Environ. Sci. Technol. 1994, 28, 504-513
Modeling Ozone Deposition onto Indoor Residential Surfaces Richard Reiss, P. Barry Ryan,’ and Petros Koutrakis
Department of Environmental Health, Environmental Science and Engineering Program, Harvard University School of Public Health, 665 Huntington Avenue, Boston, Massachusetts 021 15 Modeling the deposition of pollutants onto surfaces requires the inclusion of two separate components: (1) the transport of the pollutant to the surface and (2) the subsequent uptake of the pollutant onto the surface. The relationship of these two components to the deposition velocity can be written in the form of two resistances corresponding to the two components (Le., the boundary layer resistance and the surface uptake resistance). In order to calculate the surface uptake resistance, the mass accommodation (or “sticking”)coefficient is required. We present an experimental method for determining accurately the mass accommodation coefficient and report the results of measurements on several common indoor surfaces. For ozone deposition onto glass, latex paint, and vinyl and paper wallpaper, the mass accommodation coefficients were in the range of 10-5-10-7. It was found that for the surfaces tested, the deposition was governed by one of three conditions, depending on the airflow conditions: (1)surface uptake is rate limiting, (2) boundary layer transport is rate limiting, or (3) both boundary layer transport and surface uptake are important.
Introduction Tropospheric ozone has been identified as a criteria air pollutant by the U S . Environmental Protection Agency since it is known to cause acute health effects, and there is evidence that it may be responsible for more severe chronic effects (1). An individual’s exposure to a pollutant such as ozone can be characterized as the sum of exposures in the microenvironments where the individual spends his or her time. One delineation of these microenvironments is outdoors versus indoors. Ambient ozone is known to infiltrate indoors (2), resulting in indoor concentrations from about 20 to 80% of the outdoor concentration (3). However, individuals spend about 90% of their time indoors (41, suggesting that the indoor environment constitutes a significant ozone exposure. One of the most important variables affecting indoor ozone concentrations is the deposition of ozone onto indoor surfaces. This deposition is the principal reason that indoor ozone concentrations are lower than outdoor concentrations (5). Ozone also reacts with nitric oxide, which is present indoors as a result of the infiltration of ambient air and indoor combustion sources, and in some instances this results in a significant removal of ozone, (e.g., see ref 6). Deposited ozone may also react on surfaces to form other pollutants. For example, ozone is known to react with carpet to form several aldehyde compounds (7). For these reasons, it is important to understand the factors that influence the deposition velocity. Surface deposition is dependent on two processes: the transport of the pollutant to the surface and the subsequent uptake onto the surface. The transport of a pollutant to
the surface is dependent on the thickness of the boundary layer, which in turn is dependent on the nature of the near-surface airflow in the residence. The surface uptake is dependent on the mass accommodation coefficient, defined as the number of “sticks” of a molecule colliding with a surface divided by the total number of collisions. One of the purposes of this study is to determine the relative importance of the transport and surface uptake processes for the surfaces tested. Generally, for large boundary layer thicknesses (which occur during stagnant airflow conditions), the boundary layer transport is rate limiting, while for small mass accommodation coefficients, the surface uptake process is rate limiting. Wilson (8)has shown that sulfur dioxide is removed at less than the transport-limited rate, indicating that both boundary layer transport and surface uptake may be important for this pollutant. This paper presents an experimental technique for measuring deposition velocities using a laminar flow tube and presents measurement results for several common indoor surfaces. These results will be incorporated into a model that will be useful for examining the factors that result in a significant variabilityof ozone indoor to outdoor ratios among different residences. The model will also be useful for the study of indoor heterogeneous chemistry, which is dependent on pollutant deposition. Finally, the model will help provide the understanding needed to develop strategies to reduce exposures.
Background Indoor pollutant deposition is normally modeled by the concept of the deposition velocity, defined as the flux of the pollutant to the surface divided by its mean concentration in air (9). This can be written as
Kd = JIC,
* Address correspondence to this author; e-mail address:
[email protected].
