Cough Aerosol Cloud Parameters

. This work is a further development of the authors' COVID-19 pandemic consequences research. The dynamics of the cough aerosol cloud was studied. An experimental setup for fixing spatial and temporal distributions of aerosol cloud velocities was used. Flags were placed on the threads of the experimental setup. On the first and second frames, the area and shape of the flags were different. The process of air passing through the frames was recorded by photographic equipment. The footage was compared by a computer program to identify differences.The results of an experiment with five adults (18–22 years, men), volunteered for study participation, are presented. The method of aerosol cloud visualization is applied. The dynamic parameters of the aerosol cloud are estimated. The velocity of the air flow arising from coughing was measured. The shape of the flow was determined depending on the time. It was found that the flow front moves with acceleration at the initial stage of propagation and with a constant velocity at the final stage. A nonlinear dependence of the change in the volume of cough air flow aerosol on time was established.


Introduction
Aerosols are a substance that determines the existence of living organisms on Earth [1].Multi-kilometer aerosol clouds [2] move around the planet and carry bacteria, fungal spores and mold over huge distances.The transport of aerosols [3] is cyclical and has a significant impact on the functioning of ecosystems [4].Moisture particles in the air exhaled by humans and animals may contain viruses [5].In this way viruses can migrate [6] and transmitted from one carrier to another [7].Such an exchange of small particles between living organisms through the transfer of an aerosol can be both positive and negative, associated with the transfer of dangerous viruses and bacteria [8].To understand the mechanisms of transmission of viruses from one organism to another, it is necessary to know the laws of the aerosol cloud movement [9] that arises during breathing, sneezing and coughing [10].The transfer of bacteria and viruses can occur on moisture droplets [11] contained in the exhaled air, and represent an ideal transport mechanism for the microorganisms.An obstacle to the transfer is the high rate of evaporation [12] of moisture particles when they get into the environment.The evaporation process depends on the parameters [13] of the environment: temperature, pressure, humidity.In addition, it should be taken into account that the drops can connect with each other, the resulting large drop leaves the cloud quickly enough.The evaporation rate of droplets [14] depends primarily on their size and is negligible for micron-sized droplets [15].When determining the lifetime of liquid droplets in an aerosol cloud, it is necessary to take into account the drop rate under the influence of gravity, as well as drops movement associated with air convection [16].It is important to take into account the statistics of the distribution of aerosol cloud droplets by size [17,18].
The main mechanism of moisture droplets transfer in this experiment is the transfer of an exhaled air jet containing aerosol cloud.It is necessary to take into account the next expansion of the jet due to the difference between an air pressure in the lungs and the atmospheric pressure.
Such a pressure difference can be 40-300 mm of mercury.The flow rate is 4-7 liters per second, the maximum volume of exhaled air can reach 3-4 liters.The parameters of each specific single cough are individual, their exact reproducibility is difficult.The experiments carried out make it possible to estimate the rate of propagation of exhaled air during coughing and visualize the shape of the front of the spreading air.

