WEBVTT 00:00:10.940 --> 00:00:13.080 PROFESSOR: So let's talk about the transfer 00:00:13.080 --> 00:00:16.500 of respiratory pathogens, and in particular, contagious 00:00:16.500 --> 00:00:19.930 pathogens such as viruses and bacteria, 00:00:19.930 --> 00:00:22.750 that infect the respiratory system. 00:00:22.750 --> 00:00:25.690 The way that such pathogens are normally transferred 00:00:25.690 --> 00:00:29.860 is through droplets which are emitted by respiration, which 00:00:29.860 --> 00:00:33.910 could be by just normal breathing, coughing, sneezing, 00:00:33.910 --> 00:00:35.580 et cetera. 00:00:35.580 --> 00:00:38.730 And so here is a sketch of an infected person who 00:00:38.730 --> 00:00:44.730 is undergoing respiration and is emitting droplets into the air. 00:00:44.730 --> 00:00:48.150 And so let's think about what is the fate of those droplets, 00:00:48.150 --> 00:00:49.350 what it could be. 00:00:49.350 --> 00:00:51.930 So one possibility is if the droplets are very heavy, 00:00:51.930 --> 00:00:54.240 they're just going to settle to the ground. 00:00:54.240 --> 00:00:57.330 And then they may collect on the ground 00:00:57.330 --> 00:00:59.370 or on some other surface. 00:00:59.370 --> 00:01:02.040 And then somebody else could touch that surface 00:01:02.040 --> 00:01:03.960 and transmit it, perhaps by touching 00:01:03.960 --> 00:01:05.700 their eyes or some other-- 00:01:05.700 --> 00:01:10.320 or their nose or some bodily entrance point. 00:01:10.320 --> 00:01:15.970 And that sort of transmission is called fomite transmission. 00:01:15.970 --> 00:01:19.750 So these dried up bits of droplets 00:01:19.750 --> 00:01:22.030 on the surface are called fomites. 00:01:22.030 --> 00:01:27.430 And this mode of transfer would involve 00:01:27.430 --> 00:01:31.930 settling of those droplets to the surface, to a surface, OK? 00:01:31.930 --> 00:01:36.250 Now, another possibility is that the droplets kind of float 00:01:36.250 --> 00:01:38.650 around, and if they're small enough, 00:01:38.650 --> 00:01:43.390 they might actually evaporate and they might disappear. 00:01:43.390 --> 00:01:45.070 So they might evaporate. 00:01:47.680 --> 00:01:49.729 And at that point, if there's a pathogen in them, 00:01:49.729 --> 00:01:51.680 that pathogen may still be around, 00:01:51.680 --> 00:01:53.810 but perhaps if it loses enough fluid 00:01:53.810 --> 00:01:56.240 it's going to lose its viability. 00:01:56.240 --> 00:02:00.050 And so perhaps those droplets would be eliminated. 00:02:00.050 --> 00:02:01.670 And then finally, there are droplets 00:02:01.670 --> 00:02:05.000 which undergo neither of these and remain 00:02:05.000 --> 00:02:08.130 floating indefinitely, or at least for long periods of time, 00:02:08.130 --> 00:02:10.639 let's say for hours, in the space. 00:02:10.639 --> 00:02:14.240 And these are called aerosol droplets. 00:02:14.240 --> 00:02:16.310 So these are droplets that are very small. 00:02:16.310 --> 00:02:20.220 They don't really settle in a reasonable amount of time. 00:02:20.220 --> 00:02:22.260 But they're not necessarily evaporating either. 00:02:22.260 --> 00:02:23.260 And so they are present. 00:02:23.260 --> 00:02:25.670 And if another person is here, they can very easily 00:02:25.670 --> 00:02:28.310 breathe in those droplets, OK? 00:02:28.310 --> 00:02:31.520 Now, how do we know which of these outcomes 00:02:31.520 --> 00:02:37.260 is possible for droplets that are emitted from respiration? 