(1) where J is the flux to the surface (units of mass deposited per area per time) and Cf is the free-stream concentration, which is assumed to be uniform throughout the indoor space. The concept also assumes that the loss process is first-order. Deposition velocities for ozone have been reported for specific surfaces in experimental chambers and for actual indoor environments. Deposition is known to vary considerably depending on the surface (5), suggesting that surface effects are important. Mueller et al. (10) observed that the relative humidity had a dramatic effect on ozone deposition onto aluminum. Also, Sabersky et al. (5) filled a residence with ozone and observed a doubling of the ozone decomposition rate when an internal recirculation system was turned on, indicating that room airflows may be important. For atmospheric deposition modeling, the deposition velocity depends on the convective and diffusive flows transporting the pollutant to the surface (e.g., ground, building surfaces, etc.) and the probability of “sticking” upon collision with the surface. For this reason, the deposition velocity is often written as the combination of
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0013-936X/94/0928-0504$04.50/0
Environ. Sci. Technol., Vol. 28, No. 3, 1994
0 1994 Arnerlcan Chemical Society
three resistances: the aerodynamic resistance, r,; the boundary layer resistance, rb; and the surface uptake resistance, rs, as (11)
discussion, we will summarize the theoretical results of these researchers. The surface uptake resistance can be written as
r, = 4JaU The first resistance term accounts for the mixing of the pollutant in the core region above the surface. This term is generally independent of the pollutant properties. Rather it is defined by the wind speed and turbulence. The second term corresponds to the movement of the pollutant across the surface boundary layer to the surface. This resistance is determined by the diffusion coefficient of the pollutant in air and the thickness of the surface boundary layer. Finally, the surface uptake resistance corresponds to the rate at which pollutants adsorb onto surfaces and re,-releasefrom the surface. It is dependent on the nature of the absorbate (Le.,the gaseous pollutant) and the absorbent (Le.,the surface). This concept can be extended to indoor pollutant deposition with some modifications. Indoor airflows are often assumed to follow the boundary layer assumption. In this situation, the air away from the surface (in the core region) of an enclosure is assumed to be well mixed while air movement within the boundary layer is assumed to diminish to zero at the surface. Pollutants are transported to the surface by diffusing across the boundary layer to the edge of the surface and then being taken up by the surface. The airflow in the enclosure determines the size of the boundary layer, with higher airflows resulting in a smaller boundary layer thickness. The assumption that the core region is well-mixed renders the aerodynamic resistance negligible. Thus, for indoor pollutant deposition, the important resistances are the boundary layer and surface uptake resistances. The analogous deposition velocity formula for indoor environments can be written as
Kd
1 ‘b -k
(3)
‘8
The transport-limited deposition velocity is the inverse of the boundary layer resistance, and similarly, the surface uptake-limited deposition velocity is the inverse of the surface uptake resistance. Normally surface reactions are modeled according to the following sequence: (1)transport of the gas to the surface, (2) adsorption onto the surface, and (3) reaction or re-release from the surface (see ref 12). Thus, the surface uptake resistance contains two components: adsorption onto the surface and reaction with the surface. Adsorption onto the surface can be reversible, and it is feasible that material adsorbed onto the surface will re-release without modification. However, in several of our laboratory experiments, ozone flow across a surface was turned off after a period of deposition. It was observed that no ozone desorbed from these surfaces. Therefore, it is assumed that all adsorbed ozone molecules will react without desorbing. In this case, the mass accommodation coefficient can also be called the reaction probability. To compare the effect of the surface uptake and boundary layer processes, it is necessary to quantify the two resistances, which can be determined by evaluating the pollutant fluxes to the surface for each process. CanoRuiz et al. (13)have presented an approach to this problem relying on the kinetic theory of gases. For clarity in
(4)
where CY is the mass accommodation coefficient and 0 is the mean thermal speed. The mean thermal speed can be defined as (5)
where k b is the Boltzmann constant, T is the absolute temperature, and M is the mass of the pollutant molecule. The boundary layer resistance is a function of the nearsurface airflow in the residence. Three near-surface airflow scenarios were considered: (1)forced laminar convection parallel to a flat plate, (2) laminar natural convection flow along an isothermal vertical plate, and (3) homogeneous turbulence in an enclosure. Natural convection flow normally occurs during the low ozone winter season when windows are closed and air movement may arise from temperature gradients between interior and exterior walls. High ozone periods normally occur during warmer periods when windows are usually open and airflow is governed by infiltration flows that can be modeled by scenarios 1 and 3. Thus, we will consider only these two scenarios. For scenario 1, pollutant transport is governed by molecular diffusion across the boundary layer, and the resistance can be written as rbl
%
6JDg
(6)
where 6 is the average boundary layer thickness and D, is the ozone diffusion coefficient. For scenario 3, the flux to the surface due to turbulent diffusion can be written as
Jt
KJ,- dC
(7) dY where K, is the turbulence intensity, m is an empirical coefficient, and y is a length variable normal to the surface. For gases, such as ozone, which have molecular diffusivities equal to the kinematic viscosity of air, the resistance to mass transport can be written as
It should be noted that these equations assume a smooth surface. Some residential materials are porous solidswhere we may expect that porous diffusion processes will also be important. To do their analysis, Cano-Ruizet al. (13)used published data on ozone deposition in chambers. However, in most of these experiments, the flow conditions were not described; so they estimated the transport-limited deposition velocities in order to calculate the mass accommodation coefficients. In this paper, we present a method for experimentally determining the mass accommodation coefficient under well-characterized flow conditions.
Materials and Methods
Description of Apparatus. A schematic of the apparatus is shown in Figure 1. Air streams are mixed in two bottles as shown in Figure 2. One is for zero-air (i-e., pure air) only and is used to condition the chamber at the Envlron. Sci. Technol., Vol. 28, No. 3, 1994 505
Angus-Esterline
r----LJ1
Flgure 1.
