The Chamber Wall Index for GasâWall Interactions in Atmospheric

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Environmental Measurements Methods

The Chamber Wall Index for Gas-Wall Interactions in Atmospheric Environmental Enclosures William H. Brune Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.8b06260 • Publication Date (Web): 06 Mar 2019 Downloaded from http://pubs.acs.org on March 10, 2019

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Environmental Science & Technology

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The Chamber Wall Index for Gas-Wall Interactions

2

in Atmospheric Environmental Enclosures

3

William H. Brune*

4

Department of Meteorology and Atmospheric Science, Pennsylvania State University, University

5

Park, PA, 16802, USA

6

ABSTRACT

7

Secondary organic aerosol (SOA) particles, which are formed and aged in Earth’s oxidizing

8

atmosphere, influence climate and human health. Quantifying properties of SOA particles and

9

oxidized organic compounds (OVOCs) requires controlled experiments in enclosures, but

10

enclosures have walls that can alter the chemistry. Comparing wall effects for widely used large

11

environmental chambers (ECs) and portable oxidative flow reactors (OFRs) is difficult. In this

12

paper, the Chamber Wall Index (𝐶𝑊𝐼) is developed as the minimum ratio of the initial wall uptake

13

time constant divided by the enclosure residence time. This index demonstrates that walls alter the

14

chemistry less in OFRs than in ECs, due primarily to shorter residence times. Much shorter

15

residence times may not be feasible because oxidation chemistry and microphysics need time to

16

produce atmospherically relevant SOA and SVOCs. While all current OFRs have wall effects, it

17

may be possible to develop a “wall-less” OFR.

ACS Paragon Plus Environment


18

Introduction

19 20

Atmospheric oxidation chemistry dictates the fate of the thousands of chemical species emitted

21

into the atmosphere and the production of the atmospheric pollutants ozone (O3) and secondary

22

organic aerosol (SOA). Developing predictive capability for these pollutants requires improved

23

chemical theory and modeling, field measurements, and laboratory studies. These laboratory

24

studies provide the chemical mechanisms, rate coefficients, and product yields that are embedded

25

in the models, which can then be tested against field measurements and used to predict pollutant

26

production.

27 28

Laboratory-derived chemical mechanisms, rates, and yields are useful for models only if the

29

chemistry occurring in the experiment enclosures accurately simulates the chemistry occurring in

30

the atmosphere. There are several challenges to achieving results relevant to the atmosphere.1,2

31

First, the chamber radiation should affect the enclosure chemistry in the same way that solar

32

radiation affects atmospheric chemistry. Second, the initial abundances of gases such as volatile

33

organic compounds (VOCs) and nitrogen oxides (NOx=NO+NO2) should be similar to

34

atmospheric abundances. Third, the residence time (𝜏𝑟𝑒𝑠) should be great enough to allow the gas-

35

phase, heterogeneous, and particle chemical reactions and the microphysics of nucleation,

36

condensation, evaporation, and diffusion to happen the way they would in the atmosphere. Fourth,

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the enclosure walls should not have unwanted influence on the chemistry and microphysics that

38

are being studied. All past and existing environmental enclosures compromise on one or more of

39

these challenges.

40


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Most enclosures can be grouped into three types: flow tubes, oxidative flow reactors, or

42

environmental chambers. Flow tubes (FTs) have long been used to study laboratory gas-phase

43

kinetics of simple systems, such as bimolecular or heterogeneous reactions.3-5 The typical FT

44

residence time of a few seconds means that FTs are difficult to use for complex, multi-step

45

chemistry. Thus, they are not included in the analysis below.

46 47

Oxidative flow reactors (OFRs) are similar to flow tubes in that they have flowing gas, but they

48

have greater residence times (𝜏𝑟𝑒𝑠) and lower gas velocities than flow tubes to allow multi-step

49

chemistry.6-11 They also have greater volume-to-surface area ratios (𝑉/𝐴) in an attempt to reduce

50

the influence of the walls on the chemistry. The flow within the OFR is laminar but stirred by

51

eddies, complicating the analysis of chemical kinetics because the distance down the reactor does

52

not always correspond directly with the time in the reactor. For SOA studies, OFRs often use

53

amounts of reactive gases such as hydroxyl (OH) or ozone (O3) that are 10 to 1000 times greater

54

than in the atmosphere to accelerate the chemistry so that a few minutes in the OFR is equivalent

55

to many hours to many days in the atmosphere.

56 57

Environmental chambers (ECs) are typically made of thin Teflon walls that allow the ultraviolet

58

(UV) radiation to pass from lamps outside the chamber to inside the chamber where the chemistry

59

occurs.1,2,12-14 ECs have the greatest 𝑉/𝐴 and 𝜏𝑟𝑒𝑠 of all, with volumes of ~1 to 270 m3 and

60

residence times of tens of minutes to hours. They are usually operated in a static or quasi-static

61

mode. Stirring by natural convection, fans, or vibration mixes the chemical constituents throughout

62

the bulk gas, producing uniform chemistry throughout the chamber, except in the thin boundary

63

layer near the walls. Instruments sample this well-mixed air through lines that penetrate the



64

chamber floor or walls. Even in the largest chambers, the reactants and particles are brought by

65

eddies to the walls within minutes or tens of minutes, although methods have been developed to

66

account for the particle loss.15-17

67 68

In 2010, Matsunaga and Ziemann18 showed that the EC walls were taking up the semi-volatile

69

organic compounds (SVOCs) involved in SOA formation. Other oxygenated VOCs (OVOCs),

70

such as low-volatility VOCs (LVOCs) and intermediate-volatility VOCs (IVOCs), are also

71

involved in SOA formation and are likely affected by the walls. This wall uptake likely

72

substantially reduced the measured SOA yields from precursor gases in some previous EC

73

studies.19 Several others studies followed and examined ways to quantify this OVOC loss and to

74

correct for this uptake.14,20-27

75 76

Atmospheric environmental enclosures come in so many different sizes, shapes, and flow

77

characteristics that it is difficult to determine which ones have less wall influence on the chemistry.

