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Atmospheric Environment Pergamon Press 1971. Vol. 5. pp. 571-578. Primed in Great Britain.
RESIDENCE TIME OF PARTICLES IN URBAN AIR*
Nurtan A. EsMfcNt and Morion Corn Department of Occupational Health, Graduate School of Public Health, University of Pittsburgh
' Pittsburgh, Pennsylvania 15213, U.S.A.
(First received 3 June 1970 and in final form 18 November 1970)
Abstract--A preliminary set of experiments to determine particle residence time in the dry
atmosphere was conducted. Using a membrane filler exposed in the horizontal plane and another membrane filter for sampling the ground level concentration of suspended particulate matter, ground level concentration, and flux of atmospheric aerosol were measured. Assuming
a ceiling height of 2 km the mean residence time of atmospheric aerosol was calculated. The preliminary results indicate that the mean residence time of submicron particles in the absence of precipitation is on the order of lO'-IO' h. Particles in the range of I 10 pm have residence
times on the order of 10-100 h.
INTRODUCTION
In order to maintain a balance between the input of both natural and artificial
particulate contaminants of the atmosphere and the concentrations which exist at any given place and time, there must be a very significant removal of particles from the
atmosphere. The mechanisms of removal of particulate matter from the atmosphere include diffusion, sedimentation, capture by cloud droplets and scrubbing by
precipitation.
If capture by cloud droplets and the scrubbing effect of rain are considered together
as the process of "wet removal" and sedimentation is considered "dry removal", one
may express the total removal as the sum of these three components, i.c. diffusion,
wet removal and dry removal. The net diffusion of particles out of a control volume of
at mo .pliers
be neglected as being several orders of magnitude smaller than the
other mechanisms of removal. Of the remaining two mechanisms, in terms of efficiency
and the total particulate bulk cleared from the atmosphere in a short period of time,
the more important is that of "wet removal". The enormous quantity of water w hich
cycles continuously in the atmsophere is responsible for the bulk of particulate removal, but the dry removal process essentially determines the life of aerosols in the
air. This apparently contradictory assertion can be defended as follow's. After a
significant precipitation, there is a drastic reduction in the particulate concentration
of the lower atmosphere. The build up and equilibrium concentrations attained between two subsequent intervals of precipitation is governed solely by the dry
removal process provided that the input conditions do not alter significantly. The latter is, in most cases, a reasonable assumption in an air basin. Hence, if one assumes
that a steady state is reached for addition and removal of particulate matter to and from the atmosphere, during periods between precipitation it is possible to derive an
expression for the mean residence time of suspended particulate matter injected into the air.
The determination and basic understanding of dry removal of particles from the atmosphere has been at best scanty. Junge (1963) calculated the residence time
This investigation was supported by Public Health Service Research Grant No. AP 00431-05, National Center for Air Pollution Control.
* Present add'crs: University of Dela^-iT. Newark Delaware 19711. U.S.A.
571
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572 Nurtan A. Esmen *r.J Morton Corn
of particulate matter based on their fall velocities and assumed a 5 km ceiling for the uniform mixing depth above the earth. His results were not experimentally verified. McDonald (McDonald, 1961) attempted to approximate such a residence time using available values of concentration of suspended particulate matter and dustfall. The result he obtained for the mean residence time of atmospheric particles was on the order of 10 h. This result was based on data which by its very nature, led to calcul ations of residence time based on wet and dry removal processes. This result applied to the entire size spectrum of airborne particles. It is clear that the removal of airborne particles from the atmosphere depends on aerodynamic particle size. This result, therefore, leaves much to be desired. It does not permit one to associate a residence time with a particle of given size after it is injected into the atmosphere.
Chamberlain (Chamberlain, 1966) made measurements in the field and in a wind tunnel of the transport of Lycopodium spores of approximately 30 ym dia. and 1.175 g cm'* density to.grass and other surfaces. Wind tunnel experiments were also performed with particles as small as 0.08 ym. For release at a height of 10 m, it was estimated that half the spores could travel a distance of 10 km.