Schematic diagram of tube flow apparatus.
I
---
Figure 2. Flow diagram of zerc-air system.
relative humidity of the experiment prior to ozone exposure. The other is acomhinationof zero-air andozone and is used for ozone exposure tests. First, a room air stream is scrubbed with charcoal and Purafill (permanganate coated alumina) to remove organics, and then it is dried by passing it through silica gel. One portion of this dry stream is sent directly to the zero-air mixing bottle while another portion is sent to the ozone mixing bottle. A second room air stream, after being scrubbed with charcoal and Purafill, is passed over a Milli-Q (Millipore Corp.) water bath to produce a wet stream. The Milli-Q is maintained a t a constant temperature. In-line water traps prevent water condensation in the chamber. A 500 Envirwl. Sd. Technci.. Vol. 28. NO. 3. I994
portion of this wet stream is then mixed with the dry stream in the zero-air mixing bottle to give the desired relative humidity. Another portion of the wet stream is sent to the ozone mixing bottle. A third room air stream is scrubbed with charcoal and Purafill and sent to the UV photometric ozone calibrator (TECO 49PS)where ozone is generated. This stream then combines with wet and dry zero-air streams in the ozone mixing bottle to give the desired relative humidity of the ozone stream. Flow through the test section is achieved in two ways. A pump pulls air through a t the end of the chamber, and air going into the mixing bottles pushes mixed air out of the bottles and into the test section. A vent to the atmosphere before the test chamber allows excess air to be vented to the room. Ozone concentrations are measured just before and after the test section with two ozone analyzers (Monitor Labs Model 8410). The analyzers determine ozone concentrations hy measuring the light flux from the chemiluminescent reaction between ozone and ethylene. Continuous measurements of temperature and relative humidity are also monitored using temperature and relative humidity probes (Omega 411). Data me recorded hothon two,multi-channeled Esterline-Angus strip chart recorders and on a real-time computer monitoring system. All flows are monitored with calibrated rotometers. The test section has a 2.1-cm i.d. and a 3C60-cm length depending on the experiment. Several materials that are commonly found on indoor surfaces were tested including latex paint, vinyl wallpaper, and paper wallpaper. For latex paint, the inside of the test section was simply painted, while the wallpaper was glued to the inside of the test section. Two different brands of latex paint were tested. For a typical experiment, a test section was placed in line and the relative humidity was adjusted to a desired level. The test section was exposed to a zero-air stream for about 2 h for conditioning and then exposed to ozone for about 24 h. Usually the incoming ozone concentration
to the test section was a nominal 70-100 ppb. Ozone removal, defined as the percentage of ozone depositing on the test section, was measured over the course of the experiment. Mass Accommodation Coefficient Calculation. Careful consideration must be given to the design of a laminar flow reactor for measuring mass accommodation coefficients. First, there needs to be a measurable deposition on the test section. One can increase deposition by increasing the test section length, decreasing the test section radius, and/or decreasing the flow rate. However, there must also be appreciable differentiation between materials with different mass accommodation coefficients. A t small lengths, for a given radius and flow rate, there is little deposition for all mass accommodation coefficients, thus no differentiation. At larger lengths, there is significant deposition for all mass accommodationcoefficients with similar differentiation problems. Therefore, one must choose an intermediate length based on the expected range of mass accommodation coefficients. McMurry and Stolzenburg (14) provide a model for measuring mass accommodation coefficients using a laminar flow tube. This model was used to design our apparatus. For a gas penetrating in a cylindrical tube with fully developed laminar flow, the appropriate steadystate convective transport equation is
where C(r,z)is the concentration of the pollutant species, r is the radial distance from the center of the tube, ro is the tube radius, z is the axial distance, and ii is the mean flow speed in the axial direction, which is defined as the volumetric flow rate divided by the cross-sectional area. The term on the left side of eq 9 represents the convective flow while the term on the right side represents diffusive flows, both radial and axial. McMurry and Stolzenburg (14) solved eq 9 subject to the following boundary conditions:
before it becomes fully developed. Bird et al. (15)provide an empirical formula for this entrance length:
Le = O.O7Or0Re
(14)
where Re is the Reynold’s number for a fluid flowing in a cylindrical tube. The Reynold’s number is defined as
Dii Re=- v
(15)
where D is the diameter of the tube and v is the kinematic viscosity of air. For tube flow, an Re below 2100 is considered laminar (15). For our apparatus, Re = 160 for a typical flow rate of 2.35 L/min, which is safely in the laminar region. This gives an entrance length of 12 cm. The entrance length was, thus, set at 18 cm to ensure fully developed flow. In its current form, eq 9 is difficult to solve. However, the axial term of eq 9 can be neglected if the dimensionless Peclet number, which is a measure of the relative flux due to convective flow compared to the flux due to axial diffusive flow, is greater than 100. The Peclet number is defined as
2iir, Pe = -
Dk?
