A theoretical evaluation on the HNO3 artifact of the annular denuder system due to evaporation and diffusional deposition of NH4NO3-containing aerosols

A theoretical evaluation on the HNO

₃

artifact of the annular

denuder system due to evaporation and diffusional deposition

of NH

₄

NO

₃

-containing aerosols

Kuanfoo Chang

, Chungsying Lu

*, Hsunling Bai

, Guor-Cheng Fang

a

Department of Environmental Engineering, National Chung-Hsing University, Taichung 402, Taiwan

b

Institute of Environmental Engineering, National Chiao-Tung University, 75, Pa-Ai Street, Hsinchu 300, Taiwan

c

Air Toxic and Environmental Analysis Laboratory, Hungkuang Institute of Technology, Sha-Lu, Taichung 433, Taiwan Received 7 July 2001; accepted 17 May 2002

Abstract

A mathematical model was developed to evaluate HNO3artifact of the annular denuder system due to evaporation

and diffusional deposition of nitrate-containing aerosols. The model performance was validated by comparing its numerical solutions with laboratory and numerical data available in the literature for evaporation and diffusional deposition of monodisperse and polydisperse NH4NO3aerosols. Measurement artifacts were evaluated by varying

typical sampling ranges of ambient temperature, HNO3gas concentration, aerosol number concentration, aerosol mass

median diameter, and nitrate mass fraction ofo2.5 mm aerosols to see their respective effects. Potential application of the present model on estimating HNO3artifacts was demonstrated using literature data sampled in USA, Taiwan,

Netherlands, Korea and Japan. Significant measurement artifact could be found in Taiwan and Netherlands due either to low HNO3gas concentration and high nitrate concentration ino2.5 mm aerosols or to high ambient temperature.

r2002 Elsevier Science Ltd. All rights reserved.

Keywords: Annular denuder system; Measurement artifact; HNO3; NH4NO3; Evaporation; Mass accommodation coefficient

1. Introduction

The annular denuder system is an instrument being widely employed for sampling and collecting reactive gases such as SO2, HNO3, NH3and organic vapors in

the atmosphere (Koutrakis et al., 1988; Benner et al., 1991; Lee et al., 1993; Matsumoto and Okita, 1998). The sampling mechanism of the denuder is the diffusion of gaseous pollutants onto the denuder walls coated with reactive substances. Despite the fact that the denuder has advantages of allowing high sampling velocities and possessing large sampling capacities, measurement artifacts are possible and may be significant.

As the gaseous pollutants are absorbed onto the denuder wall, the state of equilibrium between the aerosol and gas-phases is disturbed, which may result in evaporation of aerosols and release of additional gaseous pollutants. Therefore, an excessive amount of gaseous pollutants is being sampled. This phenomenon may particularly be true for volatile aerosols such as NH4NO3 and NH4Cl and their associated gases.

Furthermore, the diffusional deposition of aerosols containing compounds similar to the sampling gases may also introduce additional gaseous pollutants.

Durham et al. (1987) conducted a study on the nitric acid–nitrate aerosol measurements by a tubular diffu-sion denuder and compared their experiment data with those predicted by the Gormley–Kennedy equation (Gormley and Kennedy, 1949). The relative errors, which are defined as the difference between measured

*Corresponding author. Fax: +886-4-22862587. E-mail address:cslu@enve.ev.nchu.edu.tw (C. Lu).

1352-2310/02/$ - see front matterr 2002 Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 2 - 2 3 1 0 ( 0 2 ) 0 0 3 5 2 - 7

and theoretical results divided by the theoretical result, were in the range of 10–90%. They attributed the deviations to the deposition of gaseous N-compound that is extracted and analyzed as NO3

or the released of HNO3gas from NH4NO3aerosols during transit in the

denuder. Measurement artifacts were found for sam-pling HNO3gas in the study of Bai and Wen (2000). The

relative errors strongly depend on the atmospheric HNO3concentration and may be as high as over 80%.

Sampling artifacts of the denuder due to evaporation of NH4NO3aerosols have been theoretically studied by

Pratsinis et al. (1989) and Biswas et al. (1990). Over 200% excessive absorbed NH3gases may occur at 351C.

