We are told that, on the one hand, heads should roll for not providing health-care workers with enough masks to save their lives, and on the other, that masks will not aid us the people in trying to survive the virus. We smell a rat. Further, the frail elderly among us have grown sceptical of the words of professional bureaucrats and politicians -- we would rather know the raw facts and live or die based on our own judgement. It’s all a bit life and death. So, here are the facts. They do not rely on an elevated position in a bureaucracy but rather on fifty years hands-on experience with fluid dynamics and particle dynamics.
The virus is a respiratory virus, meaning that it attacks the respiratory system and finds new hosts by the process of exhalation. The human skin is a desert of dead cells and, although it produces most of household dust by shedding, it is mute of malice in spreading the virus. The virus makes its living by getting from an infected respiratory tract to an uninfected one. It can only do this by being carried in droplets of liquid. Left alone in the air, it cannot move relative to the air and is not a happy camper. So, let’s look into droplet production by exhalation.
In normal breathing, we produce a range of droplets. Our yardstick is the micron -- there are 100 microns in a hair’s breadth and the droplets we produce range in size from submicron to 1000 microns. The smallest droplets are produced by thelittle ducts that lead to the alveoli (the tiny little balloons in the lungs). The ducts close, at the bottom of the lungs at the end of inhalation and then open, producing bubbles that break and release the submicron drops. These are carried away in the breath. Surprisingly, the main producer of droplets is the vocal cords. These rattle something terrible when you speak or cough and shake loose little bits of liquid. You produce more of these when speaking loudly than when coughing. The droplets are carried by the stream of your breath into the space in front of you.
Modern measurements show that normal breath travels at about a metre and a half per second, while coughing and sneezing get up to four and a half metres per second. So, this exhalation carries a range of drops from submicron up to about 200 microns, for normal breathing and speaking.
When the particles get into the fresh air, they start evaporating. They are relatively warm, and the little ones evaporate much, much faster than the big ones because they have more surface area per molecule of liquid. In the high, hot desert, they evaporate very fast. In Louisiana, they don’t.
What about this two-meter business? Imagine that you send out a breath. It goes out at 1.5m/s and has the form of a speaking trumpet, spreading out a little as it moves. It is surrounded by a toroidal vortex that, in the old days, was visible as a smoke ring. This vortex insulates it from the still air, so it goes a long way -- metres. Assume that it is going straight out in front of the person who is breathing on you. Then, it takes 1.3 seconds to cover two meters. During that time a one-micron particle has fallen 0.17mm, a ten-micron particle falls 2mm and 100-micron particle falls 300 mm. So, which size droplet is going to get you? Well, the Wells equation predicts that in a hospital, all particles smaller than 50 microns will evaporate in a second and leave the virus high and dry (and dead).
So, in a hospital and in theory, only particles larger than 50 microns are a danger to a socially distant person. And then there is this concept called,” in practice.” If you are walking in a gentle breeze (Beaufort scale 2, or 4 m/s), then all bets are off because it will cover the two metres in half the time and 10 to 20-micron particles, with almost no falling, can get you.
What of masks? Do they work? Well, you cannot make a mesh aperture down to a micron. Forget the notion of marbles being too big to go through a strainer. So, modern masks jumble a whole lot of very thin fibres into a space and draw the air through them. Because the passages available to flow are so narrow and so twisted, two things happen. Firstly, there is considerable resistance to flow and you have to suck quite hard to get your air. Secondly, the little particles, barrelling along the passages, bash into the walls. This leads to mechanical entrapment and all sorts of surface interactions that stick the particle to the wall. The bigger the particle, the more likely it is to come upon the corners and get trapped. This is the reason why they rate masks as trapping 95% of particles -- it has to be statistical. Because of the resistance to air flow, the masks tend to seal all around the face while sucking -- except where the nose tents them up. Intuitively, it would seem that about 90% of the inflow would go down this space. Not good. (Speaking in a racially insensitive manner, many Orientals are better off because the bridge of their nose is lower). You want a better than 10% improvement when you wear a mask, so this is not good enough. When you exhale, the same thing happens, and you blow a jet of air into your eyes and mist up your glasses. The turbulence around your eyes also encourages free floating droplets in the atmosphere to rattle around and perhaps become trapped in your moist eyes.
From our frail, elderly viewpoint, what should we do then?
You should buy a mask that has provision to seal off around the bridge of your nose. You can tape it down to your cheeks if you need to. With this mask, even if it is quite poor -- a P1 or N90 -- you will be okay at two meters. If you are in a room with people, you definitely need an N95 or P3 mask, sealed over the nose or, preferably, you need to leave the building.
How worried should we be? If you live in the USA, then about 3 million people must die every year of old age. Speaking as a 73-year-old, with leukaemia, I can afford to be quite matter of fact about stepping off the twig. We, the elderly, tend to prefer this level of plain speaking (preferably loudly). So, three million of us are going to die every year, mostly from the comorbidities that we have picked up along the way. Statistics seem to show that a lot better than 90% of people who die from the virus have comorbidities. Clearly, what is happening is that when we are old and frail, the weakest of us will die preferentially. But, in the U.S., the very worst prediction is that a total of 100,000 will die in this epidemic. Contrast that with the three million who are going to die anyway and note that this is merely 3% of that number. An examination of the actuarial tables will show you that this is not your greatest fear. In fact, it is nothing, compared with the real danger of being bored to death by the frenetic media. Certainly, the danger to us is not worth ruining the economy for very marginal gain. In the scheme of things, we weren’t going to last very long, anyway