Because of the scarcity of data, and in order to obtain a method to compare the relative removal efficiencies and magnitudes of wet and dry removal we performed a preliminary set of experiments to determine particle residence time in the atmosphere. This residence time was calculated from the particle flux to the ground and the ground level concentration of particles segregated into size groups.
TH FORTH CAL CONFIDE RATIONS
Consider a vertical distribution of particle concentration C(li) with boundary conditions C(0) - C0 and C(H) - CH at heights 0 and H above ground. From the studies on the vertical distribution of aerosol concentration in the atmosphere (Hamilton, 1966; Aiilquist and Charlson, 1968) it is reasonable to assume that this concentration function is monotonic non-increasing and < < C0 (Fig. 1). We can also consider a monotonic non-increasing particle flux./(/i), orthogonal to a horizontal surface element on the ground, with boundary conditions J(0) = J0 and J(,H) -- 0. Furthermore, it is assumed that a steady state is established over the entire region under consideration and C(/i)> C"'(h) and J(h) are integrable. Then,
J(h) = C(h)0t(h)
(1)
at any given height h and the particle removal velocity 0K(lt) is in the direction of the flux. We can calculate the arithmetic mean particle residence time, r, by assuming that the only contribution to particle removal on the vertical axis is described by On, the mean particle velocity.
r = tf/2 On
(2)
But
` 7/J _ l f MJih) VnV>) d/l " H J CCl(/i) d/i.
Fig I. Variation o
When the ground level possible to determine a 1 and define the distributio
Now we consider equatic
The value of the inn theorem of integral calci
By the definition of the ft
And simi..'ly since fi) i
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PRODUCED BY FORD
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`
, k*d a 5 km ceiling for the penmentally \enhca. Wa residence time using
matter and dustfall. The
-.cric particles was on the ery nature, led to calculresses. This result applied it the removal of airborne panicle size. This result, e to associate a residence umosphere. n the field and in a wind itely 30 pm dia. and 1.175 jl experiments were also t a height of 10 m. it was
m. t method to compare the
:m. value performed a time in the atmosphere. > to the ground and the groups.
NS ' 'll) with boundary ... ground. From the
.non in the atmosphere inable to assume that this "*: < C0 (Fig. 1). We can v . ,-^nogonal to a horizontal '".7(0) = J0 and J(H) - 0. >ed over the entire region ble. Then.
(1)
'i) is in the direction of the :nce time, r, by assuming -tical axis is described by
(2)
dh. (3)
Residence Time of Particles in Urban Air
573
Pig. 1. Variation of particle concentration between ground level and height H.
When the ground level concentration C,, and ground level flux J0 are measured it is possible to determine a limiting value for CK. Let the normalizing function ^ be:
>P *= 1 -- h/H, 0 < ^ 1
(4)
and define the distribution functions g(>p) and f(tp) for J(<p) and C(<P) respectively.
C('P)^CoA'P) 0</W)<l
(51
A<P) = JoSW Now we consider equation (3):
0 sS g{+) s: 1.
((
fj`_-h! )0f
m;)djlh~Jco Jrmg(<P) '0
d<p
O)
The value of the integral above may be investigated using the mean value theorem of integral calculus:
ii
m "r fix)
V
By the definition of the function g(<P): 1
j ) d>P m 1.
0s'l-
(8) W
And similarly since f(ip) is normalized: 0 < f(J') < 1.
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PRODUCED BY FORD
574 Nurtan A. Esmin and Morton Corn Hence the right hand side of equation (8) is:
jk !*>***' o And therefore using equation (11):
1
01)
J A*)
(12)
Therefore, from equation (7) On < Ua.
Therefore from equation (2) t > H/2 U0 = C0H/2 J0.
