CORONA VIRUS: SIZE DOES MATTER
I decided to teach my grandchildren about orders of magnitude. Most of us ignore THAT which we cannot see, and some believe that what we cannot see is not really there. And yet those things we cannot see can do us great harm, as everybody surely knows by now.
I decided to stick with metric, because it is a lot easier. A meter is a little more than the average stride. 1.8 meters is about 5 foot 10 and is just above an average height for a male adult human.
Once we have a good feel for this, we use prefixes to expand these names. We all know what size a kilometer is roughly, but of course it is exactly 1,000 meters. Similarly, a millimeter is exactly 1/1,000 of a meter (or, put another way, 1,000 millimeters make a meter). These prefixes expand out in both directions, so that kilo-, mega-, giga- , and tera-, become a thousand, a million, a billion, and some number I don’t know, respectively.
Scientists make this more concise by writing 10 with a superscript number like 106 for a million. (The 6 here is called the exponent, or the power, or the number of zeros). Kilo- is 1 with 3 zeros, mega- is 1 with 6 zeros, giga- is 1 with 9 zeros, and tera-, as in 1 tera-byte of memory, is a 1 with 12 zeros! In 1969 when I first programed computers as part of my summer job in High Energy Physics at the University of Toronto, I used an IBM 360/365 computer, and I had to set delimiters for my volume of memory from 8 to 16 kilobytes. You can go into just about any computer accessories store now, and buy some storage device for one terabyte of memory, essentially 1,000,000,000 times the amount of memory I could eek out of that old IBM, a computer that consumed a lot of Convocation Hall at University of Toronto (about the size of a house).
Again, similarly, the meter can be further subdivided to milli-, micro-, nano- and pico-. This gets tricky, because we are now dividing by tens instead of multiplying and writing this out like the fraction representing milli-, micro-, nano-, and pico-, gets very cumbersome. Scientists just use the exponent of ten again, but now with a negative number to show we are dividing by that many, not multiplying. A millimeter is 10-3 meters. A micro-meter thus becomes 10-6. One one millionth of a meter, or 1/1,000,000 of a meter. Have I lost you? This is pretty small. It is smaller than can be seen by the naked eye, and its other common name is the micron. But to give you an idea, the width of a human hair is often 50 microns or fifty micro-meters. Remember, 20 human hairs side by side, is 1 millimeter wide, because one milli-meter is 1,000 micro-meters. (Well, trust me. 20 x 50 = 1,000). Microns are neat…some cells are 10 microns in size, but they have this magnitude in all three dimensions. We cannot see them.
But can we really see that small, as small as 50 microns, the width of a human hair? Well, you see hair. And if you pull one out and look at it, you see a single human hair, usually, especially with your glasses on. Try it. It hurts a bit, but it is worth it. Can we really see 50 microns? In truth, our limit is probably mostly above 100 microns, or 0.1 millimeter. The reason we can see the human hair is because it has length as well as width (and depth), and the length is well within our ability to see…just not the width (or depth). Amazing, eh? Can you see a thread of a spider’s web? Yup. And yet it is only about 7 microns or 0.007 millimeters wide. But the length could be several centimeters. This gives you a glimpse of human perception, a whole other, but important topic.
The usual smallest division on a ruler in System International, is the millimeter, about the size of an ‘i’ and a little bit smaller than an ‘m’. 1,000 microns.
In fact, if you cut 50 microns off the end of the hair, so now the piece is a tube, 50 microns in both diameters and fifty microns long, you probably will not see it at all (I welcome you to try, but you will need a very sharp knife, a powerful magnifying glass and a strong light source). Take it from me, you cannot see it! Weird.
A closely related issue, but complicated by trigonometry and geography, as well as atmospheric interference and pollution, is how big an object you can see at a distance. This turns out to be about 0.3 meter (a little more than a foot) at a distance of one kilometer (a little less than 2/3 of a mile). Take it from me, that is like looking at 300 microns from as close as you can get your eye to the page and still be able to focus.
So, fifty microns is quite small, right at or just below your limit of your sight. And what you see depends on all three dimensions, not just one or two.
How big is Corona virus? Well, it’s about 125 nanometers, equivalent to 0.125 micro-meters, or microns. One micron is 1,000 nanometers. The smallest we can maybe see is 50,000 nanometers (or 50,000,000 pico-meters…save that for later), but that was the width of a human hair, and we really only see that because it has length. 400 corona viruses lying side to side would be about the width of a human hair.
But if masks can stop airborne (naked, no water droplet around them, and this requires high quality N95 masks really) corona virus, won’t that stop oxygen? Nope.
