The Uptake of Gases by Liquid Droplets - ACS Symposium Series

Chapter 32

The

Uptake of Gases by Liquid Droplets Sulfur Dioxide 1,3

1

1,4

James A. Gardner , Lyn R. Watson , Yusuf G. Adewuyi , Jane M . Van Doren , Paul Davidovits , Douglas R. Worsnop , Mark S. Zahniser , and Charles E. Kolb 1

1

Downloaded by CORNELL UNIV on October 11, 2016 | http://pubs.acs.org Publication Date: April 27, 1989 | doi: 10.1021/bk-1989-0393.ch032

2

2

2

1

Department of Chemistry, Boston College, Chestnut Hill, MA 02167 Aerodyne Research, Inc., 45 Manning Road, Billerica, MA 01821 2

Heterogeneous reactions involving water droplets in clouds and fogs are important mechanisms for the chemical transformation of atmospheric trace gases. The principal factors affecting the uptake of trace gases by liquid droplets are the mass accommodation coefficient of the trace gas, the gas phase diffusion of the species to the droplet surface and Henry's Law saturation of the liquid. The saturation process in turn involves liquid phase diffusion and chemical reactions within the liquid droplet. The individual processes are discussed quantitatively and are illustrated by the results of experiments which measure the uptake of SO2 by water droplets. Heterogeneous reactions involving water droplets in clouds and fogs are increasingly recognized as major mechanisms for the chemical transformation of atmospheric trace gases (1-5). In such heterogeneous reactions, the rate of trace gas uptake is a pivotal factor in understanding the transformation process. An example of an atmospherically important heterogeneous process is the transformation of S 0 gas into sulfurous acid and then sulfuric acid as represented in Equations l a and lb. 2

In equilibrium the concentrations of the sulfur (IV) compounds are determined by the Henry's Law Constant Η«ο2 respectively. The curves in Figure 2 are plots of Equation 7 with three assumed values for 7: 0.08,0.11 and 0.14. The best fit to tne experimental values of 7d is provided by 7 = 0.11. Since gas uptake could be further limited by liquid phase phenomena as discussed in the following section, 7502 0.11 is a lower limit to the true mass accommodation coefficient for S 0 on water. 2

2

2

2

2

m

2

a n (

m

m

2


=

2

Henry's Law Equilibrium. The equilibrium relationship between molecules in the gas phase at a pressure p and the molecules dissolved in the liquid is given by Heniy's Law. n! = p . H = n RTH

(8)

g

Here nj and n are the liquid and gas phase concentrations is moles per liter, and H is the Henry's Law coefficient which for S 0 in water at 25°C is 1.3 M atm-i (11). As equilibrium is approached, the net uptake of gas decreases and with it the observed mass accommodation coefficient 7 b*. Once equilibrium is reached, the rate of absorption of the gas is balanced by the rate of desorption from the liquid and the net uptake of gas is zero. Under dynamic conditions such as found in our experiment, the surface may saturate long before the trace species penetrates into the whole droplet. At that point, the rate of gas uptake is controlled by the rate of liquid phase diffusion of the dissolved molecule away from the surface. The surface density and characteristic time r for the surface to reach saturation can be derived as follows. The net flux J of trace species entering the liquid is g

2

0

p

7

n

J = "g ^ = l*c 4 4

(9)

Here 6 is the desorption coefficient which can be related to 7 and the equilibrium liquid phase density of the trace species ni° as ng7 = ni°*. Using the relationship ni°/n = RTH, 6 can be expressed as 6 = 7 / R T H and J can be written as g

c7

J=

4RTH [ n ^ - n j

(10)

In the absence of a chemical reaction in the liquid phase, the density ni can be expressed approximately as n, = J L AX

Saltzman and Cooper; Biogenic Sulfur in the Environment ACS Symposium Series; American Chemical Society: Washington, DC, 1989.