78

In this paper, I describe a simple metric, the Chamber Wall Index (𝐶𝑊𝐼). This index indicates the

79

degree to which the chemistry in an enclosure is free from unwanted wall effects, either uptake or

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surface chemistry, as determined by the sampled gas-phase chemical constituents. Using this

81

metric, we can compare existing and future enclosures for potential wall effects and thus determine

82

which type of enclosures are best to use for different research goals. The focus of this paper is on

83

gas-phase chemical species related to SOA-forming chemistry, although a 𝐶𝑊𝐼 could be

84

developed for SOA, with a few modifications due to factors such as slower diffusivity and

85

gravitational settling.15-17

86


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87


Defining the Chamber Wall Index (𝐶𝑊𝐼)

88 89 90

An equation for freedom from wall effects is composed of three common-sense properties that are known to slow wall loss (eq 1).

91 92

𝑄=

(𝑉 𝐴)

1 1 𝑣𝑑𝜏𝑟𝑒𝑠

(1)

93 94

𝑄 is a unit-less index; 𝑉 𝐴 is the ratio of the volume to the surface area of the enclosure (m); 𝑣𝑑 is

95

the deposition velocity (m s-1); and 𝜏𝑟𝑒𝑠 is the enclosure residence time (s). Larger 𝑉 𝐴, smaller 𝑣𝑑,

96

and shorter 𝜏𝑟𝑒𝑠 all decrease wall effects on the chemistry and increase 𝑄.

97 98 99

The first two terms on the right-hand side of eq 1 are equal to the characteristic time of wall loss (𝑠), as in eq 2.26

100 101

𝜏𝑤𝑎𝑙𝑙 =

(𝑉 𝐴)

1 𝑣𝑑

(2)

102 103

Substituting this characteristic time for wall loss in eq 1 gives eq 3.

104 105

𝑄=

𝜏𝑤𝑎𝑙𝑙 𝜏𝑟𝑒𝑠

106 107


(3)


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108

The characteristic time of wall loss can be different for each gas-phase chemical species, whether

109

they are the initial VOC or the OVOC products. 𝜏𝑤𝑎𝑙𝑙 can vary by several orders of magnitude

110

because some gas-phase chemical species are taken up by the wall on almost every collision while

111

others are essentially not taken up at all. While it is possible to calculate a different 𝑄 for each

112

chemical species if their uptake is known, this approach does not account for unknown gas-phase

113

oxidation products, unknown uptake, or chemical reactions occurring on or in the wall. However,

114

the minimum value of 𝑄 provides a worst-case scenario, which assumes that any wall interactions

115

might affect the chamber chemistry and the quantity and character of sampled OVOCs and SOA.

116

This minimum value for 𝑄 is called the Chamber Wall Index (𝐶𝑊𝐼), as given in eq 4.

117 118

𝐶𝑊𝐼 =

( ) 𝜏𝑤𝑎𝑙𝑙 𝜏𝑟𝑒𝑠

𝑚𝑖𝑛

(4)

119 120

A chamber with a greater 𝐶𝑊𝐼 will have fewer wall effects on the chemistry within. The 𝐶𝑊𝐼

121

does not indicate that the chemistry will be affected by the walls, only that it has the potential to

122

be affected by the walls. The recent revelations about OVOC wall effects and the uncertainties in

123

heterogeneous and surface wall chemistry suggest that we should assume that the walls are having

124

an impact on the chemistry until it can be proved otherwise. The lower the 𝐶𝑊𝐼, the greater the

125

potential for wall effects and the more important it is to either prove otherwise or devise

126

corrections.

127 128

Consider the 𝐶𝑊𝐼 in terms on the factors in eq 1. Increasing 𝑉 𝐴 can decrease wall effects by

129

making it less likely that the sampled air contains constituents that are been affected by the walls.

130

Decreasing 𝜏𝑟𝑒𝑠 reduces the opportunity for transport within the enclosure to carry wall-affected


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131

air to the sampling ports. Of course, decreasing 𝜏𝑟𝑒𝑠 too much means that the desired chemistry or

132

microphysics may not be achievable before constituents are sampled from the enclosure.27-31

133

Decreasing 𝑣𝑑 reduces the ability of transport within the enclosure to carry air with wall-affected

134

VOCs or OVOCs to the sampling ports.

135 136 137

Huang et al.26 provide a derivation and thorough description of the deposition velocity (m s-1) in an EC under equilibrium conditions. Using their notation, their eq S9 leads to eq 5.

