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