(16)
Weschler et al. (16) estimated the ozone diffusion coefficient to be 0.15 cm2/s using the Hirschfelder approximation. Assuming a typical flow rate of 2.35 L/min and a tube radius of 1.05 cm, Pe = 160 for the apparatus in this study. Therefore, the axial diffusion term can be dropped from eq 9. For flow rates less than 1.5 L/min, this term must be included. Sideman et al. (17)provide a convenient solution to eq 9, with the axial term removed, that can easily be programmed into a computer. The solution is in the form of a “mixing cup concentration”, which is defined as the radially integrated concentration at a point ‘z’ divided by the (radially integrated) inlet concentration. In that, for our apparatus, the inlet and outlet sampling provide a radially integrated ozone concentration measurement at each location, this solution provides an ideal analysis tool. The mixing cup concentration is given by
Equation 10 simply states that the inlet concentration is C, at all r. Equation 11 states that the concentration is maximized in the radial direction at r = 0 (i.e.,the center of the tube). Equation 12 states that the net diffusional flux to the surface equals the rate of uptake, which is calculated from the kinetic theory of gases. I t assumes that the re-release of ozone from the surface can be neglected. Equation 9 requires fully developed flow at the entrance of the apparatus. Fully developed flow occurs in a cylinder when the velocity profile of the fluid becomes completely parabolic and the boundary layer fills the entire tube. Quantitatively, this means that the velocity in the tube is governed by the following formula:
where the dimensionless radial variable, p , can be written as
u(r)= ~ 1 (r/r,)’) (13) A fluid must flow for some length (“entrance length”)
An
The dimensionless length variable, 4, can be written as
t=(+2iir, E, is an eigenfunction defined as
P = rho (20) is the nth eigenvalue of the following equation which Environ. Sci. Technoi., Vol. 28, No. 3, 1094
507
0
20
40
60
80
100
Tube Length (cm) Figure 3. Deposition versustube length for three mass accommodatlon coefficients.Flow rate is 2.35 L/min and tube diameter is 2.1 cm. (D) a = 1 x 10-4; (e)a = I x 10-5; (m) a = 1 x 10-6. includes the function Y,(p)
a2yn
ay,
(21)
-+--++X,2(1-p2)Y,=O ap2 P d p
subject to the corresponding boundary conditions
-8
-6
-4
-2
0
Log of the Mass Accommodation Coefficient Figure 4. Ozone deposition versus mass accommodation coefficient. Flow rate is 2.35 L/min, tube length is 30 cm, and tube diameter Is 2.1 cm. it is not possible to differentiate between mass accommodation coefficients for ozone depositions above about 70%. This corresponds to a mass accommodation coefficient of 10"'. Therefore, for depositions above about 70 % ,it willmerely be stated that the mass accommodation coefficient is above
Results and Discussion
Sideman et al. ( 1 7 ) show how to calculate the partial derivatives in eq 19. A computer program, written in the C programming language, was used to determine the mixing cup concentration, given the mass accommodation coefficient. The mass accommodation coefficient for a particular experiment (Le., with a particular mixing cup concentration) was then determined by an iterative trial and error procedure. Figure 3 shows predicted mixing cup concentration ratios for three mass accommodation coefficients in the expected range versus the length of the cylinder. The flow rate is assumed to be 2.35 L/min. One needs to choose a tube length where there is a detectable difference in deposition between surfaces with different mass accommodation coefficients. The figure shows that there is considerable spread between the curves above lengths of 10 cm; thus, a length of 30 cm was chosen for the apparatus. The apparatus allows the tube length to be increased when needed. For example, several experiments have been conducted using 60-cm tubes. Once the boundary layer transport becomes rate limiting, higher mass accommodation coefficients will not result in higher depositions. Therefore, there can be no further differentiation of surfaces with different mass accommodation coefficients above the threshold where boundary layer transport becomes rate limiting. Figure 4 shows a plot of the log of the mass accommodation coefficient versus the ozone deposition. One can see that 508
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1994
Chamber Deposition Results. Table 1showsselected results from the chamber study. The mass accommodation coefficients ranged from lo-' for glass surfaces to greater than lo4 for one brand of latex paint. The mass accommodation coefficients listed in Table 1are actually values obtained after 20 h of ozone exposure. For each experiment, the deposition started at a higher value and then decreased to a more or less constant value at about 20 h. Figure 5 shows a plot of the mass accommodation coefficientversus time for a typical latex paint experiment. It shows that there is a considerable difference between a new surface and one that has been exposed for a period of time. However, in most cases, surfaces in indoor environments can be considered Yexposednfor modeling purposes, particularly during the high ozone periods of most interest. Thus, the 20-h values presented in Table 1 are the most relevant. The discussion of results that follows will concentrate on the exposure and modeling implications. A detailed description of the surface chemistry involved will be provided elsewhere, (see ref 18). The deposition of ozone onto these surfaces was observed to be first order with respect to ozone (i.e.,the percentage deposition or the mass accommodation coefficient was not dependent on the ozone concentration). This effect is shown in Figure 6, which is a plot of percentage ozone deposition in our chamber versus time for two experiments, with inlet concentrations of 75 and 150 ppb. Given measurement uncertainty, there is no discernible difference between these two experiments. Mueller et al. (IO) observed first-order kinetics for ozone decomposition onto
_____
Table 1. Summary of Ozone Deposition Results mass ozone relative humidity deposition accommodation coeff (%)a (%)
experiment no.