(11)

512

BIOGENIC SULFUR IN THE ENVIRONMENT

Here AX is the average penetration depth into the droplet by the trace species during time t. This depth is approximately AX

= (D^/2

(12)

= 1.8 x where D| is the diffusion coefficient of the trace species in the liquid (D| = IO" cm s- for SO2 in water at 25°C) (2). In this derivation it is assumed[that th AX is smaller than the radius of the droplet. Using Equations 10,11 and 12, we obtain an expression for n\ as 5

2

1

n, = Downloaded by CORNELL UNIV on October 11, 2016 | http://pubs.acs.org Publication Date: April 27, 1989 | doi: 10.1021/bk-1989-0393.ch032

t

4

»£ ,4RTH(D /t)V

(13) 2

1

C

7

We define the characteristic time, r , for the equilibrium between gas and liquid phases as p

2

r = (4RTH/c ) D! p

(14)

7

which allows us to rewrite Equation 13 as n, =

5£ 1 + (r /t)V2

(15)

p

This expression is developed in a more rigorous treatment by Schwartz and Freiberg (H). From our measurements of SO? uptake, we know that 7 is at least equal to our experimental value of 7 = 0.11 shown in Figure 2. This corresponds to Tp = 3 x 10* s which is considerably shorter than the transit time of the droplet through the reaction zone. The characteristic time r represents the minimum time for saturation of the surface if there were no chemical removal of the species within the droplet. In fact, as is indicated in Equation 1, sulfur (IV) is dissolved in the liquid also in the form of HSO3- and SO3- . The capacity of the liquid to hold S(I V) is therefore increased, and saturation is delayed. The equilibrium concentration of the total amount of S(IV) dissolved in the liquid can be expressed according to Schwartz (2) in terms of an effective Henry's Law coefficient H* as 8

p

2

n

n

H

S(IV)j/ SO^g) = * S ( I V )

R T

1 6

( )

For the S 0 equilibrium H*s(iv) is given by (2) 2

H* (IV) - H S

s o

Al + 2

+

(17)

+

[H ]

[H

+]2 2

8

The equilibrium constants K and K are 1.39 x 10* M and 6.5 x 10* M, respectively (fi). With these values, H* is 23 at a pH of 3.0 and is 4200 at a p H of 5.2. Taking into account all the S(IV) species and assuming sufficiently rapid equilibration among them, the liquid phase S(IV) concentration, n (iy)i, is x

2

S


32. GARDNER ETAL. n

The Uptake ofGasesby LiquidDroplets

n

S(IV)l = S 0 ( g )

RTH

2

H

H

n

*S(IV) = ( * S ( I V ) / S 0 ) S0 (l) 2

2

513 1 8

( )

In this case, Equation 10 becomes

J

=

[ n 0 s

I V

,

n s

^4 rR^T H *< ) > " (

I V

S(IV

)

, 1

( 1 9 )

and Equation 13 becomes n n

S(TV)l

=

1

l


°S(IV)l

^4RTH' flV)(D /t) / S

2

(20)

l

Using this equation and substituting r from Equation 14, we obtain p

n

1

s(IV 1

)i = " V O > l + (H« /H o )(rp/t)l/2 s ( I V )

S

(21)

2

The observed mass accommodation coefficient 7 b is obtained from G

s

"g^obs = J 4

(22)

Rearranging terms and using Equations 19, 21 and 22, we obtain a time dependent expression for (H* fobsCO

88

fobs(°)

S ( I V

) / H ^ ) (r /t)V2 S

p

(23) l + CH'sdVHsoJCVOV

2

If the equilibrium between the S(IV) species were reached instantaneously, 7 bs(P) would be simply the gas diffusion limited mass accommodation coefficient 7 d given by Equation 7. Equation 21 may be rewritten by substituting Equation 14 for r 0

p

7obs(t)

=

7obs

(0)/[l +

£ 7 o b s ( 0 )

(t/DOl/2] 4RTH* (iv)

(24)

S

In Figure 3 we plot experimental values of f c c as a function of the droplet transit time t for two values of H*s(jvy 23 and 4200. These values were obtained by setting thepH of the droplets surface at 3.0 and 5.2, respectively. This p H includes the effect of the acidification due to the absorbed SO2 gas. The contact time was varied by the inlet position of the trace gas and by the velocity of the droplets. These data were taken under conditions of water vapor pressure on the order of 20 torr, or as in Figure 2 , 1 / D -0.20. The solid lines are plots of Equation 23, where 7 K (0) is assumed to be 0.059. A more exact treatment, valid for droplets of arbitraiy diameter, has been presented by Danckwerts (12). In the region of applicability, our simplified derivation is in quantitative agreement with that work. 7 0

g

p

s


514

BIOGENIC SULFUR IN THE ENVIRONMENT


T

.001

I

1

1

0

5

10*

—

1

15

1

20

Time (msec)