00:02:37.260 --> 00:02:42.600 So what it really depends on at the simplest level 00:02:42.600 --> 00:02:44.040 is the size of the droplet. 00:02:46.600 --> 00:02:53.870 So the droplet fate depends on its size. 00:02:53.870 --> 00:02:57.079 So why don't we do some simple estimates 00:02:57.079 --> 00:03:00.660 of these different processes? 00:03:00.660 --> 00:03:06.720 So the first would be looking at settling. 00:03:06.720 --> 00:03:14.600 So the settling time from a height L, 00:03:14.600 --> 00:03:17.480 which might be the height of a person, a typical number that's 00:03:17.480 --> 00:03:23.300 taken is 2 meters for a settling problem like this. 00:03:23.300 --> 00:03:25.010 It's given by the following formula, 00:03:25.010 --> 00:03:27.590 assuming we have so-called Stokes' 00:03:27.590 --> 00:03:30.590 law of settling is valid, which it usually 00:03:30.590 --> 00:03:32.510 is for small droplets. 00:03:32.510 --> 00:03:35.210 And that would be that-- 00:03:35.210 --> 00:03:38.890 I'll just write the formula first. 00:03:38.890 --> 00:03:41.150 2 rho g R^2. 00:03:41.150 --> 00:03:43.120 So basically, there's a 9/2. 00:03:43.120 --> 00:03:45.050 L is the height which they're going to fall. 00:03:45.050 --> 00:03:53.520 So basically this is L. And mu_a is the viscosity of the air, 00:03:53.520 --> 00:03:56.790 rho is the density of the air-- or density the droplet, 00:03:56.790 --> 00:03:58.329 excuse me, of the liquid. 00:03:58.329 --> 00:04:01.180 And g is the gravitational acceleration, 00:04:01.180 --> 00:04:03.140 and R is the size of the droplet. 00:04:03.140 --> 00:04:08.330 So the size of the droplet is R -- or that's the radius. 00:04:08.330 --> 00:04:11.990 So what you see here is that when the radius gets bigger, 00:04:11.990 --> 00:04:15.390 the drops fall faster, and hence the time goes down. 00:04:15.390 --> 00:04:18.500 So very large droplets will very quickly settle out. 00:04:18.500 --> 00:04:21.350 Others -- as R goes to be smaller and smaller -- 00:04:21.350 --> 00:04:24.770 they might be suspended and become aerosols. 00:04:24.770 --> 00:04:30.260 We also might worry about evaporation, for the smaller 00:04:30.260 --> 00:04:32.490 droplets especially. 00:04:32.490 --> 00:04:36.780 And the evaporation time, again with a fairly simple 00:04:36.780 --> 00:04:40.260 approximation of pure liquid which is evaporating. 00:04:40.260 --> 00:04:42.730 Basically, just as it's getting more highly curved, 00:04:42.730 --> 00:04:46.290 the molecules will have a bigger driving force to be removed. 00:04:46.290 --> 00:04:49.330 And if it's a diffusion-limited process, 00:04:49.330 --> 00:04:51.900 which is basically water vapor has to diffuse away 00:04:51.900 --> 00:04:55.620 into the environment, then you can show the evaporation time 00:04:55.620 --> 00:04:58.500 is the initial size of the droplet, R_0 -- 00:04:58.500 --> 00:05:00.420 so let's just say R_0 is the initial size. 00:05:00.420 --> 00:05:02.050 And maybe here, when it's settling, 00:05:02.050 --> 00:05:03.300 it could still be evaporating. 00:05:03.300 --> 00:05:04.320 So R could be varying. 00:05:04.320 --> 00:05:06.780 But why don't we just neglect that 00:05:06.780 --> 00:05:08.070 for droplets settling quickly. 00:05:08.070 --> 00:05:10.800 Maybe that's roughly the initial size. 00:05:10.800 --> 00:05:15.060 And here for evaporation, there is a constant, 00:05:15.060 --> 00:05:16.980 which I'll call D_bar, which is just something 00:05:16.980 --> 00:05:18.660 that has units of diffusivity. 