Modeling studies of the concurrent growth and neutralization of sulfuric acid aerosols under conditions in the human airways

%NVIRONMENTAL

RESEARCH

35, 79-96

(1984)

Modeling Studies of the Concurrent Growth and Neutralization of Sulfuric Acid Aerosols under Conditions the Human Airways

in

ALAN T.COCKS AND W. JOHN MCELROY CEGB, Central Electricity Research Laboratories, Kelvin Atzenue. Leatherhead. Surrey KT22 7SE, United Kingdom Received January 11, 1983 A kinetic model of coupled droplet growth, gas uptake, and chemical reaction has been used to examine the possible changes to sulfuric acid aerosols as a result of exposure to respiratory ammonia under the conditions in the human airways. Results for a wide range of initial droplet sizes and concentrations spanning the extremes of likely atmospheric conditions are presented. It is predicted that gas phase reactions of SO? will not significantly affect the neutralizing capability of airways ammonia. The effects of physical and chemical parameters on aerosol neutralization and growth are discussed and in particular, predictions of neutralization in typical inhalation times for aerosols characteristic of severe persistent London fogs and modern urban conditions are compared. The analysis supports the suggestion that the London fog episodes were unique in the relationship of the acid droplets formed to the neutralizing capability of ammonia in the human airways and that simple extrapolation of mortality and morbidity data from such episodes to modern conditions is unlikely to be valid.

INTRODUCTION

A recent reappraisal of the effects of H,SO, aerosols on human respiratory function (International Electric Research Exchange, 1981) concludes, from a number of experimental human exposures, that submicron H,S04 aerosols in concentrations ranging up to 1000 kg me3 do not constitute a significant respiratory stress for short exposures. A similar conclusion is reached by Kerr et ul. (1981) from exposures of 100 kg me3 lasting 4 hr. The IERE reassessment concurs with the suggestion of Larson er al. (1977) that this is most likely due to aerosol neutralization by ammonia generated by bacterial action in the upper respiratory tract. Measured ammonia concentrations in expired air lie in the range 210-700 kg mm3 (Kupprat et al., 1976) for quiet mouth breathing and lo-50 pg mP3 for quiet nose breathing (Larson et al., 1977). The IERE study contrasts this situation with the observations of Lawther and Waller (1977) that short exposures to coarser aerosols (2-4 pm diam) were found to be intensely irritating at concentrations above 300 pg mB3 and intolerable at concentrations above 1000 p,g mei although subjects became more tolerant to longer exposures. Large droplets of sulfuric acid with pH ca. 2 were observed in the London fogs of the 1950s (Waller, 1963) and the projected levels of H,SO, in the worst episodes probably exceeded 500 pg mP3. The IERE study discusses the possibility that the respiratory stress induced by the London fogs was due primarily to the inhalation of droplets of H$O,, particularly in the case of those suffering from advanced respiratory and 79 0013-9351184

$3.00

80

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AND

MC

ELROY

cardiovascular disorders, and theoretical modeling of the neutralization of fixedvolume droplets in the human airways using simple (Larson et al., 1978) and more sophisticated (Cocks and McElroy, unpublished calculations cited in IERE, 1981) models suggests that this may be due to the inability of oral and nasal ammonia to neutralize large H,SO, droplets at high loadings. The concentration of acid in an inhaled droplet may also be reduced upon inhalation by hydration of the aerosol and recent calculations, using fundamental heat and mass transfer concepts (Cocks and Fernando, 1982) have indicated that for concentrated (>1 M) droplets, a dilution factor > 10 may be achieved in typical inhalation times. However, these independent growth and neutralization models suggest that these processes occur in similar time scales and, therefore, that neutralization might be significantly affected by droplet growth. The present work reports the application of a combined gas uptake/droplet growth/chemical reaction model, in which concentration and temperature effects on thermodynamic parameters are adequately treated, to the neutralization and growth of sulfuric acid aerosols under conditions present in the human airways, and was undertaken to determine more accurately the possible acidity changes of such particles upon inhalation. In addition, calculations of the possible effects of inhaled SO, on the availability of ammonia for sulfuric acid neutralization are presented. CALCULATIONS Droplet model. In the model the uptake of ammonia is described by a modified version of Frosslings equations (Frossling, 1938) shown in Eq. (1). The symbols are defined in the Appendix. dcs2& dt

?(

g

-CH s

YNS)*

(1)

