] indicate that over 70% of the respondents wearing masks reported feeling discomfort on their faces. Of all the people who felt discomfort, 62.7% reported that the main symptom was facial fever, 25.4% reported symptoms of dyspnea and 9.1% experienced an accelerated heartbeat, which may have been caused by an increase in temperature in the mask space. People who wear masks prefer lower ambient temperatures [15]. A certain solution to neutralize the increase in temperature in the space of the mask is to remove the mask from the face and take a break from wearing the mask [4] of course, if the working conditions allow it. Healthcare workers are advised to change masks every two hours [16]. Comparing the increase in temperature and humidity in the space of the mask, a faster increase in temperature in the mask was observed compared to air humidity [17]. The increase in humidity in the mask space may have a negative effect on the facial skin [18]. Wearing a mask may also contribute to the growth of colonies of bacteria and fungi on the surface of the mask [19,20,21,22,23,24], which is undoubtedly related to the accumulation of moisture between the mask and the face, the main source of which is the human. Mask humidity also affects the filtration efficiency of electret FFP masks when worn in real conditions [25].

In modeling the flow of mass and heat in masks, Computational Fluid Dynamics (CFD) numerical calculations are most often used [26,27,28,29]. Three-dimensional numerical methods are quite complicated due to spatial grids and may be associated with significant discrepancies [28] in the computational results between CFD models [28].

Due to the problems caused by air humidity when wearing a protective mask [6,13,14,15,16,17,18,19,20,21,22,23,24], it is important to carefully examine the course of changes in air humidity as a function of time in the protective space of the mask.

In the literature, no evaluation of the microclimate under the masks in terms of temperature and humidity, as well as algorithms that would allow predicting the humidity in the space of the mask, have been found.

The aim of the publication is to assess the microclimate in terms of temperature and humidity in the mask space based on the adopted standards [1,3] and to develop a simplified model of humidity as a function of time for selected types of masks.

The following sections present the remainder of this publication. Section 2 describes the types of masks and the method of measuring temperature and humidity in the mask space. In Section 3, the microclimate in the mask space was assessed based on the measured temperature and humidity. Then, a simplified model of humidity in the mask space was built. The last part of this publication contains conclusions.

2. Materials and Methods

The tests were carried out for five types of protective masks in an office located in the city of Bialystok in Poland in the temperate climate zone. The temperate climate in Poland is characterized by high weather variability throughout the year. Winters can be frosty or mild, while summers can be rainy or hot [30]. The office room is equipped with stack ventilation with an average number of air changes per hour equal to 0.25 1/h.

The measurements were taken in conditions similar to those experienced by many millions of people during the COVID-19 pandemic. To ensure that we did not harm human beings, we obtained informed consent from all individuals participating in the research. The data that support the findings of this study are available from the first author but restrictions apply to the availability of these data, which were used under license for the current study, and so are not publicly available. Data are however available from the authors upon reasonable request and with permission of first author.

The research was conducted in conditions where masks were mandatory at work and outside. The types of masks tested were worn during the COVID-19 pandemic. All types of masks tested were permitted. The research was conducted during normal office work and did not interfere with people’s functioning and their work.

Preview photos of the tested masks are shown in Figure 1. The number 1 three-layer flat mask, in accordance with the EN 14683 [31] standard, was made of non-woven polypropylene. The hand-made mask number 2 was made of three layers of 100% cotton material with a weight of 125 g/m² during the COVID-19 pandemic when masks were not available on the local market. The number 3 double-layer flat mask was made of non-woven polypropylene. The number 4 convex KN95 mask in accordance with EN 149: 2001 + A1: 2009/GB2626-2006 [32,33] was made of polypropylene. Mask number 5 type FFP2 in accordance with the EN 149: 2001 [32] standard was made of polypropylene and was equipped with an exhalation check valve.

Four adults with the following characteristics participated in the study:

-

Person A: Female, age 35, height 164 cm, weight 64 kg.

-

Person B: Female, age 57, height 171 cm, weight 102 kg.

-

Person C: Male, age 43, height 180 cm, weight 87 kg.

-

Person D: Male, age 58, height 178 cm, weight 100 kg.