138

(

139

1

―1 1 𝑣𝑒

) (

𝑣𝑑 = 1 + 𝐾𝑤

1

)

―1

(5)

+ 𝑣𝑐

140 141

𝑣𝑒 (𝑚 𝑠 ―1) is velocity associated with the molecular and eddy diffusion transporting the chemical

142

species to and from the wall and 𝑣𝑐 (𝑚 𝑠 ―1) is the velocity associated with the accommodation of

143

the chemical species on the wall. 𝑣𝑑 (𝑚 𝑠 ―1) can be decreased by reducing either the transport of

144

the chemical species to or from the enclosure walls or the accommodation of the constituent to the

145

walls. 𝐾𝑤 is the equilibrium partitioning coefficient between the gas phase and the wall for each

146

chemical constituent.

147 148

The transport velocity, 𝑣𝑒, is given in eq 6.26

149 150

𝑣𝑒 =

𝑘𝑒𝐷𝑔

( )

𝑎𝑟𝑐𝑡𝑎𝑛 𝛿𝑐

𝑘𝑒 𝐷𝑔

151


(6)


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𝐷𝑔 is the gas-phase diffusion coefficient of the chemical species (m2 s-1), 𝑘𝑒 is the eddy diffusion

153

frequency (s-1), and 𝛿𝑐 is the chemical boundary layer depth (m), usually called the concentration

154

boundary layer depth. Its growth into being fully developed is related to the growth of the more

155

common momentum boundary layer depth, 𝛿, by the Schmidt number, 𝑆𝑐 = 𝜈 𝐷𝑔.32 𝜈 is the

156

kinematic viscosity and equals 1.5 × 10 ―5 m2 s-1 for typical laboratory conditions.33 In fully

157

developed flow, 𝛿𝑐 and 𝛿 are equal. The value for 𝐷𝑔 depends on the molecular species, particularly

158

the molar mass. For water vapor, it is 2.6x10-5 m2s-1 at 298 K34 and for a typical SVOC with a

159

molar mass of 200 g mole-1, it is about 5x10-6 m2s-1.26 If

160

≪ 1, 𝑣𝑒 = 𝐷𝑔/𝛿𝑐. In the first case, eddy diffusion dominates molecular diffusion, while in the

161

second case, molecular diffusion dominates. Eddy diffusion dominates in all current OFRs and

162

ECs.

𝛿𝑐2𝑘𝑒 𝐷𝑔

2

≫ 1, 𝑣𝑒 = 𝜋 𝑘𝑒𝐷𝑔. However, if

𝛿𝑐2𝑘𝑒 𝐷𝑔

163 164

The eddy diffusion is taken as the eddy diffusion frequency, 𝑘𝑒, times the square of a chemical

165

transport distance, which in this case is assumed to be the enclosure chemical boundary layer

166

depth, 𝛿𝑐. An expression derived for 𝑘𝑒 is given in eq 7.14,30,35

167 168

𝑘𝑒 = 0.004 + 10 ―2.25𝑉0.74

(7)

169 170

V is the enclosure volume (m3). This expression has been derived for static environmental

171

chambers and has been applied to an OFR.30 Under some circumstances, it is possible to reduce

172

eddy diffusion, but, for a given temperature and pressure, molecular diffusion cannot be reduced

173

and sets the minimum molecular transport to and from the walls.

174


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175

In OFRs, the primary eddies are due to convection, which are driven by small thermal gradients

176

in the walls or between the walls and the gas. As these eddies rise vertically and accelerate, some

177

vertical motion is converted into horizontal motion, stirring the gas. A second source of eddies is

178

an uneven distribution of the velocities of air entering the OFR, which cause large eddies that are

179

not readily damped by viscosity. These eddies stir wall-affected chemical species throughout the

180

enclosure volume.

181 182 183

The velocity associated with the accommodation of the chemical species with the wall, 𝑣𝑐, is given by eq 8.26

184 185

𝑣𝑐 =

𝑎𝑤𝜔 4

(8)

186 187

𝑎𝑤 is the accommodation coefficient for the chemical species on the wall and 𝜔 is the molecular

188

speed of the chemical species, which is typically about 180 m s-1 for molecules with a mass of

189

OVOCs. 𝑎𝑤 varies over orders of magnitude depending on the chemical species and the wall

190

material. Accommodation on the wall is only one aspect of the interaction between the gas and the

191

wall. It is also possible for gases to come off the wall to establish an equilibrium between

192

partitioning in the wall and in the gas phase.19 The equilibrium constant, 𝐾𝑤, depends on chemical

193

species and its saturation vapor pressure. If equilibrium is established, the continued loss to the

194

walls can decrease and the effective uptake can become quite small, even though the wall has taken

195

up some of the chemical species that otherwise could condense on aerosol particles. However, if

196

the OVOCs are being created or destroyed by chemistry faster than equilibrium can be achieved,

197

then the OVOC concentrations will not achieve true equilibrium.



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198 199

With all these considerations, the 𝑄 index can be written as eq 9.