Methods
An experimental installation created by N.A.Parfentyev [19] was used (Figure 1) to fix the spatial and temporal distributions of the air flow velocities created by coughing.The installation is a pair of frames with horizontal threads.Flags are placed on the thread, which are deflected by the pressure of the air flow [20].The sizes of the flags of the first and second frames differ.The dynamics of the process was recorded by photographic equipment.Then computer processing of the received images and their comparison was carried out.The volunteer was at a distance of about one meter from the first frame (right one), the second frame was about half a meter away from the first.There were two frames in the camera's field of view at once.Thus, it was possible to fix the disturbance front in two cross sections.The time of propagation of the front through the frame and the distribution of deviations of the frame flags corresponding to the spatial distribution of air flow velocities were recorded.
The process was recorded on a high resolution video camera.Then the video frames were selected.Then such selected frames were compared with each other.The video recording frequency was equal to 30 frames per second.The frames separated by 1/15 seconds were compared.Successive changes in the position of the flags of the left frame of the experiment installation are shown in Figure 2. The sequential change in the position of the frame flags when the airflow front passes through the frame is shown in Figure 3.The total time of the process shown was about 1.2 seconds, the time between the two comparative pictures was about 2/15 seconds.
The total distance from the second frame to the source of the cough was 160 cm.The first frame was at 41 cm closer to the source.
Table 1 shows the parameters of the air flow from the source to the frame.The Start1 parameter shows the time (unit of measurement 1/30 of a second, the time between two consecutive shooting frames) between the moment of the cough beginning and the beginning of the flags disturbance in the first frame, Start2 -the time between the cough beginning and the beginning of the flags disturbance in the second frame, Stop1 -the time between the beginning of the cough and the end of the process of rejection of the flags in the first frame.The Stop2 parameter shows the time between the beginning of the cough and the end of the process of rejecting the flags in the second frame.The time of the flags movement stopping is a rather subjective value and depends on the criterion of the movement stop fixing.Small fluctuations of individual flags continue for a long time due to both the cyclic dynamics of the air mass movement process and possible residual fluctuations of the flags themselves.However, the developed subjective criterion for stopping the process allows you to record the moments of the beginning and end of the air flow.
Another method used to determine the spatial and temporal characteristics of the airflow created by coughing was the visualization method.The inhaled air was tinted with the smoke from an electronic smoking device and then exhaled in the form of a cough.The spread of the tinted air mass was recorded by photographic equipment.The snapshots were compared using a computational program.As a result, a picture of the propagating air flow was obtained.The source of the cough (volunteer) was located on the right slice of the image -we can see the profile of the real person face.The size of the area in the frame is approximately 60 cm (horizontal) by 40 cm (vertical) (Figure 4), the time step of the pictures is 1/30 sec.(Figure 5).

Results
The velocity of the airflow between the frames is 1.3 -3.0 m/s with a "strong" cough, and 0.3-0.7 m/s with a "weak" cough.The spread of values is significant between the five subjects.The measurements were carried out indoors at an air temperature of about 26 degrees Celsius.The distance from volunteer mouth to airflow front with time is shown on left part of Figure 6.Dependence of the flow area from time is shown on the right part of the Figure 6.As follows from the graph, the first 1.5 seconds the front moves with the acceleration, after that the velocity of its propagation becomes almost constant.The first 0.5 seconds the movement of the front is directed downward at an angle of about π/4 to the horizon level.The front surface (ellipse) is located below the level of the source (mouth).Then there is a change in the shape of the surface with its transition to a circle.The surface of the front rises above the horizontal line of the mouth.At the fourth second of propagation, the surface of the flow front rises to the level of the top of the person's head -the source of the cough.
In the interval from the beginning of the process to 1.3 seconds the entire volume of the flow is within the framework of the figure and it is possible to calculate the change in the area of the propagating flow.At the initial stage, the increase in the area of the spot depends almost linearly on time, then the dependence change to a nonlinear one.