surface
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
glass glass latex paint A latex paint A latex paint A latex paint A latex paint A latex paint A latex paint A latex paint A latex paint A latex paint A latex paint A latex paint A latex paint A latex paint B latex paint B latex paint B vinyl wallpaper vinyl wallpaper vinyl wallpaper vinyl wallpaper paper wallpaper paper wallpaper paper wallpaper paper wallpaper paper wallpaper
4 X 10-I 2 x 10-7 2.7 X 10" 1.6 X lo4 3.0 X lo4 2.5 X 10-6 2.2 x 10-6 4.9 x 10-6 6.3 X lo4 4.2 X 10" 5.6 X 2.2 x 10-5 1.2 x 10" 2.7 X lk5 5.0 x 10-5
2
6-9 89-90 6-11 4 23-27 25-29 41-46 48-53 48-49 50-55 53-56 79-85 66-71 83-85 89-94 66-67 45-49 53-56 6-7 5-6 68-75 71-77 6-9 4-8 67-71 73-77 65-77
1 11 7 12 10 9 18 22 16 20 41 34 51 62 71 21 70 15 33b 21 2Ib 5 9 4 3
>lo4
5.9 x 10-6 >lo-'
3.9 x 10-6 5.0 X lo4 5.9 x 10-6 3.8 x 10-6 1.2 x 10-6 2.2 x 10-6 9 x 10-7 7 x 10-7 1.2 x 10-6
lob
0
20
10
30
Time (hours) Flgure 6. Ozone depositionversus time for two latex paint experiments with different inlet ozone concentrations.(El) [ozone],, = 75 ppb; (+) [ozone],, = 150 ppb.
*
70
The uncertainty on these measurements is about 3%. 60-cm tube.
60 -4.6 50 -4.8
. I
Y
. I
o
-5.0
40
g-a
30
0
20
-5.2 10
-5.4 0
20
40
60
ao
100
Relative Humidity (percent)
-5.6
0
10
20
30
40
Time (hr) Flgure 5. Mass accommodation coefficlent versus time for a typical latex paint experiment. Relative humidlty is 56%.
an aluminum surface. The fact that the deposition is firstorder is important because it is an assumption for using deposition velocities. There is considerable difference in deposition for latex paint brands A and B, with about 1 order of magnitude difference in the mass accommodation coefficient at high relative humidities. This "intramaterial" variability is interesting, especially for a surface such as latex paint which is so prevalent in indoor settings. It may be that the brand of latex paint used in a house is a significant factor in the indoor ozone concentration. Also, the relative humidity had a large effect on deposition. For brand A,
Flgure 7. Ozone deposition (at 20 h) versus relative humldlty for latex paint brand A.
the deposition was relatively constant for relative humidities between 0 and 50% and then increased linearly above about 50%. This effect is shown in Figure 7. For low relative humidities, the mass accommodation coefwhile for high relative ficient was on the order of 1 X humidities, the mass accommodation coefficient is about 5 X 104-5 X Also, for brand B there is a large difference between experiments in the 45 and 55 % relative humidity range. Table 2 shows the results of several experiments done on tubes that had been previously exposed. The table shows results for tubes that were exposed once or several times after their original exposures, denoted in Table 2 as the second, third, or fourth exposure. Between exposures, Envlron. Sci. Technol., Vol. 28, No. 3, 1994 509
these tubes were stored in the laboratory where they were exposed to small amounts of ozone as they would be in a residence. For latex paint brand A, there is a considerable aging effect. For the two brand A experiments with relative humidities less than 50%, the mass accommodation which coefficients appear to be in the range of 5 X is similar to glass. Experiments A3-A4 are third and fourth, high relative humidity exposures, which have mass accommodation coefficients about 1 order of magnitude lower than the corresponding mass accommodation coefficients for newer tubes at similar relative humidities. Experiment A5 has a much higher mass accommodation coefficient, perhaps because it is the only experiment with a high relative humidity during a second exposure. This indicates that the relative humidity effect observed for new tubes may also be present for old tubes, The deposition onto vinyl and paper wallpaper was generally lower than latex paint, but still significant. For vinyl wallpaper, the mass accommodation coefficients averaged about 5 X lo4, while for paper wallpaper they averaged about 1 X lo4. Also, the relative humidity had no effect on the deposition onto vinyl and paper wallpaper. Glass had virtually no discernible deposition as, given measurement uncertainties, we cannot differentiate these deposition values form zero. Thus, if there is any deposition onto glass, it is surface uptake limited. Comparison of Boundary Layer and Surface Uptake Resistances. In order to compare the surface uptake and boundary layer transport processes, we will calculate the ratio, rb/(rb + r8). For values of this "resistance ratio" near unity, the boundary layer transport process is dominant, while for values near zero, the surface uptake process is rate limiting. We will determine this resistance ratio for the surface mass accommodation coefficients measured in this study considering the air flow scenarios described earlier. In order to determine the transport-limited deposition velocity for forced laminar flow, we need to determine the thickness of the boundary layer. There are actually several types of boundary layers that influence mass transfer: (1) the momentum boundary layer, which is determined by air velocities, (2) the thermal boundary layer, and (3) the concentration boundary layer. Nazaroff et al. (19) note that for gases in indoor environments, these three boundary layers are approximately equal. We will estimate the boundary layer by air flows. This can be done by calculating the mass-transfer coefficient (20).For forced laminar convective flow past a flat plate, the average masstransfer coefficient can be determined by the following correlation (21) (24) Re,
