key: cord-0837411-h1zm94p4
authors: Carelli, Pasquale
title: A physicist's approach to COVID-19 transmission via expiratory droplets
date: 2020-06-17
journal: Med Hypotheses
DOI: 10.1016/j.mehy.2020.109997
sha: 49669d100425e5a1e711eeaf7c59e3de64bd97c8
doc_id: 837411
cord_uid: h1zm94p4

In this paper, a physicist's approach is given to support the necessity to wear surgical masks during the COVID-19 pandemics; they have become compulsory in Eastern countries, while in Western countries they are still an optional. My thesis is supported and described on the basis of a physicist's model which studies the droplets behavior when emitted by the respiratory apparatus of an infected person, symptomatic or not. The intermediate dimensioned droplets are proved to be changed into aerosol, losing their water content and becoming seriously contagious, but in their initial phase they could be easily caught by a simple surgical mask. The actual efficiency of FFP3 masks has been examined and found to be lower than expected.

While the COVID-19 pandemic is spreading around all over the world in a dramatic way, I think it is necessary to state a reference date in order to make any reflections, I chose the 3rd April 2020.

On that date in Italy there were 14,681 dead people and 119,827 infected, the situation was dramatically changing with a number of deaths higher than 500 a day.

That rate (mortality) caused by the virus is of 0·11 (deaths/population).

At the same date in South Korea there were 120 dead people and 9,037 infected, mortality was of 0·002% with a lethality rate (deaths/infected people) of 1·3%. As the population in South Korea has a life expectation very similar to the Italian one (even if Koreans are younger than Italians[1]), the Korean data about lethality is more plausible.

One of the reasons of such a serious pandemic in Italy and afterwards in many other western countries, could be the following: in Asian countries surgical masks have been widely worn for many years as a means to protect other people. This habit, There are non doubts about the fact that expiratory particles transmit the pandemic, but we must make a coarse distinction among droplets and their dynamic evolutions when emitted by infected people. This paper wants to afford the problem from a physical point of view.

The airborne disease is caused by violent coughing [3] and sneezing [4] , but many infected people were minimally symptomatic or asymptomatic at all [5, 6, 7] and transmission of virus from asymptomatic carriers has been identified [8] . We always emit a large quantity of droplets[9,10] even just breathing and speaking.

Whatever is the possible expiratory particle source, I assume that the smallest droplets are more numerous than the bigger ones and I won't distinguish between speaking and any other more violent expiratory events.

A single initial very large droplet (R0=1 cm radius, V0=4·2 cm 3 volume) containing a large viral load (10 8 virions for milliliters [8] ) splits in many smaller droplets (the largest droplets having a radius of R3=50 µm ). The model that I propose assumes that the number of fragments with a radius between r1 and r2 is given by:

where A is a dimensionless constant. A is simply 3 times the cube of ratio between R0

and R3 because the volume of the initial droplet must be equal to that of all the smaller droplets; in this specific case A's value is 24000. , their viral load is absolutely negligible. Those particles cannot be stopped by a surgical mask, but there is no reason to intercept them because they are just water or mucous. For the aerosol the gravity has a negligible effect, unless it is in an environment with brackish air.

The second group (in green in Fig.1) , is made of droplets with the biggest size, having a radius larger than 25 µm, they are a bit more than 15,000. They constitute almost the total volume of the initial large droplet and then they contain most of the viral load. They follow a parabolic trajectory and constitute what is called fomite [12] , which can contaminate surfaces where they settle.

The third group (in black in Fig.1) is made of droplets with an initial radius between 2·5 µm and 25 µm, they are about 55,000. Their dynamic is strongly dependent from the Stokes law, that states that a spherical droplet of radius R, moving in the air, undergoes a drag force given by:

where µ[13] is the air viscosity.

At first they don't behave like the aerosol, because the gravity action has an important role compared with the drag force; anyway at the end the two equal and opposite forces rapidly balance and the droplet reaches a descending speed limit. That movement is slow and it allows the evaporation of water, till the droplet is reduced to its particulate or virus and it has become aerosol.

These droplets have a substantial viral load, they are quite numerous, some thousands of them can contain just one single virion each and they are probably the most contagious and dangerous elements[14]; if not stopped on time, they constitute the real element of airborne infection [15] . Take note that at the starting phase, when they are larger, they could be easily caught by a common surgical mask. The evolution of those droplets has been roughly studied a long time ago by Wells [16] ;

more recently it has been deeply analyzed [17] . Of course the distinction of the three different typologies of droplets is purely as an indication, they are not exact measurements.

In the fluids dynamics we define fluidodynamical resistance the ratio between the gas flux (usually measured in liter/s) and the pressure difference. In a normal person breathing through the nose, the fluidodynamical resistance is about 250 Pa liter/s [18].

FFP3 masks [19] have very specific technical characteristics, they should have a fluidodynamical resistance lower than 63 Pa liter/s and filters at least 99% of airborne particles larger than 0·3 µm. We know that virions of SARS-CoV2 are about 0·1 µm. Fig.2 shows a drawing on scale of a filter (simulating the FFP3 mask filters) with holes of 800 nm diameter and a particulate with a 300 nm diameter (down, smaller than the canal): I presume that in 99% of the cases, whatever is the coming direction, it will hit the wall and it will be stopped. The other particulate with a 100 nm diameter, moving on the same direction and angle, goes inside in the same position, but it passes through the canal without being stopped. Therefore a filter able to stop particulates of 300 nm diameter in 99% of cases, can't have the same efficiency for smaller particles.

Shortage of FFP3 masks has been considered a very bad event, but I don't believe we need them so much: as a matter of fact, to be an absolutely safe protection they should cling to the face completely, which is impossible, especially when worn by bearded men.

Success in fighting against a virus depends on how deep is knowledge of its characteristics: to understand how the virus aerosol changes after being emitted from the otorhinolaryngological apparatus is important in order to recommend a widely spread use of surgical masks everywhere people speak, especially indoors. Moreover I underline how FFP3 masks are poorly efficient in preventing infection, considering the nature of infectious aerosol. Waiting for a new vaccine we could hope to extirpate the SARS-CoV-2 like it happened for Smallpox [19] .

A cough aerosol simulator for the study of disease transmission by human cough-generated aerosols

Violent expiratory events: on coughing and sneezing

Kin-Hang Kokn and others, A familial cluster of pneumonia associated with the 2019 novel coronavirus indicating person-to-person transmission: a study of a family cluster

Xingwang Li and others, A novel coronavirus from patients with pneumonia in China

Guangfu Jin, and others, Clinical characteristics of 24 asymptomatic infections with COVID-19 screened among close contacts in Nanjing, China

Gisela Bretzel and others, Transmission of 2019-nCoV infection from an asymptomatic contact in Germany

The size and the duration of air-carriage of respiratory droplets and droplets-nuclei

The size distribution of droplets in the exhaled breath of healthy human subjects

Holbrook and others, Aerosol and surface stability of SARS-CoV-2 as compared with SARS-CoV-1

On air-borne infection: Study II. Droplets and Droplet nuclei

How far droplets can move in indoor environments--revisiting the Wells evaporation-falling curve

Zdenek Jezek, and others, Smallpox and its eradication