Gas phase depletion by solution uptake is allowed for in the model. Knudsen effects are not important for ammonia uptake by droplets in the size range considered in this paper. Droplet growth is calculated by solving the fundamental heat and mass transfer equations as described previously (Cocks and Fernando, 1982). Knudsen effects are more important for water accretion as the condensation coefficient is low (Fukuta and Walter, 1970; Cocks and Fernando, 1982). Activity coefficients for ionic species in solution for Z < 0.5 are calculated from extended Debye-Htickel theory (Debye and Htickel, 1923). For Z < 0.5, mean activity coefficients from literature data are input as simple polynominal functions of Z and T. The activity coefficient of undissociated species in solution (the only neutral species of importance in the present study is ammonia), is calculated by consideration of primary and secondary solvation effects (Bockris and Reddy, 1970). Water activity in the multicomponent solutions of the aerosol droplets is calculated from binary osmotic coefficients by the method of Reilly, et al. (1971) ignoring solute-solute interaction terms. Activities are corrected for the effect of surface tension using the Kelvin equation (Nair and Vohra, 1975).

NEUTRALIZATION

EQUILIBRIA

OF

SULFURIC

ACID

AEROSOLS

TABLE 1 IN THE NHJAQUEOUS

H,SO,

SYSTEM

81

NH, (gas) = NH, (solution) NH, (solution) + H+ = NH,+ Hz0 = H+ + OHH,SO, = H’ + HSO,HSO,= H’ + SO;-

Equilibrium constants in terms of activity, obtained from literature data are input as simple polynomial functions of T. Henry’s law coefficients (again only important for ammonia in the present study) are calculated from solubility data at low concentrations. Rate constants for chemical reactions in solution are input directly and where necessary, reverse rate constants are calculated from the equilibrium constants. The computer program derived from the model integrates the coupled differential equations for gas uptake, droplet growth, and solution reaction kinetics using a Gear algorithm (Gear, 1971). At each integration step, the droplet temperature is calculated assuming steady state conditions for water vapor diffusion and the equilibrium constants are evaluated. Activities of solution species and water are also recalculated at each step to account for the effects of changes in temperature and solution composition. Input parameters. Equilibria involved in the NH,/aqueous sulfuric acid system are shown in Table 1. Simple polynomial expressions for the equilibrium constants in terms of activities as a function of temperature were derived from the data of Sillen (1964). The Henry’s law constant for ammonia was calculated at various temperatures using total solubility data at low partial pressures (Pigford and Colburn, 1950), and the temperature dependence was expressed as a simple polynomial fit. For ionic species in solution at Z < 0.5, the extended Debye-Htickel theory (Debye and Hiickel, 1923) was used in conjunction with individual ionic hydration diameters obtained from the compilation of Kielland (1937) to obtain activity coefficients. The hydration diameter for hydrogen sulfate was assumed to be identical to that for sulfate. For Z > 0.5, mean activity coefficient relationships (Robinson and Stokes, 1959) were expressed as simple polynomial functions of I. Values for the NH,OH system were assumed to be the same as those for KOH. The effective activity of undissociated ammonia in solution was calculated (Bockris and Reddy, 1970) from literature values of partial molar volume (Treybal, 1968), dipole moment and refractive index (CRC Handbook of Chemistry and Physics, 1980), and molecular polarizability (Landholt-Biirnstein, 1952). Solvation number and primary hydration radius were estimated from reported activity coefficient values under specific conditions (Harned and Owen, 1958). The osmotic coefficient and hence the water activity of a multicomponent aqueous solution was calculated from the individual binary osmotic coefficients of the salts comprising the mixture using the expression derived by Reilly et al. (1971), and for Z > 0.5 the solution was assumed to be the appropriate composite

82

COCKS

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ELROY

mixture of H$O, and NH4HS04. (NH&SO, was not considered, as HSO,- is the dominant S(V1) ion for Z > 0.5. The binary osmotic coefficients for H,SO, were obtained from water activity data over H,SO, solutions at 298” K (Robinson and Stokes, 1959), and the activity was expressed as a polynomial function of S(V1) concentration. The activity was corrected for temperature using Eq. (2) (Cocks and Fernando, 1982), a&t’,)

= aJ298”K)exp

- (F

(ri2z)).

