1
00:00:10,940 --> 00:00:13,080
PROFESSOR: So let's
talk about the transfer

2
00:00:13,080 --> 00:00:16,500
of respiratory pathogens, and
in particular, contagious

3
00:00:16,500 --> 00:00:19,930
pathogens such as
viruses and bacteria,

4
00:00:19,930 --> 00:00:22,750
that infect the
respiratory system.

5
00:00:22,750 --> 00:00:25,690
The way that such pathogens
are normally transferred

6
00:00:25,690 --> 00:00:29,860
is through droplets which are
emitted by respiration, which

7
00:00:29,860 --> 00:00:33,910
could be by just normal
breathing, coughing, sneezing,

8
00:00:33,910 --> 00:00:35,580
et cetera.

9
00:00:35,580 --> 00:00:38,730
And so here is a sketch
of an infected person who

10
00:00:38,730 --> 00:00:44,730
is undergoing respiration and is
emitting droplets into the air.

11
00:00:44,730 --> 00:00:48,150
And so let's think about what
is the fate of those droplets,

12
00:00:48,150 --> 00:00:49,350
what it could be.

13
00:00:49,350 --> 00:00:51,930
So one possibility is if
the droplets are very heavy,

14
00:00:51,930 --> 00:00:54,240
they're just going to
settle to the ground.

15
00:00:54,240 --> 00:00:57,330
And then they may
collect on the ground

16
00:00:57,330 --> 00:00:59,370
or on some other surface.

17
00:00:59,370 --> 00:01:02,040
And then somebody else
could touch that surface

18
00:01:02,040 --> 00:01:03,960
and transmit it,
perhaps by touching

19
00:01:03,960 --> 00:01:05,700
their eyes or some other--

20
00:01:05,700 --> 00:01:10,320
or their nose or some
bodily entrance point.

21
00:01:10,320 --> 00:01:15,970
And that sort of transmission
is called fomite transmission.

22
00:01:15,970 --> 00:01:19,750
So these dried up
bits of droplets

23
00:01:19,750 --> 00:01:22,030
on the surface are
called fomites.

24
00:01:22,030 --> 00:01:27,430
And this mode of
transfer would involve

25
00:01:27,430 --> 00:01:31,930
settling of those droplets to
the surface, to a surface, OK?

26
00:01:31,930 --> 00:01:36,250
Now, another possibility is
that the droplets kind of float

27
00:01:36,250 --> 00:01:38,650
around, and if
they're small enough,

28
00:01:38,650 --> 00:01:43,390
they might actually evaporate
and they might disappear.

29
00:01:43,390 --> 00:01:45,070
So they might evaporate.

30
00:01:47,680 --> 00:01:49,729
And at that point, if
there's a pathogen in them,

31
00:01:49,729 --> 00:01:51,680
that pathogen may
still be around,

32
00:01:51,680 --> 00:01:53,810
but perhaps if it
loses enough fluid

33
00:01:53,810 --> 00:01:56,240
it's going to lose
its viability.

34
00:01:56,240 --> 00:02:00,050
And so perhaps those
droplets would be eliminated.

35
00:02:00,050 --> 00:02:01,670
And then finally,
there are droplets

36
00:02:01,670 --> 00:02:05,000
which undergo neither
of these and remain

37
00:02:05,000 --> 00:02:08,130
floating indefinitely, or at
least for long periods of time,

38
00:02:08,130 --> 00:02:10,639
let's say for
hours, in the space.

39
00:02:10,639 --> 00:02:14,240
And these are called
aerosol droplets.

40
00:02:14,240 --> 00:02:16,310
So these are droplets
that are very small.

41
00:02:16,310 --> 00:02:20,220
They don't really settle in
a reasonable amount of time.

42
00:02:20,220 --> 00:02:22,260
But they're not necessarily
evaporating either.

43
00:02:22,260 --> 00:02:23,260
And so they are present.

44
00:02:23,260 --> 00:02:25,670
And if another person is
here, they can very easily

45
00:02:25,670 --> 00:02:28,310
breathe in those droplets, OK?

46
00:02:28,310 --> 00:02:31,520
Now, how do we know
which of these outcomes

47
00:02:31,520 --> 00:02:37,260
is possible for droplets that
are emitted from respiration?

