The mechanical effect of moisturization on airborne COVID-19 transmission and its potential use as control technique.

Mounting evidence from scientific community seems to suggest that COVID-19 virus can potentially spread by airborne transmission. As a result, methods and techniques for preventing environmental contagious, such as ventilation or air filtration have been proposed. Here, it is investigated the effect of moisturization on airborne COVID-19 transmission from a mechanical point of view in which comparatively large water droplets promote the growth -by collision and coalescence, of suspended airborne COVID-19 and then accelerating its gravitational settling. Utilizing a classical raindrop collisional model from cloud science and the available experimental data an expression for the removal time of suspended airborne COVID-19 as function of the relative humidity was derived. The mechanical model is in good agreement with the recent reported experimental research in which high temperature and high relative humidity reduce COVID-19 contagious and then is a point in favor of the mechanic model of the effect of moisture in the COVID-19 airborne transmission. The results encourage further research on the deliberate moisturization of room air (by using ceiling mounted humidifiers) as a potential technique for control of airborne COVID-19 transmission.

Introduction

Until not long ago it was believed that COVID-19 -henceforth covid, spread from person-to-person mostly through respiratory droplets with diameters larger than m produced when an infected person coughs or sneezes, (Li et al., 2020). However, mounting evidence seems to suggest that covid can potentially spread by airborne transmission, i.e., via microscopic particles (m) which are small enough to stay suspended in the air for hours, (Domingo et al., 2020; Morawska and Milton, 2020; Wilson et al., 2020; Tropea et al., 2007; WHO 2020; Bontempi, 2020; Jayaweera et al., 2020.), and as a result, methods and techniques for preventing airborne transmission, such as ventilation, (Bhagat et al., 2020) or air filtration (Zhao et al., 2020), have been explored.

The object of this work was to analyze a new approach, namely the deliberate moisturization of air (by using humidifiers) in order to promote the growth of suspended airborne covid -by collision and coalescence with water drops, and then accelerating its gravitational settling. In the next sections and utilizing a raindrop collisional model used in meteorology science together with available experimental data the efficiency of this approach is investigated. At this point, it interesting to see that actually it has been demonstrated that the relative humidity of environment reduces the spread of the virus but the reasons either biological or mechanical behind are still unclear. The proposed model confirm that, at least from a mechanical point of view, relative humidity reduces the spread of the virus.

Materials and methods

Raindrop collisional model

Let us consider the mechanistic model used in cloud physics in which raindrops falling from the sky are growing during their path by a collisional process with other tiny drops encountered during the downward travel, (Rogers, 1976). The raindrop collisional model is based in the calculation of an effective collisional cross section as sketched in Fig. 1 , in which a falling drop (the collector drop) will only collide with a second stationary drop (the collected drop) if this drop is inside of a certain area which is less than the geometric area because the air streamlines bowing out around the collector drop carry the smaller drops with them around the drop, and then the effective cross-section becomes less than the actual cross-section. For small travel distances it is allowable to neglect evaporation and growth of the collector drop owing to the environment humidity as well, the validity of this assumption is demonstrated in the appendix. The raindrop collision efficiency, ε, is defined as (Rogers, 1976),where R and are the radius of the collector and collected drop, respectively, and is the critical value of the impact parameter within which a collision is certain to occur and outside of which the droplet will be deflected out of the path of the drop (see Fig. 1). The collection efficiency, would be the product of collision efficiency times coalescence efficiency, however, when the collected drops are smaller than 100 μm it is usually assumed that the coalescence efficiency is unity, and then the collection efficiency is identical to the collision efficiency, (Rogers, 1976). Mathematically the collisional cross section is given bywhich considering Eq. (1) becomes

Fig. 1

Air flow around a falling particle. Only the air in innermost streamline collides with the particle, the rest goes around it. Credit. Lamb and Verlinde (2011).

Collection rate

Once defined the cross section of collision, Eq. (3), it is possible to infer the rate of collection. Because for contagious what seems relevant is if a given water drop is contaminated and it makes no difference whether if inside the drop there is only one or many viruses then for first estimation we can assume that all the virus inside a drop can be considered as a single virus. Then if the cloud formed by the waters drops coming from an infected person are all contaminated by using the diffusion equation we havewhere is the absorption rate per unit of volume and time of particles of covid, the concentration per volume of particles of covid suspended in the air; and is the flux of water (collector) drops per unit of area and time.

The flux can be reckoned considering the expressionwhere is the concentration per unit of volume of the collector water drops; and is the approaching velocity which is equal to the gravitational terminal velocity (see Fig. 1). The concentration of water drops suspended in air can be measured by the relative humidity h of the environment according with the following equation, derived in Appendix.where f is a function of temperature. Taking into account Eq. (6), Eq. (5) becomesInserting Eq. (7) and Eq. (3) into Eq. (4) one obtainswhere an absorption time, τ, was defined asSolving Eq. (8) yieldswhere is the initial concentration of suspended particles of covid at time .