200

201

𝑄=

(𝑉 𝐴) (1 + )( 1 𝜏𝑟𝑒𝑠

1 𝐾𝑤

( )

𝑎𝑟𝑐𝑡𝑎𝑛 𝛿𝑐

𝑘𝑒𝐷𝑔

𝑘𝑒 𝐷𝑔

4

)

+ 𝑎𝑤𝜔

(9)

202 203

The actual impact of the enclosure walls on the OVOC and SOA chemistry depends on 𝑎𝑤 and

204

𝐾𝑤, which are functions of the OVOCs being studied, the SOA composition and concentration,

205

and wall material. The goal here is to rank enclosures with the 𝐶𝑊𝐼 based on the greatest possible

206

initial uptake of initial VOCs and reaction-product OVOCs by the walls. The initial wall uptake

207

with 𝑎𝑤 = 1 gives a better measure of worst-case wall interactions of uptake and chemistry that

208

the 𝐶𝑊𝐼 is meant to define.

209 210

Determining the 𝐶𝑊𝐼 for different enclosures

211 212

Here 𝑄 and the 𝐶𝑊𝐼 are found for different existing enclosures that have been used to study

213

atmospheric SOA chemistry and for two cases of an optimal OFR, which will be discussed in a

214

later section. In this paper, the analysis assumes typical laboratory temperature and pressure and

215

an OVOC mass and 𝐷𝑔, but the 𝐶𝑊𝐼 is not strongly dependent on reasonable ranges of laboratory

216

pressure and temperature or on 𝐷𝑔.36 The quantities needed to calculate 𝑄 and the 𝐶𝑊𝐼 are V, A,

217

𝜏𝑟𝑒𝑠, 𝑘𝑒, 𝛿, 𝐷𝑔, 𝑎𝑤, 𝜔. The well-known quantities of enclosure volume, surface area, volume-to-

218

surface area ratio, and typical residence time were taken from the literature (Table 1). Residence


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219

times were equated to measured mean residence times for OFRs. For ECs, they were equated to

220

the experiment run times because the longer the experiment runs, the greater the opportunity for

221

the initial VOCs and the evolving reaction-product OVOCs to interact with the wall.

222 223

An uncertain quantity is the enclosure boundary layer depth, although for eddy-dominated flow,

224

the calculation of 𝑣𝑒 and 𝑣𝑑, and thus 𝑄 and the 𝐶𝑊𝐼, are insensitive to 𝛿𝑐. For the Caltech EC,

225

Huang et al.26 assigned 𝛿𝑐 a value of 0.10 m, but allowed for values between 0.01 m and 1 m. For

226

ECs, the multiplicative uncertainty factor (∆𝛿) is assumed to be in the range from 1/10 to 10 (Table

227

1). For eddy-dominated diffusion in OFRs, 𝛿𝑐 is taken to be half the vertical dimension. The

228

multiplicative uncertainty factors (∆𝛿𝑐) are assumed to be ½ to 2 for OFRs (Table 1).

229 230

The eddy diffusion coefficient, 𝑘𝑒, and the molecular diffusion coefficient, 𝐷𝑔, are also

231

uncertain. For 𝑘𝑒 determined using eq 7, the uncertainty is assumed to be a multiplicative

232

uncertainty factor in a normal distribution out to 3 standard deviations, with 1𝜎 confidence that it

233

lies between 1/1.5 and 1.5. The uncertainty factor of 1.5 was estimated based on scatter in the wall

234

uptake data in McMurry and Grosjean16. 𝐷𝑔 is assumed to have any value between 3x10-6 and

235

9x10-6 m2 s-1,36 and that 𝑀𝑊 can have any value between 120 and 280 g mole-1, which covers most

236

of the range for SVOCs in Huang et al..26

237 238 239 Table 1. Chamber parameter measurements and estimates



#

Chamber

1

FZJ Saphir EC

2

V (m3)

A (m2)

V/A (m)

270

270

1.0

2x104

0.1 (10)

Rohrer et al., 2005

Caltech EC

24

48

2.0

2x104

0.1 (10)

Cocker et al., 2001; Huang et al., 2018

3

CU EC

8.2

24.4

3.0

1.5x104

0.1 (10)

Yeh and Ziemann, 2015; Krechmer et al., 2016

4

CMU EC

10

24

2.4

1x104

0.1 (10)

Hildebrandt et al., 2009

5

Caltech CPOT OFR

0.054

1.28

0.042 600

0.06 (2)

Huang et al., 2017

6

UT TPOT OFR

0.0014

0.078 0.018 100

0.075 (2)

George et al., 2007

7

PAM OFR

0.013

0.325 0.040 150

0.1 (2)

Lambe et al., 2011

8

New PAM OFR (no 𝑘𝑒)

0.013

0.32

0.041 150

0.1 (1.2)

This paper

9

New PAM OFR (no 𝑘𝑒, ℎ 2 = 1.4𝛿)

0.025

0.49

0.050 150

0.11 (1.2)

This paper

𝜏𝑟𝑒𝑠 (s)

𝛿 (∆𝛿) (m)

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Reference for chamber

240 241 242

These uncertainty estimates are used to find the uncertainty for 𝜏𝑤𝑎𝑙𝑙, 𝑄, and the 𝐶𝑊𝐼. Using a

243

Monte Carlo method, 𝑘𝑒, 𝛿𝑐, 𝐷𝑔, and 𝑀𝑊 are independently and randomly varied a million times

244

within their uncertainty ranges. 𝜏𝑤𝑎𝑙𝑙 and the 𝐶𝑊𝐼 are calculated each time. From these many runs,

245

the probability distribution function, mean value, and standard deviation were found for each

246

chamber. The standard deviation is for a normal distribution and may not apply quantitatively to

247

these distributions, but it is adequate for giving a sense of the effects of changing parameter values,

248

its only use in this paper. Sensitivity of these results is also examined by doubling the 𝑘𝑒

249

uncertainty range and by considering the effects of each uncertainty individually or in pairs.


