A model for the relative humidity effect on the readings of the PM10 beta-gauge monitor

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A model for the relative humidity e%ect on the

readings of the PM10

beta-gauge monitor

C.T. Chang, C.J. Tsai

∗

Institute of Environmental Engineering, National Chiao Tung University, No. 75 Poai Street, Hsinchu 300, Taiwan

Received13 February 2003; accepted23 June 2003

Abstract

In the previous paper (Atmos. Environ. 15 (1981) 1087), we foundthat the PM10 concentrations detected

by the Wedding beta-gauge PM10 monitor andthose measuredby the manual hi-vol PM10 sampler were quite

close when the ambient relative humidity (RH) was lower than the deliquescence RH (DRH) of aerosols. However, when the deliquescent point was exceeded, PM10 concentrations of the beta-gauge were foundto be

higher and di%erences increased with an increasing ambient RH. In addition, theoretical water mass calculated by a thermodynamic model (ISORROPIA model, (Aquat. Geochem. 4 (1998) 123)) was found to be much higher than the actual values. In this study, models were developed to determine water evaporation loss from collectedparticles on the <lter tape of the beta-gauge during sampling andin the monitoring room. Simulated results show that all absorbedwater will evaporate completely at RH lower than about 85%. However, absorbedwater does not evaporate completely at RH higher than about 85%, andremaining water in particles accounts for higher beta-gauge readings than the hi-vol concentrations. The simulated daily beta-gauge PM10

Keywords: Beta-gauge; PM10; Aerosol mass monitor; Humidity e%ect

1. Introduction

There are 72 ambient air quality monitoring stations in Taiwan’s air quality monitoring network, where automatic Wedding beta-gauge PM10 monitors are usedto measure hourly PM10

concen-trations. The Wedding beta-gauge PM10 system has a cyclone as the PM10 inlet, andthe Bow rate

∗_{Corresponding author. Tel.: +886-3-5731880; fax:+886-3-5727835.}

E-mail address: [email protected](C.J. Tsai).

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Nomenclature

a speci<c surface area of particle bed, m−1

A <ltration area, m2

Cc Cunningham slip correction factor

D di%usion coeGcient of water vapor, m2_s−1

Dp particle diameter, m

HDp average particle diameter, m

DRH deliquescence relative humidity, %

Jv evaporatedBux of water vapor, kg m−2 s−1

k mass transfer coeGcient, m s−1

K2 dust cake resistance coeGcient, s−1

K2;st theoretical dust cake resistance coeGcient, s−1

L thickness of dust cake, m

mev1 evaporatedwater mass during sampling, kg

mev2 evaporatedwater mass during beta-counting, kg

n ratio of cake thickness to the diameter of particle (L= HDp)

P0 pressure at upstream of sampler, N m−2

Pe Peclet number

Qin air Bow rate at the upstream dust cake, m3s−1

Qout air Bow rate at the downstream dust cake (Qin=(1 − )); m3s−1

RR-H resistance factor, Happel’s cell model

RH relative humidity, %

SB saturation ratio of water vapor in monitoring room

Sh Sherwoodnumber

Sin saturation ratio of vapor at upstream dust cake (in=e)

Sout saturation ratio of vapor at downstream dust cake (out=e)

u0 super<cial Buidvelocity when pressure is equal to P0, m s−1

Vf face velocity, m s−1

W mass area density of cake, kg m−2

x traveling direction of Bowing Buid

Greek letters

a dimensionless parameter in Eq. (1) a dimensionless parameter in Eq. (1) a dimensionless parameter in Eq. (1) JP pressure drop of particle bed, N m−2 Jt time periodof sampling, s