Adults of working age were included in the study. In Poland, according to the Statistics Poland [34], the working age for men refers to the group aged from 18 to 64, and in the case of women, the working age is from 18 to 59. People of working age were selected from the most representative groups in terms of percentages according to the age pyramid of the Polish population [35].

Each person tested all types of masks five times. The research was carried out in the following months: January, March, April, September, November and December. During the study, all persons performed light office work classified in accordance with the standard [36,37] in class W1. Work activity in class W1 [36,37,38], is light manual work, including writing, typing, drawing, work in the chemical laboratory, inspection, assembly or sorting of lightweight materials. For the measurement of humidity and temperature, a Testo 435 data logger with measuring probes with the following parameters was used: humidity, measuring range: +10 to +98% RH, resolution 0.1% RH, accuracy ±1%RH, temperature, measuring range: 0 and +50 °C, resolution 0.1 °C, accuracy ±0.3 °C. The humidity and temperature measuring point was located in the lower part of the zygomaticus major muscle in the mask space (Figure 2). Humidity and temperature measurements in the mask space were taken in a series of measurements at one-minute intervals during a one-hour experiment. Then, based on the one-hour measurement series, arithmetic mean values of humidity and temperature were determined. During the tests, the ambient air parameters ranged from 19.5 °C to 25.0 °C, and the relative humidity ranged from 35% to 64%.

3. Results and Discussion

Table 1. Average values of temperature, relative humidity, absolute humidity for one hour of use of masks.

Mask Number	Tm	Tm_min	Tm_max	σTm
-	°C	°C	°C	°C
Mask 1	31.7	30.1	33.7	1.3
Mask 2	32.2	29.3	34.1	2.1
Mask 3	30.5	27.1	33.9	3.7
Mask 4	32.7	29.2	33.8	1.4
Mask 5	32.6	30.5	34.1	1.5
Mask Number	ϕm	ϕm_min	ϕm_max	σϕm
-	%	%	%	%
Mask 1	82.5	76.0	92.9	5.8
Mask 2	87.1	79.0	92.9	5.7
Mask 3	83.5	81.9	87.1	2.4
Mask 4	85.5	78.7	93.7	4.1
Mask 5	80.8	75.3	86.4	5.2
Mask Number	ωm	ωm_min	ωm_max	σωm
-	g/m3	g/m3	g/m3	g/m3
Mask 1	27.5	24.0	32.5	3.4
Mask 2	29.8	24.1	33.4	3.6
Mask 3	25.7	21.8	30.7	4.8
Mask 4	29.9	24.9	34.8	3.0
Mask 5	28.2	26.3	31.0	2.1

presents the mean, minimum, maximum values and standard deviations for temperature (T_m, T_{m_min}, T_{m_max}, σT_m, respectively), relative humidity (ϕ_m, ϕ_{m_min}, ϕ_{m_max}, σϕ_m, respectively) and absolute humidity (ω_m, ω_{m_min}, ω_{m_max}, σω_m, respectively) in the space between the mask and the face for individual masks after one hour of use in office work for the selected five mask types. The values of air parameters in the mask space, which are presented in Table 1, refer to 20 averaged tests of individual masks (from 20 measurement series). The average temperature in the mask space was in the range of 30.5–32.7 °C, while the average relative humidity was in the range of 80.8–87.1%. In the work [6], the temperature in the tested masks was in the range of 35.5–37.9 °C and these values are higher than the temperatures obtained in this work. The discrepancies between the average temperatures of this work and publication [6] result from the fact that in the work [6] the tests were carried out at a much higher ambient temperature, equal to 28 °C, which resulted in less heat exchange between the mask space and the external environment. In the article [29], the measured temperatures in the mask space were similar to the temperatures in the mask in this work, which may be due to similar temperatures in the room.

The lowest average hourly temperature was obtained in mask no. 3, which was made of two layers of material and has the thinnest wall thickness compared to the other masks. Under the adopted test conditions, heat was transported from the mask space to the external environment. According to Fourier’s law [39], which describes the thermal conductivity of solids, the heat flux that flows through the mask wall depends on the thickness of the mask wall. In the case of mask No. 3, due to the small wall thickness, the heat exchange was the most intense compared to the other masks, and therefore the temperature in mask No. 3 turned out to be the lowest.