Discussion
We measured the air flow velocity from coughing.There is a significant spread of measurement results from person to person.Two subjects cough strongly, the flow rate is 2-3 m / s, three people -weakly (1.3 -0.4 m /s) with a "strong" cough.With a "weak" cough, the indicators are approximately similar (0.3-0.9 m/s), with the exception of two subjects.One of them always had a "strong" cough, while for the other it was not possible to measure the velocity of a "weak" cough flow.This means that for a set of statistics, it is necessary to pre-test the subjects and divide them into groups, depending on the purpose of the study, as well as increase the number of subjects for the improvement of the statistic data.Nevertheless, it is possible to estimate the length and velocity of the spreading flow, which is important for assessing the safe distance when coughing.
With "frames" method we can measure the transverse area of the flow depending on time and calculate the volume of ejected air during one act of coughing.This allows us to estimate the necessary ventilation rate of the room for people to stay safely in it.When visualizing the exhaled air, the shape of the air flow and its change over time, the direction of propagation at the beginning of the process and the change in direction over time were evaluated.The shape of the flow was observed well: an ellipse turning into a circle.For a detailed study of the shape and its changes over time, it is necessary to find the suitable shooting parameters and increase the contrast and to achieve absolute static background condition.
An increase in the processed surface of the image can allow us to measure more accurately the dependence of the volume of exhaled air on time and to measure the parameters of the expansion of air after exhalation.An interesting fact is that the direction of propagation of the air jet during coughing occurs downwards, at an angle up to π/4 to the horizon level.This fact was noted by the authors in previous works.
A new observation is that about a second after the onset of coughing, the shape of the exhaled air flow front changes and this front rises to the level of the top of the person's head -the source of the cough.Meanwhile, the distance from a person to the flow front is about half a meter (for the "weak" cough).It is necessary to verify this fact with different initial cough parameters.In addition, it is interesting to see and evaluate the effect of the inevitable convective flows in the room on the propagation of the cloud.
The mechanism of moisture transfer associated with the ballistic flight of large (up to 100 microns) droplets from person to person was not considered in this work.Observations in bright light shows, that such a transfer is possible at a distance of 1.5-2 m.A drop of moisture that has escaped from a person's tongue during a conversation, overcomes such distance in a fraction of a second.Droplets with 100 microns size have a significant "lifetime" and are the most dangerous from the point of view of the transfer of viruses and bacteria.Since such a transfer mechanism is possible when talking, coughing and sneezing, it is necessary to study it and take it into account for the safe distance estimation.

Conclusions
Based on the visualization method, the nonlinear dependence of the distance from the source to the flow front on the time at the initial (up to 1.5 seconds from the start of the process) stage was measured.The linear dependence of the front movement on time at the final stage is found.The dependence of the volume of air exhaled during coughing on time measured, the nonlinear nature of such dependence is noted.
Using the "framework" method, the parameters of the air flow created when a person coughs were experimentally determined.It is shown that the starting flow rate can vary in the range of 0.3 -3 m/s (depends on the cough source person).The possibility of measuring the cross section of an air jet over time is shown.The possibility of fixing the velocity fields of the cough air flow is demonstrated.

Fig. 1 .
Fig. 1.The installation used in the experiments (compiled by the authors).

Fig. 2 .
Fig. 2. Consecutive pictures of the second frame (interval -1/15 sec.) and their comparison (compiled by the authors).The right picture in the Figure 2 shows the result of the computer comparison of the central and left images.The white margins on the right picture show the changes in the central picture in comparison with the left picture.The left picture was recorded earlier.The sequential change in the position of the frame flags when the airflow front passes through the frame is shown in Figure3.The total time of the process shown was about 1.2 seconds, the time between the two comparative pictures was about 2/15 seconds.The total distance from the second frame to the source of the cough was 160 cm.The first frame was at 41 cm closer to the source.Table1shows the parameters of the air flow from the source to the frame.The Start1 parameter shows the time (unit of measurement 1/30 of a second, the time between two consecutive shooting frames) between the moment of the cough beginning and the beginning of the flags disturbance in the first frame, Start2 -the time between the cough beginning and the beginning of the flags disturbance in the second frame, Stop1 -the time between the beginning of the cough and the end of the process of rejection of the flags in the first frame.The Stop2 parameter shows the time between the beginning of the cough and the end of the process of rejecting the flags in the second frame.

Fig. 3 .
Fig. 3. Flow rates change in the cross section of the left frame, increment 2/15 sec (compiled by the authors).

Fig. 4 .
Fig. 4. Location of human and cloud front (compiled by the authors).

Fig. 6 .
Fig. 6.The distance from volunteer mouth to airflow front with time (left part) and flow area (right part) (compiled by the authors).

Table 1 .
Strong cough flow (compiled by the authors).

Table 2 .
Weak cough flow (compiled by the authors).