However, in their studies, the aerosol stream was assumed to contain a monodisperse aerosol. A moment model approximating the aerosol-size distribution by a lognormal function was developed by Bai et al. (1995) to evaluate the evaporation rate of dry NH4NO3 and

NH4Cl aerosols. The model was then employed to derive

the denuder performance equation for sampling atmo-spheric HNO3 gas (Lu et al., 1995). The aerosol

polydispersity leads to a significant reduction in the evaporation rate of dry NH4NO3and NH4Cl aerosols as

compared to the monodisperse aerosol. Therefore, the actual measurement artifact may not be as significant as predicted by Pratsinis et al. (1989) and Biswas et al. (1990).

On the other hand, Forrest et al. (1982) and Larson and Taylor (1983) conducted an experiment on the evaporation of NH4NO3aerosols in a tubular diffusion

denuder and a parallel-plate stripper, respectively. They

concluded that the HNO3 gas evaporated from

NH4NO3 aerosols could be neglected as compared to

measured HNO3 gas concentration. Koutrakis et al.

(1988) demonstrated the high performance of the Harvard-EPA denuder for sampling atmospheric SO2,

HNO3 and HNO2 gases. The differences between

measured and calculated collection efficiencies were small in their study. Tsai et al. (2000) found that positive HNO3artifact due to volatilization of NH4NO3

aerosols is generally negligible compared to measured nitrate-containing particles for an annular denuder and a honeycomb denuder system. According to these studies, the measurement artifacts seem unimportant in a denuder system. However, most of their emphases are on the evaporation of aerosols. Many factors such as ambient temperature, HNO3 concentration, NH4NO3

concentration as well as aerosol size distribution may simultaneously influence the accuracy of HNO3

measurement.

The mass accommodation coefficient, a; is a kinetics-originating factor describing the interface limitations to the mass transfer between the aerosol and gas-phases. The coefficient is yet not well understood; the process is believed to be inhibited by a resistance in transport of molecules across the particle/air interfaces (Dassios and

Pandis, 1999). Bai et al. (1995) used a of 0.1–1 to fit the change of radius of dry NH4NO3aerosol in the denuder.

Recently, Dassios and Pandis (1999) found that the a decreases from 0.8 to 0.5 as the temperature increases from 211C to 271C. In order to evaluate the effect of organic compounds on the NH4NO3evaporation, Cruz

et al. (2000) coated the NH4NO3particles of 100–200 nm

diameter with dioctyl phthalate (DOP) and allowed them to evaporate in a constant temperature laminar flow reactor. A decrease, up to 50%, in the evaporation rate of NH4NO3 aerosol due to the presence of DOP

film was observed which corresponds to the decrease of a from 0.4 to 0.25.

The goals of this study were to develop a mathema-tical model for identifying atmospheric conditions that may lead to significant HNO3artifacts. Major sampling

artifacts under consideration are from evaporation and diffusional deposition of NH4NO3-containing aerosols.

Effects of the two mechanisms on the HNO3artifacts for

a typical range of atmospheric aerosol and gas proper-ties are evaluated and quantitatively determined.

2. Theory

When NH4NO3 aerosols in equilibrium with HNO3

and NH3gases enter the denuder, HNO3gas is removed

by diffusional absorption at the denuder walls with which the equilibrium is distorted. This results in evaporation of NH4NO3 aerosols and release of

addi-tional HNO3and NH3gases.

2.1. Basic assumptions

The following major assumptions are made in developing a mathematical model to study the HNO3

artifacts in the denuder:

1. The system is in a steady-state operating condition. 2. The flow field in the denuder is a fully developed

laminar flow.

3. Only dry atmospheric aerosols are considered, that is, the relative humidity of the atmosphere is below the deliquescent humidity of investigated aerosols. 4. Effect of diffusion in the direction of flow is neglected

as compared to convection. This is a valid assump-tion since the Peclet number of the denuder is much greater than unity.

5. No production or reaction of the gas or aerosol occurs in the denuder.

6. Gas-particle equilibrium, with a modification by introducing a of less than unity, is assumed at the interfaces of solid particles and their surrounding gases and is independent of the denuder residence time.