The assessment of the microclimate in the mask space in terms of temperature and humidity can be performed based on the ASHRAE [1] guidelines and literature [3]. It should be noted that no standards have been found in the literature that define the parameters and quality of air in the mask space. For ASHRAE [1] the allowable temperature and humidity range was not met. In the case of publication [3], the microclimate assessment was divided into four ratings: “Good” (for the condition 24 °C < T ≤ 27 °C), “Intermediate” (for the condition T ≤ 24 °C and 30% < ϕ ≤50% or 24 °C < T ≤ 27 °C and ϕ ≤ 30% or 24 °C < T ≤ 27 °C and ϕ > 50% or T > 27 °C and 30% < ϕ ≤ 50%) and “Bad” (for condition T ≤ 24 °C and ϕ > 50% or T ≤ 24 °C and ϕ ≤ 30% or T > 27 °C and ϕ > 50% or T > 27 °C and ϕ ≤ 30%).

The average values from one hour of mask use indicate a “Bad” rating. It should be noted here that the parameters of the ambient air inside the laboratory met the ASHRAE [1] guidelines, while in the case of evaluation according to publication [3] the air was rated “Intermediate” and “Good”. A solution to the problem of poor air quality under the mask may be to take a break from using the mask by removing it from the face [4]. Figure 3 shows the graphical results of the calculations from Table 1 on a psychrometric chart with the comfort area marked for a clothing level of 0.65 clo and a metabolic rate of 1.40 met based on ASHRAE implemented in the application [40]. The marked points of air parameters inside the mask space 1–4 are located outside the thermal comfort area. Despite significant humidity in the mask space, people wearing masks during the one-hour period did not report any problems. In [8], approximately 83.8% of people reported problems with using the mask, which may be caused by the much longer time of wearing the mask compared to the one-hour period.

Figure 4 shows a box plot for absolute humidity. Based on the box plot, it can be seen that the smallest data dispersion occurs in mask no. 5, which may be due to the operation of the check valve in this mask. The largest interquartile range occurs in masks no. 1, 2 and 3, while the smallest interquartile range occurs in masks no. 4 and 5. The differences in moisture dispersion are probably caused by the type of construction of the masks. Masks No. 1, 2 and 3 are loosely woven [41] masks, while masks 4 and 5 are layered fine-woven masks that provide better protection [41]. Perhaps the lower material density of masks 1, 2 and 3 contributes to a greater dispersion of absolute humidity values. According to publication [42], the relative humidity value has no effect on the hydraulic resistance generated by the masks.

Figure 5 shows the relationship between the absolute humidity in the mask space and the absolute humidity inside the room. The coefficient of determination R², which was 0.77, indicates a strong correlation between the absolute humidity in the mask space and the absolute humidity of the environment outside the mask. Lowering the humidity by drying the air inside the room where people wearing masks are present may contribute to reducing the humidity in the mask space.

Due to the significant number of measurement series,

Table 2. Average values of temperature, relative humidity and absolute humidity for one-hour use of masks for selected measurement series.

Number of Measurement Series	Person	Mask	Month	Average Ambient Temperature	Average Ambient Relative Humidity	Average Ambient Absolute Humidity	Average Temperature in the Mask Space	Average Relative Humidity in the Mask Space	Average Absolute Humidity in the Mask Space
							Tm	ϕm	ωm
-	-	-	-	°C	%	g/m3	°C	%	g/m3
S1	B	1	September	22.0	52.0	10.1	33.2	90.9	32.5
S2	D	1	April	20.3	41.5	7.3	30.6	82.3	26.7
S3	D	2	April	19.5	50.9	8.5	29.7	90.5	27.3
S4	C	2	September	22.6	63.5	12.8	33.3	99.1	36.1
S5	B	3	September	22.0	45.0	8.7	33.7	81.6	31.2
S6	D	3	March	18.7	35.0	5.6	27.2	82.1	21.7
S7	C	4	November	24.5	37.0	8.3	33.7	93.0	34.6
S8	B	4	September	20.4	52.0	9.2	31.6	85.5	28.3
S9	A	5	April	21.0	35.6	6.5	32.4	77.0	26.8
S10	D	5	April	20.3	45.0	7.9	30.4	83.4	26.0
S11	B	1	December	19.8	37.0	6.3	30.9	75.8	24.4

and Figure 6 present a selection of 11 measurement series that were performed for different absolute humidity values in the room. Figure 6 presents representative measurement series of absolute humidity as a function of time for one-hour mask use for selected masks and people, while Table 2 describes the average values of temperature, relative and absolute humidity of the ambient air in the office and in the mask space, and the type of mask with the tester.