(13) (14)
Equation (14) indicates that the mean particle residence time calculated using measured ground level particle concentration and flux represents the lower bound of mean particle residence time, i.e. all values of mean particle residence time should exceed or be equal to this value. Of course, this result is only applicable within the framework of the assumptions made here.
In order to extend this argument to cover a larger class of cases we can investigate the efTects of local deviations from monotonic behavior. It is clearly evident that if the average value of C(/i) does not exceed C0 and the behavior ot J(h) is as assumed the conclusions arrived at above will still be valid. The experimental values available (Mwiii.tox, 1966: Aiilquist and Charlson, 1968) on the vertical distribution of
atmo'r.lvric jerosol seem- to iustify the acceptance of this limiting condition provided that J(lt) behaves as assumed. Now we can investigate the strength of the monotonie
behavior assumption of J(li). Suppose due to the increase in local eddy diffusivity JUi) between h, and h} is increased in a manner that the monotonic balance is dis
turbed. Then we expect a local build up of aerosol at a level below /i,, say /t0. The removal velocity between /;, and h0 being the same these will be increased in con
centration and hence there will be an increase in the flux in that direction, increasing the flux all the way to the ground level. This, of course, will again establish the
monotonic behavior of the flux. Because the sampling time in the studies to be described is relatively long (1-4 h) it is expected that these deviations will be smoothed
and on the average a quasi equilibrium may be assumed. These arguments will, of course, be invalidated if the atmospheric stability is such that there is a very high ceiling (above the assumed height) with strong fumigation and.or local sources have a strong influence. By a judicious choice of sampling site and time these exceptional cases may be excluded from the investigation and the validity of the results would not
be affected. The upper bound of the mean particle residence time may be determined as follows.
The particle removal velocity is composed of several components (equation (IS)].
VK TM v, H- V4 -r U,
(151
where U, -- Particle terminal settling velocity /
( ,. ................. v eiocit*. L x Particle icniovui velocity due to reaction ano ai . oli-.c. ciiccu.
e^on OKb
It is as: velocity co explorator interest, i.<
Thus, tl values bas
In each particles fi Public He; paniculate to the filte for one ra the effects by gluing in its centi distortionby Davies microscop calculated in botli c.i
The gro the nearby level shou
The sai three day humidity
11 VI VIV independe of approx filters diag atmosphemicroscor paper this millipore I to that fill and a trei mem brant h:!r'd,ine
PBOm Tr-m uv com
(12)
(13)
(14) :alculated using lower bound of nee time should table within the
: can investigate v evident that if
is as assumed values available distribution of ' provided
ntonotonic tody diffusivity
balance is disx, say lt0. The
jsed in conN-rtcfn, increasing
in establish the e studies to be fill be smoothed -.uments will, of : is a very high :al sources have iese exceptional .suits would not
lined as follows, uation (15)].
(15)
effects.
Residence Time of Particles in Urban Air
J75
It is asvumcJ that V, i- always in the direction of (but that oth-:
oval
vcl>ciiy components may be in opposing directions for short durations oi i . .. jn the
exploratory study reported here, averages over appreciable time periods were of
interest, i.e.. hours. Hence: it is reasonable to assume that:
U* > V,
(16)
Thus, the range of residence time, as calculated from C0 and J0, and the limiting
values based on U,, are given by equation f!7).