7. The collection efficiencies of HNO3 gas and

NH4NO3-containing aerosols are 100% on the

collector wall surface. 2.2. Model development

For NH4NO3 aerosols undergoing simultaneous

diffusion and evaporation in the denuder, the steady-state general dynamic equation is expressed as (Fried-lander, 1977) Uavf ðrÞ qn qz¼ 1 r q qr r qðDpnÞ qr
 þqðGnÞ qv ; ð1Þ

where Uavis the average gas velocity in the denuder, f ðrÞ is the flow profile, r is the radial distance, n is the volume distribution function, z is the axial distance, Dp is the particle diffusivity, G is the volume evaporation/ condensation rate (Go0 when evaporation is faster than condensation), and v is the volume of an aerosol. The left-hand side (LHS) term accounts for convection of aerosol stream. The first term on the right-hand side (RHS) accounts for radial diffusion of particles. The second RHS term accounts for the loss or gain of particles by evaporation/condensation at rate G: The fully developed flow profile in the denuder is written as (Bird et al., 1960)

f ðrÞ ¼2½ð1
k 2_Þlnðr=r

0Þ þ lnð1=kÞð1
r2=r20Þ

ð1 þ k2_{Þlnð1=kÞ
ð1
k}2_Þ ; ð2Þ where k is the inner-to-outer radius ratio, r0is the outer radius of the denuder. The G can be expressed as (Friedlander, 1977) G ¼dv dt¼ 2pDmMdpðp1
pdÞ Rr_pT  1 þ Kn 1 þ 0:3773Kn þ 1:33Knð1 þ KnÞ=a   ð3Þ where Dmis the diffusivity of NH4NO3monomer, M is

the molecule weight, dp is the particle diameter, p1and pdare the vapor pressures of NH4NO3monomer in the

bulk phase and in equilibrium with the aerosol surface, R is the gas constant, r_pis the particle density, T is the absolute temperature in K, Kn is the Knudsen number of the particle (Kn is defined as 2l=dp; with l the mean free path of gas molecules).

The evaporation of NH4NO3 aerosol leads to the

release of HNO3 and NH3 gases. The mass balance

equation of the gaseous species j is expressed as (Lu et al., 1995) Uavf ðrÞ qCj qz ¼ Dj r q qr r qCj qr  
1 vm Z N 0 Gn dv; ð4Þ

where Cj is the concentration of species j (j¼ HNO3or NH3), Dj is the diffusivity of species j; vmis the molar volume of NH4NO3 aerosol. The LHS term considers

convection of species j: The first RHS term considers

radial diffusion of species j while the second RHS term considers the gain of species j by aerosol evaporation.

The sectional approach was employed for simulating the evolution of aerosol size distribution along the denuder (Gelbard et al., 1980). The studies of Landgrebe and Pratsinis (1990) showed that the volume-square-based model provided a better prediction on the evolution of aerosol-size distribution than the number-based and number-based models. Therefore, the volume-square-based model was employed in this study. By dividing the entire aerosol-size domain into L arbitrary sections, the volume-squared size distribution is approximated as follows:

QI¼ Z vI

vI
1

nðvÞv2dv; ð5Þ

where QIis the aerosol volume-squared concentration in section I ð1pIpLÞ; vI
1 and vI represent the volumes of the smallest and largest aerosols, respectively, in section I.

The governing equations for the sectional volume-squared distribution can be deduced from Eqs. (1) and (4) to give the following partial differential equations (PDEs): qQIðr; zÞ qz ¼ 1 er q qr r q qrðoQIðr; zÞÞ   þ 1 Uavf ðrÞ ðwIQI
HIþ HI
1Þ; ð6Þ Uavf ðrÞ qCNH3 qz ¼ DNH3 r q qr r qCNH3 qr  
ðS
1ÞzcX I ¼L I ¼1 QI ðvI
vI
1Þ ; ð7Þ Uavf ðrÞ qCHNO3 qz ¼ DHNO3 r q qr r qCHNO3 qr  
ðS
1ÞzcX I ¼L I ¼1 QI ðvI
vI
1Þ ; ð8Þ

where S is the system saturation ratio (S is defined as CHNO3CNH3=KP; with KP the equilibrium constant of NH4NO3particles with the two associated gases, HNO3

and NH3). When the S value is unity, the system is in an

external state of equilibrium. The driving force of the evaporation process of NH4NO3particles is determined

by ð1
SÞ: The definitions of e; z; o; w; HI; HI
1; z and c are listed in Table 1.