Analyzing the course of absolute humidity (Figure 6) as a function of time, a rapid increase in humidity can be observed within a few minutes until the mask is put on the face. After a few minutes, the absolute humidity stabilizes, its final value depends primarily on the moisture content in the ambient air and the temperature inside the room (Table 2). Ambient temperature has an effect on human humidity generation. People who used the mask at lower temperatures experienced less discomfort [14]. It should be noted here that the value of moisture generated by humans depends primarily on physical activity [43]. One of the physical activities is office work in a sitting position, for which all protective mask testing studies have been carried out.

The moisture content of the outdoor air in a temperate climate depends largely on the season, the ventilation and heating system and the number of people in the room. Figure 7 presents the course of absolute humidity in 2021 in the room where the tests were conducted. The lowest values of absolute humidity occur in winter and the highest in summer. The stabilized absolute humidity values presented in Figure 6 depend primarily on the absolute humidity in the room, which in turn depends on the season. During the measurements, the highest average absolute humidity values in the room and in the mask space were recorded in September, and the lowest absolute humidity values in January and December.

Figure 8 shows the effect of removing mask 4 from the face on the absolute humidity measurements and the course of changes in the absolute humidity value in the tested room. After removing the mask from the face, there was a sudden drop in absolute humidity. A similar trend of changes in humidity was obtained in [4]. Removing the mask from the face reduces the absolute humidity to the absolute humidity value close to the room.

4. Simplified One-Dimensional Model of Absolute Humidity in the Mask Space

One-dimensional models can be used for prediction and simple analysis of air parameters related to air quality and microclimate, such as air temperature [44,45] or carbon dioxide concentration in the air [46,47]. Despite the simplifying assumptions made when formulating the differential equations, one-dimensional models can give good convergence to the experiment and provide better computational performance compared to complicated three-dimensional models.

The basis of the one-dimensional simplified model of absolute humidity ω [g/m³] in the mask space is the humidity balance, which consists of the humidity discharged from the mask space and supplied to the mask from the outside Q_n [g/h] and the human-generated humidity Q_g [g/h]:

$$V{\displaystyle \frac{d\omega }{dt}}=Q_n+Q_g,$$

(1)

where V [m³] is tidal volume, t [h] is time.

The tidal volume parameter, according to the standard [37], is related to the work rate class, which is determined on the basis of the activities performed [37]. The adopted model assumes a work rate class of the W1 type [37], which is characterized by light work related, among others, to writing and working in the laboratory. For the work rate class W1, the tidal volume was assumed to be 1.5 dm³, in accordance with the standard [36,38]. It should be noted here that the mask during use is pressed against the face and has a small volume in relation to the tidal volume, therefore only the tidal volume was assumed in the model without taking into account the volume of the mask. Human-generated humidity Q_g [g/h] was assumed on the basis of the relationship determined in publication [48]. The values of moisture from human origin determined from formula [48] for representative measurement series 1–11 are presented in

Table 3. Values of human-generated moisture, determined from the formula according to publication [48] for representative measurement series 1–11.

Number of Measurement Series	S1	S2	S3	S4	S5	S6	S7	S8	S9	S10	S11
Human-generated moisture Qg [g/h]	32.7	28.4	26.3	34.2	32.7	24.2	38.4	28.6	30.2	28.4	27.1

.

Humidity Q_amb discharged from the mask to the environment and supplied to the mask from the outside is described by the following relationship:

$$Q_n=nV({\omega }_{amb}-\omega ),$$

(2)

where ω [g/m³] is the absolute humidity inside the mask, ω_amb [g/m³] is the absolute humidity outside, and n is the number of air changes in the mask [1/h].