48
00:02:37,260 --> 00:02:42,600
So what it really depends
on at the simplest level

49
00:02:42,600 --> 00:02:44,040
is the size of the droplet.

50
00:02:46,600 --> 00:02:53,870
So the droplet fate
depends on its size.

51
00:02:53,870 --> 00:02:57,079
So why don't we do
some simple estimates

52
00:02:57,079 --> 00:03:00,660
of these different processes?

53
00:03:00,660 --> 00:03:06,720
So the first would be
looking at settling.

54
00:03:06,720 --> 00:03:14,600
So the settling time
from a height L,

55
00:03:14,600 --> 00:03:17,480
which might be the height of a
person, a typical number that's

56
00:03:17,480 --> 00:03:23,300
taken is 2 meters for a
settling problem like this.

57
00:03:23,300 --> 00:03:25,010
It's given by the
following formula,

58
00:03:25,010 --> 00:03:27,590
assuming we have
so-called Stokes'

59
00:03:27,590 --> 00:03:30,590
law of settling is
valid, which it usually

60
00:03:30,590 --> 00:03:32,510
is for small droplets.

61
00:03:32,510 --> 00:03:35,210
And that would be that--

62
00:03:35,210 --> 00:03:38,890
I'll just write
the formula first.

63
00:03:38,890 --> 00:03:41,150
2 rho g R^2.

64
00:03:41,150 --> 00:03:43,120
So basically, there's a 9/2.

65
00:03:43,120 --> 00:03:45,050
L is the height which
they're going to fall.

66
00:03:45,050 --> 00:03:53,520
So basically this is L. And mu_a
is the viscosity of the air,

67
00:03:53,520 --> 00:03:56,790
rho is the density of the
air-- or density the droplet,

68
00:03:56,790 --> 00:03:58,329
excuse me, of the liquid.

69
00:03:58,329 --> 00:04:01,180
And g is the gravitational
acceleration,

70
00:04:01,180 --> 00:04:03,140
and R is the size
of the droplet.

71
00:04:03,140 --> 00:04:08,330
So the size of the droplet
is R -- or that's the radius.

72
00:04:08,330 --> 00:04:11,990
So what you see here is that
when the radius gets bigger,

73
00:04:11,990 --> 00:04:15,390
the drops fall faster, and
hence the time goes down.

74
00:04:15,390 --> 00:04:18,500
So very large droplets will
very quickly settle out.

75
00:04:18,500 --> 00:04:21,350
Others -- as R goes to
be smaller and smaller --

76
00:04:21,350 --> 00:04:24,770
they might be suspended
and become aerosols.

77
00:04:24,770 --> 00:04:30,260
We also might worry about
evaporation, for the smaller

78
00:04:30,260 --> 00:04:32,490
droplets especially.

79
00:04:32,490 --> 00:04:36,780
And the evaporation time,
again with a fairly simple

80
00:04:36,780 --> 00:04:40,260
approximation of pure
liquid which is evaporating.

81
00:04:40,260 --> 00:04:42,730
Basically, just as it's
getting more highly curved,

82
00:04:42,730 --> 00:04:46,290
the molecules will have a bigger
driving force to be removed.

83
00:04:46,290 --> 00:04:49,330
And if it's a
diffusion-limited process,

84
00:04:49,330 --> 00:04:51,900
which is basically water
vapor has to diffuse away

85
00:04:51,900 --> 00:04:55,620
into the environment, then you
can show the evaporation time

86
00:04:55,620 --> 00:04:58,500
is the initial size
of the droplet, R_0 --

87
00:04:58,500 --> 00:05:00,420
so let's just say R_0
is the initial size.

88
00:05:00,420 --> 00:05:02,050
And maybe here,
when it's settling,

89
00:05:02,050 --> 00:05:03,300
it could still be evaporating.

90
00:05:03,300 --> 00:05:04,320
So R could be varying.

91
00:05:04,320 --> 00:05:06,780
But why don't we
just neglect that

92
00:05:06,780 --> 00:05:08,070
for droplets settling quickly.

93
00:05:08,070 --> 00:05:10,800
Maybe that's roughly
the initial size.