It is assumed that the NH4NO3 aerosols and

associated gases, HNO3and NH3,reach equilibrium at

the denuder inlet (S ¼ 1 at z ¼ 0). So the inlet NH3

concentration can be assumed to be CNH3;in¼

Kp=CHNO3;in: The Kp value is taken from Mozurkewich (1993) and can be expressed as

ln Kp¼ 118:87
24084

The initial condition for the inlet aerosols is QIðr; 0Þ ¼

Z I I
1

v2nðv; 0Þ dv: ð10Þ

The denuder wall is designed as perfect sink for

NH4NO3 aerosol ðQI¼ 0Þ and HNO3 gas

(CHNO3 ¼ 0), but inert for NH3 gas (CNH3=qr ¼ 0). The physical quantity of QI¼ 0 means the aerosol volume-squared concentration is equal to zero at the denuder wall.

Eq. (6) describes aerosol diffusion and evaporation while Eqs. (7) and (8) consider the diffusion of NH3and

HNO3gases and the source term from evaporation of

NH4HNO3 aerosol. These equations along with the

appropriate boundary conditions constitute a set of coupled PDEs. Using an explicit-finite difference scheme at P radial points across the denuder, the three PDEs are transformed to ordinary differential equations (ODEs). These ODEs are then solved by a stiff ODE solver, DIVPAG (IMSL, 1987). The integrations are solved using the Gauss–Lagendre quadrature method (Horn-beck, 1982). The cup-mixing average is used to evaluate effects of process parameter on the evolution of the aerosol and the gaseous concentrations.

3. Results and discussion 3.1. Numerical stability analysis

Prior to analysis of the denuder performance, the numerical stability of the model is checked. The

stability of numerical solutions as a function of grid size ðDr; DzÞ and number of sections ðLÞ employed in the model was investigated by a sensitivity analysis. Trials with varying P radial points from 10 to 30, Dz from 10
6 to 10
4cm, and L from 5 to 20 were conducted and the results showed that nearly identical solutions are achieved for P radial points X20, Dzp10
4 and LX10: Therefore, radial points of 20, Dz of 10
4cm, and L of 10 were used in the following studies.

3.2. Model verification for diffusional deposition of HNO3gas and NH4NO3aerosol

The present model for diffusional deposition of HNO3 gas and NH4NO3 aerosol was first examined

by comparing its numerical solutions with those predicted by the Gormley–Kennedy equation (Gormley and Kennedy, 1949) in a tubular pipe. The inner-to-outer radius ratio, k; was set to zero and the flow profile is set to f ðrÞ ¼ 2ð1
r2_=r2

0Þ: The boundary conditions were set to axis of symmetry and zero wall concentration. The aerosol diffusivity was estimated by the Stokes–Einstein expression (Friedlander, 1977) while the diffusivities of NH3, HNO3 and NH4NO3

monomer were chosen as 0.227, 0.118 (Winiwarter, 1989) and 6.03  10
2cm2/s (Bai et al., 1995), respec-tively. The comparison results showed that the numer-ical solutions predicted by the present model are in excellent agreement with the Gormley–Kennedy solution.

Table 1

Definitions of parameters used in the governing equations

w ₁ ðvI
vI
1Þ 12DmMðp1
pdÞ Rr_pT RvI vI
1 1 d2 p 1 þ Kn 1 þ 0:3773Kn þ 1:33Knð1 þ KnÞ=a ! dv e Uavf ðrÞR_vv_I
1I 1=v2dv ¼ Uavf ðrÞð1=vI
1
1=vIÞ o RvI vI
1kbTCc=v 2_3pmd pdv j RvI þ1 vI ðdp=v 2_{Þð1 þ KnÞ=ð1 þ 0:3773Kn þ 1:33Knð1 þ KnÞ=aÞ dv} z ð1=vmÞð2pDmpdM=rpRTÞ HI mI=ðmI þ1
mIÞwQI HI
1 mI
1=ðmI
mI
1ÞwI
1QI
1

Note: v; volume of an aerosol; Dm; diffusivity of NH4NO3monomer; M; molecular weight; dp; particle diameter; p1; bulk phase vapor

pressure of NH4NO3 monomer; pd; equilibrium vapor pressure of NH4NO3 monomer; R; gas constant; rp; particle density; Kn;

Knudsen number; a; accommodation coefficient; Uav; average gas velocity; f ðrÞ; flow profile; r; radial distance; kb; Boltzmann’s

constant; T; ambient temperature; Cc; Cunningham correction factor; m; dynamic viscosity; vm; molar volume of NH4NO3aerosol;

mI ¼ VI=NI; VI; aerosol volume in section I; NI; aerosol number in section I; and QI; aerosol volume-squared concentration in

3.3. Model verification for evaporation of a monodisperse NH4NO3aerosol

The present model for evaporation of a monodisperse NH4NO3 aerosol was then evaluated by the measured

data of Dassios and Pandis (1999). The NH4NO3

aerosols of 80–220 nm diameter were evaporated in the reactor under relative humidity of around 10% and temperature of 20–271C. An average residence time of 30 s was employed in most experiments. The a value is unknown and needs to be justified.