The number of exchanges was determined as the ratio of the airflow volumetric flow q and the tidal volume V:

$$n={\displaystyle \frac{q}{V}},$$

(3)

In accordance with the testing guidelines for protective masks [36,37,38] for the work rate class W1, the masks are tested for two air flows of 10 L/h and 35 L/h. The volume flow of air was assumed as q = 24 L/h.

After substituting Formula (4) into relation (3), the absolute humidity balance takes the form:

$$V{\displaystyle \frac{d\omega }{dt}}=nV({\omega }_{amb}-\omega )+Q_g,$$

(4)

After integrating the above equation with respect to time, the model of absolute humidity (ω = ω_num) change as a function of time t in the mask space was determined:

$${\omega }_{num}={\omega }_{amb}+{\displaystyle \frac{Q_g}{nV}}+\left({\omega }_{t=0}-{\omega }_{amb}-{\displaystyle \frac{Q_g}{nV}}\right)e^{-nt},$$

(5)

The calculation results of the model (5) for an air flow of 24 l/h were compared with the data from the experiment. The relative error was determined according to the following formula:

$$\delta {\omega }_{num}=\left|{\displaystyle \frac{{\omega }_{\exp }-{\omega }_{num}}{{\omega }_{\exp }}}\right|100\%$$

(6)

where ω_exp is the absolute humidity from the experiment, while ω_num is the value determined from the model (5). The average value of the relative error determined according to the Formula (6) from all measurement series amounted to 7.4%.

A graphical comparison of the calculation results of the model (5) with the experiment for the selected eleven measurement series is shown in Figure 6. For greater clarity, Figure 8 shows a graphical comparison of the model with the experiment only for the measurement series No. 1. As can be seen in Figure 6 and Figure 9, the results obtained from the one-dimensional model achieved good agreement with the experimental data. Comparing the solution of model (5) with the experiment (Figure 9), it can be seen that the model function is a smooth function in a given one-hour time interval, while the results of the experiment are characterized by fluctuations. Fluctuations in absolute humidity are probably caused by the nature of office work, in which the head makes small movements while working at the computer, which may interfere with the flow of air through the mask. The simplified model (5) can be used to estimate the humidity in the mask space for different types of masks and for different climatic conditions and different physical activities.

5. Conclusions

Wearing a mask causes an increase in temperature and humidity in the air in the mask space during light office work from the moment the mask is put on the face. Absolute humidity values stabilize after a few minutes and depend on the temperature and humidity of the ambient air in the room. The average values of temperature and humidity during one-hour use of the mask significantly exceeded the recommended levels presented in the standards [1]. During the use of the mask, discomfort may occur due to the simultaneous increase in temperature and air humidity. Research has shown that the average relative humidity in the mask space is approximately twice as high as the relative humidity of the ambient air, while the average temperature inside protective masks is approximately one and a half times higher than the ambient air temperature. The research was carried out in different seasons in the temperate climate zone, which is characterized by high variability of both temperature and humidity as a function of time. The average temperature and average relative humidity values in the mask space during one hour of mask use exceeded thirty degrees Celsius and eighty percent, respectively. It should be noted here that the general trends in providing thermal and humidity comfort for people assume that the higher the value of air humidity, the lower the value of air temperature should be.

Research has shown that removing the mask causes a drop in temperature and air humidity in the space where the temperature and humidity were measured. Removing the mask is undoubtedly a simple method that can restore the air parameters from before wearing the mask.

The simplified model of absolute humidity in the space of the mask developed in the work can be used to predict the course of absolute humidity in the space of the mask based on the temperature and air humidity in rooms where people are present. It should be noted here that the developed model was tested in office conditions while working at a computer. The calculation results indicate that the people taking part in the experiment generated humidity from 26.3 g/h to 38.4 g/h. In subsequent research, the model will be validated for other physical activities.

In the next research works, it is planned to confirm the results of this work for a larger number of measurement series and conduct research on methods to reduce high temperature and humidity in the mask space. Accumulation of air humidity in the mask can be optionally reduced by using a suitable material that lets moisture out. The temperature in the mask space can be lowered by using materials from which the mask is made with a higher thermal conductivity coefficient, which may contribute to greater heat transfer outside the mask.