94
00:05:10,800 --> 00:05:15,060
And here for evaporation,
there is a constant,

95
00:05:15,060 --> 00:05:16,980
which I'll call D_bar,
which is just something

96
00:05:16,980 --> 00:05:18,660
that has units of diffusivity.

97
00:05:18,660 --> 00:05:20,580
So length squared per time.

98
00:05:20,580 --> 00:05:25,300
And then (1-RH), where
RH is the relative humidity.

99
00:05:25,300 --> 00:05:28,620
So basically, the tendency
for the water droplets

100
00:05:28,620 --> 00:05:34,080
to be removed from a liquid
droplet end up in the air

101
00:05:34,080 --> 00:05:36,090
has to do with the relative
humidity of the air.

102
00:05:36,090 --> 00:05:39,400
So that's another factor
that comes in here.

103
00:05:39,400 --> 00:05:43,800
So if we plot these
two results, we

104
00:05:43,800 --> 00:05:46,750
arrive at the
so-called Wells curve,

105
00:05:46,750 --> 00:05:53,800
which was first formulated by
epidemiologist Wells in 1934.

106
00:05:53,800 --> 00:05:55,500
And I'll draw that over here.

107
00:05:58,480 --> 00:06:02,720
And the Wells curve
is sketched like this.

108
00:06:02,720 --> 00:06:10,250
It says that if we have the
drop size R_0 on one axis,

109
00:06:10,250 --> 00:06:16,970
and on the other axis we have
the time of settling-- the time

110
00:06:16,970 --> 00:06:21,260
that the droplet
has left the mouth,

111
00:06:21,260 --> 00:06:23,910
then you have basically
two expressions here.

112
00:06:23,910 --> 00:06:29,120
So the settling is
something like this,

113
00:06:29,120 --> 00:06:35,810
where it's a function that
goes to 0, like 1/R squared.

114
00:06:35,810 --> 00:06:38,680
On the other hand,
evaporation is the fastest

115
00:06:38,680 --> 00:06:39,770
for the smallest droplets.

116
00:06:39,770 --> 00:06:41,310
You see that it goes
like (R_0)^2.

117
00:06:41,310 --> 00:06:45,720
So it has a dependence
more like this.

118
00:06:45,720 --> 00:06:50,610
And so basically, these curves
intersect at a certain point

119
00:06:50,610 --> 00:06:51,370
here.

120
00:06:51,370 --> 00:06:54,550
And if you ask yourself,
if I am a droplet of,

121
00:06:54,550 --> 00:06:58,290
let's say, this size here,
then as time goes on,

122
00:06:58,290 --> 00:07:03,340
I hit this point, and
this is where I evaporate.

123
00:07:03,340 --> 00:07:06,610
So for just a pure liquid
droplet, at that time,

124
00:07:06,610 --> 00:07:08,850
that droplet would disappear.

125
00:07:08,850 --> 00:07:14,440
On the other hand, if I
have a larger droplet that's

126
00:07:14,440 --> 00:07:16,410
going to hit this
other curve first,

127
00:07:16,410 --> 00:07:20,540
then these droplets will
settle, because before they

128
00:07:20,540 --> 00:07:22,340
have time to evaporate,
which would require

129
00:07:22,340 --> 00:07:23,600
all the way going
to here, they've

130
00:07:23,600 --> 00:07:24,800
already fallen to the ground.

131
00:07:24,800 --> 00:07:27,290
They may continue
evaporating on the ground,

132
00:07:27,290 --> 00:07:30,420
and you're eventually left
with a dried up residue

133
00:07:30,420 --> 00:07:32,480
of some of the
material that may have

134
00:07:32,480 --> 00:07:34,760
been contained in the droplet.

135
00:07:34,760 --> 00:07:37,520
And then there's a crossover.

136
00:07:37,520 --> 00:07:40,400
And so generically, you
expect this kind of behavior

137
00:07:40,400 --> 00:07:43,230
for droplets that are
evaporating and settling.

138
00:07:46,100 --> 00:07:50,740
So the Wells curve was
first formulated in 1934.

139
00:07:50,740 --> 00:07:53,120
And if we just want to put
some numbers on here, if we're

140
00:07:53,120 --> 00:07:57,680
talking about pure water,
then this crossover

141
00:07:57,680 --> 00:08:00,590
happens around 70 microns.