Fig. 1 shows the change in size of the NH4NO3

aerosols at 211C predicted by the present model and measured by Dassios and Pandis (1999). The employed a values were equal to 0.5, 0.8 and 1. As can be seen, close agreement was obtained between the predicted and measured results in the a range of 0.5–1.0. The a ¼ 0:8 case provides a best fit to the measured data and was used in the following studies.

3.4. Model verification for evaporation of a polydisperse NH4NO3aerosol

The present model for evaporation of a polydisperse NH4NO3aerosol in the denuder was also tested by the

measured data of Harrison et al. (1990). The inlet NH4NO3aerosols were lognormally distributed with a

geometric mean radius of 0.46 mm and a standard deviation of 1.6. The temperature and relative humidity were 20721C and 30–60%, respectively. The inlet number concentration of NH4NO3 aerosol was set to

105/cm3(Bai et al., 1995).

Fig. 2 shows the measured and predicted results on the change of particle radius of dry NH4NO3aerosols in

the denuder. It is seen that the predicted results agree well with the measured data.

3.5. Model application in the field study

The present model was then applied to predict the measured data of Bai and Wen (2000) for the relative sampling errors of HNO3 gas by the annular denuder

system. Bai and Wen (2000) used three or four denuders in series coated with NaCl for HNO3 sampling.

Assuming that the absorption efficiency of HNO3 gas

ðZÞ is high and the absorption efficiency of the interfering species ðZ_intÞ is low, the first and second denuders collected both HNO3gas and interfering species (CHNO3 and Cint) and the third and fourth denuders collected interfering species only; the collected gas concentrations by each denuder are

first denuder ¼ CHNO3Z þ CintZint; ð14Þ

second denuder ¼ CHNO3ð1
ZÞ þ CintZint; ð15Þ third denuder ¼ fourth denuder ¼ CintZint: ð16Þ The HNO3gas concentration can thus be calculated

by subtracting double the concentration collected by the third from the sum of those collected by the first and second denuders. The percentage excess of absorbed HNO3 gas is calculated as CintZint=CHNO3 100%: Detailed information concerning HNO3artifact can be

seen in Bai and Wen, 2000. Because the size distribution of the atmospheric aerosols was not measured in their study, the atmospheric aerosol and gas properties of the Hsinchu area are adopted from average values of a typical range available in the literature (Lee and Hsu, 1996; Bai and Wen, 1998) and are listed in Table 2.

Fig. 3 shows the predicted and measured results on the percentage excess of absorbed HNO3 gas in the

denuder. As can be seen, the percentage excess of absorbed HNO3gas was underpredicted by the present

model. This can be attributed to the oxidation of other Inlet particle diameter (nm)

50 100 150 200 250 Final particle diameter (nm) 0 50 100 150 200 250 Measured data This study ( α α=0.5) This study ( α α=0.8) This study ( α α=1.0)

Fig. 1. Comparisons of the change in size for a monodisperse NH4NO3aerosol at 211C predicted by the present model and

measured by Dassios and Pandis (1999).

0 6 12 18 24 30 36 Particle geometric mean radius ( µ m) 0.0 0.1 0.2 0.3 0.4 0.5 Measured data This study

Residence time of aerosol in the denuder (min)

Fig. 2. Comparisons of the change in size for a polydisperse NH4NO3aerosol predicted by the present model and measured

gaseous N-compounds such as HNO2 and NOX to HNO3 gas, which was not considered in this study.

These reactions are still unclear in the literature and further studies are needed to determine the real mechanisms of oxidation and whether they can be controlled. Significant deviations were observed for inlet HNO3concentrationso0.2 mg/m3and could be as high

as 40%. However, as the inlet HNO3 concentrations

increased to 1.0 mg/m3, the deviations between the measured and predicted results became small. This is because for the same amount of HNO3 artifact the

percentage error is high for low inlet HNO3

concentra-tion since the denominator in the calculaconcentra-tion is low.