JtB time periodof beta-counting, s

ratio of JP=P0

porosity of dust cake

a dimensionless variable in Eq. (6) dynamic viscosity of air, N s m−2

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concentrations of water vapor, kg m−3

e saturation concentration of water vapor, kg m−3

in concentration of water vapor at upstream of particle bed

out concentration of water vapor at downstream of particle bed

p density of particle, kg m−3 g geometric standard deviation

a parameter in Eq. (7)

is 18:9 l=min. It is an equivalent methodfor PM10 designated by the US EPA. Before a sampling cycle begins, the 14_{C source of the monitor will emit beta-particles through a reference position of} the <lter tape. After detecting the initial or background count rate through the reference position of the <lter tape, the tape is movedto the sampling position under the inlet exhaust tube andbegins a sampling cycle (Wedding & Weigand, 1993). After 54 min: of the sampling cycle, the sampling manifoldwill start to open, andthe <lter tape with collectedparticles is returnedunder the 14_C source, andthe sampling manifoldis closedautomatically. The time that the <lter tape exposes in the monitoring room as the sampling manifoldopens is about 40 s. After that, the beta-gauge begins to measure the attenuatedcount rate for 5 min: and20 s andthe PM10 concentration in ambient air in that hour is estimated.

Manual Sierra–Anderson SA1200 hi-vol and Wedding hi-vol PM10 sampler are the designated reference methods for PM10 by the US EPA. Both samplers are usedwidely in Taiwan for am-bient PM10 study. The Wedding hi-vol PM10 sampler has a cyclonic PM10 inlet with a Bow rate of 1:13 m3_{=min. Its PM}₁₀ _{inlet has been testedfor particle penetration eGciency by many di%erent} tunnel facilities in the laboratory at di%erent wind speeds (Ranade, Woods, Chen, Purdue, & Rehme, 1990). The inlet of Sierra–Anderson SA1200 is a single-stage multi-jet impactor, the Bow rate is 1:13 m3_{=min andhas been testedin a windtunnel (}_{McFarland& Ortiz, 1987}_{). Since the <lter of} the manual Sierra–Anderson SA1200 and Wedding PM10 hi-vol samples are conditioned before and after sampling, the measuredconcentrations are close to dry PM10 concentrations. According to the standard operation procedure for weighing PM10 <lters, the average temperature of the weighting environment shouldbe kept between 15◦_{C and30}◦_{C, andthe temperature variation shouldbe} main-tainedwithin ±3:0◦_{C, whereas, the average RH of the environment shouldbe kept between 20%} and45%, andthe RH variation shouldbe maintainedwithin ±5:0% (US EPA, 1987). Therefore, it is expectedthat the readings of the beta-gauge monitor will be higher than the hi-vol sampler at RH higher than DRH when aerosol particles absorbs water during sampling process of the beta-gauge monitor.

Because of the frequent occurrence of high relative humidity in the ambient air of Taiwan, the Taiwan EPA is interested to know the e%ect of humidity on the readings of the automatic Wedding beta-gauge PM10 monitors. We conducteda <eldstudy at four stations (Chung-Shan, Ta-Yuan, Chu-Shan andTa-Liao) in Taiwan as shown in Fig. 1 andfoundthat the PM10 concentrations of the Wedding beta-gauge were quite close to the measured values of manual hi-vol samplers when the ambient RH was lower than the DRH of aerosols (Chang et al., 2001). However, when the deliquescent point was exceeded, PM10 concentrations of the beta-gauge were foundto be higher than those the manual hi-vol sampler andthe di%erences increasedwith increasing ambient RH.

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Fig. 1. The location of four sampling stations.

The experimental PM10 concentration ratio of beta-gauge versus hi-vol sampler in Chang et al.

(2001) is further comparedwith the theoretical ratio assuming that the water content calculatedby the thermodynamic model (ISORROPIA model, Nenes, Pandis, & Pilinis, 1998) is entirely associ-atedin the particles of the beta-gauge monitor, as shown in Figs. 2(a) and(b). The <gures show that the experimental PM10 concentration ratio starts to increase from 1.0 when RH is higher than 80–85%. In most cases, the thermodynamic model seems to over-predict water content in particles of the beta-gauge monitor andthe di%erence increases with an increasing RH. Also shown in Fig. 2 is the more reasonable theoretical ratio calculated by the models that we have developed in this study. The thermodynamic model calculates the water content of particles assuming they are in thermody-namic equilibrium with a prescribedambient condition. However, when particles are collectedon a <lter, water evaporation may occur due to the pressure drop through the dust cake and changes in the ambient conditions. These non-equilibrium conditions reduce the humidity e%ect on the beta-gauge readings.