(2)

Values of h(X) were taken from the extensive compilation by Giauque et al. (1959) and expressed as a polynomial function of S(VI)%. The binary osmotic coefficient for NH,HSO, was derived from water activity data over NH,HSO, solutions determined at 298°K by Tang and Munkelwitz (1977). The water activity was expressed as a polynomial in S(W) concentration, and no temperature correction was applied as h(X) is small and no reliable measurements are available. For Z < 0.5, extrapolation of experimental values of binary osmotic coefficients, which are normally measured at high concentration, are unreliable and for low concentrations they were calculated using the extended Debye-Htickel theory and Bjerrum’s equation which relates the solute activity coefficient to the solute osmotic coefficient. Values for the hydration diameters were calculated by fitting the calculations for solutions containing H+ , NH4+, HS04-, and SOd2- to known osmotic coefficients at 0.1 M (Robinson and Stokes, 1959). Except for SOd2-, these are identical to the values given by Kielland (1937). Density data for H,SO,, NH,HSO,, and (NH,),S04 solutions have been reviewed recently (Stelson and Seinfeld, 1981) and for the concentration range considered in the present note, the densities of solutions of the ammonium salts can be equated. Density data for H2S0, (Liley and Gambill, 1974) and (NH,),SO, (International Critical Tables, 1933a) were expressed as polynomial functions of molarity and temperature (310 + 10°K). The water activity of a droplet is modified by surface tension (Kelvin effect) and polynomial expressions for the surface tension in terms of molarity and temperature were derived from literature compilations for H2S04 (Sabinina and Terpugow, 1935) and (NH,),S04 (International Critical Tables, 1933a) solutions. The surface tension for (NHJHSO, was assumed identical to that of (NH,),SO, (Cocks and Fernando, 1982). For application of the Kelvin correction the partial molar volume was equated to that of pure water (Cocks and Fernando, 1982). Calculation of droplet growth by the application of fundamental heat and mass transfer considerations to water accretion (Cocks and Fernando, 1982) requires values for the latent heat of vaporization of water, the thermal conductivity of air, and the Knudsen correction terms f, and fa for heat and mass transfer, respectively. Data for the latent heat of vaporization of water for sulfuric acid solutions (International Critical Tables, 1933b) were expressed as a function of temperature. The latent heat of vaporization of water for both (NH,)HSO, and (NH,),SO, solutions was taken to be that of pure water as the enthalpy of mixing of water

NEUTRALIZATION

OF

SULFURIC

ACID

AEROSOLS

83

is negligible for solutions of these compounds (Cocks and Fernando, 1982). An expression for the temperature dependence of the thermal conductivity of air was derived from tabulated data (CRC Handbook of Tables for Applied Engineering Sciences, 1973). The calculation of the Knudsen correction terms requires values for the accommodation and condensation coefficients together with the diffusion coefficient and mean free path of water in air. The accommodation coefficient for water was assumed to be unity and the condensation coefficient was taken to be 0.04 (Fukuta and Walter, 1970; Cocks and Fernando, 1982). The diffusion coefficient for water in air at 273°K was taken from literature data and a T7’4 dependence assumed (American Institute of Physics Handbook, 1972). The mean free path was calculated neglecting water-water collisions (Moelwyn-Hughes, 1961) using a value of 0.3133 nm for the mean molecular diameter (Welty et al., 1976). The relative humidity of the respiratory tract was assumed to be 99.5% at 310°K (Ferron. 1977). The diffusion coefficient for ammonia in air and at 273°K was taken as I .92 x 1O-5 m2 set-’ and a T7’4 dependence was assumed (Pigford and Colburn, 1950). Rate constants at 298°K for the bimolecular chemical reactions depicted in Table 1 were obtained from the measurements of Eigen et al. (1964). The value for the reaction associated with first ionization of sulfuric acid was assumed to be equal to that for the second. These rate constants were assumed to be temperature and composition independent and the associated first-order rate constants for the reverse reactions were calculated from the equilibrium constants. Errors introduced by ascribing all temperature and ionic strength effects to the forward rate constants are negligible in the case of the very fast reactions considered in this paper. Conditions simulated. Neutralization and growth of sulfuric acid droplets was investigated at body temperature (310.16”K) for times up to 10 set, well in excess of the residence time of inhaled air during quiet breathing. Sulfuric acid loadings of 1000 and 100 kg me3 were used and are representative of urban conditions ranging from those found in the worst London fog episodes (Lawther, 1963) to projected peak U.S. burdens (Kerr et al., 1981). Neutralization by ammonia loadings of 500 p.g rnm3, corresponding to mean levels measured during mouth breathing (Larson et al., 1977; Kupprat et al., 1976; Sulfur Oxides, 1978), and 50 to the highest levels measured during nose breathing pg mA3 corresponding (Larson et al., 1977) was modeled. Initial droplet compositions defined by relative humidities of 99.97, 99.5, 80, and 60% were considered. These humidities correspond to severe London fog conditions [calculated from the observation of an equilibrium pH of 2 (Wallet+, 1963)], respiratory tract conditions, and two representative values of ambient conditions, respectively. Droplets with initial diameters of 5 and 1 pm were modeled in all cases, and in addition, droplets with initial diameters of 15 km were investigated at 99.97% rh, and droplets with initial diameters of 0.5 and 0.1 pm were investigated at 80 and 60% rh. Depletion of ammonia by SO,. The reaction of gaseous SO, and NH, in humid air at 296°K to form solid reaction products has been studied experimentally by