H 1 C0H 2 U* ' Jo 2'
(17)
EXPERIMENTAL METHODS
In each test, a membrane filter (Millipore HA) was exposed to collect settled
particles for four hours in the horizontal plane on the roof of the Graduate School of Public Health. University of Pittsburgh. The ground level concentration of suspended
particulate matter was measured by simultaneously sampling at 6.5 l.min*1 adjacent to the filter with another membrane filter (Millipore HA) oriented in the vertical plane
for one randomly selected hour within the four hour interval. In order to minimize the effects of cross-wind a leak tight filter holder (Gussman et a!.. 1962) was modified
by gluing to the filter holder face a 12 cm dia.. 1 in. thick plate with a 7.5 mm i.d. hole in its center. This geometry of the collecting filter will not introduce sampling velocity distortions for 40pm dia. particles in winds up to 40 km h"', according to calculations by Davies (Davies, 1968). After the sample was collected, particles on each tiller were microscopically sized and counted, using two magnifications and overlapping the calculated concentrations. The magnifications used were 20 X ocular, 1.25 opiovar in both cases, 25 x and 63 objective for larger and smaller fractions, respectively.
The ground level measurements were not made due to the expected distortion from the nearby buildings. However, for the purpose of the study, measurements at the roof level should be sufficiently accurate to estimate the residence time of the particles.
The sampling periods were selected when there was no precipitation for at least three days prior to the sampling period and during the sampling period relative humidity was less than 70 per cent.
VERIFICATION OF SAMPLING METHOD
In order to investigate the effect of sampling surface on the flux measurements five independent tests at a different locality were conducted. On four corners of a square of approximately 1 m a Whatman 40 filter paper, a glass slide and two Millipore HA filters diagonally opposing each other were placed. These surfaces were exposed to the atmospheric dust for a duration of four hours and the deposited particles were sized microscopically. Due to the difficulty in assessing the size distribution on Whatman paper this verification was performed on panicles larger than 2.0 pm only. One of the millipore filters was assumed to be a correct evaluation and the others were compared to that filter. The results show that the deviations are well within experimental error and a trend does not seem to exist between sampling media (Table 1). The use of
membrane filters is well justified in terms of the ease in the particle size assessment and handling. Although glass slides are easy to use in conjunction with the microscope,
handling and cleaning presents some difficulties.
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Tabu 1. CoMTAiuaoN or DtrmENT couacroa aunTAcn in the meaiummixt or rune
-2.
S. Collector $ surface
Membrane II
Whatman 40
Glass slide
-
Comparative flux measurement (Membrane filter I taken as 1.00)
Test Particle diameter
No.
2.0-4.8 pm
4.8-9.6 pm
> 9,6 fin
1 0.98 1.05 0.90 2 1.08 0.96 1.00
3 1.12 1.00 1.02 4 0.90 0.96 1.09 S 0.95 0.99 1.02
1 1.09 0.98 1.10 2 1.12 1.00 1.09 3 0.90 1.1! 0.90
4 0.91 1.05 0.92 S 1.10 1.02 0.91 ] . 1.00 0.90 0.90
2 0.95 0.98 0.87 3 0.92 1.09 0.90
4 1.08 1.01 1.09 5 1.13 0.95 1.10
RESULTS
.
Five preliminary tests were performed. Test data were reduced io the following
way: (1) From microscopic sizing and counting of particles on each filter a ground level
particle concentration and a ground level particle flux were defined for each particle
size group. (2) The particle size data were then reduced to particle aerodynamic equivalent
size, d,, using a mean particle shape factor of 1.29 (Stein el al., 1969). (3) From C0 and J0, l/* (0) and r were calculated by assuming that the maximum
aerosol height, H, was 2000 m above the ground level. (4) t/*(0) was then compared to particle terminal settling velocity in calm air, V,,
based on calculated values of dr The results of these procedures are shown in Figs. 2-4.
DISCUSSION OF RESULTS
The preliminary results indicate that the mean residence time of submicron particles in the absence of precipitation is on the order of lO'-lO1 h. Particles in the aero dynamic equivalent diameter range 10 pm to 1 pm have residence times of 10-100 h, respectively. These times are long compared to those reported by McDonald (McDonald, 1961); but compare favorably with Junge's results (Junoe, 1963). McDonald utilized National Air Sampling Network data to calculate residence time. These data included the removal effect by rainfall. As expected, the effect of precipi tation appears to be Urge.