Evaporation of volatile particulate species such as ammonium chloride and ammonium nitrate due to the evaporation when the pressure drop increases across the <lter during sampling has been studied extensively (Appel & Tokiwa, 1981;Zhang & McMurry, 1987, 1992; Cheng & Tsai, 1997). However, evaporation of particle-boundwater during sampling process has rarely been mentioned in the literature, despite that water can be one of the most abundant species in particles when RH is higher than DRH.

The schematic of the role of water vapor on beta-gauge readings during sampling and beta-counting is depicted in Figs. 3(a) and(b). During aerosol sampling, airborne particles absorb water when RH is greater than DRH. However, particle-bound water will evaporate during sampling mainly due to

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0.6 0.7 0.8 0.9 1 RH 0 1 2 3 Ratio Ta-Liao (Nov.23-Nov.28, 1999) Ta-Liao (Nov.11-Nov.23, 2000) Chung-Shan (Sep.29-Oct.13, 2000) ISORROPIA Present models 0. 6 0 .7 0.8 0.9 1 RH 0 1 2 3 Ratio Ta-Liao (Nov.18-Nov.28, 2000) Chu-Shan (Oct.20-Oct.30, 2000) Ta-Yuan (Sep.30-Oct.7, 2000) ISORROPIA Present models (a) (b)

Fig. 2. Ratio of daily average PM10 concentrations of Wedding beta-gauge to (a) Wedding (b) Andersen hi-vol sampler

versus RH. Experimental data are in Chang et al. (2001). The long dashed line: The ratio is based on the theoretical water content of the beta-gauge calculatedby the ISORROPIA model; solidline: The ratio is basedon the beta-gauge concentrations calculatedby the present models.

the pressure drop across the dust cake, as shown in Fig. 3(a). Before beta-counting process, the time when the sampling manifoldopens for about 40 s, the dust cake is exposedto the monitoring room with air conditioning, where the humidity and temperature are most likely lower than the ambient air. Particle-boundwater will evaporate during the periodof 40 s. During beta-counting, the space between the <lter tape andbeta source or detector is very small, therefore, the amount of water evaporatedwill be limited, as shown in Fig. 3(b). In this study, water evaporation is assumed to be negligible during beta-counting.

In the following, models developed to calculate water evaporation of collected particles during sampling andin the monitoring room will be presentedandthe simulatedbeta-gauge concentrations will be comparedwith the actual readings.

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Fig. 3. (a) Water evaporation loss occurs during sampling, and(b) when the sampling manifoldis openedbefore beta-counting. During beta-counting, evaporation loss is negligible.

2. Theoretical models

2.1. Water evaporation during sampling

To calculate the evaporated water mass in particles during sampling, the model originally de-velopedby Cheng andTsai (1997) is used. In the model, the evaporation loss from collected particles on the <lter is considered as a mass transfer problem of a particle bed. According to the model, the saturation ratio of water vapor concentration at the downstream of the <lter, Sout, can be calculatedas

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where = 1 +_nP4 e + 24(1 − )Sh P2 e ; =nP₂e; = 1 1 +_{6n(1 − )S}Pe h ;

where n is the ratio of dust cake thickness to the average particle diameter, L= HDp; Sin the saturation

ratio of water vapor at the upstream of dust cake; the ratio of pressure drop across the particle bed to the pressure at the upstream of the sampler, JP=P0; and the porosity of dust cake. Sherwood

number, Sh, is de<ned as Sh= k HDp=D; andPeclet number, Pe, is de<ned as Pe= Vf HDp=D.

The total evaporatedmass of water of the collectedparticles during the sampling periodJt can be foundas

mev1= e(SoutQout− SinQin)Jt; (2)

where Qin is the Bow rate at the upstream of dust cake; Qout(=Qin=(1 − )) the Bow rate at the

downstream of dust cake; and e the saturation concentration of water vapor. Other details of the

model can be found in Cheng andTsai (1997).