84

COCKSANDMCELROY

Hartley and Matteson (1975) for a range of relative humidities. However, the experimental system employed by these workers did not unambiguously exclude contributions from heterogeneous and solution phase processes, particularly on the filters used to collect the particulate product. Thus, the kinetic results probably represent an upper limit for the homogeneous reaction. The second-order rate constant was in the range 1 to 6 x lo5 liter mole1 set-l and tended towards the higher value as an upper limit at high relative humidities. Allowing for a realistic activation energy a second-order rate constant of 1 x lo6 liter mol- ’ set- 1 was taken as a reasonable value under conditions found in the human bronchial tract and lungs (relative humidity 99.5%, temperature 310°K). Calculations, assuming simple homogeneous second-order behavior and allowing for gas phase depletion were performed to examine the possible removal of ammonia in the concentration range 500 to 50 pg me3 by SO, in the concentration range 5000- 100 ug rnm3. The SO, range corresponds to the highest levels recorded in severe London fog episodes and modern urban levels. RESULTS

Results are presented in Tables 2-5 showing the extent of neutralization and the relative change in volume of sulfuric acid droplets after exposure to ammonia for 0.1, 0.3, 1.O, 3.0, and 10.0 set for the conditions modeled. Reduction of actual acidity is expressed as [H+]/[H+], for the various reaction times and neutralization is expressed as [NH,+]&2 * ([HSO,-] + [S04*-I)) since neutralization is complete when the ammonia ion concentration is twice that of the sulfur (VI) ionic concentration. The contribution of droplet growth toward the change in acidity is expressed as the volume ratio VJV. For an initial sulfuric acid concentration of 0.139 M (99.5% rh-Table 4) the droplet is already at equilibrium with lung conditions and no growth occurs. When sufficient ammonia is available to allow complete neutralization, droplet radius is the dominant factor governing the neutralization rate. The sulfuric acid loading exerts relatively little influence, whereas the gas phase ammonia concentration has a significant effect in determining this rate. Under conditions of no growth, the acidity of the droplets is entirely determined by the concentration of absorbed ammonia. On increasing the sulfuric acid concentration to 3.29 and 5.08 M (80% rhTable 3 and 60% rh-Table 2, respectively) the rate of neutralization decreases for similar sulfuric acid and ammonia loadings and droplet diameters. Substantial droplet growth occurs at these H,SO, concentrations which results in significant reductions in droplet acidity due to growth even when the rate of neutralization by ammonia is slow or complete neutralization cannot be achieved. Tables 2 and 3 reveal the strong dependence of the neutralization rate on gas phase ammonia concentration particularly for droplets of 5 pm diameter. The influence of H,SO, loading is only apparent after 1 set and droplet acidity is controlled by growth rather than neutralization under these conditions. For sulfuric acid droplets with an initial concentration 7.0 x 10e3 M (pH 2.0, rh 99.973%-Table 5) neutralization is very rapid and absorption of ammonia is essentially complete within 1 set, except for the largest drops (15 pm). Since the