00:05:18.660 --> 00:05:20.580 So length squared per time. 00:05:20.580 --> 00:05:25.300 And then (1-RH), where RH is the relative humidity. 00:05:25.300 --> 00:05:28.620 So basically, the tendency for the water droplets 00:05:28.620 --> 00:05:34.080 to be removed from a liquid droplet end up in the air 00:05:34.080 --> 00:05:36.090 has to do with the relative humidity of the air. 00:05:36.090 --> 00:05:39.400 So that's another factor that comes in here. 00:05:39.400 --> 00:05:43.800 So if we plot these two results, we 00:05:43.800 --> 00:05:46.750 arrive at the so-called Wells curve, 00:05:46.750 --> 00:05:53.800 which was first formulated by epidemiologist Wells in 1934. 00:05:53.800 --> 00:05:55.500 And I'll draw that over here. 00:05:58.480 --> 00:06:02.720 And the Wells curve is sketched like this. 00:06:02.720 --> 00:06:10.250 It says that if we have the drop size R_0 on one axis, 00:06:10.250 --> 00:06:16.970 and on the other axis we have the time of settling-- the time 00:06:16.970 --> 00:06:21.260 that the droplet has left the mouth, 00:06:21.260 --> 00:06:23.910 then you have basically two expressions here. 00:06:23.910 --> 00:06:29.120 So the settling is something like this, 00:06:29.120 --> 00:06:35.810 where it's a function that goes to 0, like 1/R squared. 00:06:35.810 --> 00:06:38.680 On the other hand, evaporation is the fastest 00:06:38.680 --> 00:06:39.770 for the smallest droplets. 00:06:39.770 --> 00:06:41.310 You see that it goes like (R_0)^2. 00:06:41.310 --> 00:06:45.720 So it has a dependence more like this. 00:06:45.720 --> 00:06:50.610 And so basically, these curves intersect at a certain point 00:06:50.610 --> 00:06:51.370 here. 00:06:51.370 --> 00:06:54.550 And if you ask yourself, if I am a droplet of, 00:06:54.550 --> 00:06:58.290 let's say, this size here, then as time goes on, 00:06:58.290 --> 00:07:03.340 I hit this point, and this is where I evaporate. 00:07:03.340 --> 00:07:06.610 So for just a pure liquid droplet, at that time, 00:07:06.610 --> 00:07:08.850 that droplet would disappear. 00:07:08.850 --> 00:07:14.440 On the other hand, if I have a larger droplet that's 00:07:14.440 --> 00:07:16.410 going to hit this other curve first, 00:07:16.410 --> 00:07:20.540 then these droplets will settle, because before they 00:07:20.540 --> 00:07:22.340 have time to evaporate, which would require 00:07:22.340 --> 00:07:23.600 all the way going to here, they've 00:07:23.600 --> 00:07:24.800 already fallen to the ground. 00:07:24.800 --> 00:07:27.290 They may continue evaporating on the ground, 00:07:27.290 --> 00:07:30.420 and you're eventually left with a dried up residue 00:07:30.420 --> 00:07:32.480 of some of the material that may have 00:07:32.480 --> 00:07:34.760 been contained in the droplet. 00:07:34.760 --> 00:07:37.520 And then there's a crossover. 00:07:37.520 --> 00:07:40.400 And so generically, you expect this kind of behavior 00:07:40.400 --> 00:07:43.230 for droplets that are evaporating and settling. 00:07:46.100 --> 00:07:50.740 So the Wells curve was first formulated in 1934. 00:07:50.740 --> 00:07:53.120 And if we just want to put some numbers on here, if we're 00:07:53.120 --> 00:07:57.680 talking about pure water, then this crossover 00:07:57.680 --> 00:08:00.590 happens around 70 microns. 