3.6. Predicting the excess of absorbed HNO3gas

Having established the accuracy and consistency of the present model on the evaporation and diffusional deposition of NH4NO3 aerosol in the denuder, a

sensitivity analysis of the important parameters on the HNO3artifact was carried out. The denuder described in

the study of Bai and Wen (2000) was employed. The

investigated parameters are: inlet aerosol number con-centration (Ni), inlet mass median diameter (MMDi),

nitrate mass fraction of o2.5 mm aerosols ðMfÞ; and inlet HNO3gas concentration (Ci). The employed values

of Table 2 are selected as the base case. Trials are conducted for each parameter in the high and low levels, keeping all other variables constants as the base case.

Figs. 4–7 show the predicted percentage excess of absorbed HNO3 as a function of ambient temperature

for varying Ni; MMDi, Mf and Ci; respectively. The residence time of aerosols in the denuder system was set to 1.0 s. The employed ambient temperature was in the range of 15–351C which is the typical temperature range

Table 2

Typical range of the atmospheric aerosol and gas properties Parameters Typical range Employed values Ni(#/cm3) 104–106 105

MMDi(mm) 0.1–1.0 0.6

Mf(%) 4–12 8

Ci(mg/m3) 0.2–1.0 0.6

Note: Ni; inlet aerosol number concentration; MMDi, inlet

aerosol mass medium diameter; Mf; nitrate mass fraction of less

than 2.5 mm aerosols; and Ci, initial HNO3gas concentration.

Initial HNO₃concentration (µg/m3₎

0 2 4 6 8 Percentage excess o f absorbed HNO 3 gas (% ) 0 20 40 60 80 100 Measured data This study

Fig. 3. Comparisons of the percentage excess of absorbed HNO3gas predicted by the present model and measured by Bai

and Wen (2000). Ambient temperature (oC) 0 10 20 30 40 Percentage excess of absorbed HNO 3 (% ) 0 20 40 60 80 100 120 140 Ni= 104/cm3 Ni= 105/cm3 Ni= 106/cm3

Fig. 4. Predicted percentage excess of absorbed HNO3gas as a

function of ambient temperature for varying inlet aerosol number concentration (Ni) with inlet conditions of aerosol mass

median diameter=0.6 mm, nitrate mass fraction of o2.5 mm aerosols=0.08, and inlet HNO3gas concentration=0.6 mg/m3.

Ambient temperature (o_C) 0 10 20 30 40 Percentage excess of absorbed HNO 3 (% ) 0 20 40 60 80 100 120 140 MMD = 1.0µm MMD = 0.6µm MMD = 0.1µm

Fig. 5. Predicted percentage excess of absorbed HNO3gas as a

function of ambient temperature for varying inlet aerosol mass median diameter (MMDi) with inlet conditions of aerosol

number concentration=105_/cm3_{, nitrate mass fraction of}

o2.5 mm aerosols=0.08, and inlet HNO3 gas

in Taiwan. It is seen that the percentage excess of absorbed HNO3 increased as the ambient temperature

increased. This can be attributed to the fact that the NH4NO3 evaporation rate is dependent on the partial

pressure driving force, p1
pd as indicated in Eq. (3). The pdis a function of ambient temperature. An increase of ambient temperature causes an increase of pd; and thus results in an increase of partial pressure driving force and NH4NO3evaporation rate.

As can be noted in Fig. 4, the percentage excess of absorbed HNO3 gas increased as Ni increased. This is due to the fact that an increase of Niprovides a higher NH4NO3mass available for evaporation and release of

more HNO3 gases. Furthermore, more NH4NO3

-con-taining aerosols were deposited on the denuder wall for a higher Ni; which may also enhance the HNO3artifact.

The Ni=106 case has a very significant effect on the HNO3 artifact under ambient temperature >301C. At

an ambient temperature of 301C, the percentage excess (artifact concentration) of absorbed HNO3 gas was

equal to 33% (0.2 mg/m3), 5% (0.03 mg/m3) and 1% (0.006 mg/m3) for aerosols with Ni of 104, 105 and 106cm
3, respectively.

