On pollen and airborne virus transmission

This study investigates how airborne pollen pellets (or grains) can cause severe respiratory-related problems in humans. Given that pollen pellets can capture ribonucleic acid viruses, we show that airborne pollen grains could transport airborne virus particles such as the airborne coronavirus (CoV) disease (COVID-19) or others. We consider the environmental conditions featuring the highest pollen concentration season and conduct computational multiphysics, multiscale modeling and simulations. The investigation concerns a prototype problem comprising the transport of 104 airborne pollen grains dropped from a mature willow tree at a wind speed of (Uwind=4 km/h). We show how pollen grains can increase the coronavirus (CoV) transmission rate in a group of people, including some infected persons. In the case of high pollen grains concentrations in the air or during pollination in the spring, the social distance of 2 m does not hold as a health safety measure for an outdoor crowd. Thus, the public authorities should revise the social distancing guidelines.


I. INTRODUCTION
In plant biology, pollen is a microscopic grain discharged from the male part of a flower that can fertilize the female ovule to which pollen is transported in huge numbers by wind or in small numbers by insects such as bees. Pollination is the transport of pollen grains from their male site of production, i.e., tree and grass flowers, to the female landing site. Pollen grains size can range from some micrometers to tens or hundreds of micrometers. Their topology is very complex, and their shape generally varies from spherical to oval depending on the complex through a not fully understood dehydration process that occurs during pollination. Thus, the environmental conditions of the surrounding environment, i.e., ambient air temperature (T air ), relative humidity (RH), and wind speed (U wind ) play a crucial role in the pollination and the changing shape of pollen grains. Figure 1(i) shows an example of some pollen grains from electron microscopic images revealing different topologies. 1 Figure 1(ii) 2 shows an example of the shape change in pollen grains due to dehydration. Some of the airborne pollen grain species are known to cause human severe respiratory diseases. 3 The knowledge of airborne pollen transport, environmental effects, and the pollen interaction with other airborne viruses or aerosols is scarce. Madanes and Dadon 4 and Velasco-Jim enez et al. 5 made essential efforts to quantify the best sample location and the minimum required sample types of airborne pollen grains required to characterize site-scale airborne pollen. They found that increasing pollen counts from 150 to above 2700 does not yield different results among the dominant and subdominant types, which account for 70%-80% of the pollen sum. Sado and Inouye 6 conducted a statistical study on airborne pollen grains. Plotting the number of days as a function of a specific type of airborne pollens, they found a normal distribution. Damialis et al. 7 investigated the effects of wind direction, speed, and persistence on the transport of airborne pollen into a city. They revealed the significance of wind persistence in pollen transport, mainly when a breeze prevails for a considerable part of the year, i.e., the spring season. Tampieri et al. 8 studied the transport of airborne pollen. Their work evaluated the area concerned with pollen dispersion coming from a distant source. They estimated, from travel time and the viability of the pollen itself, an extended distance within which the exchange of genetic material can occur. Buitink et al. 9 investigated the calorimetric properties of dehydrating pollen by analyzing a desiccation-tolerant and an intolerant species.
The present study sheds light on the link between the increase in the coronavirus disease (COVID-19) infections among humans and pollination during March, April, and May, where specific outdoor temperature, relative humidity, and wind conditions exist. The above is based on the hypothesis that an airborne coronavirus (CoV) particle or airborne infected saliva droplet can adhere to a pollen grain. Past research supports evidence for the above as follows: • Molecular detection of ribonucleic acid (RNA) viruses in pollen pellets. 10 • Airborne pollen is likely a seasonal factor in inhibiting flu-like epidemics. 11,12 • Airborne pollen grains can be present for a long period in the environment outdoor in cities but also indoor such as in streetlevel shops. 13  For the first time, through advanced computational multiphysics multiscale modeling and simulations, we investigate the effect of pollination on increasing airborne virus transmission. We will show how pollen grains dropped from a mature tree and transported by a breeze toward a crowd (including some infected individuals) can significantly contribute to an increase in the coronavirus transmission rate. Finally, we will emphasize the role of social distancing in reducing airborne virus transmission in the presence of airborne pollen.

II. COMPUTATIONAL MODELS, DOMAIN AND BOUNDARY CONDITIONS
The Lagrangian multiphysics, multiscale computational fluid dynamics (CFD) solvers (transient numerical models) developed in Refs. 18-22 are applied in this study. We consider the coupled fluid dynamics and heat transfer equations at the scale of the pollen grains. Thus, we account for the effects of the change in calorimetric properties as a function of the relative humidity, temperature, and wind speed of the ambient air, e.g., particle size and drag and lift force variations due to the evaporation/dehydration of pollen grains. 9 All the equations are discretized in space in a finite volume method 23 framework, and the k À x À SST turbulence model was applied as the turbulence model. The environmental conditions in the computational domain are imposed to values as those close to ones corresponding to a spring season with T air ¼ 22 C; 2T ground ¼ 17 C; 1RH ¼ 50%. The boundary temperature of the crowd is applied as A complete 3D model of a willow tree is created with a considerable number of tree leaves as sources of pollination (see Fig. 3) that ejects 10 4 pollen grains due to a breeze at U wind ¼ 4 km=h. Furthermore, we introduce a realistic 3D model for a crowd of people into the computational domain at a vital distance away from the tree, as shown in the bottom side of Fig. 3. The velocity and pressure boundary conditions on the extremities of the computational domain are imposed as freestream boundary conditions. For pressure, this ensures an outlet-inlet condition that uses the velocity orientation to blend between zero gradients for standard inlet continuously and a fixed value for normal outlet flow: left side of the domain in Fig. 3 upstream of the tree. For the velocity, this ensures an inlet-outlet boundary condition that uses the velocity orientation to continuously blend between fixed value for standard inlet (U wind ¼ 4 km=h) and zero gradients for outlet flow: right side of Fig. 3 downstream of the crowd.
We consider initially each pollen grain to have a density of q p 0 ¼ 1435 kg m À3 and C p 0 ¼ 2000 J kg À1 K À1 corresponding to an initial 0.1 water content mass fraction (see Ref. 9). The initial size distribution of the pollen grains diameters attached to the tree leaves is imposed as a normal distribution law f ðd p Þ such that (1) with a mean value l ¼ 25 lm and a variance r ¼ 2 lm. These values are in the approximate correct statistical range of data for willow pollen grain diameters.