00:08:00.590 --> 00:08:06.900 And the time is around 3 seconds. 00:08:09.890 --> 00:08:11.440 So that gives you a sense, basically, 00:08:11.440 --> 00:08:14.020 of how quickly the larger droplets are settling faster 00:08:14.020 --> 00:08:18.790 than 3 seconds, and then the small droplets are evaporating 00:08:18.790 --> 00:08:19.680 a lot faster. 00:08:19.680 --> 00:08:21.850 And by the way, to get a sense of how fast they are, 00:08:21.850 --> 00:08:25.010 if we look at the dependents, each of these is squared. 00:08:25.010 --> 00:08:27.860 So if we want to go by a factor of 100, if you go to, 00:08:27.860 --> 00:08:33.909 let's say, 0.7 microns, which is 700 nanometers, 00:08:33.909 --> 00:08:35.500 it's a factor of 100. 00:08:35.500 --> 00:08:37.640 But the time comes in squared. 00:08:37.640 --> 00:08:42.640 So it's 3e-4 seconds. 00:08:42.640 --> 00:08:45.400 So we're talking 0.3 milliseconds. 00:08:45.400 --> 00:08:49.450 So basically, droplets that are in the 1 micron or below range, 00:08:49.450 --> 00:08:52.900 if they're pure liquid, they'll evaporate extremely quickly. 00:08:52.900 --> 00:08:55.390 And conversely, if we consider much larger droplets, 00:08:55.390 --> 00:08:58.450 let's say that are bigger by a factor of 10 or 100, 00:08:58.450 --> 00:09:00.700 that also comes in squared in terms of the settling 00:09:00.700 --> 00:09:02.360 time being reduced. 00:09:02.360 --> 00:09:06.730 And so we would then end up with 100, or up to even 10,000 times 00:09:06.730 --> 00:09:07.780 smaller settling time. 00:09:07.780 --> 00:09:09.280 Although it won't be quite as small, 00:09:09.280 --> 00:09:12.610 because also, the particles need to accelerate to that speed. 00:09:12.610 --> 00:09:18.910 This settling speed here is the terminal velocity of a drop. 00:09:18.910 --> 00:09:21.760 And there is a short acceleration time 00:09:21.760 --> 00:09:23.860 for very small particles. 00:09:23.860 --> 00:09:25.720 And for very long particles, you may still 00:09:25.720 --> 00:09:28.310 be actually in that acceleration time when you hit the ground. 00:09:28.310 --> 00:09:29.970 So basically, it might not be that long. 00:09:29.970 --> 00:09:32.650 But basically, the time, at large times, 00:09:32.650 --> 00:09:35.830 is also quite a bit reduced for large particles. 00:09:35.830 --> 00:09:40.130 Now, there's also the humidity effect, which can be seen here. 00:09:40.130 --> 00:09:43.840 So for example, if we're at 90% relative humidity, 00:09:43.840 --> 00:09:46.100 this factor here is a factor of 10. 00:09:46.100 --> 00:09:48.350 So what was on the order of a few seconds, 00:09:48.350 --> 00:09:50.260 if we're at higher humidity, then 00:09:50.260 --> 00:09:52.750 this curve ends up looking more like this. 00:09:52.750 --> 00:09:54.760 And we may follow this curve a little bit 00:09:54.760 --> 00:09:58.880 further and end up with something like this. 00:09:58.880 --> 00:10:04.510 This would be high humidity. 00:10:04.510 --> 00:10:06.640 I'll say higher, because I haven't gone that far. 00:10:06.640 --> 00:10:09.150 There's another curve that I could draw where this even 00:10:09.150 --> 00:10:12.030 goes further this way, and where this 00:10:12.030 --> 00:10:15.600 could start turning into, say, 30 seconds 00:10:15.600 --> 00:10:16.890 where that crossover occurs. 00:10:16.890 --> 00:10:20.150 But in any case, there is a crossover at some point. 