Figure 3. Experimental values and fits calculated by Equation (23) (assuming 7 = 0.059) for 7 b as a function of the droplet transit time for two values of H*s(iv) Lower curve - H* (i ) = 23; upper curve - H*SQV) 4200. These values were obtained by setting the pH of the droplets surface at 3.0 and 5.2, respectively. 0

s

:

=

S

V


32.

GARDNER ET AL.

515

The Uptake of Gases by Liquid Droplets

Rate of Liquid Phase Reactions. The uptake of gas by a droplet can be affected by the rate of liquid phase chemistry within the droplet. A n example is provided by the uptake of SO2. In the previous section we showed that the uptake of S 0 by the liquid is enhanced due to the fact that S(IV) is dissolved in the liquid not only as S0 (aq) but also in the form of HSO3" ^ SO3 ". However, in the derivation of Equation 23 it was assumed that equilibrium between the S(IV) species is reached instantaneously. This is not the case. The conversion of S0 (aq) to HSO3- occurs at a finite rate kj and the corresponding reaction time is 7 ™ = (kx)- ( H ) . If r is longer than r„ then a significant fraction of S0 (aq) can evaporate before reacting to form HSO3-. In that case, Equation 23 as it stands is not applicable. The finite reaction rate can be taken into account by modifying 7(0) in Equation 23. Early in the absorption process, where the reverse reaction HSO3" — > S0 (aq) can be neglected, the change in the number density of S0 (aq) at distance from the surface, x, is given by 2

a n

2

2

2

1

r x n


2

2

2

anso (1)00

Dl * nso (l)(x)

"so © t o

2

2

=

ax

d t

(25) r

2

rxn

Both Tnuj and r are short compared to the millisecond scale transit time of droplets through the reaction zone. Therefore, steady state conditions can be applied to Equation 25 and the solution is p

1/2

n o (l)to = n o (i)(x=0) exp[-x/(trxnDl) ] S

2

S

(26)

2

The flux of trace species at the interface on the liquid side of x = 0 is an«o (Y\

2

J = D,

U

=(D /T 1

rxn

)V2n

ax

ri)(0)

S0

(27)

2

This flux is set equal to the flux as calculated earlier in Equation 10 which yields at the interface the steady state ratio n

°so (i)

n

so (l)(0)

2

- 1+

(28)

o

The approximations used in the derivation make this expression valid for times t > 7 but still early in the absorption process. In this early period, 7 b s « y(t = P

0

0).

As before, using the relationship n c 7(0) t/4 = Jt we obtain, consistent with Reference (2) and (2), g

fobs ~

1

1 + (WTp) /

2

We can compute from this expression a theoretical upper limit for 7 bc. The rate for the conversion S0 (aq) to HSC>3' was measured by Eigen et al. (12) as 3.6 x 10 s which gives a characteristic reaction time = 2.8 x 10* s. 0

2

6

_1


7

516

BIOGENIC SULFUR IN THE ENVIRONMENT 10

With the maximum possible value of 7 = 1, we obtain 7 - = 3 x 10- s yielding the upper limit for 7 t, as 0.03. From Equation 7 and Figure 2 we have 7 = 0. 11. correcting 7 ^ for gas phase diffusion limitations. This value implies that the rate for the conversion of SO> to HSO3 is at least twelve times higher than the one measured by Eigen. However, their results are not necessarily contradicted by this observation. The conversion reaction studied by Eigen occurs in the bulk of the liquid whereas the process observed in our experiment occurs near the interface. It appears that the conversion rate is faster near the surface than in the bulk of the liquid. The conversion rate mav be so rapid at the interface that the species enters the liquid as HSO3- rather than SCWaq). A more complete presentation and analysis of our data on the uptake and conversion of SO2 by water droplets has been prepared and submitted for publication (15). Downloaded by CORNELL UNIV on October 11, 2016 | http://pubs.acs.org Publication Date: April 27, 1989 | doi: 10.1021/bk-1989-0393.ch032