< 500 000
where k, is the mean mass-transfer coefficient and L is the length of wall. ReL is the Reynold's number for flow past a flat plate and can be written as Re, = ULIv
(25)
where U is the free-stream air velocity. Sc is the Schmidt number and can be written as Sc = v/D,
(26)
The mean mass-transfer coefficient can be approximated 510
Environ. Sci. Technol., Vol. 28, No. 3, 1994
S u m m a r y of Aged Latex Paint Experiments
Table 2. experiment no.
surface
AI A2" A3" A4" A5
latex paint A latex paint A latex paint A latex paint A latex paint A
age of tube (months)
relative mass humidity accommodation (%) coeff
11 (2nd exposure) 4-5 9 (2nd exposure) 45-46 9 (3rd exposure) 70-78 10 (4th exposure) 72-74
10 (2nd exposure) 78-80
7 X 10-7 4 X 10-7 1.2 X 10" 1.2 X 1o-B 6.7 X 10"
Experiment numbers A2-A4 are consecutive exposures on the same tube.
Table 3. S u m m a r y of A i r Velocity Measurements ref
measurement location
air velocities (cm/s)
22
six occupied homes in East Tennessee during summer months
23
summer and winter measurements in offices in southern Finland; spaces were ventilated two rooms within a mobile home trailer
total for all six homes: median, 5.3 mean, 7.2 maximum, 57 HVAC off median, 4.4 HVAC on median, 15.0 mean, 7.2
24
small room: central region, 14 along wall, 24 large room: central region, 19 along wall, 40
as (21)
E , = D,/6
(27)
which is equal to the transport-limited deposition velocity. The mean mass-transfer coefficient was determined from eq 24 to give the transport-limited deposition velocity for forced laminar convection flow
D
db = 0.6442Re,1/2Sc1'3 (28) L where db is the transport-limited deposition velocity. In order to calculate the transport-limited deposition velocity, we need a value for the air velocity in a residence. Air velocity measurements from several studies are shown in Table 3. Most of the data are for offices and other spaces with ventilation systems. The only data specific to residences is Matthews et al. (22). The authors observed a sharp increase in air flow when the HVAC was turned on. Assuming a = 5 x lo4 (a typical value for the mass accommodation coefficientof surfaces tested in this study) and a surface length of 5 m, for forced laminar convection flow, the resistance ratio defined earlier is 0.66 for the HVAC off-air velocity and 0.50 for the HVAC on-air velocity. The corresponding deposition velocities are 0.016 cm/s for HVAC off and 0.022 cm/s for HVAC on. For a smaller surface length of 2 m, the resistance ratio is 0.55 for the HVAC off-air velocity and 0.39 for the HVAC onair velocity. The corresponding deposition velocities are 0.021 cm/s for HVAC off and 0.028 cm/s for HVAC on. This indicates that for a typical surface in this study, which includes some of the most prominent indoor surfaces, both boundary layer transport and surface uptake are important. For surfaces with lower mass accommodation coefficients (e.g.,paper wallpaper), surface uptake is more important, while for surfaces with higher mass accommodation coefficients (e.g.,latex paint brand B),boundary
layer transport is more important. The observation of Irwin and Paumier (see ref 24) that air flow along walls was about twice as high as air flow in the center region is interesting. I t may mean that boundary layers are smaller than what would be calculated from air velocity measurements in the center of rooms. To calculate the transport-limited deposition velocity for homogeneous turbulent flow, we need values for the turbulent intensity, K e , and the empirical coefficient, m. Nazaroff et al. (25) found, with m = 2, that mean values of K e for five museums were in the range of 0.4-2 s-l. Using as before, the resistance a K , of 1.2 s-1 and CY = 5 X ratio is 0.10 and the deposition velocity is 0.041 cmls. For this situation, surface effects are almost completely dominant. For the high relative humidity experiments with latex paint brand B where the mass accommodation coefficient and L was >lo4, the resistance ratio (assuming CY = = 3 m) is 0.97 for the HVAC-off condition and 0.94 for the HVAC-on condition for forced laminar flow conditions. Both of these are transport limited. This also points to an additional advantage of our apparatus design. When a deposition measurement is transport limited in the chamber, it is also transport limited in indoor environments where the air flow can be approximated as forced laminar convection flow. Thus, for the large mass accommodation coefficients that the apparatus cannot differentiate, the deposition in a residence with this type of air flow is transport limited anyway and there would be no need to determine the actual mass accommodation coefficient. However, for homogeneous turbulent flow, the resistance ratio is 0.68 for these conditions, indicating that both boundary layer transport and surface uptake are important. For these cases, it would be helpful to have an apparatus that could measure mass accommodation coefficients higher than Latex paint and wallpaper cover a large woportion of the surfaces commonly found in indoor environments. One other common surface is carpet. However, because carpet has a rough surface, the mass accommodation coefficient cannot be measured in our apparatus. Our technique requires that t,he flow conditions are laminar, and the surface roughness of carpet