During sampling, water evaporation is calculatedbasedon the pressure drop, JP, through the particle cake, which can be calculatedas

JP = K2WVf; K2= K2;stRR−H= 18 pHD2P;21Cc · 3 + 2(1 − )5=3 3 − 4:5(1 − )1=3_{+ 4:5(1 − )}5=3_{− 3(1 − )}2; HDP;21= ∞ 0 D3Pf0(DP) dDP _∞ 0 DPf0(DP) dDP 1=2 ; (3)

where K2 is the dust cake resistance coeGcient, W the mass area density of cake, Vf the face

velocity, and Cc the Cunningham slip correction factor. The Bow resistance, K2 can be foundby

multiplying the theoretical dust cake resistant coeGcient, K2;st, by a correction factor RR−H based

on the Happel’s cell model (Gupta, Novick, Biswas, & Monson, 1993). 2.2. Water evaporation in the monitoring room

To determine the evaporation loss of particle-bound water in the monitoring room during the periodwhen the sampling manifoldis openedbefore beta-counting, the convection–di%usion equation of the dust cake has to be solved. Neglecting the convection term, the governing equation for

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the dust cake is Dd2

dx2 + ak(e− ) = 0: (4)

To solve Eq. (4), the boundary conditions for a packed bed are used

= Soute at x = 0; (5a)

d

dx = 0 at x = L: (5b)

The concentration of water vapor in the dust cake can be calculated as (x) =(SB− 1)e 1 + e2√L (e √_x + e2√L_e−√x_{) +} e; =ak_D; (6)

where SB is the saturation ratio of water vapor in monitoring room. Applying the Fick’s law at the

surface of the dust cake (at x = 0), the evaporatedBux Jv of water vapor can be foundas

Jv= e2n _{− 1} e2n _{+ 1} (1 − SB)e_DD p ; =6(1 − )Sh: (7)

The total evaporatedwater mass of the collectedparticles during beta-counting, JtB, can be

shown as mev2= e2n _{− 1} e2n _{+ 1} (1 − SB)e_DD p AJtB: (8)

In the above models, the data of the hourly relative humidity and temperature were obtained from the Central Weather Bureau in Taiwan, and the actual readings of the automatic Wedding beta-gauge monitor of the four stations were obtained from the Taiwan EPA. The mass median of aerodynamic diameter (MMAD) and geometric standard deviation g were measuredby a micro-ori<ce uniform

deposit impactor (MOUDI) to be 0.47 and 1:19 m for <ne particles, and3.10 and1:54 m for coarse particles, respectively. The di%usion coeGcient of water vapor is calculated according to Chapman andEnskog theory (Poling, Prausnitz, & O’Connell, 2001) andequals 0:25 cm2_{=s at 20}◦_C. A BET surface analyzer (Micromeritics ASAP 2000) was usedto measure the speci<c surface area andporosity of the dust cake on the <lter tape in the beta-gauge. The average porosity of particle cake of six samples was foundto be 0:66±0:09. Further, temperature andRH in the monitoring room of the automatic Wedding beta-gauge monitor was measured to be 24:2 ± 3:2◦_{C and69:8 ± 10:1%} in this study during beta-counting.

3. Results and discussion

3.1. Simulated results of water evaporation

The theoretical hourly dry PM10 concentration andionic concentration obtainedin Chang et al. (2001) were used in the thermodynamic model to calculate the theoretical water content, and

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07:00 13:00 19:00 01:00 07:00 Hour 0 400 300 200 100 PM 10 concentration, µ g/m 3 Beta-gauge PM10 Manual PM10 (average) Inferred hourly dry PM10

07:00 13:00 19:00 01:00 07:00 Hour 292 296 300 304 308 Temperature, Deg K 0.6 0.7 0.8 0.9 1.0 RH Relative humidity Temperature (a) (b)

Fig. 4. (a) Temperature andrelative humidity, and(b) PM10 concentration versus time at Ta-Liao, November 23, 1999.

in the present models to calculate the evaporated water mass of dust cake during sampling and beta-counting. Two 1-h periods were taken as an example at Ta-Liao station in November 23, 1999 to explain the detailedvariation of particle andwater mass with time during the 1-h periodof sampling andbeta-counting. RH andtemperature at Ta-Liao in November 23, 1999 are shown in Fig. 4(a). The <rst 1-h periodis from 11:00 am–12:00 pm, when RH andtemperature are about 62.3%, and303:6 K, respectively. Water content is shown to be low in Fig. 5(a). The second1-h periodis from 2:00–3:00 am in November 24, 1999, when RH equals 95.3% andtemperature is 295:2 K. Water content is as high as 180:8 gm−3 _{as shown in Fig.} ₅_(b).