0

s

Implications for Atmospheric Sulfur Oxidation The large S 0 mass accommodation coefficient (7 = 0.11) indicates that interfacial mass transport will not limit the rate of SOj uptake into clean aqueous cloud and fog droplets. Either gas phase diffusion, Henry's law solubility, or aqueous reactivity will control the overall rate of aqueous S(IV) chemistry. This conclusion is demonstrated by modeling studies of SOo oxidation in clouds by Chamedies (2) showing that the conversion time of S(IV) to S(IV) is independent of the mass accommodation coefficient for 1 £ 7 > 10"* Schwartz (16) has also shown that, with 7 as large as our measured value, the interfacial mass transport is unlikely to inhibit the oxidation of SO2 by O* or H7O2 in cloud droplets for gas concentrations typical of non-urban industrialized regions. 2

Summary Heterogeneous reactions involving water droplets in clouds and fogs are important mechanisms for the chemical transformation of atmospheric trace gases. The principal factors affecting the uptake of trace gases by liquid droplets are the mass accommodation coefficient of the trace gas, the gas phase diffusion of the species to the droplet surface and Henry's Law saturation of the liquid. The saturation process in turn involves liquid phase diffusion and chemical reactions within the liquid droplet. The individual processes are discussed quantitatively and are illustrated by the results of experiments which measured the uptake 01SO2 by water droplets.

Acknowledgments This work has been supported by funds from the Coordinating Research Council (contract number CAPA-21-80(2-84)) and the Electric Power Research Institute (contract number RP 2023-8) to Aerodyne Research, Inc. and by grants from the National Science Foundation (ATM-8400748) and the Environmental Protection Agency (CR 812296-01-0) to Boston College. Literature Cited 1. 2. 3. 4.

Graedel, T. E.; Goldberg, K. I. J. Geophys. Res., 1983, 88, 10865-82. Heikes, B. G.; Thompson, A . M . J. Geophys. Res., 198388,10883-95. Chameides, W. L. J. Geophys. Res. 1984,89,4739-55. Schwartz, S. E. J. Geophys. Res. 1984,89,11589-98. Saltzman and Cooper; Biogenic Sulfur in the Environment ACS Symposium Series; American Chemical Society: Washington, DC, 1989.


32. GARDNER ETAL.

The Uptake ofGases by Liquid Droplets

517

5. Jacob, D. J. J. Geophys. Res. 1986, 91, 9807-26. 6. Sherwood, T. K.; Pigford, R. L.; White, C. R. Mass Transfer; McGraw-Hill, 1975. 7. Gardner, J. A.; Watson, L. R.; Adewuyi, Y . G.; Davidovits, P.; Zahniser, M . S.; Worsnop, D. R.; Kolb, C. E. J. Geophys. Res. 1987, 92, 10887-95. 8. Fuchs, N. A.; Sutugin, A . G. High Dispersed Aerosols; Hidy, G. M.; Brock, J. R., Eds.; Pergamon: Oxford, 1971; pp 1-60. 9. Schwartz, S. E. Chemistry of Multiphase Atmospheric Systems: Jaeschke, W., Ed.; N A T O ASI Series: Sprinter-Verlag, Berlin, 1986; Vol. G6, pp 415-71. 10. Kimpton, D. D.; Wall, F. T. J. Phys. Chem. 1952, 56, 715-7. 11. Schwartz, S. E.; Freiberg, J. E. Atmos. Environ. 1981, 15, 1129-44. 12. Goldberg, R. N.; Parker, V. B. J. Res. N.B.S. 1985, 90, 341-58. 13. Danckwerts, P. V. Trans Faraday Soc. 1951, 47, 1014-23. 14. Eigen, M.; Kustin, K.; Maass, G. Z. Phys. Chem. N.F. 1961, 30, 130-6. 15. Worsnop, D. R.; Zahniser, M . S.; Kolb, C. E.; Gardner, J. A.; Watson, L . R.; Van Doren, J. M.; Jayne, J. T.; Davidovits, P. J. Phys. Chem., in press. 16. Schwartz, S. E. Atmos. Environ., submitted. RECEIVED December 19, 1988


The Uptake of Gases by Liquid Droplets - ACS Symposium Series

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