It is seen in Fig. 5 that a higher sampling artifact is introduced for aerosols with a larger MMDi. This is due

to the fact that for NH4NO3-containing aerosols with

same Mf and Ni; a larger MMDiaerosol has a higher

NH4NO3 mass available for the evaporation and

diffusional deposition processes. At an ambient tem-perature of 301C, the percentage excess (artifact concentration) of absorbed HNO3 gas was equal to

45% (0.27 mg/m3), 20% (0.12 mg/m3) and 2% (0.012 mg/ m3_{) for aerosols with MMD}

i of 1.0, 0.6 and 0.1 mm,

respectively.

It is noted in Fig. 6 that the percentage excess of absorbed HNO3gas increased as Mf increased. This is again due to a high NH4NO3 mass available for

evaporation and diffusional deposition processes. However, the effect of Mf on the HNO3 artifact is

relatively small as compared to other parameters. This is because the typical value of Mf in Taiwan was usually _{o0.1 (Chang et al. 2001). Hence, the M}f was changed only by a factor of three. At an ambient temperature of 301C the percentage excess (artifact concentration) of absorbed HNO3 gas increased from

2% (0.012 mg/m3) to 4% (0.024 mg/m3) as Mf increased from 0.04 to 0.12.

As can be seen from Fig. 7, an increase of Ciresults in a reduction of the percentage excess of absorbed HNO3

gas increased as Cidecreased, but an opposite trend was observed for artifact concentration. For example, at an ambient temperature of 401C the percentage excess of absorbed HNO3gas decreased from 55% to 18% as Ci increased from 0.2 to 1.0 mg/m3, respectively, but the artifact concentration increased from 0.11 to 0.18 mg/m3. This is because the NH3–HNO3–NH4NO3 system was

assumed to be in equilibrium at the entrance of the denuder. Therefore, the inlet NH3 gas concentration

depends on the inlet HNO3 gas concentration. For a

high inlet HNO3gas concentration, the inlet NH3 gas

concentration is low. As the HNO3 gas is being

absorbed rapidly at the denuder wall upon entering the denuder, the evaporation driving force, S
1; would be high, which caused a high NH4NO3 evaporation rate

and thus led to the release of more HNO3gas. However,

when expressed as the percentage excess of absorbed HNO3gas, the artifact becomes relatively low for a high

inlet HNO3 gas concentration since the denominator

is high. Ambient temperature (o_C) 0 10 20 30 40 Percentage excess of absorbed HNO 3 (% ) 0 2 4 6 8 10 12 14 16 18 Mf= 0.12 M_f= 0.08 Mf= 0.04

Fig. 6. Predicted percentage excess of absorbed HNO3gas as a

function of ambient temperature for varying nitrate mass fraction of o2.5 mm aerosols ðMfÞ with inlet conditions of

aerosol mass median diameter=0.6 mm, aerosol number con-centration=105/cm3, and HNO3gas concentration=0.6 mg/m

3 . Ambient temperature (oC) 0 10 20 30 40 Percentage excess o f absorbed HNO 3 gas (% ) 0 10 20 30 40 50 60 Ci= 1.0µg/m3 Ci= 0.6µg/m3 Ci= 0.2µg/m3

Fig. 7. Predicted percentage excess of absorbed HNO3gas as a

function of ambient temperature for varying inlet HNO3gas

concentration (Ci) with inlet conditions of aerosol mass median

diameter=0.6 mm, aerosol number concentration=105/cm3, and nitrate mass fraction ofo2.5 mm aerosols=0.08.

Fig. 8 shows the effects of the residence time of aerosols in the denuder from 0 to 5 s on the percentage excess of absorbed HNO3 gas. With the exception

of Ci; the parameter values were adopted from the base

case of sensitivity analysis. The Ciwas set to 0.1 mg/m3. As can be seen, the magnitude of HNO3 artifact

was proportional to the residence time of aerosols in the denuder. This is because more HNO3 gases

were evaporated from nitrate-containing aerosols and diffused to the denuder wall at a longer residence time.

3.7. Practical application of the present model

Potential application of the present model was demonstrated on estimating the HNO3 artifact using

literature data sampled in USA (Keeler and Spengler, 1991), Taiwan (Perng, 1995), Netherlands (Hoek et al., 1996), Korea (Lee et al., 1997) and Japan (Matsumoto and Okita, 1998) and the results were listed in Table 3. These studies provided the measured data of HNO3gas

concentration and nitrate concentration in o2.5 mm aerosols. However, the information of aerosol size distribution and ambient temperatures was not avail-able. Therefore, it is assumed that the size distribution of o2.5 mm aerosols was lognormally distributed with Ni of 105/cm3 and MMDi of 0.6 mm. The HNO3 artifact

was estimated using the highest monthly average temperature in 1 yr. As can be seen in Table 3, 0 1 2 3 4 5 Percentage excess of absorbed HNO 3 gas (% ) 0 20 40 60 80