Page 13 of 32


250 251

The accommodation coefficient, 𝑎𝑤, can vary from 1 to below 10-7. 𝑄 is calculated for four

252

values: 1, 10-5, 10-6, and 10-7 for all enclosures. For Teflon film, 𝑎𝑤 > 2 × 10 ―3 applies to LVOCs,

253

𝑎𝑤 from 2 × 10 ―3 ―3 × 10 ―5 applies to SVOCs, and 𝑎𝑤 < 3 × 10 ―5 applies to IVOCs.14,26 For

254

a metal surface, the 𝑎𝑤 are generally larger for LVOCs and SVOCs. In a separate analysis, the

255

dependence of 𝑄 is calculated for the entire range of 𝑎𝑤 for one EC and one OFR to show for

256

which types of OVOCs the 𝐶𝑊𝐼 value applies.

257 258

Results

259

260 261

Figure 1. The wall loss time scale for nine different chambers, which are numbered in Table 1.

262

𝑀𝑊, 𝐷𝑔, 𝑘𝑒, and 𝛿𝑐 were varied repeatedly as described in the text to produce mirror-image

263

probability distribution functions (pdfs) for 𝜏𝑤𝑎𝑙𝑙 for each enclosure (pdfs are along the vertical).



264

These pdfs are shown for four values of 𝑎𝑤: 1 (red), 10-5 (green), 10-6 (yellow), and 10-7 (blue).

265

The mean values are shown as gray horizontal lines, with 𝑎𝑤 = 1 being darker.

266

First consider the mean calculated wall loss time scale, 𝜏𝑤𝑎𝑙𝑙 (Figure 1). It depends on 𝑎𝑤 – the

267

smaller 𝑎𝑤, the greater 𝜏𝑤𝑎𝑙𝑙. 𝜏𝑤𝑎𝑙𝑙 is greater for ECs than for OFRs. For 𝑎𝑤 = 10 ―5, 𝜏𝑤𝑎𝑙𝑙 is

268

1900-3300 s for the ECs, which is consistent with the measured 𝜏𝑤𝑎𝑙𝑙 for SVOCs of 1800 s in the

269

Caltech chamber23, and 170-410 s for existing OFRs, which is consistent with the measured 𝜏𝑤𝑎𝑙𝑙

270

for SVOCs of 70-600 s in OFRs.9,30 The differences between the different enclosure types are

271

caused by differences in 𝑣𝑒, primarily through 𝑉 𝐴, because 𝑣𝑐 is the same for all enclosures for

272

the same 𝑎𝑤 and chemical species.

273 274

The mean 𝐶𝑊𝐼 for the seven existing enclosures is 0.05-0.14 for ECs and 0.5-2.1 for the OFRs

275

(Figure 2). The Q values show that for all 𝑎𝑤, the relative ranking of the different enclosures

276

remains qualitatively the same, although as 𝑎𝑤 gets small, all enclosures become effectively wall-

277

less. The 𝐶𝑊𝐼 values show that OFRs have substantially less wall effects than ECs for the same

278

OVOC.

279 280

How robust is this conclusion? When the uncertainties in 𝑘𝑒, 𝛿𝑐, 𝐷𝑔, and 𝑀𝑊 were turned on or

281

off individually or in pairs, or when the uncertainty in 𝑘𝑒 was doubled, the width of the 𝐶𝑊𝐼

282

uncertainty pdf was sensitive to changes in these input uncertainties. The greatest contributor to

283

the 𝐶𝑊𝐼 uncertainty is 𝑘𝑒. The uncertainty in 𝑘𝑒 accounts for (80-90)% of the total 𝐶𝑊𝐼 uncertainty

284

for ECs and (60-70)% of the total 𝐶𝑊𝐼 uncertainty for OFRs. The contribution of the uncertainty

285

in 𝑘𝑒 to the shape of the pdf for 𝐶𝑊𝐼 uncertainty can be seen by comparing the more symmetric


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286

pdf shapes for enclosures 1 through 7 that have eddy diffusion to those for enclosures 8 and 9 that

287

have only a skewed uncertainty in molecular diffusion. However, the mean 𝐶𝑊𝐼 did not change

288

in any case for any chamber no matter which uncertainties were used. Thus, the 𝐶𝑊𝐼 and the

289

relative ranking of the enclosures is robust.

290

291 292

Figure 2. The Chamber Wall Index (𝐶𝑊𝐼) (red) and Q values for 𝑎𝑤 of 10-5 (green), 10-6 (yellow),

293

and 10-7 (blue), which are shown for the nine different chambers numbered in Table 1. 𝑀𝑊, 𝐷𝑔,

294

𝑘𝑒, and 𝛿𝑐 were varied repeatedly as described in the text to produce mirror-image probability

295

distribution functions (pdfs) for 𝜏𝑤𝑎𝑙𝑙 for each enclosure (pdfs are along the vertical). Mean values

296

for each enclosure 𝐶𝑊𝐼, 𝑄, and 𝑎𝑤 are shown as gray horizontal bars, , with 𝑎𝑤 = 1 being darker.