00:10:20.150 --> 00:10:22.540 And at high relative humidity, the evaporation is slower, 00:10:22.540 --> 00:10:26.140 and so we are more following the settling droplets. 00:10:26.140 --> 00:10:28.560 And so this is an important set of concepts 00:10:28.560 --> 00:10:30.930 in the field of aerosol science involving 00:10:30.930 --> 00:10:34.740 droplets, and especially for respiratory diseases. 00:10:34.740 --> 00:10:36.720 But it's still oversimplified. 00:10:36.720 --> 00:10:41.520 So recent research has showed that, in fact, many droplets 00:10:41.520 --> 00:10:43.260 that are present from respiration 00:10:43.260 --> 00:10:46.620 do not evaporate on these kind of fast timescales. 00:10:46.620 --> 00:10:48.630 And in fact, they can linger and can 00:10:48.630 --> 00:10:52.470 be way into this small size range of aerosols 00:10:52.470 --> 00:10:53.730 and not disappear. 00:10:53.730 --> 00:10:56.610 And it's possible, then, to breathe them in and transmit 00:10:56.610 --> 00:10:57.870 disease with them. 00:10:57.870 --> 00:11:00.690 So what's missing here is that the droplet fate 00:11:00.690 --> 00:11:05.070 depends not only on the size of the droplet, 00:11:05.070 --> 00:11:08.870 but also on solutes. 00:11:16.310 --> 00:11:20.660 So what I mean by that is that, of course, a droplet coming out 00:11:20.660 --> 00:11:23.900 of your lungs and passing through your pharynx, 00:11:23.900 --> 00:11:26.780 your vocal chords, is not just pure water. 00:11:26.780 --> 00:11:28.460 It's even not pure saliva. 00:11:28.460 --> 00:11:30.510 In fact, it contains many other molecules. 00:11:30.510 --> 00:11:33.950 So of course, it contains the pathogens themselves, 00:11:33.950 --> 00:11:35.750 which are solids, and they don't evaporate. 00:11:35.750 --> 00:11:40.220 So whether it's bacteria or virus, some of that material 00:11:40.220 --> 00:11:41.630 has to stay behind. 00:11:41.630 --> 00:11:47.280 There's all kinds of organic molecules, 00:11:47.280 --> 00:11:49.770 because in fact, the mucus that comes out 00:11:49.770 --> 00:11:51.750 of your lungs as a non-Newtonian fluid that's 00:11:51.750 --> 00:11:54.570 full of macromolecules of different types. 00:11:54.570 --> 00:11:56.580 Those molecules are usually charged, 00:11:56.580 --> 00:12:02.680 as are, in fact, the viruses and other pathogens as well. 00:12:02.680 --> 00:12:06.120 And so there could also be hydration, 00:12:06.120 --> 00:12:09.310 water, so that those water molecules, 00:12:09.310 --> 00:12:12.060 which are not freely in solution but were strongly interacting 00:12:12.060 --> 00:12:14.580 with charge services, or charged molecules, 00:12:14.580 --> 00:12:18.210 and form so-called hydration shells around those molecules. 00:12:18.210 --> 00:12:20.880 And finally, there could also be salts, 00:12:20.880 --> 00:12:24.150 because we all know that our body is, in many cases, 00:12:24.150 --> 00:12:27.570 similar to seawater, and has fluids which contain 00:12:27.570 --> 00:12:28.920 a large number of salts. 00:12:28.920 --> 00:12:32.190 For example, sodium chloride or calcium. 00:12:32.190 --> 00:12:35.080 And salts love water. 00:12:35.080 --> 00:12:38.700 So in fact, it's been shown that some respiratory aerosols are 00:12:38.700 --> 00:12:41.100 actually observed to be growing after they're 00:12:41.100 --> 00:12:42.420 emitted from the body. 00:12:42.420 --> 00:12:44.190 In a humid environment, water may actually 00:12:44.190 --> 00:12:45.780 be condensing onto those particles 00:12:45.780 --> 00:12:47.400 and causing them to grow, because it 00:12:47.400 --> 00:12:49.950 has molecules that love water. 