Oxygen (made up of two oxygen atoms), molecular oxygen, not the atom, is about 150 pico-meters. (I told you to save that). The pico-meter is 1/1,000 of a nanometer, so a thousand oxygen molecules can line up beside a corona virus and be about the same size (125,000/150 = 833 actually, but close). Masks do not block oxygen or carbon dioxide, in either direction, in or out, but they certainly can block corona virus. And corona virus is most often contained in 50-micron droplets or larger, which lots of face coverings and even those silly plexiglass plates in front of the cashier, can catch.
So, wear a mask! (Psst, even behind those plexiglass shields, wear a mask, especially if you are at risk.)
DISTANCE DOES MATTER
Why does distance help prevent Covid?
I think the first answer really should be, “It doesn’t.” If you are in the room of a patient, or patients, spewing corona virus with every breath, every spoken word, every cough, every song, it doesn’t take long to fill the room. Sure, big droplets will slowly sink to the floor. If the air is humid, and the droplets get bigger, they fall faster, but that would be like a sauna where water was dripping off every piece of metal in the place. Mostly, especially during winter, the air is dry, and the droplets which may start as 50 micron (0.050 millimeter) bundles of water, well, they shrink incredibly quickly by evaporation to 1 micron, or 0.1 micron (remember, the width of a thread of a spider’s web, which you can see, is 5 microns), well, these droplets are so light they will float in the air currents and follow the breeze wherever it goes.
But let’s say you are outside, in quiet, still air, no enclosure to your space…say it is dusk and nothing is moving. The sun is down and no longer beating down on surfaces, heating them up and changing all the air currents. Someone with you, maybe one of those 40% who have Covid and spread it unknowingly, never ever getting symptoms but spreading the illness like Typhoid Mary…say they cough. The puff of air, the head of steam if you will, spreads out like ripples from a stone thrown into the water, but in all dimensions, not just the surface. This is like a bubble, like the light from a candle, like the sound waves from a speaker. The intensity reduces quickly with distance. The question is, how quickly?
With many physical phenomena, like light, the reduction is related to the inverse square law. Scientists often speak of some substance like this as flux. If you start with stuff at the centre, and it travels out to one meter, you figure it had spread equally over the imaginary surface like a bubble, a sphere. The area of that surface is related to the distance, ‘r’, from the original centre by a proportion related to the radius ‘r’ squared. Well the density of the virus distributed across that sphere proportional to something divided by that area, so is proportional to 1/4πr2. You can ignore the constant terms, and just think of the amount coming your way at distance r to be proportional to 1/r2.
Take it from me, you probably learned, and actively forgot, this formula for the surface area of a sphere. The important issue is that the amount of stuff that started at the centre decreases with every meter your move from the origin. So, whatever you have at one meter, is reduced by one quarter at two meters, and one ninth at three meters, one sixteenth at four meters, and so it goes forever.
If you cough in someone’s face at a one foot distance, the amount of virus at two feet is one quarter what it was at one foot.
In fact, it may be even less than that, because the virus doesn’t all keep going. Some of it stops, bumping into other particles in the air, and so the inverse square law may deviate towards the inverse cube law, closer to 1/r3. The stuff at one meter becomes 1/8 at 2 meters, and 1/27 at three meters.
If this makes no sense, don’t worry. Just understand that the amount of virus spewing your way goes down quickly with distance, but never goes to zero.
But that is really only out in the open, or maybe in a large department store where ventilation is forcing air up and out. Nevertheless, distance reduces the amount of virus that hits you, and that is important.
Also, the droplets that are heavy, and carry some momentum, travel in a straight line. These are the 50 micron droplets or greater. Full of corona virus, they splat onto the plexiglass plate, or the mask, or the goggles, and end up being cleaned up later. The droplets that are smaller, or the naked virus which is only 125 nano-meters (remember, 1 one thousandth of a micron, 1 billionth of a meter!), these all travel with the flow of air, and do not have enough momentum to bump into walls and corners when the air flow turns around. They continue with the middle of the stream, because they are not heavy enough to break away and travel in a straight line.
Let’s pause here and think. If the 50 micron droplets go splat on the barrier between you and the cashier, what happens to the 1 micron droplets and less. Think about sitting in the backseat of a car and going around a corner. Say you are sitting beside a person you really do not want anything to do with. There is effort you have to produce to prevent leaning into that person. The 50 micron droplet has the same problem. If it hits the wall, it gets stuck. If it goes with the flow, it escapes to carry on.