297 298

The dependence of 𝑄 on 𝑎𝑤 is examined here for the Caltech EC and the PAM OFR (Figure 3).

299

𝑄 is independent of 𝑎𝑤 when 𝑎𝑤 is greater than 10-4, which is close to the transition point between



300

accommodation control regime and gas-phase transport control regime.26 Although the 𝐶𝑊𝐼 is

301

defined for 𝑎𝑤 = 1, 𝑄 equals the 𝐶𝑊𝐼 for 𝑎𝑤 = 1 to 𝑎𝑤 < 10 ―4. This range of 𝑎𝑤 encompasses

302

all LVOCs and most SVOCs, which are probably the most important gas-phase contributors to

303

SOA because of their low volatility. Thus, the 𝐶𝑊𝐼 is a good indicator of the freedom from

304

potential wall effects that an enclosure has for OVOC and SOA studies.

305

306 307

Figure 3. 𝑄 versus accommodation coefficient for the Caltech EC (green line) and the PAM OFR

308

(blue line). The 𝐶𝑊𝐼 = 𝑄 when 𝑎𝑤 = 1 and is shown as red x’s on the EC and OFR curves. Ranges

309

of 𝑎𝑤 for different OVOC types on Teflon is shown with double arrows.14,26

310

For all 𝑎𝑤 values, the primary factor driving this large difference in the 𝐶𝑊𝐼 between ECs and

311

OFRs is 𝜏𝑟𝑒𝑠, not 𝜏𝑤𝑎𝑙𝑙 (Figure 4). In fact, 𝜏𝑤𝑎𝑙𝑙 is less in OFRs than in ECs, which reduces the EC

312

and OFR difference that is caused by 𝜏𝑟𝑒𝑠. For existing enclosures, the slope of this relationship

313

between the 𝐶𝑊𝐼 and 𝜏𝑟𝑒𝑠 is approximately 0.5 in log10 space. The conclusion from this analysis

314

might be that the lower 𝜏𝑟𝑒𝑠, the better. However, 𝜏𝑟𝑒𝑠 must be longer than the time required to

315

complete the gas-phase, heterogeneous, and particle chemical reactions and the microphysics of


Page 16 of 32

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316

nucleation, condensation, evaporation, and diffusion needed to produce atmospherically relevant

317

SOA.

318

319 320 321

Figure 4. 𝐶𝑊𝐼 as a function of residence time for 𝑎𝑤 = 1. The dashed vertical line indicates the

322

approximate longest known SVOC isomerization time scale.27

323 324

Discussion

325 326

Is it possible to produce an enclosure that is wall-less to the chemistry? If a wall material could

327

be found for which VOCs, OVOCs, and SOA had 𝑎𝑤 < 10 ―7 and on which no chemistry could

328

occur, then the enclosure made of this material would be effectively wall-less to the chemistry. I

329

know of no such material, but it makes sense to use a material for which 𝑎𝑤 is as small as possible

330

for the VOCs, OVOCs, and SOA being studied.



331 332

Can an EC be made wall-less to the chemistry by manipulating the properties in eq. 1? The 𝑉 𝐴

333

ratio is already large. To increase the 𝐶𝑊𝐼, oxidant levels could be increased so that 𝜏𝑟𝑒𝑠 could be

334

reduced to accomplish the same chemistry or the eddy diffusion could be reduced. However, ECs

335

need to be well mixed so that the chemistry sampled through different sampling ports is the same

336

and so that random noise is not introduced into the sampling of chemical constituents because air

337

parcels with different chemistry histories move past the sampling ports. For uniform chemistry,

338

𝜏𝑟𝑒𝑠 needs to be much greater than the EC mixing timescale, which is driven by strong eddy

339

diffusion, so 𝜏𝑟𝑒𝑠 probably cannot be reduced to less than ~1 h. Therefore, it is probably not

340

possible to improve the 𝐶𝑊𝐼 for an EC by as much as a factor of 10. Thus, the wall uptake

341

corrections developed by many are necessary.

342 343

It may be possible to improve the 𝐶𝑊𝐼 for an OFR. For simplicity, consider a rectangular OFR

344

with a height ℎ (𝑚) and width ℎ, a length 𝑥 (𝑚) between the entrance and the sampling point, a

345

mean centerline velocity 𝑈 (𝑚𝑠 ―1), and a residence time 𝜏𝑟𝑒𝑠, which is 𝑥 divided by the mean

346

velocity for the sampled air parcels. The sample is taken through a tube that protrudes into the

347

OFR on the centerline. Only a small fraction of the total flow that is sufficient for the sampling

348

instruments is pulled into the centerline sampling tube.

349 350

A way to optimize the 𝐶𝑊𝐼 is to minimize 𝑣𝑒 by minimizing eddy diffusion, which leaves

351

molecular diffusion mainly transporting wall-affected air from the walls to the sampling port. For

352

OVOCs with 𝑎𝑤 > 10 ―5, transport by molecular diffusion, 𝑣𝑒, is much smaller than the

353

accommodation velocity, 𝑣𝑐, so that the deposition velocity depends only on molecular diffusion.