142
00:08:00,590 --> 00:08:06,900
And the time is
around 3 seconds.

143
00:08:09,890 --> 00:08:11,440
So that gives you
a sense, basically,

144
00:08:11,440 --> 00:08:14,020
of how quickly the larger
droplets are settling faster

145
00:08:14,020 --> 00:08:18,790
than 3 seconds, and then the
small droplets are evaporating

146
00:08:18,790 --> 00:08:19,680
a lot faster.

147
00:08:19,680 --> 00:08:21,850
And by the way, to get a
sense of how fast they are,

148
00:08:21,850 --> 00:08:25,010
if we look at the dependents,
each of these is squared.

149
00:08:25,010 --> 00:08:27,860
So if we want to go by a
factor of 100, if you go to,

150
00:08:27,860 --> 00:08:33,909
let's say, 0.7 microns,
which is 700 nanometers,

151
00:08:33,909 --> 00:08:35,500
it's a factor of 100.

152
00:08:35,500 --> 00:08:37,640
But the time comes in squared.

153
00:08:37,640 --> 00:08:42,640
So it's 3e-4 seconds.

154
00:08:42,640 --> 00:08:45,400
So we're talking
0.3 milliseconds.

155
00:08:45,400 --> 00:08:49,450
So basically, droplets that are
in the 1 micron or below range,

156
00:08:49,450 --> 00:08:52,900
if they're pure liquid, they'll
evaporate extremely quickly.

157
00:08:52,900 --> 00:08:55,390
And conversely, if we
consider much larger droplets,

158
00:08:55,390 --> 00:08:58,450
let's say that are bigger
by a factor of 10 or 100,

159
00:08:58,450 --> 00:09:00,700
that also comes in squared
in terms of the settling

160
00:09:00,700 --> 00:09:02,360
time being reduced.

161
00:09:02,360 --> 00:09:06,730
And so we would then end up with
100, or up to even 10,000 times

162
00:09:06,730 --> 00:09:07,780
smaller settling time.

163
00:09:07,780 --> 00:09:09,280
Although it won't
be quite as small,

164
00:09:09,280 --> 00:09:12,610
because also, the particles need
to accelerate to that speed.

165
00:09:12,610 --> 00:09:18,910
This settling speed here is the
terminal velocity of a drop.

166
00:09:18,910 --> 00:09:21,760
And there is a short
acceleration time

167
00:09:21,760 --> 00:09:23,860
for very small particles.

168
00:09:23,860 --> 00:09:25,720
And for very long
particles, you may still

169
00:09:25,720 --> 00:09:28,310
be actually in that acceleration
time when you hit the ground.

170
00:09:28,310 --> 00:09:29,970
So basically, it might
not be that long.

171
00:09:29,970 --> 00:09:32,650
But basically, the
time, at large times,

172
00:09:32,650 --> 00:09:35,830
is also quite a bit reduced
for large particles.

173
00:09:35,830 --> 00:09:40,130
Now, there's also the humidity
effect, which can be seen here.

174
00:09:40,130 --> 00:09:43,840
So for example, if we're
at 90% relative humidity,

175
00:09:43,840 --> 00:09:46,100
this factor here
is a factor of 10.

176
00:09:46,100 --> 00:09:48,350
So what was on the
order of a few seconds,

177
00:09:48,350 --> 00:09:50,260
if we're at higher
humidity, then

178
00:09:50,260 --> 00:09:52,750
this curve ends up
looking more like this.

179
00:09:52,750 --> 00:09:54,760
And we may follow this
curve a little bit

180
00:09:54,760 --> 00:09:58,880
further and end up with
something like this.

181
00:09:58,880 --> 00:10:04,510
This would be high humidity.

182
00:10:04,510 --> 00:10:06,640
I'll say higher, because
I haven't gone that far.

183
00:10:06,640 --> 00:10:09,150
There's another curve that
I could draw where this even

184
00:10:09,150 --> 00:10:12,030
goes further this
way, and where this

185
00:10:12,030 --> 00:10:15,600
could start turning
into, say, 30 seconds

186
00:10:15,600 --> 00:10:16,890
where that crossover occurs.

187
00:10:16,890 --> 00:10:20,150
But in any case, there is
a crossover at some point.