00:12:49.950 --> 00:12:54.300 And in fact, these kinds of molecules or particles 00:12:54.300 --> 00:12:59.080 that attract and hold water are so-called hygroscopic 00:12:59.080 --> 00:13:01.520 materials. 00:13:01.520 --> 00:13:03.540 And many respiratory-- a significant number 00:13:03.540 --> 00:13:07.040 of respiratory droplets are, in fact, hygroscopic. 00:13:07.040 --> 00:13:09.910 So this whole picture of evaporation settling really 00:13:09.910 --> 00:13:10.790 needs to be modified. 00:13:10.790 --> 00:13:13.760 The settling part is going to always be there. 00:13:13.760 --> 00:13:16.520 Even a solid particle which is settling in air 00:13:16.520 --> 00:13:20.210 is going to obey this Stokes settling velocity. 00:13:20.210 --> 00:13:22.760 But the evaporation part of it is certainly 00:13:22.760 --> 00:13:26.330 true for pure water, but is not necessarily the right way 00:13:26.330 --> 00:13:28.000 to think about respiratory aerosols. 00:13:31.040 --> 00:13:35.690 So finally then, I'll just sketch 00:13:35.690 --> 00:13:38.900 what happens when people have measured 00:13:38.900 --> 00:13:42.290 respiratory distributions of particles, 00:13:42.290 --> 00:13:44.150 and focusing on the aerosol range 00:13:44.150 --> 00:13:47.180 of the really small particles that might remain suspended. 00:13:47.180 --> 00:13:50.360 So these are particles like this guy right here, which 00:13:50.360 --> 00:13:53.780 are around 1 micron, and will have settling times 00:13:53.780 --> 00:13:55.770 that are on the order of hours. 00:13:55.770 --> 00:13:57.320 So those particles that can linger 00:13:57.320 --> 00:14:00.450 in the air for long periods of time. 00:14:00.450 --> 00:14:02.690 And so if we look at the number of droplets 00:14:02.690 --> 00:14:06.920 that we have at different sizes, and this 00:14:06.920 --> 00:14:08.960 is for different kinds of respiration-- 00:14:08.960 --> 00:14:11.000 and I'll draw this to sketch what it would look 00:14:11.000 --> 00:14:12.600 like on a log scale. 00:14:12.600 --> 00:14:18.080 So here I'll put 0.01 microns, which is 100 nanometers. 00:14:18.080 --> 00:14:25.080 And then I'll put 1 micron, and then 10 microns, and then 00:14:25.080 --> 00:14:27.910 100 microns. 00:14:27.910 --> 00:14:32.810 So when you breathe, speak, cough, 00:14:32.810 --> 00:14:34.900 sneeze, you're letting out a distribution 00:14:34.900 --> 00:14:37.750 of particles of all these different types of droplets. 00:14:37.750 --> 00:14:39.460 And those droplets will typically 00:14:39.460 --> 00:14:42.970 contain pathogens, such as bacteria or virus. 00:14:42.970 --> 00:14:45.760 And the way these things look is because 00:14:45.760 --> 00:14:49.880 of these hygroscopic solutes, in fact, 00:14:49.880 --> 00:14:52.840 we don't see that all the little ones are evaporating it away 00:14:52.840 --> 00:14:55.390 in a tiny timescale like milliseconds, 00:14:55.390 --> 00:14:56.560 but in fact, they do linger. 00:14:56.560 --> 00:14:59.770 And you do have respiratory aerosols that can be observed. 00:14:59.770 --> 00:15:01.900 And so what these distributions actually look like, 00:15:01.900 --> 00:15:06.490 they tend to have a peak around half a micron in diameter, 00:15:06.490 --> 00:15:09.960 or a radius even smaller than that would be a quarter micron. 