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354

To ensure that air that contacted the wall is not sampled, the sampling must be in the chemical

355

entrance (or transition) region of the OFR, where the chemical boundary layer has not yet

356

converged to the centerline from all sides.

357 358 359

The minimum optimum Chamber Wall Index, 𝐶𝑊𝐼𝑜𝑝𝑡 𝑚𝑖𝑛, is given by eq 10, which is derived in the Supporting Information.

360 361

𝐶𝑊𝐼𝑜𝑝𝑡 𝑚𝑖𝑛 =

𝛿𝑐

𝑥 𝑅ℎ𝑆𝑐

(10)

362 363

This equation is valid only for sampling in the enclosure entrance region. For a given 𝑅ℎ, the

364

𝛿 𝐶𝑊𝐼𝑜𝑝𝑡 𝑚𝑖𝑛 depends on 𝑐 𝑥, which defines the chemical boundary layer growth in the entrance region.

365

For flow in an OFR with a square cross section, the relationship between 𝑥 and 𝛿𝑐 must be

366

computed for the OFR chemical entrance region.37 𝐶𝑊𝐼𝑜𝑝𝑡 𝑚𝑖𝑛 can also be defined in terms of different

367

quantities, as in eq S19, which is reproduced as eq 11.

368 369

𝐶𝑊𝐼𝑜𝑝𝑡 𝑚𝑖𝑛 =

𝛿𝑐ℎ 4𝜏𝑟𝑒𝑠𝐷𝑔

(11)

370 371 372

From eq S14, the square OFR height (and width) that is needed to meet the absolute minimum 𝐶𝑊𝐼𝑜𝑝𝑡 𝑚𝑖𝑛 is obtained as a function of 𝜏𝑟𝑒𝑠 in eq 12.

373 374

ℎ=

𝐷𝑔𝜏𝑟𝑒𝑠 0.03

375


(12)


376 377

378 379

Figure 5. The OFR height / width required to achieve the 𝐶𝑊𝐼𝑜𝑝𝑡 𝑚𝑖𝑛 as a function of residence

380

time. The dashed vertical line indicates the approximate longest known SVOC isomerization time

381

scale.

382 383

As the desired 𝜏𝑟𝑒𝑠 gets larger, ℎ must increase (Fig. 5). For the OFR with no eddy diffusion,

384

and the values 𝜏𝑟𝑒𝑠 = 150 𝑠, 𝐷𝑔 = 5 × 10 ―6𝑚2𝑠 ―1, 𝑈 = 0.0033 𝑚 𝑠 ―1, and 𝑥 = 0.5 𝑚, the

385

enclosure height and width to achieve 𝐶𝑊𝐼𝑜𝑝𝑡 𝑚𝑖𝑛 is ℎ = 0.16 𝑚. If eddy diffusion could be

386

suppressed in existing PAM OFRs, they could achieve the 𝐶𝑊𝐼𝑜𝑝𝑡 𝑚𝑖𝑛 with a residence time of ~150

387

s. TPOT and CPOT would need to sample only a small fraction of the air near their centerlines to

388

𝑜𝑝𝑡 achieve the 𝐶𝑊𝐼𝑜𝑝𝑡 𝑚𝑖𝑛 with a residence time of (100-130) s. To achieve the 𝐶𝑊𝐼𝑚𝑖𝑛 for 𝜏𝑟𝑒𝑠 = 500

389

s, the eddy-less OFR must have a height of at least 0.3 m. Experience with eddy suppression

390

38 suggests that achieving the 𝐶𝑊𝐼𝑜𝑝𝑡 𝑚𝑖𝑛 for this height is possible , but the larger the chamber and the

391

longer the residence time, the more difficult it is to maintain eddy-less flow.

392


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393

For the new PAM OFR with ℎ = 0.16 𝑚, 𝜏𝑟𝑒𝑠 = 150 𝑠, and 𝛿𝑐 = 0.99 × ℎ 2, the resulting value

394

for 𝐶𝑊𝐼𝑜𝑝𝑡 𝑚𝑖𝑛 is 4.2 ± 1.6 (Fig. 2). The uncertainty (2𝜎 confidence) comes mostly from the

395

uncertainty assigned to 𝐷𝑔. This value is the absolute minimum 𝐶𝑊𝐼 to achieve the wall-less

396

condition for chemistry for this residence time. An enclosure with a lower 𝐶𝑊𝐼 has the potential

397

for wall effects on the chemistry. The lower the 𝐶𝑊𝐼, the greater the potential.

398 399

In practice, ℎ will almost certainly need to be larger, which is equivalent to taking the sample at

400

a distance x shorter than the chemical entrance length. The reason: a fraction of the OFR airflow

401

is drawn through the sampling port by the instruments measuring VOCs, OVOCs, and SOA. Using

402

the absolute minimum 𝐶𝑊𝐼𝑜𝑝𝑡 𝑚𝑖𝑛 is possible only if the sampling flow is negligible. For more

403

realistic sampling flow needs, a larger cross-section around the centerline will need to be outside

404

of the converging chemical boundary layers.