The consistent lack of particles larger than approximately 20 pm in statistically significant numbers indicates that the mean residence time of these particles is on the order of, or less than, the transport time necessary Tor their arrival at the sampling site. Furthermore, for particles greater than 20 pm. the upward draft would have to be
Fig. 2. Re Fig. 3. Rc
PRODUCED BY FORD
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yVis/^EMEWt or mix
(Membrane ) ster i > 9.6 pm
0.90 1.00 1.02 1.09
1.02 1.10
1.09 0.90 0.92 0.91 0.90 0.87 0.90 1.09 1.10
:d in the following
ilter a ground level ach particle
jjuamic equivalent 969). 'at the maximum
' jty in calm air, U,,
submicron particles rticles in the aeroce times of 10-100 'ed by McDonald
or. 1963;. .dence time, r- of precipi-
pm in statistically e particles is on the val at the sampling ft would have to be
Residence Time of Panicles in Urban Air
577
M
1s
l;iii. 2. Relationship between calculated panicle removal velocity and particle sire (</,). calculated from measured panicle projected area diameters.
*3t >yc v
Fig. 3. Relationship between particle sire id,) and the ratio of particle terminal settling velocity to panicle removal velocity.
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PRODUCED BY FORD
571
' L..
Nurtan A. Esmkn and Motion Cotn
Atmospheric Ettrit
V.
Fio. 4. Relationship between panicle mean residence time and panicle site.'
about 0.1 km h' 1 in order to distribute them up to the assumed ceiling of 2 km above the surface. This will lead to a further complexity of calculating the residence time of the large particles.
Because the concentration of particles in precipitation was not determined in this study, we cannot compare the calculated dry and wet removal particle velocities.
The results discussed above are based on a model with severe restrictions and assumptions pertaining to the atmospheric ceiling height for particle dispersion and to the nature of the distribution of particles within this layer. However, the results offer a first order approximation to the residence time of particles injected into an
urban atmosphere.
REFERENCES Ahlquist N. C. and Chaalson R. J. (1968) Measurement of the vertical and horizontal profile of
aerosol concentration in urban air with the integrating nephelomeler. Environ, Sei. Techno!. 2, 363. Chamberlain A. C. (1966) Transport of lycopodium spores and other small particles to rough surfaces, Proc. Roy. Soc. A-296, 45. Hamilton P. M. (1966) The use of lidar in air pollution studies, hi. J. Air Water Potlul. 10, 427. Davies C. N. (1968) The entry of aerosols into sampling filter and heads. Bri. J. appl. Phys., (Ser. 2) I, 921. Gussman R. A.. Dennis R. and Silverman L. (1962) Notes on the design and leak testing of sampling filter holders. Am. Ind. Hyp. Ass. J. 23, 480. JitNtir. C. E. (1963) Air Chemistry and Radioactivity, p. 291 IT. Academic Press, New York. McDonald J. E. (1961) Mean atmospheric residence times for particulate air pollutants. Bull. Am. . Meieorol. Soc. 42,664. Stein F,, Esmen N. A. and Corn M. (1969) The shape of atmospheric particles in Pittsburgh air. Atmospheric Environment 3, 443. ^ ,
Abstract--Air more (rcplicat. cvntrations of' (2) "respirable equivalent as i Likely causes < numbers of pa' lion, anisokine components. w
The results comparison rawere between 0 0.16 and 5.4. a for CAS l-CA With all aampl. location was b.
In general, it estimated the t. underestimated was found thin and relative p proha blv is not made an integr
Sampling an a transport and c
tracer as inlcrrc obtain an empit
model. Such st (McLi.rov, 196
tempered by an eentration or its
the quantity wl rcprcsentativcnc
data upon whic the data used U
The difference and what is mea
measurement. 1 resulting from r
random or syste from the ideal c
Work supported t Present address:
PRODUCED BY FORD
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.145-165. i
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Atmospheric Environment Pergumon Press 1971. Vol. 5, pp. iiiSv lv>0. Printed in orent Britain.