188
00:10:20,150 --> 00:10:22,540
And at high relative humidity,
the evaporation is slower,

189
00:10:22,540 --> 00:10:26,140
and so we are more following
the settling droplets.

190
00:10:26,140 --> 00:10:28,560
And so this is an
important set of concepts

191
00:10:28,560 --> 00:10:30,930
in the field of aerosol
science involving

192
00:10:30,930 --> 00:10:34,740
droplets, and especially
for respiratory diseases.

193
00:10:34,740 --> 00:10:36,720
But it's still oversimplified.

194
00:10:36,720 --> 00:10:41,520
So recent research has showed
that, in fact, many droplets

195
00:10:41,520 --> 00:10:43,260
that are present
from respiration

196
00:10:43,260 --> 00:10:46,620
do not evaporate on these
kind of fast timescales.

197
00:10:46,620 --> 00:10:48,630
And in fact, they
can linger and can

198
00:10:48,630 --> 00:10:52,470
be way into this small
size range of aerosols

199
00:10:52,470 --> 00:10:53,730
and not disappear.

200
00:10:53,730 --> 00:10:56,610
And it's possible, then, to
breathe them in and transmit

201
00:10:56,610 --> 00:10:57,870
disease with them.

202
00:10:57,870 --> 00:11:00,690
So what's missing here
is that the droplet fate

203
00:11:00,690 --> 00:11:05,070
depends not only on the
size of the droplet,

204
00:11:05,070 --> 00:11:08,870
but also on solutes.

205
00:11:16,310 --> 00:11:20,660
So what I mean by that is that,
of course, a droplet coming out

206
00:11:20,660 --> 00:11:23,900
of your lungs and passing
through your pharynx,

207
00:11:23,900 --> 00:11:26,780
your vocal chords, is
not just pure water.

208
00:11:26,780 --> 00:11:28,460
It's even not pure saliva.

209
00:11:28,460 --> 00:11:30,510
In fact, it contains
many other molecules.

210
00:11:30,510 --> 00:11:33,950
So of course, it contains
the pathogens themselves,

211
00:11:33,950 --> 00:11:35,750
which are solids, and
they don't evaporate.

212
00:11:35,750 --> 00:11:40,220
So whether it's bacteria or
virus, some of that material

213
00:11:40,220 --> 00:11:41,630
has to stay behind.

214
00:11:41,630 --> 00:11:47,280
There's all kinds of
organic molecules,

215
00:11:47,280 --> 00:11:49,770
because in fact, the
mucus that comes out

216
00:11:49,770 --> 00:11:51,750
of your lungs as a
non-Newtonian fluid that's

217
00:11:51,750 --> 00:11:54,570
full of macromolecules
of different types.

218
00:11:54,570 --> 00:11:56,580
Those molecules are
usually charged,

219
00:11:56,580 --> 00:12:02,680
as are, in fact, the viruses
and other pathogens as well.

220
00:12:02,680 --> 00:12:06,120
And so there could
also be hydration,

221
00:12:06,120 --> 00:12:09,310
water, so that those
water molecules,

222
00:12:09,310 --> 00:12:12,060
which are not freely in solution
but were strongly interacting

223
00:12:12,060 --> 00:12:14,580
with charge services,
or charged molecules,

224
00:12:14,580 --> 00:12:18,210
and form so-called hydration
shells around those molecules.

225
00:12:18,210 --> 00:12:20,880
And finally, there
could also be salts,

226
00:12:20,880 --> 00:12:24,150
because we all know that
our body is, in many cases,

227
00:12:24,150 --> 00:12:27,570
similar to seawater, and
has fluids which contain

228
00:12:27,570 --> 00:12:28,920
a large number of salts.

229
00:12:28,920 --> 00:12:32,190
For example, sodium
chloride or calcium.

230
00:12:32,190 --> 00:12:35,080
And salts love water.

231
00:12:35,080 --> 00:12:38,700
So in fact, it's been shown that
some respiratory aerosols are

232
00:12:38,700 --> 00:12:41,100
actually observed to be
growing after they're

233
00:12:41,100 --> 00:12:42,420
emitted from the body.