In Fig. 5(a) when RH is around62.3%, water absorbedby particles, which are collectedon the <lter tape of the beta-gauge, evaporates entirely during sampling, and the actual reading of beta-gauge (120:9 g m−3_{) is close to the theoretical concentration (106:6 g m}−3_{). PM}₁₀ _{mass, water mass} andevaporatedwater mass shown in Fig. 5 are calculatedfrom PM10 concentration, Bow rate and sampling time (Fig. 4b). In comparison, if water evaporation is not considered, the sum of dry PM10 concentration andwater content calculatedby the thermodynamic model, 143:28 g m−3_{, is higher} than the actual beta-gauge reading.

When RH = 95:3%, the water content is very high and if water evaporation is not considered, the theoretical beta-gauge concentration will be much higher than the actual reading, as shown

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0 900 1800 2700 3600 Time, sec 0 5e-005 0.0001 0.00015 0.0002 0.00025 Accumulated mass, g 0 50 100 150 200 Concentration, µ g/m 3 RH = 62.3 % T = 303.6 K PM10 = 106.6µg/m3 Water content = 36.68µg/m3 (ISORROPIA) Actual beta -gauge reading Simul. beta -gauge conc. Dry PM10 + theo. water Dry PM10

Dry PM10 + theo. water

- evap. water 0 900 1800 2700 3600 Time, sec 0 0.0002 0.0004 0.0006 0.0008 Accumul ated mass, g 0 200 400 600 Conce ntr a tion, µ g/m 3 RH = 95.3 % T = 295.2 K PM10 = 175.65µg/m3 Water content = 366.72 µg/m3 (ISORROPIA) Actual beta -gauge reading

Dry PM10 + theo. water

- evap. water Dry PM10 + theo. water Dry PM10 Simul. beta -gauge conc. (b) (a)

Fig. 5. SimulatedPM10 mass in the beta-gauge versus time during sampling and beta-counting at Ta-Liao, (a) 23rd,

November 1999 (11:00 am–12:00 pm) (b) 24th, November 1999 (2:00–3:00 am).

in Fig. 5(b). Only a small fraction of water is foundto evaporate during sampling. However, an appreciable amount of water in particles is evaporatedduring the periodwhen the sampling manifoldis openedbefore beta-counting. The simulatedbeta-gauge concentration, 336:39 g m−3 (range: 290.57–377:61 g m−3_{), is foundto be very close to the actual reading, 329:7 g m}−3_. 3.2. Comparison between simulated and actual beta-gauge concentrations

The comparison between the hourly simulatedbeta-gauge concentrations andthe actual readings is shown in Figs. 6(a) for high ambient RH andaerosol water content area (Ta-Liao in Novem-ber 23, 1999), andFig. 6(b) for low ambient RH andaerosol water content area (Chung-Shan in October 29, 2000). Three cases assuming the average, highest andlowest RHs (70%, 80% and 60%) in the monitoring room are also calculated. Here the actual hourly beta-gauge readings are obtainedfrom the Taiwan EPA, the simulatedbeta-gauge concentrations equal the sum of hourly dry PM10 concentration (Chang et al., 2001) andthe hourly theoretical water content calculatedby the

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60 160 260 360 460 560

Actual beta-gauge reading, µg/m3

60 160 260 360 460 560

Simulated Beta-gauge conc.,

µ g/m 3 60 % 70 % 80 % ISORROPIA Present model Y = 1.05 X - 33.75 R2_{= 0.905} RH 10 30 50 70 90

10 30 50 70 90 Simulated beta-gaugeconc., µ g/m 3 Y = 1.02 X - 4.43 R2 = 0.982 60 % 70 % 80 % ISORROPIA Present model RH (a) (b)

Fig. 6. Comparison between the hourly simulatedandactual beta-gauge concentrations versus RH in the monitoring room, (a) Ta-Liao (November 23, 1999) (b) Chung-Shan (October 29, 2000).

thermodynamic model, minus the hourly evaporated water mass calculated by the present models. Also indicated in the <gures with data points labeled “ISORROPIA” are the theoretical concentra-tions without considering water evaporation, andwater content is calculatedby the thermodynamic model.