00:15:09.960 --> 00:15:13.730 And so they look something like this. 00:15:13.730 --> 00:15:15.790 And if you're breathing at rest, it 00:15:15.790 --> 00:15:18.850 might look something like that. 00:15:18.850 --> 00:15:20.890 And actually, the volume fraction, 00:15:20.890 --> 00:15:22.890 if we were to convert this to a volume fraction, 00:15:22.890 --> 00:15:26.130 ends up being around 1e-16 parts 00:15:26.130 --> 00:15:28.930 of liquid per volume of air. 00:15:28.930 --> 00:15:31.920 So these are very small droplets. 00:15:31.920 --> 00:15:34.740 And you can't see them, but they're there. 00:15:34.740 --> 00:15:37.410 If you're resting breathing, you might have something like that. 00:15:37.410 --> 00:15:40.600 There's also an important effect of the type of respiration. 00:15:40.600 --> 00:15:43.020 So if I start talking, then it turns out 00:15:43.020 --> 00:15:45.750 I'm still releasing quite a few these aerosols, 00:15:45.750 --> 00:15:49.170 but now I'm also releasing some much larger droplets. 00:15:49.170 --> 00:15:50.780 I might even be having-- 00:15:50.780 --> 00:15:54.840 depending how I'm speaking, and in fact, my personal physiology 00:15:54.840 --> 00:15:56.800 may vary from person to person, I 00:15:56.800 --> 00:15:59.010 might be emitting even more of these larger droplets. 00:15:59.010 --> 00:16:01.560 Or also, the aerosol droplets as well. 00:16:01.560 --> 00:16:03.060 And then there are other activities, 00:16:03.060 --> 00:16:09.810 such as singing or exercise, where 00:16:09.810 --> 00:16:12.180 you're breathing very heavily, where 00:16:12.180 --> 00:16:14.190 you emit even more droplets. 00:16:14.190 --> 00:16:16.140 And you can see vocalizations, singing, 00:16:16.140 --> 00:16:19.350 and this can be, for example, talking, 00:16:19.350 --> 00:16:21.480 that those lead to more emissions. 00:16:21.480 --> 00:16:23.820 But the important thing is that there is 00:16:23.820 --> 00:16:29.520 a big population of particles. 00:16:29.520 --> 00:16:32.310 In fact, the majority of particles, 00:16:32.310 --> 00:16:39.040 by number or even by volume, is over here in the aerosol range. 00:16:39.040 --> 00:16:41.430 So these are particles that do hang around. 00:16:41.430 --> 00:16:42.840 And they float around the room. 00:16:42.840 --> 00:16:45.030 And they can do so for minutes or even hours, 00:16:45.030 --> 00:16:48.900 depending on their size and the conditions of the room. 00:16:48.900 --> 00:16:56.020 These here are the large drops which will sediment out 00:16:56.020 --> 00:16:57.510 according to this formula here. 00:16:57.510 --> 00:16:59.560 So the Stokes formula is still going to be valid 00:16:59.560 --> 00:17:00.790 regardless of evaporation. 00:17:00.790 --> 00:17:02.380 If we know the size, we have a sense 00:17:02.380 --> 00:17:04.720 of how quickly the droplets are falling. 00:17:04.720 --> 00:17:06.849 But the ones we're really going to want to focus on 00:17:06.849 --> 00:17:10.329 are these aerosols for viruses, because viruses are small. 00:17:10.329 --> 00:17:12.730 Whereas bacteria are big and they 00:17:12.730 --> 00:17:15.520 might have to be transmitting more of the enlarged drops. 00:17:15.520 --> 00:17:19.000 So now let's talk a bit about the biology of viruses 00:17:19.000 --> 00:17:20.680 and bacteria and see how that might 00:17:20.680 --> 00:17:25.530 connect to the physics of droplet transmission.