NEUTRALIZATION

OF

SULFURIC

ACID

AEROSOLS

8.5

H,SO, concentration is much lower than the equilibrium value of 0.139 M at 99.5% rh, surface evaporation of water occurs. For a l-pm droplet, the final equilibrium diameter of 0.27 pm is attained corresponding to a XVI) concentration of 0.364 M indicating a significant Kelvin effect. This ‘Lconcentration” effect is less marked for a 5-pm droplet and negligible for larger diameters. Droplet acidity is initially lowered by neutralization but increases at longer times due to evaporation. Where complete neutralization is achieved this increase is relatively small. However, where ammonia levels are low compared with initial H,SO, loadings the acidity may rise to a level many times its initial value (e.g., H,SO,, 1000 kg rnw3; NH,. 50 p.g mP3; diameter 1 pm). In all the calculations performed, the rate of growth is virtually unaffected by the gas phase ammonia concentration confirming that the properties of H,SO,, NH,HSO,, and (NH&SO, in solution are very similar in their influence on droplet growth (Cocks and Fernando, 1982). Figures I and 2 illustrate the predicted gas phase removal of ammonia by sulfur dioxide at loadings of 100 and 5000 p,g m -3, respectively. At the low loading only a small fraction (ca. 2%) is removed after 10 set whereas up to 50% may be removed at the high SO, loading in this time. However, even at high SO, loadings, less than 10% of the ammonia is predicted to be removed after 1 sec. DISCUSSION

Over the wide range of SO, concentrations considered in this work, gas phase reaction calculations indicate that it is unlikely that SO, would significantly affect the neutralizing capacity of ammonia in the human airways. The droplet model predicts that under conditions of low growth and ammonia depletion, the effects of variations in the chemical and physical parameters up to 80% neutralization and those expected from Frossling’s equation in which the concentration term is approximately constant. For a fixed sulfuric acid concentration, the extent of neutralization in a given time is inversely proportional to rz and is proportional to NH, loading. For fixed volume and NH, loading, the extent of neutralization is inversely proportional to initial sulfuric acid concentration and for a fixed NH, loading and mass of sulfuric acid per droplet, it is proportional to r. Under conditions of negligible ammonia depletion, the linear dependence of neutralization on ammonia loading is also found to hold for a growing droplet because the rates of growth of H,SO,, NH,HSO,, and (NH&SO, are virtually identical (Cocks and Fernando, 1982). Droplet growth enhances neutralization by increasing the surface area for uptake. For submicron droplets, the Kelvin effect reduces the rate and extent of growth and the equilibrium acidity following inhalation, even after complete neutralization, increases with decreasing droplet size. However, this effect is insufficient to overcome the favorable surface/volume ratio of small droplets in the size range considered in the present work, and for a given acid loading, a finely dispersed aerosol would be more readily neutralized than a smaller number of larger droplets. From a simple consideration of uptake, for acid droplets of a given initial radius,

50

500

NH, 6.~2 m-‘)

0.1

0.5

1

5

0.1

0.5

1

5

Diameter (w-4

H V N H V N H V N H

H V N H V N H V N H V N

*

0.1

TABLE AND GROWTH

0.074 0.073 5.42 0.064

1.43

0.400 0.398 0.04 0.116 0.115

0.400 0.398 0.42 0.090 0.115 14.3 0.015 0.074 54.2 6.2 x 1O-5 0.078 99.5

NEUTRALIZATION

1.43

0.241 0.241

0.3

OF H,SO,

0.247 0.241 0.14 0.071 0.070 4.46 0.044 0.047 11.6 0.064

0.028 0.070 44.6 4.7 x 10-S 0.054 99.6 6.2 x 1O-5 0.077 99.5

2

0.032 0.036 14.2 0.064

11.0

0.139 0.133 0.56 0.040 0.042

0.030 0.033 14.2 0.031 0.034 14.2 0.064

1.90

0.087 0.080

2.0 x 10-s 0.032 99.9 4.4 x 10-5 0.049 99.6 6.2 x 1O-5 0.077 99.5

2.9 x 1O-s 0.043 99.9 4.4 x 10-5 0.049 99.6 6.2 x 1O-5 0.077 99.5

3.0 0.063 0.081 19.0

1.0

Time (se4

0.126 0.134 5.43

DROPLETSO

0.049 0.047 6.16 0.028 0.031 14.3 0.031 0.034 14.2 0.064

10-f 0.029 99.9 4.4 x 10-5 0.049 99.6 6.2 x 1O-5 0.077 99.5 1.8 x

61.5

0.011 0.048

10

Is M L 2

z

E

IIa

* H = [H+]/[H’],. ’ Initial relative

100

0.1

0.5

1

5

0.1

0.5

1

5

H V N H V N H V N H V N

H V N H V N H V N H V N

0.075 14.3

M.