Fig. 2 shows the field of the collisional efficiency ε for drops of radius R with droplets of radius r from Rogers (1976) and derived from data from Mason (1971). In this figure it is easy to see that the efficiency for collection of airborne covid (particles with radius around m or less) may be a at most for very coarse atomization with droplets with radius around m. However, such a coarse atomization (with radius of the droplet similar than that observed in rain droplets) would be unpractical, and a value between semi-fine to semi-coarse atomization around m seems tolerable, and then a maximum upper limit of the efficiency of collection would be around a . Finally, we can asses the efficiency in the control of covid by the deliberate moisturization of the air as follows.

Fig. 2

Field of the collisional efficiency ε for drops of radius R with droplets of radius r from Rogers (1976), and derived from data from Morawska and Milton, 2020).

Results

Control of a suspended cloud

We assume that a cloud of covid is already suspended in the air, and then the water drops generated by the humidifiers located at the top of the building are approaching the cloud with a velocity which is equal than the terminal velocity of the water drop. For spherical drops with radius R a density ρ much more larger than the air density , i.e., -and then neglecting buoyancy, the terminal velocity is given bywhere g is gravity and is the drag coefficient (approximately close to 0.4 for spheres). Thus, inserting Eq. (11) into Eq. (9) we have

To obtain some idea of the effectiveness of collection which is given by the absorption time τ predicted by Eq. (12), we assume some values of the parameters: a Drop radius of m; covid airborne particles of m; m and with collection efficiencies and , respectively, derived from Fig. 2; m/s2; kg/m3; kg/m3; . The resulting curves are shown in Figs. 3 and 4 for temperatures of 20C and 5C, respectively. It is seen that for relative humidities between 30 and 70 -where humans can be comfortable, the absorption time can be reduced to a few seconds. Contrariwise, for dry air the time in which the covid can be stay suspended in air is in the order of hours. In the same figures, by comparison, it is seen that an increase in the temperature translates into a decrease of the absorption time, i.e., into an increase of the accelerated settling. This results is in good agreement with recent investigation which conclude that high temperature and high relative humidity reduce covid cases, deaths and improve recovery, (Sarkodie and Owusu, 2020; Azuma et al., 2020).

Fig. 3

Absorption time τ as a function of the relative humidity h for collector drops of m and airborne particles of m and m and a temperature of 20C.

Fig. 4

Absorption time τ as a function of the relative humidity h for collector drops of m and airborne particles of m and m and a temperature of 5C.

Finally, because the simultaneous dependence of the airborne transmission in temperature and relative humidity, its seems more suitable the use of absolute humidity H rather than relative humidity h. Fig. 5 shows the absorption time τ as a function of the absolute humidity H for collector drops of m and airborne collected particles of m and m; and Fig. 6 shows the absolute humidity H as function of temperature for several values of relative humidity h.

Fig. 5

Absorption time τ as a function of the absolute humidity H for collector drops of m and airborne particles of m and m and a temperature of 20C.

Fig. 6

Absolute humidity H as function of temperature for several values of relative humidity h.

Biological effects

Although the scope of the present work is strictly restricted to the mechanical effect of moisturization on airborne covid and its possible use as technique for control in which microscopic water drops are deliberately used to sweep up suspended covid, nonetheless, it is worthy to mention, at least, some recent studies on the virus stability under different environmental conditions including relatively or absolute humidity. The interested reader is referred to Carducci et al. (2020), who recently reviewed survival experiments on corona viruses (and their surrogates), air monitoring and epidemiological-air flow model studies. In those experiments interesting results were obtained by Prussin et al. (2018), who demonstrated that the relation between survival and relative humidity shows a typical U-shaped curve: the coronavirus surrogate survived better at high () and low () humidity, with a significant decrease in infectivity at middle range of relative humidity (60%–85%). Then, the effect of humidity is not the same for all viruses, for example H1N1 survival was higher at 70% relative humidity compared with lower relative humidity values (Doremalen et al., 2013; Peng and Jimenez, 2020).

Floor water puddle

Continuous moisturization, i.e., continuous injection of water into the environment may not be the most efficient strategy and a better approach could be by using intermittent discharges of moisturization. Such discharges could be performed in a similar fashion than commercial electric air fresheners and controlled either by continuous monitoring and surveillance of the air or by fixed intervals of time.