III. RESULTS AND DISCUSSION
In this section, we present results for pollination for wind speed of U wind ¼ 4 km=h ð% 1:1 m=sÞ, air temperature T air ¼ 22 C, However, there is a significant flow diversion upwards. Figure 5 also reveals higher wind speeds surrounding the larger group. We attribute the above behavior to several reasons: • The denser and larger crowd creates a rougher surface over which flowing air is perturbed, leading to recirculation regions and turbulence. • The more significant number of people creates several small gaps that trap the flowing air leading to vortical structures.
• The vortical structures have a downward effect on the deflection in the case of a larger crowd. The above scenarios provide a qualitative comparison of the effects of larger vs smaller crowds on the environmental flow. • Thermal gradients induce buoyancy effects. Individuals have higher boundary temperature, T air ¼ 30 C, compared to the ambient air T air ¼ 22 C.

B. Pollination: Airborne virus transmission
The 10 4 pollen grains released from the tree do not reach the crowd's boundary at t ¼ 10 s [ Fig. 6 (Multimedia view)]. Some pollen grains start coming to the crowd's edge at t ¼ 20 s, consistent with the U wind ¼ 4 km=h ¼ 1:1 m=s speed of the breeze and the 20 m distance separating the crowd from the tree. At t ¼ 30 s, the pollen grains completely penetrate the crowd in the wind's direction (left to right) but without significant dispersion perpendicularly. A side perspective of the results is shown in Fig. 7 (Multimedia view). The pollen grains field continues to preserve its major flow direction, aligned with the breeze, without major dispersion in the gravitational direction. At t ¼ 40 s; t ¼ 50 s; and t ¼ 60 s, pollen grain dispersion takes place in   Physics of Fluids ARTICLE scitation.org/journal/phf with the wind than a saliva droplet. This is because a pollen particle is lighter, with less water content, and it is very much more porous than a saliva droplet. The above analysis leads to a critical conclusion that in environmental conditions like those in Figs. 6 and 7, pollen may increase the airborne virus transmission rate.

C. Airborne pollen dynamics-Case of a group of people
We investigate what happens if the crowd is reduced to only 11 individuals instead of 97 under the same breeze speed, temperature and boundary conditions. The results of Figs. 9 (Multimedia view) and 10 (Multimedia view) reveal that the pollen grains detached from the tree and transported by the wind do not disperse all around the areas, covering the individuals' positions. Therefore, in high pollen grain concentrations in the air or during pollination in the spring, the minimum social distance of 2 m does not hold as a safety measure for a crowd outdoor. Thus, it should be revised by public authorities.

D. Quantitative analysis
We calculated the total number of airborne pollen grains suspended in the air in three different zones that envelop the crowd of 97 individuals and 11 individuals (Figs. 11-13). The numerous pollen grains at the ground level y ¼ 0 were not counted. In the volumetric zone at 20 x 40 m; y 2:5 m, the pollen cloud traverses the group of people (Fig. 11) for (t ! 50 s). Both the residential time and the total number of pollen grains are higher in the crowd of 97 than 11

IV. CONCLUSION AND PERSPECTIVES
We showed that at some environmental conditions of ambient air temperature (T air ), relative humidity (RH), and wind speed (U wind ), airborne pollen grains play a non-negligible contributing role to transporting airborne virus particles. Under the scenario of a spring season conditions outdoor at T air ¼ 22 C; T ground ¼ 17 C; RH ¼ 50%, we investigated the transport of 10 4 airborne pollen grains dropped from a mature willow tree due to a breeze at U wind ¼ 4 km=h.
Assuming that a coronavirus particle can adhere to a pollen pellet's surface, 10 we showed how airborne pollen pellets transported by a light wind can penetrate and disperse into a crowd of individuals, even when the social distance of 2 m is maintained. We showed that if only some persons in this crowd are infected, then the pollen grains dynamics can increase the airborne virus transmission rate.
Studying a smaller group of people under the same conditions, we found that the minimum social distance of 2 m is not sufficient as a health safety measure for a crowd outdoor at high pollen grain concentration or during pollination in the spring, i.e., March to May. Thus, public authorities should revise the social distancing recommendations. The above should be adapted accordingly in different countries, which may have different pollen seasonality. 25 Future work will investigate the influence of different environmental conditions, i.e., parameters like the air temperature, relative humidity, and wind speed on the airborne virus transmission rate induced by pollination with critical pollen grain concentrations in the atmosphere.

ACKNOWLEDGMENTS
The authors would like to thank the Editor-in-Chief and Physics of Fluids staff for their assistance during the peer-review and publication of the manuscript.   The numerous pollen grains at the ground level y ¼ 0 are not counted. The simulations concern pollination of 10 4 pollen grains detached from a mature willow tree at U wind ¼ 4 km=h; T air ¼ 22 C; T ground ¼ 17 C; RH ¼ 50%.

DATA AVAILABILITY
The data that support the findings of this study are available on request from the corresponding author upon reasonable request.