0.400 0.398 0.04 0.118 0.115 1.50 0.073 0.073 6.64 6.8 x lo-’ 0.078 94.4

0.400 0.398 0.42 0.088 0.115 15.0 7.8 x lO-3 0.07’4 66.5 2.0 x 10-5 0.077 99.8

V = I’,#,, N = % neutralization. humidity = 60%. Initial [H$O,] = 5.08-5.17

50

500

V N

0.247 0.241 0.14 0.071 0.070 5.25 0.035 0.047 21.9 5.6 x IO-“ 0.078 95.3

0.241 0.241 1.44 0.022 0.070 52.5 1.5 x 10-5 0.054 99.9 2.0 x 10-5 0.077 99.8

0.075 14.3

0.139 0.133 0.57 0.034 0.043 19.6 7.1 x 10-3 0.035 66.8 5.6 x 10m4 0.078 95.3

0.126 0.133 5.73 9.4 x 10-h 0.043 99.9 1.4 x 10-s 0.049 99.9 2.0 x 10-5 0.077 99.8

0.075 14.3

0.087 0.080 2.02 0.010 0.033 56.1 1.9 x 10-4 0.032 98.8 5.6 x lO-4 0.078 95.3

0.075 14.3 0.061 0.081 20.2 6.4 x l0-h 0.032 100 1.4 x 10-j 0.049 99.9 2.0 x 10-5 0.077 99.8 0.048 0.047 7.85 1.8 x 10-4 0.029 98.7 1.9 x 1om4 0.032 98.8 5.6 x lO-4 0.078 95.3

0.075 14.3 5.5 x 10-s 0.048 78.3 5.9 x 10-h 0.029 100 1.4 x 10-S 0.049 99.9 2.0 x 10-s 0.077 99.8

E cn

8

is

Pi E;

s E

z 5;

%

z =: s

F z

3

1000

NH,

50

500

OLg me31

0.1

0.5

1

5

0.1

0.5

1

5

(eLmI

Diameter

TABLE

0.100

0.321 0.314 0.20 0.097 0.096 5.67 0.063 0.069 12.8 0.100

0.511 0.505 0.06 0.159 0.156 1.91 0.103 0.104 6.85

H V N H V N H V N H

0.310 0.314 1.99 0.026 0.097 56.7 7.1 x 10-5 0.081 99.6 9.7 x 10-x 0.125 99.5

0.506 0.505 0.59 0.109 0.156 19.1 0.010 0.106 68.5 9.7 x 10-S 0.125 99.5

H V N H V N H V N H V N

OF H,SO,

0.1

3

0.1

AND GROWTH

*

NEUTRALIZATION

0.160 0.177 7.68

1.0

Time (set)

0.184 0.178 0.77 0.056 0.060 12.3 0.050 0.55 14.2 0.100

99.5

0.125

6.8 x 1O-5 0.077 99.6 9.7 x 10-5

99.9

0.060

4.1 x 10-5

DROPLETS~

0.100

0.116 0.108 2.53 0.045 0.049 14.4 0.049 0.054 14.2

6.8 x lo-’ 0.077 99.6 9.7 x 10-S 0.125 99.5

100

25.3 3.0 x 10-5 0.047

0.109

0.073

3.0

0.065 0.065 7.64 0.044 0.048 14.4 0.049 0.054 14.2 O.lW

99.5

0.125

8.4 x 10-X 0.065 76.3 2.8 x 10-5 0.045 100 6.8 x 10-S 0.077 99.6 9.7 x 10-S

10

E 2

E

m

a(1 s! in

50

500

* H = [H+]J[H+],, V = ’ Initial relative humidity

100

H V N H V N H V N H V N

H V N H V N H V N H V N

0.125 14.3

M

0.511 0.505 0.059 0.159 0.159 2.04 0.099 0.104 9.03 8.7 x lO-4 0.125 99.5

0.506 0.505 0.59 0.105 0.156 20.4 2.0 x 10-X 0.106 90.2 3.2 x lO-5 0.125 99.8

V,,W,. N = % neutralization. = 80%, initial [H$O,] = 3.29-3.46

0.1

0.5

1

5

0.1

0.5

1

5

V N

0.321 0.314 0.200 0.095 0.096 7.05 0.044 0.069 29.0 8.6 x 10-d 0.125 99.5

0.310 0.314 2.00 0.016 0.097 70.4 2.3 x lO-5 0.081 99.9 3.2 x lo-” 0.125 99.8

0.125 14.3

0.183 0.177 0.788 0.042 0.060 25.7 5.4 x 10-j 0.054 81.3 8.6 x 10-A 0.054 81.3

0.160 0.177 7.88 1.3 x 10-5 0.060 100 2.2 x 10-5 0.077 99.9 3.2 x lO-5 0.125 99.8