RESIDENCE TIME OF PARTICLES IN URBAN AIR*
Tnt ursini Nrt time of 0.1 to 1.0 pm radius particles in urban air seems to lie on the order of one day based on several wars experience in measuring atmospheric turbidity by optical means. This qualitative conclusion n'is.. ;-nm observing the na! variation in turbidity which iniiinally increases during the day but decreases during the night. The increase is due to two factors: 11) the direct production of particles by human activities and by turbulent lifting of natural particles, and (-1 by production of particles by photochemical reactions of trace gases in the air. Both of these pri'cesscs arc at least reduced at night. Since the turbidity decreases then, there must be a removal mechanism, at least as rapid in the dark as ill the light: possibly more rapid, due to reduction in atmospheric turbulence, lissn s and Corn correctly called this mechanism "dry removal". The observed changes in turbidity overnight in conditions of "dry removal" only lead to a mean lifetime for this si/c range of particles of 17-39 h. The day-time mean lifetime may be slightly longer due to meteorological parameters, so that
an estimate of lO'-IO* h would seem warranted. The dillcrcncc between this result and Ihc 10MOJ h given by I-Smi n and Corn may arise from two reasons: (I) the assumption of steady state made by them, and (2) the low collection and optical detection efficiencies of these small particles.
Atmospheric Sciences Research Center
State University of New York at Albany 1400 Washington Avenue Albany, New York 12203, US.A.
William H. Fiscirtat
AUTHORS' REPLY
Although atmospheric turbidity measurements show a diurnal variation, we fail to sec a con tradiction between our results and the diurnal variation in turbidity. This can be shown by a few simple calculations. The turbidity is defined as (Dxvtrs, 1966):
' K~noEl
where
n nunvbcr of particles a panicle projected area proportional to particle diameter squared
E particle extinction coefficient I thickness of light path.
(1)
We now let the turbidity at nightfall he A'fO), and investipale the value of K(t) after a time r. assuming no generation and greatly reduced mixing. This can he accomplished by investigating the
behavior of an exponential decay model for A'(r). Our results indicate that
r ~ 150/r/
where tl = particle aerodynamic diameter in microns r mean residence lime in hours. From the exponential model we can calculate the n(tf,t) variation or partide count
(2)
n(rf, t) -- o (<0 exp (-- r/r) - exp
(3)
From conations (ll-(3) we get
(4)
* P.SMrs N. A. nmJ Corn M., Atmospheric Enrironment 5, 571-57# 0971). t Present address: Natiohal Center for Atmospheric Research. P.O.Box 1470, Boulder,Colorado 80302. U.S.A.
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Discussions
"Integrating this value between </*() and rf 20
>:'
K-
AjU) Atn
dx
150 20t
HS)-
To make the calculations easy we can take t - 7.5 h. Hence
(5)
A(6) ~ 1-7 A'(7-S)
(6)
This indicates a 70 per cent reduction in turbidity. Considering the other removal mechanisms, partial generation and further complicating atmospheric effects, this figure is certainly reasonable. On the oilier hand, if we take r approximately 1/4 of the values reported here, as suggested by Fischer
we will obtain (by similar calculations)
- A'(0) - 16 A'(7.5)
(7)
This value seems excessive. Therefore, we feel that our results are at least a good first ap proximation to the true value of the dry removal residence time under equilibrium conditions.
Groiluotr School of Public Health Unkenity ofI'iitshmuh Pittsburgh, Pcnnsylrunia 15213, U.S.A.
N. A. Csmi.n* and M. Corn
REFERENCE
.
Davies C. N. (F.d.) (lOfiOj Aerosol Science. Academic Press, Nciv York.
* Present address: University of Delaware.
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bundle many computer jobs, but its prioe starts at 52700, Wang says.
6000 0152
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