405 406

The cost of shorter OFR residence times is the possibility of incomplete chemistry, condensation

407

on aerosol particles, or loss of SOA by excessive gas-phase oxidation of SVOCs by the time the

408

air is sampled.30 Currently there is no definitive answer on the ability of OFRs to produce

409

atmospherically relevant SOA particles with 𝜏𝑟𝑒𝑠 of 100-200 seconds. Several observational

410

studies provide evidence that SOA particles produced in OFRs have chemical properties similar

411

to those produced in the atmosphere.6,30,35,39-42

412 413

This similarity stands in contrast to the suggestion that the OFR 𝜏𝑟𝑒𝑠 is too short to allow enough

414

time for some SVOC-producing initial auto-oxidation processes to occur.28 These auto-oxidation

415

processes require O2 addition and isomerization, with the initial isomerization step calculated to



416

take from less than a second to about 500 seconds, depending on the precursor gas (Figure 5).28 If

417

the slower auto-oxidation processes are important for SOA formation, then studies are needed to

418

determine if the enhanced OH amounts in OFRs increase the initial isomerization rates by

419

providing more radical sites on the OVOC molecules.

420 421

Another modeling study suggests that SOA aging in OFRs occurs more by heterogeneous

422

oxidation and less by SVOC gas-phase oxidation than is occurring in the atmosphere.29 However,

423

the kinetic simulations in this study assumed an SOA mass in the OFR that was 100 times larger

424

than that assumed for the atmosphere, whereas it is known that using larger-than-atmospheric

425

amounts of VOCs and SOA leads to less oxidized SOA.39 It is essential to use atmospherically

426

relevant amounts of the initial SOA or VOCs when comparing the SOA or OVOCs produced in

427

an EC or an OFR to those produced in the atmosphere.

428 429

While some studies mentioned above have compared SOA and SVOC from ECs and OFRs,

430

there has been no systematic study to examine the trade-off between 𝜏𝑟𝑒𝑠 and OH concentration

431

([OH], units: cm-3) using SOA, VOC, and OVOC measuring instruments. It still needs to be

432

determined if SOA produced in OFRs and the atmosphere are different enough to cause differences

433

in OVOCs concentrations or the most important SOA properties, such as hygroscopicity, optical

434

absorption, or interactions with human cells.

435 436

A suggested limit for the contamination from the chemical boundary layer could be 1%.

437

However, to quantify the 𝑥 and ℎ needed to meet this limit for a given 𝜏𝑟𝑒𝑠 requires knowledge of

438

𝛿𝑐 𝑥 as a function of 𝑅ℎ, or equivalently 𝛿𝑐 𝜏𝑟𝑒𝑠 as a function of ℎ, in the entrance region.37 While


Page 22 of 32

Page 23 of 32


439

Cebeci and Bradshaw provide some guidance, the best approach is to find these ratios as a function

440

of 𝑅ℎ or ℎ using a computation fluid dynamics model. In the interim, if the sampling on the

441

centerline draws 15% of the total air flow, then ℎ should be chosen to be ~40% greater than ℎ = 2𝛿𝑐

442

for a given choice of 𝜏𝑟𝑒𝑠 to assure that none of the sample is contaminated with chemical boundary

443

layer air. For an enclosure with 𝜏𝑟𝑒𝑠 = 150 𝑠 and ℎ = 0.22 𝑚, the recommended 𝐶𝑊𝐼 is ~6, as

444

shown in Fig. 2 for enclosure 9.

445 446

Finally, this paper provides guidance for creating an OFR in which the potential for wall effects

447

on the sampled chemistry is negligible. Despite the low Reynolds number and developing laminar

448

flow in OFRs, the jetting of the input air and convection bring air from near the walls to the

449

sampling tube. This eddy diffusion must be minimized. Convection is the easiest eddy source to

450

reduce. Heating the entering air at the chamber’s top and cooling the chamber’s bottom suppresses

451

convection.38 Less than a few Co are needed, although additional heating along the top and cooling

452

along the bottom may be needed to maintain the temperature gradient all the way to the sampling

453

port. A more difficult problem is suppressing the horizontal eddies driven by inhomogeneity in the

454

incoming flows and by the sampling itself. These eddies remain a challenge, but if they can be

455

minimized, truly wall-less OFR laboratory and field experiments will be possible, assuming that

456

effects of sampling line walls can be minimized. The 𝐶𝑊𝐼 is a good metric for determining how

457

close current and future enclosures are to realizing this goal of being chemically wall-less

458

enclosures.

459 460

ASSOCIATED CONTENT



Page 24 of 32

461

Supporting Information. Derivation of the minimum optimal Chamber Wall Index (𝐶𝑊𝐼𝑜𝑝𝑡 𝑚𝑖𝑛). This

462

material is available free of charge via the Internet at http://pubs.acs.org.

463 464

AUTHOR INFORMATION

465

Corresponding Author: *Email: [email protected] , Tel.: (814) 865-3286

466 467

ACKNOWLEDGMENT

468

I thank Ying Pan, Andrew Lambe, John Crounse, Jordan Krechmer, and Jose Jimenez for helpful

469

conversations, Jena Jenkins and Devin Wang for insights into chamber design, and the anonymous

470

reviewers for their comments. This work was supported by the US National Science Foundation

471

grant AGS-1537009.

472 473

ABBREVIATIONS

474

SOA, Secondary Organic Aerosol; SVOC, Semi-volatile organic compound; FT, Flow tube; EC,

475

Environmental Chamber; OFR, Oxidative Flow Reactor; CWI, Chamber Wall Index

476 477

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478

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