234
00:12:42,420 --> 00:12:44,190
In a humid environment,
water may actually

235
00:12:44,190 --> 00:12:45,780
be condensing onto
those particles

236
00:12:45,780 --> 00:12:47,400
and causing them
to grow, because it

237
00:12:47,400 --> 00:12:49,950
has molecules that love water.

238
00:12:49,950 --> 00:12:54,300
And in fact, these kinds
of molecules or particles

239
00:12:54,300 --> 00:12:59,080
that attract and hold water
are so-called hygroscopic

240
00:12:59,080 --> 00:13:01,520
materials.

241
00:13:01,520 --> 00:13:03,540
And many respiratory--
a significant number

242
00:13:03,540 --> 00:13:07,040
of respiratory droplets
are, in fact, hygroscopic.

243
00:13:07,040 --> 00:13:09,910
So this whole picture of
evaporation settling really

244
00:13:09,910 --> 00:13:10,790
needs to be modified.

245
00:13:10,790 --> 00:13:13,760
The settling part is
going to always be there.

246
00:13:13,760 --> 00:13:16,520
Even a solid particle
which is settling in air

247
00:13:16,520 --> 00:13:20,210
is going to obey this
Stokes settling velocity.

248
00:13:20,210 --> 00:13:22,760
But the evaporation
part of it is certainly

249
00:13:22,760 --> 00:13:26,330
true for pure water, but is
not necessarily the right way

250
00:13:26,330 --> 00:13:28,000
to think about
respiratory aerosols.

251
00:13:31,040 --> 00:13:35,690
So finally then,
I'll just sketch

252
00:13:35,690 --> 00:13:38,900
what happens when
people have measured

253
00:13:38,900 --> 00:13:42,290
respiratory distributions
of particles,

254
00:13:42,290 --> 00:13:44,150
and focusing on
the aerosol range

255
00:13:44,150 --> 00:13:47,180
of the really small particles
that might remain suspended.

256
00:13:47,180 --> 00:13:50,360
So these are particles like
this guy right here, which

257
00:13:50,360 --> 00:13:53,780
are around 1 micron, and
will have settling times

258
00:13:53,780 --> 00:13:55,770
that are on the order of hours.

259
00:13:55,770 --> 00:13:57,320
So those particles
that can linger

260
00:13:57,320 --> 00:14:00,450
in the air for long
periods of time.

261
00:14:00,450 --> 00:14:02,690
And so if we look at
the number of droplets

262
00:14:02,690 --> 00:14:06,920
that we have at
different sizes, and this

263
00:14:06,920 --> 00:14:08,960
is for different
kinds of respiration--

264
00:14:08,960 --> 00:14:11,000
and I'll draw this to
sketch what it would look

265
00:14:11,000 --> 00:14:12,600
like on a log scale.

266
00:14:12,600 --> 00:14:18,080
So here I'll put 0.01 microns,
which is 100 nanometers.

267
00:14:18,080 --> 00:14:25,080
And then I'll put 1 micron,
and then 10 microns, and then

268
00:14:25,080 --> 00:14:27,910
100 microns.

269
00:14:27,910 --> 00:14:32,810
So when you breathe,
speak, cough,

270
00:14:32,810 --> 00:14:34,900
sneeze, you're letting
out a distribution

271
00:14:34,900 --> 00:14:37,750
of particles of all these
different types of droplets.

272
00:14:37,750 --> 00:14:39,460
And those droplets
will typically

273
00:14:39,460 --> 00:14:42,970
contain pathogens, such
as bacteria or virus.

274
00:14:42,970 --> 00:14:45,760
And the way these
things look is because

275
00:14:45,760 --> 00:14:49,880
of these hygroscopic
solutes, in fact,

276
00:14:49,880 --> 00:14:52,840
we don't see that all the little
ones are evaporating it away

277
00:14:52,840 --> 00:14:55,390
in a tiny timescale
like milliseconds,

278
00:14:55,390 --> 00:14:56,560
but in fact, they do linger.

279
00:14:56,560 --> 00:14:59,770
And you do have respiratory
aerosols that can be observed.

280
00:14:59,770 --> 00:15:01,900
And so what these distributions
actually look like,

281
00:15:01,900 --> 00:15:06,490
they tend to have a peak around
half a micron in diameter,

282
00:15:06,490 --> 00:15:09,960
or a radius even smaller than
that would be a quarter micron.