We know that fifty-micron droplets are big enough, have enough mass (weight?) that they get smeared on the walls of any channel that turns a corner. The ten-micron droplets are not big enough to travel a straight line always. But they often get stuck in the throat instead of travelling all the way to the lungs, because that’s where the major corner in the airway is. The 0.1-micron droplets, and of course the naked virus, have no trouble at all traveling with the flow. This is possibly the distinction scientists make between ‘droplet transmission’ and ‘airborne’. Go with the flow. So droplets of corona virus get reduced as they travel, but never to zero…unless the cashier is totally enclosed in the plexiglass. And they never are, are they? In fact, when you talk to the cashier, don’t you lean around the plexiglass so your voice carries far enough that she can hear you, or you her?.
So, why do I think the smaller droplets do not hit the plexiglass but actually take a circuitous route? Because other well-known physical substances do exactly that. Here I often call upon the chocolate chip cookie analogy. If the cashier were baking chocolate chip cookies back there beside her cash register, could you smell them? How about someone in a living room striking a sulphur tipped match to light a cigarette, can you smell that? That is the big difference between droplet transmission and airborne. Small odorants, lit matches, cigarettes, and baking chocolate chip cookies have odours that permeate space and are like gaseous substances (gaseous substances are those which expand to fill their containers…this, to me, has always been consistent with the definition of a teenager!!).
The analogy is a little unfair, because some of the cookie odor, and definitely other odorants, can get to us through molecules probably even smaller than corona virus. But baking cookies does it better than cookies that have cooled down, I suspect because of water droplets, carrying the odorants, are originally produced by steam, from the heat of baking. And steam is like an aerosol, or tiny water droplets. Sure, odorants are smaller than corona virus, but small water droplets, 0.1 microns, are bigger…and that is what most often carries the wonderful smell of chocolate chip cookies, or perfume and other odorants…well they are pretty damn small. They travel with the airflow, not along the usual straight line. And the nice, smiling, coughing cashier is really not all that far away even behind a plexiglass plate, is she?
Barriers, like plexiglass, add to the distance the virus has to travel, as well as reducing the amounts that actually get to you if they hit a barrier. So, reduction, yes, but never eradication. All of these efforts are to reduce the risk, but none ever removes the risk. Sure looks to me as if the cashier should be wearing a mask as well as standing behind the plexiglass shield.
NUMBER DOES MATTER? DOESN’T IT?
I think so, but I cannot find proof.
The number of virus particles that one needs to be exposed to, to induce disease, is not clear. It is a probabilities game, really. One virus probably will not do it. It is far too easy for that virus to end up in the wrong place. We simply do not know if it takes three, or one hundred, or one million virus particles to cause symptomatic infection. We do know that a lot of people get the infection but never have symptoms. These people are still contagious.
The virus has to grow in people (occasionally animals). It cannot grow in the air or on a surface because it needs the chemicals of a human cell (or some animal cell). And we know it grows best in the back of the throat and in the lungs.
But could it be that people who get a small amount of virus initially are less likely to get symptoms? Could it be that the race between the body’s defenses (the immune system) and the total numbers of the virus (which depends on initial exposure) determines the symptoms in the end? It makes sense. Massive exposure versus minimal exposure. There seems to be evidence of this with other infectious diseases.
Children have more rapid defense mechanisms, and children tend to get symptoms from exposure far more rarely…but children can still pass it on to others. Suppose you are standing ten feet away from someone with the disease, instead of six feet. Suppose that is enough of a change in initial exposure to cause you to have fewer overall symptoms, to make the difference between someone who suffers and dies with the disease, and someone who merely gets the sniffles, or someone who remains without any symptoms and just passes it all on to someone else.
We simply do not know the answers yet, and it is very complicated anyway. But we do know that the more distance you keep from someone with Covid, the less likely you can get it and pass it on. And the more times you protect yourself by wearing a mask, the less likely you are to become part of the problem. This is the dynamic cycle Dr. Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases (NIAID), talks about. You can break that cycle by wearing a mask and keeping your distance.
Since 40% of patients with the infection do not realize it, there is no way we can know. You can get a rough idea from the numbers in your community. If your town is a hot spot, the risks are higher. If your town has not had a case in three weeks, your risks are lower.
So, wear a mask, and keep your distance from everybody who is not in your pod. Wear a mask if you can see the whites of their eyes. Keep a distance so you cannot see the whites of their eyes. Wear a mask even behind the plexiglass. It is your responsibility, to yourself, to your community, to break this cycle of Covid.
Science Fiction Doctor 
One thought on “Corona Virus: Size Matters. So Does Distance”