In Fig. 6(a), the simulatedbeta-gauge concentrations considering water evaporation basedon the present models are found to be very close to the actual readings. The slight di%erences between the simulatedbeta-gauge concentrations andactual readings are because that the theoretical hourly dry PM10 concentrations used in the models are predicted rather than actual values (Chang et al., 2001). In comparison, the simulatedbeta-gauge concentrations without considering water evapora-tion (“thermodynamic model”) are found to be much higher than the actual readings. Therefore, it is very important in the model to consider water evaporation loss. Part of water evaporation occurs during sampling, a goodfraction occurs in the monitoring room when the sampling manifoldis openedbefore beta-counting. RH in the monitoring room has a limitedinBuence on the beta-gauge

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0 100 200 300 400

Simulated beta-gauge conc.,

µ g/m 3 60 % 70 % 80 % ISORROPIA Present model Y = 0.88 X - 1.78 R2 = 0.972 RH

Fig. 7. Comparison between the daily simulatedandactual beta-gauge concentrations versus RH in the monitoring room. Data are from all four monitoring stations.

concentrations. At the maximum RH of 80% in the monitoring room when it is closer to the ambient RH of 95.3%, the amount of water evaporation is reduced, and the simulated beta-gauge concen-trations increase. In contrast, at the minimum RH of 60%, the simulatedbeta-gauge concenconcen-trations decrease because of the increase in water evaporation loss.

When the ambient RH is low, the amount of water content absorbedby particles is limited, whether or not water evaporation is considered in the model is not very important. As shown in Fig. 6(b) for Chung-Shan station where RH is low, the simulatedbeta-gauge concentrations are foundto be close to the actual readings. The simulatedbeta-gauge concentrations without consid-ering water evaporation loss (“thermodynamic model”) are found to be slightly higher than those considering water evaporation loss (present models). All water absorbed by particles almost evapo-rates completely during sampling. The inBuence of RHs (60%, 70% and 80%) in monitoring room on beta-gauge readings is limited.

The daily beta-gauge readings from the four monitoring stations (Chang et al., 2001) are pooled together andcomparedwith the simulatedbeta-gauge concentrations, as shown in Fig. 7. The sim-ulated beta-gauge concentrations of the present models are very close to the actual readings and the RH inBuence in the monitoring room is small. When the PM10 concentrations are lower than 100 g m−3_{, the simulatedbeta-gauge concentrations without considering water evaporation} (“ther-modynamic model”) are very close to the actual readings because water content is low. However, the simulatedbeta-gauge concentrations are higher than the actual readings when the PM10 concentrations are higher than 100 g m−3 _{andthe corresponding water content is also high.}

Further simulation shows that the water absorbedby particles is evaporatedentirely when RH is lower than about 85%. When RH is higher than 85%, water in particles does not evaporate entirely andremaining water will increase with increasing RH. This explains why the beta-gauge concen-tration is higher than the hi-vol sampler, andexperimental PM10 concentration ratio of beta-gauge versus hi-vol sampler is increasedappreciably higher than 1.0 as RH is increasedfrom 85%, as shown in Fig. 2.

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4. Conclusions

In this study, models were developed to calculate water evaporation loss from particles of the beta-gauge during sampling andin the monitoring room. The simulatedbeta-gauge concentrations are very close to the actual readings. Although particles absorb signi<cant amount of water when RH is higher than DRH, evaporation loss of water during sampling and in the monitoring room occurs such that actual beta-gauge readings are much lower than the theoretical PM10 concentrations

considering particle deliquescence alone. When the ambient RH is low, the amount of water absorbed by particles is small andis evaporatedentirely during sampling. When the ambient RH is higher than DRH, particles will absorb water. Only a small fraction of water is evaporatedduring sampling, while an appreciable amount of water in particles is evaporatedwhen the sampling manifoldis opened before beta-counting. Remaining water in particles explain the reason why the beta-gauge readings are higher than the concentrations of hi-vol sampler when RH is higher than 85%, andthe di%erences increase with an increasing ambient RH (Chang et al., 2001).

Acknowledgements

Authors wouldlike to thank for the support of the Taiwan NSC under the contract number NSC 90-2211-E-009-027.

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