283
00:15:09,960 --> 00:15:13,730
And so they look
something like this.

284
00:15:13,730 --> 00:15:15,790
And if you're
breathing at rest, it

285
00:15:15,790 --> 00:15:18,850
might look something like that.

286
00:15:18,850 --> 00:15:20,890
And actually, the
volume fraction,

287
00:15:20,890 --> 00:15:22,890
if we were to convert
this to a volume fraction,

288
00:15:22,890 --> 00:15:26,130
ends up being around 1e-16 parts

289
00:15:26,130 --> 00:15:28,930
of liquid per volume of air.

290
00:15:28,930 --> 00:15:31,920
So these are very
small droplets.

291
00:15:31,920 --> 00:15:34,740
And you can't see them,
but they're there.

292
00:15:34,740 --> 00:15:37,410
If you're resting breathing, you
might have something like that.

293
00:15:37,410 --> 00:15:40,600
There's also an important effect
of the type of respiration.

294
00:15:40,600 --> 00:15:43,020
So if I start talking,
then it turns out

295
00:15:43,020 --> 00:15:45,750
I'm still releasing quite
a few these aerosols,

296
00:15:45,750 --> 00:15:49,170
but now I'm also releasing
some much larger droplets.

297
00:15:49,170 --> 00:15:50,780
I might even be having--

298
00:15:50,780 --> 00:15:54,840
depending how I'm speaking, and
in fact, my personal physiology

299
00:15:54,840 --> 00:15:56,800
may vary from
person to person, I

300
00:15:56,800 --> 00:15:59,010
might be emitting even more
of these larger droplets.

301
00:15:59,010 --> 00:16:01,560
Or also, the aerosol
droplets as well.

302
00:16:01,560 --> 00:16:03,060
And then there are
other activities,

303
00:16:03,060 --> 00:16:09,810
such as singing
or exercise, where

304
00:16:09,810 --> 00:16:12,180
you're breathing
very heavily, where

305
00:16:12,180 --> 00:16:14,190
you emit even more droplets.

306
00:16:14,190 --> 00:16:16,140
And you can see
vocalizations, singing,

307
00:16:16,140 --> 00:16:19,350
and this can be, for
example, talking,

308
00:16:19,350 --> 00:16:21,480
that those lead
to more emissions.

309
00:16:21,480 --> 00:16:23,820
But the important
thing is that there is

310
00:16:23,820 --> 00:16:29,520
a big population of particles.

311
00:16:29,520 --> 00:16:32,310
In fact, the majority
of particles,

312
00:16:32,310 --> 00:16:39,040
by number or even by volume, is
over here in the aerosol range.

313
00:16:39,040 --> 00:16:41,430
So these are particles
that do hang around.

314
00:16:41,430 --> 00:16:42,840
And they float around the room.

315
00:16:42,840 --> 00:16:45,030
And they can do so for
minutes or even hours,

316
00:16:45,030 --> 00:16:48,900
depending on their size and
the conditions of the room.

317
00:16:48,900 --> 00:16:56,020
These here are the large
drops which will sediment out

318
00:16:56,020 --> 00:16:57,510
according to this formula here.

319
00:16:57,510 --> 00:16:59,560
So the Stokes formula is
still going to be valid

320
00:16:59,560 --> 00:17:00,790
regardless of evaporation.

321
00:17:00,790 --> 00:17:02,380
If we know the size,
we have a sense

322
00:17:02,380 --> 00:17:04,720
of how quickly the
droplets are falling.

323
00:17:04,720 --> 00:17:06,849
But the ones we're really
going to want to focus on

324
00:17:06,849 --> 00:17:10,329
are these aerosols for viruses,
because viruses are small.

325
00:17:10,329 --> 00:17:12,730
Whereas bacteria
are big and they

326
00:17:12,730 --> 00:17:15,520
might have to be transmitting
more of the enlarged drops.

327
00:17:15,520 --> 00:17:19,000
So now let's talk a bit
about the biology of viruses

328
00:17:19,000 --> 00:17:20,680
and bacteria and
see how that might

329
00:17:20,680 --> 00:17:25,530
connect to the physics
of droplet transmission.