For continuous monitoring and surveillance the discharges can be preformed when a certain critical threshold signal is attained in the environment. The trigger signal can be, for example, a given critical level of CO2 in the room, where it has been recently investigated that the amount of CO2 could be a suitable indicator for quantification of the amount of air exhaled by other persons and then is also a measure of the risk for contagious of covid, []. For example, the normal amount of CO2 in a open space is around 400 ppm, however, inside of rooms if the CO2 level recorded by a monitor is around 800 ppm that means that approximately the 1% of the air we are breathing is for a second time. So, discharges of moisturization could be programmed when the level of CO2 are so high that the no fresh air overcome, say, 1000 ppm. The duration of the discharge should be in the order of the absorption time τ given by Eq. (9).

However, environmental moisturization also can be performed by fixed intervals of time exactly as electric air fresheners are used in homes and buildings. For this last case, it is interesting to estimate the minimum time permissible between discharges which is mainly determined by the evaporation rate of the micro puddle of water formed in the floor if any removal system is used to prevent its formation. Indeed, because we are working with collector droplets with sizes between semi-fine to semi-coarse atomization, i.e., radius between 100 and 300 μm, they will settle down on the floor and then a water puddle will be formed as pictorially depicted in Fig. 7 . Therefore, the time between discharges must be large enough in order to allow that such a water puddle be able to evaporate, of course, if any removal system is used. This natural evaporation occurs as fog and mist droplets with varying diameter of between 10 and 15 μm and then may be removed with ease by the weak currents of air near to surface. The time of evaporation of the water puddle is controlled by surface tension of the water and the contact angle with the floor surface and can be calculated as follows.

Fig. 7

Physical model of horizontal puddle formation and evaporation.

First, inasmuch that water drops are settling on the floor a puddle is formed and spread only to the point where a maximum thickness is attained which is determined by the surface tension of water γ and the contact angle θ of the drop with the soil. The thickness of the puddle is given by, (Pierre-Gilles et al., 2002),

The above formula predicts that the evaporative time of the puddle could be reduced by controlling the contact angle θ, which is a parameter which can be controlled by suitable selection of the material covering the soil. For the sake of illustration, most of the floors are composed by ceramics which usually varies from to , (Watanabe, 2009), and then with a surface tension around mN/m, we obtain thickness between 0.4 mm and 2 mm. However, the floor could be deliberately covered with a super-hydrophilic material which can reduce the contact angle around resulting into a puddle thickness around 0.2 mm. On the other hand, the characteristic time for evaporation of this puddle can be estimated by a balance of mass in the puddle. Let us consider a large puddle with a height and surface area as depicted in the model, Fig. 7. If the puddle is large enough the mass of water of the puddle is approximated as

On the other hand, if is the evaporation i.e., the loss of water per unit of time and unit of surface (in units of kg/(m2s), then the rate of change of mass of the puddle is given byinserting Eq. (14) into Eq. (15) and after integration one obtainswhere an evaporative characteristic time , was defined aswhich after inserting Eq. (13) becomes

Many semiempirical formulations for the evaporation from an open water surface are available in the literature, one of them is the well-known Penman equation, (Penman, 1948), or the simplest adaptation due to Shuttleworth (2007), but just for the sake of illustration, from experimental data from undisturbed water pools for an air temperature around C, and relative humidity around could be around kg/m2s, (Shah, 2012), and then with a mm we obtain a characteristic time of evaporation around mins.

Therefore, if the time for discharges must be reduced below it would necessary strategies or systems to prevent the growth of the water puddle. Those strategies already exist and are well known, e.g., the use of chemical absorbent such as charcoal, road salt, etc … Finally, an alternative approach is the use of humidifier-desiccant dehumidifier closed cycle in which the humidity is collected at the bottom of the building then filtered through a desiccant unit and after that being re-humidified, pumped and re-injected in the ceiling of the building (e.g., using classical rotating drum dehumidifier). This last option not only will prevent the formation of the water puddle but also will allow the continuous moisturization of the environment for covid control.

Summary of results and conclusions

In this work a study on the effect of moisturization of room air on airborne COVID-19 transmission from a mechanical point of view was performed. Some interesting conclusions are resulting by this study as follows:

An analytical expression, Eq. (12), is derived which predicts the absorption time of airborne covid-19 as function of temperature, relative humidity and the size of water drops.

For the range of relative humidities comfortable for human standards the absorption time of airborne covid could be reduced to a few seconds.

The predictions of the mechanical model agree with reported data in which it was found that high temperature and high relative humidity reduce covid cases, deaths and improve recovery.

Its seems that a better parameter for assessment is the absolute humidity rather than relative humidity.

The results seem to indicate that the deliberate moisturization of room air (by using ceiling mounted humidifiers) could be a potential technique for control of airborne covid transmission.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.