0.125 14.3

0.115 0.108 2.78 9.2 x lO-3 0.048 69.0 3.1 x 10-4 0.052 98.8 8.6 x 10-J 0.125 99.5

0.069 0.109 27.5 9.5 x 10-6 0.047 100 2.2 x 10-S 0.077 99.9 3.2 x lO-5 0.125 99.8

0.125 14.3

0.062 0.065 10.6 2.8 x lO-4 0.045 98.7 3.1 x 10-4 0.052 98.8 8.6 x 1om4 0.125 99.5

x lo-5 0.065 100 9.0 x 10-6 0.045 100 2.2 x 1om5 0.077 99.9 3.2 x lO-5 0.125 99.8

1.41

0.125 14.3

90

COCKS

AND

MC

TABLE NEUTRALIZATION

ELROY 4

AND GROWTH

OF H,SO,

DROPLETS” Time bed

H,SO, (~3 m-9 1000

NH, (kg m-9 500

Diameter (wn) 5

1

50

5

*

0.1

0.3

1

3

H V N H V N

0.822 1.0 11.7 5.2 x 10-a 1.0 loo

0.535 1.0 32.3

0.087 1.0 81.9

5.2 x 10-h 1.0 100

H V

0.950 1.0 3.23 0.784 1.0 14.4

0.874 1.0 8.20

1

H V N

0.982 1.0 1.17 0.809 1.0 12.6

5

H V N H V N

0.815 1.0 12.1 1.7 x 10-d 1.0 100

0.486 1.0 36.1

1.7 x 10-d 1.0 100

H V N H V N H V N H V N

0.995 1.0 0.304 0.981 1.0 1.21 0.048 1.0 3.35 0.598 1.0 27.4

0.989 1.0 0.911 0.944 1.0 3.61 0.850

0.953 1.0 3.02 0.822 1.0 11.7 0.562 1.0 30.1 5.0 x 10-3 1.0 100

N

100

500

1

50

10

5

3

1

*H = [H+lJ[H+l,, ’ Relative humidity

!EO 0:180 1.0 67.4

10

0.800 1.0 13.2

0.784 1.0 14.4

0.864 1.0 8.88 0.535 1.0 32.3 0.144 1.0 72.5

0.598 1.0 27.4 0.089 1.0 81.6 5.0 x 10-j 1.0 98.8

V = V,jV,, N = % neutralization. = 99.5%, H,SO, concentration = 0.139 M.

those with the higher concentration and hence, higher mass of H2SO4, will neutralize at a slower rate, the ratios of the extent of neutralization N, and N2 at initial concentration C, and C, being given by Eq. (3) for neutralization <80% Nl -z N2

% ( I-c2 Cl

Similarly, for a given mass of sulfuric acid, droplets with smaller initial radii will neutralize at a slower rate. Hence, equilibrated atmospheric droplets of the same initial size or weight of H2SO4 will neutralize in the airways at rates correlated to atmospheric relative humidity. For equilibrium concentrations corresponding to relative humidities appreciably less than that in the lungs, the lowering of [H+] due to dilution is far greater than that due to neutralization at short exposure times. This effect is more marked for the larger initial droplet sizes and dilution is the major cause of [H+] reduction at all times in cases where complete neutralization is not possible (e.g., for H2SO4

NEUTRALIZATION

OF

SULFURIC

ACID

AEROSOLS

91

loadings of 1000 p,g m-3 and NH, loadings of 50 pg mP3 which can neutralize only 15% of the acid). Shrinkage of droplets initially at higher relative humidities than that in the lungs may be particularly important under these conditions as it may lead to a substantial increase in [H+]. Even at complete neutralization, shrinkage can substantially lower the reduction of [H+], particularly for low NH, loadings. For example, with H,SO, at 1000 p,g mP3 and NH, at 500 p,g me3, complete neutralization is obtained within 0.1 set, but [H+]/[H+l, increases from 5.6 x 10M4 at 0.1 set to 2 x lo-* at 1 sec. For H,SO, = 100 kg mm3 and NH, = 50 p,g rnM3, the [H+]/[H+], values are a factor of 10 higher. The model, as expected from the underlying fundamental factors, predicts that for a given loading and droplet size or mass of acid per droplet, the body is less able to neutralize aerosols at equilibrium at a lower atmospheric relative humidity than at a high humidity in the time for inhalation [ca. 0.5 set (Stuart, 1973)]. For example, 80% neutralization is achieved by oral NH, levels for HZS04 aerosols ~15 pm at a loading of 1000 Fg mP3 and 99.97% rh but only for those
500