will create turbulence. Sutton et al. (26) measured deposition velocities in a rectangular chamber and found a deposition velocity of 0.200 cmls for nylon carpeting and 0.087 cmls for wool carpeting. The deposition velocities were based on the nominal surface area of the carpet. In other words, the area of a flat plate parallel to the carpet surface is used to calculate the deposition velocity as opposed to the true surface area available for heterogeneous chemistry. Nonetheless, for indoor air modeling effective surface areas are normally used. These and other deposition velocities from the literature are shown in Table 4. We cannot easily compare these values because the flow conditions are unknown. However, Cano-Ruiz (13) et al. provide estimates of the mass accommodation coefficients for some of these experiments. The mass accommodation coefficients they estimated were of the same order of magnitude as the ones measured in this study. The values for carpet were some of the highest that Sutton et al. (26) calculated, suggesting that carpet may have high ozone mass accommodation coefficients and may be a major contributor to ozone deposition in indoor residences. Sabersky et al. (5) measured a high deposition onto cotton muslin, which
may indicate that furniture and clothing are important contributors to ozone deposition. A new apparatus is being designed in our laboratory to measure mass accommodation coefficients on rough surfaces, such as carpet, and on surfaces that cannot be rolled into a cylinder for use in the tube flow apparatus. The apparatus will simply be a diffusion chamber similar to that used by Tang and Lee (27). Comparison to Published Data. There are two types of experimental work in the literature that can be used to compare the results of this study. First, there is the deposition velocities that were measured in laboratory chambers. Sutton et al. (26) measured a deposition velocity of 0.002 cmls onto latex paint. While we can not directly compare this number to our mass accommodation coefficients, we note that this was one of the lowest deposition velocities that they measured. Our results indicate that latex paint has a relatively high deposition. This discrepancy may point to an even more pronounced “intramaterial” variability. There are also published values of deposition velocities measured in actual indoor environments. These values are normally determined from one-compartment models as follows:
-de - R(C,- C)- K A -C
dt dV where R is the air exchange rate, C, is the outside ozone Concentration, A is the surface area, and V is the volume of the residence. Assuming steady state, the deposition velocity can be determined by
(30) There is considerable difficulty in determining the surface to volume ratio. For a 5 X 5 X 2.5 m room without any furnishings, the AIV would be 1.6 m-l. However, most indoor surfaces have furnishing with irregular shapes, and thus the area is difficult to determine. Mueller et al. (10) used a surface-to-volume ratio of 3.3 m-l for a bedroom by assuming that all the accessories in the room could be considered as rectangular parallelepipeds. The authors state, “This is definitely an estimate of the true area since the bedroom contained irregular-shaped objects, and porous surfaces such as drapes, rugs, and bedspreads” (italics ours). It may be that assuming parallelepipeds leads to a serious underestimation of the true surface area. If the AI Vis underestimated, then the apparent deposition velocity will be an overestimate. The formula for the deposition velocityderived earlier is for the true deposition velocity, taking into account all surfaces. Nazaroff et al. (19)calculated several deposition velocities from published studies. Some of these are tabulated in Table 5. As shown, the Mueller et al. (10) surface-to-volume estimate is the highest. Therefore, it is possible that the uncertainty in this parameter leads to a .considerable uncertainty in the deposition velocity. It is interesting to look at the mass transport-limited case. For a typical air flow (10 cm/s) and surface length (3 m), d b = 0.047 cmls for forced laminar convection flow. This is also the maximum possible deposition velocity (i.e., for surfaces with high mass accommodation coefficients). Environ. Sci. Technol., Vol. 28, No. 3, 1994
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Table 4. Selected Ozone Deposition Velocities from Published Sources ref
material
5
cotton muslin lamb's wool neoprene plywood nylon polyethylene linen lucite aluminum plate glass polythylene sheet material nylon carpeting wool carpeting cotton muslin latex paint
26
Kd
(cmis)"
0.015 0.004
0.015 0.005 0.0005 0.0005 0.005 0.0005 0.0005 0.0005 0.0015 0.200 0.087 0.006 0.002
There is a need for more data on ozone deposition, Chamber studies are necessary to determine depositions onto several common indoor surfaces, for example, carpet, cloth, hardwood floors, tiles, etc. This will lead to an understanding of which surfaces are the most important for ozone deposition. The effect of aging must be studied further. Experiments underway in our laboratory will study the deposition onto tubes that were painted several years ago. Also, there is a need for more ozone field work in residences. Much of the existing data on deposition velocities is for offices and laboratories. Each type of dwelling will have unique surface and air flow characteristics that are important to the question of transport and surface limitations.