Residence time of aerosol in the denuder (sec)

Fig. 8. Predicated percentage excess of absorbed HNO3gas as

functions of residence time of aerosols in the denuder with inlet conditions of HNO3 gas concentration=0.1 mg/m

3

, aerosol mass median diameter=0.6 mm, aerosol number concentra-tion=105/cm3, nitrate mass fraction of o2.5 mm aero-sols=0.08, and ambient temperature=301C.

Table 3

Estimated measurement artifacts of HNO3gas by one annular denuder for typical gas and aerosol properties available in the literature

Country Taiwan USA Netherlands Korea Japan

Reference Perng (1995) Keeler and Spengler (1991) Hoke et al. (1996) Lee et al. (1997) Matsumoto and Okita (1998) Average HNO3gas concentration

(mg/m3₎ 0.30 1.10 0.30 0.80 1.60 [NO3
] in less than 2.5 mm aerosols (mg/m3₎ Avg. 10.0 0.4 25.0 2.50 2.24 Max. 21.6 0.79 51.4 4.53 3.20

The highest monthly average temperature in 1 ha(1C) 35 26 27 24 25 Estimated HNO3 artifactb(mg/m3) Avg. 0.11 0.0071 0.093 0.017 0.017 Max. 0.23 0.03 0.22 0.05 0.04 Estimated percentage excess of absorbed HNO3(%) Avg. 35 1.8 31 2.1 1.1 Max. 77 3.6 73 6.2 2.2

a_{Obtained fromhttp://www.wunderground.com/global/ko.html.} b_{The HNO}

3 artifact was estimated using the highest monthly average temperature in 1 yr with the assumption that the size

distribution ofo2.5 mm aerosols was lognormally distributed with inlet aerosol number concentration of 105_/cm3_{and aerosol mass}

significant measurement artifact could be found in Taiwan and Netherlands. This is due either to low HNO3 gas concentration and high nitrate

concentra-tions in_{o2.5 mm aerosols or to high ambient} tempera-ture. The estimated HNO3 artifact concentration and

the percentage excess of absorbed HNO3gas could be as

high as 0.23 mg/m3and 77%, respectively. The estimated HNO3 artifacts for the field data sampled in USA,

Korea and Japan were very low as compared to those sampled in Taiwan and Netherlands.

4. Conclusions

A mathematical model was developed to determine the HNO3 artifact in the denuder due to evaporation

and diffusional deposition of NH4NO3-containing

aerosols. The model performance was validated by comparing its predictions with the measured data for evaporation and diffusional deposition of mono-disperse and polymono-disperse NH4NO3aerosols available in

the literature. The neglect of the oxidation of other

gaseous N-compounds such as HNO2 and NOX to

HNO3 gas may lead to the underprediction of the

percentage excess of absorbed HNO3 gas measured in

the field.

The model was then applied to evaluate effects of the important parameters on the HNO3 artifact. The

investigated parameters are: inlet aerosol number con-centration (Ni), inlet mass median diameter (MMDi),

nitrate mass fraction of o2.5 mm aerosols ðMfÞ; and inlet HNO3 gas concentration (Ci). These parameters were usually neglected and unreported in the literature for evaluation of the sampling artifact in the denuder system. For the atmospheric conditions with high values of ambient temperature, Ni; MMDiand a

low value of Ci; the percentage excess of absorbed HNO3gas may be significant and therefore should be

avoided.

Potential application of the present model on estimating HNO3 artifact was demonstrated using

literature data sampled in USA, Taiwan, Netherlands, Korea and Japan. Significant measurement artifact could be found in Taiwan and Netherlands due either to low HNO3 gas concentration and high nitrate

concentrations ino2.5 mm aerosols or to high ambient temperature.

Ultimately, there are other artifact sources neglected in the present model. Therefore, further experimental and theoretical studies are needed to determine the real mechanisms of the oxidation of other N-compounds to HNO3 gas in the denuder and whether they can be

controlled. The field conditions leading to a significant measurement artifact in the denuder can then be avoided.

Acknowledgements

Support from the National Science Council, Taiwan (NSC89-2211-E-009-058) is gratefully acknowledged.

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