1000

50

NH, (w mm31

H2SO4 bg m-7

1

5

15

1

5

I.5

6.4

Diameter

H V N H V N H

H V N H V N H V N

*

AND

5.6

1O-4

0.977 1.01 2.45 0.902 1.04 11.7 1.53

1.99 100

x

100

0.1 0.736 1.01 24.5 2.8 x 1O-4 1.04

NEUTRALIZATION

GROWTH

TABLE OF H*SO,

8.9

0.945 1.02 6.15 0.936 1.13 14.3 14.6

100

x 10-j 22.8

100

0.3 0.357 1.02 61.6 3.0 x to-4 1.13

5

2.0

4.2

2.8

DROPLETS”

1 10-4

10-d

10-2

0.908 1.06 12.1 1.22 1.54 14.4 28.2

100

52.0

100 x

1.53

x

100

1.06

x

(set)

Time

0.974 1.18 14.4 3.66 5.46 14.4

100

5.21

x

1O-3

3 x 1O-4 1.18 100 1.6

3.2

9.2

5.2

1.45 1.87 14.4 14.2 24.9 14.4

100

x 1O-3 23.5

100

10

x 1o-4 1.85

F

K

%

* H = [H+I/[H+],. U Relative humidity

100

V = VdV,. = 99.973%,

50

500

H V N H V N H V N

H V N H V N H V N

N = % neutralization. H$O, concentration

I

5

I5

1

5

15

V N

= 7.0

x

IO-’

0.975 1.01 2.66 0.784 1.04 22.1 5.6 x 1O-3 1.99 99.6

0.713 1.01 26.6 9.0 x 10-S 1.04 100 1.8 x 1O-4 1.99 loo

2.00 14.4

M.

0.926 1.02 7.82 0.448 1.13 56.1 8.5 x lo-? 22.8 100

0.197 1.02 78.2 9.9 x 10-S 1.13 loo 2.9 x lo-’ 22.8 100

25.7 14.4 x 1O-5 1.06

0.769 1.06 24.3 4.2 x lo-” 1.54 100 1.9 x 10-I 52.0 100

too 1.4 x 10-4 1.53 100 6.6 x 10-j 51.9 100

9.2

51.9 14.4

0.416 1.18 60.4 1.6 x lo-” 5.22 100

1.0 x 10-4 1.18 100 5.3 x 10-d 5.21 100

x 10-j I .86 100 8.9 x lo-? 23.5

5.1

1.7 x 10-4 I .85 100 3.0 x 10-X 23.5

ki %

E

s

94

COCKS AND MC ELROY

“r 6

0

2

4

6

8

IO

TIME, s

FIG.

1. Gas-phase removal of NH, by an initial SO, loading of 100 pg rne3.

Major differences between persistent London fog conditions and modern urban conditions are the larger droplet sizes and higher acid loadings in the former case. Although initial acid concentrations in droplets are probably lower in the persistent fog situation, high levels of ammonia are needed to significantly reduce the inhaled sulfuric acid burden and the mass of sulfuric acid per droplet is likely to be higher as environmental factors such as high SO, levels and long reaction times conspire to encourage accumulation. Although the ability of the body to neutralize inhaled acid will increase with smaller burdens and smaller mass of acid per droplet, the relationship will not be a linear function passing through the origin because the nasal ammonia levels are predicted to be sufficient to effectively neutralize acidity levels in modern urban conditions. The present analysis supports the conclusion of the IERE study (1981) that simple extrapolation of mortality and morbidity data from London smog episodes to modern conditions is likely, therefore, to be invalid. 150

0

2

4

6

a

IO

TIME. s

FIG. 2.

Gas-phase removal of NH, by an initial SO, loading of 5000 pg mV3,

NEUTRALIZATION

OF SULFURIC

APPENDIX:

ACID AEROSOLS

95

NOMENCLATURE

List of Symbols

= Water activity; C, = concentration in gas phase; C, = concentration in solution; D, = gas phase diffusion coefficient; H = Henry’s law coefficient; h(X) = enthalpy of mixing of water in solution of composition X: I = ionic strength; A4, = molecular weight of water; R = gas constant; r = droplet radius; Tg = gas temperature; T, = droplet temperature; yNS = activity coefficient of neutral undissociated species in solution.

a,

ACKNOWLEDGMENTS This work was carried out at the Central Electricity Research Laboratories permission of the Central Electricity Generating Board.

and is published by

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