Glossary
These measurementswere made after a period of exposure after which time the deposition fraction settled to a constant value.
surface area of residence free-stream concentration inlet concentration transport-limited deposition velocity diameter of tube gaseous diffusion coefficient eigenfunction pollutant flux to surface turbulent flux to the surface pollutant mass-transfer coefficient Boltzmann constant deposition velocity turbulence intensity wall length entrance length empirical coefficient for turbulent flux to surface pollutant molecular mass dimensionless Peclet number radial length parameter aerodynamic resistance boundary layer resistance boundary layer resistance for forced laminar convection flow boundary layer resistance for homogenous turbulent flow tube radius surface-uptake resistance air exchange rate dimensionless Reynolds number for tube flow dimensionless Reynolds number for flow past a flat plate dimensionless Schmidt number absolute temperature tube air velocity at radius r average tube air velocity residence air velocity mean thermal speed residence volume length ordinate radial dependent variable length ordinate
Table 5. Summary of Deposition Velocities Measured in Indoor Environments ref
indoor space
10
bedroom office home, furnace off home, furnace on office office officeilab officeilab officeilab officeilab officeilab office
5 28 29 3
a
(8-l)
2.0 x 10-3
1.1 x 10-3 8 x 10-2 1.5 x 10-3 1.1x 103 1.2 x 103 1.2 x 10-3 9.0 x 10"'
1.0 x 10-3 1.1x 10-3 9.0 x 10-2 7.0 X lo4
Ai V (m-l)
Kd (cmis)
3.3 m-1 2.8 m-l 3.3 m-1 3.3 m-1 a 2.8 m-l 2.8 m-l a 2.8 m-l 2.8 m-l a 2.8 m-l 2.8 m-* a 2.8 m-1 2.8 m-l a
0.062 0.039 0.025 0.046 0.039 0.043 0.043 0.032 0.035 0.039 0.032 0.025
Estimated by Nazaroff et al. (ref 19).
The deposition velocity for ozone in a residence has been reported to be about 0.025-0.046 cm/s (see Table 5). Thus, our maximum possible deposition velocity is just out of (a typical value this range. If, for example, a = 5 X for the surfaces measured in this study), then the calculated deposition velocity would be 0.023 cm/s for forced laminar convection flow and 0.041 cm/s for homogeneous turbulent flow. These numbers are close or within the reported range. However, as discussed above, it is difficult to make comparisons between theoretical and calculated deposition velocities because of uncertainties in the measurement of the residence surface area. There is also not enough experimental data available on ozone mass accommodation coefficients to know typical or average values.
Conclusions For a typical residential environment, both mass transport and surface processes must be considered when modeling ozone deposition. The surfaces studied in this paper may be governed by any of three conditions, depending on the nature of the near surface air flow in the residence: (1) surface uptake is rate limiting, (2) mass transport is rate limiting, or (3) both boundary layer and mass transport are important. This shows that both the air flow and surface composition of a residence will affect the ozone concentration. The surface effects are further affected by the relative humidity and the age (and probably exposure history) of the surface. 512
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Greek Symbols mass accommodation coefficient F dimensionless length factor 6 boundary layer thickness An eigenvalue a
dimensionless radial length factor air viscosity
P U
Acknowledgments
This work was supported by the Center for Indoor Air Research. S u p p o r t for R.R. was provided by the National Institute of Health Training Grant ES07155. The authors would like t o acknowledge Dr. W. W. Nazaroff for a preliminary review of a shorter version of this paper. Also, the authors would like t o t h a n k Sarah Bamford for her assistance in conducting much of the experimental work.
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Received for review August 5, 1993. Revised manuscript received November 10,1993. Accepted November 18, 1993."
Abstract published in Advance ACS Abstracts,January 1,1994.
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