Amwp6e?ic hoi- , Vol. 21. No. 8. pp. 1X.5-1772 1987. olxn-69atja7 53.00+0.00

Printed in Great Britain. !K> 19X7 Perymon Journals Ltd.

MEASUREMENT OF THE ENTRAPMENT OF SULFUR DIOXIDE BY RIME ICE

DENNIS LAMB* and ROCHELLE BLUMENSTEIN

Desert Research Institute, Reno. NV 89506, U.S.A.

( First receioed 1 August 1986 ond in final form 12 January 1987)

Abstract-Experiments have heen conducted to measure the fraction of SO2 dissolved in supercooled cloud drops which remains with the ice phase following rime-ice formation. Special consideration is given lo an experimental design which simulates the atmospheric riming process realistically and to measurement uncertainties. The results of this study show the fraction/s,tv, of SO1 entrapped by the riming process to be

proportional to the drop supercooling A7, suggesting that the mechanisms of entrapment may be linked to the growth of ice during the adiabatic portion of drop freezing. A regression analysis shows

/ s,,v)= a.AT+ b,

where a = (5.8 + OS) x IO-’ K-’ and b = (1.2 f 0.6) x 10mz. No evidence was found for sulfate formation subsequent to entrapment in the rime ice.

Key word index: Cloud chemistry, ice chemistry, sulfur dioxide, riming, laboratory measurements.

I. INTRODUCIION

Rime ice is formed in the atmosphere whenever supercooled water drops impact onto a surface and freeze. This process occurs commonly in cold clouds in which ice particles have grown large enough to sedi- ment significantly relative to the small cloud drops. This accretional sweepout of supercooled cloud water, which leads to the formation of graupel and hail particles, is a primary growth mechanism of precipi- tation in mid-latitude storms. An analogous situation arises in the case of stationary surfaces past which the wind may be blowing a supercooled cloud. Such riming events are common in mountainous terrain during winter storms and can lead to significant deposition of water mass to a watershed even during non- precipitating periods.

While rime-ice formation can be very important for removing water mass from the atmosphere, the trace chemicals initially contained in the super-cooled cloud water are not necessarily removed proporlionalely. This arises in part from the fact that most substances are very much less soluble in ice than they are in liquid water. Such segregation during the phase transition is particularly important in the case of dissolved gases, since the reversibility of the absorption process permits the expulsion of the gaseous components from the freezing drops. Thus, in the limit, as might occur during slow t’rcczing or wet hail growth. the rime ice could conceivably form relatively free of any of the original gaseous species.

l Present affiliation: Department of Meteorology. The Pennsylvania Stale University. Ilniversity F’ark, PA 16802. U.S.A.

However, during most rime-forming events the impacting cloud drops freeze rapidly. particularly during the initial, adiabatic stage of freezing (Pruppacher and Klett. 1978. p. 549). It is during this stage, while the drop is warming up to 0°C. that the supercooled drop fills with a mesh of dendritic ice crystals, effectively offering opportunities for trapping many of the dissolved gas molecules before they diffuse to the drop surface and desorb back into the atmos- phere. Thus, the process of gaseous desorption during rime-ice formation is fundamentally non-equilibrium in nature, the fraction of the gas initially present that is held up being the result of compctitivc rate processes.

Past studies ofgaseous entrapment in freezing water drops have been sparse. Early laboratory work focused primarily on the segregation of non-gaseous solutes in bulk solutions which had possible application to cloud electrification (e.g. Workman and Reynolds. 1950). More recently, Iribarne et al. (1983) measured the amount of SO, held up when drops with diameters between about 0.5 and 1.0 mm were allowed to freeze on a thermally massive substrate. While these workers found that about 25% of the SO, is trapped by the frozen drops, neither the geometry nor the heat transfer in their configuration were representative of

riming conditions in the atmosphere. In this paper we describe laboratory experiments

which were designed to simulate rime-ice formation under conditions similar to those lbund in the atmos- phere. As with the experiments of lribarne et al.. we used SO, as the trace gas of interest. but extended the range of temperature in order lo gain insight into the entrapment process. Knowledge 01’ the entrapped fraction as a function of tempcraturc will find im-

mcdialc application in cloud chemistry ~noclcls which

I765

1766 DENNIS LAMB and ROCHELLE BLUMENSTEIN

are concerned with the wet deposition of sulfur compounds.

2. EXPERIMENTAL METHODS

The approach taken here to simulate rime-ice formation in the atmosphere was to generate a cloud of supercooled cloud drops in the presence ol’ known conozntrations of SO, in a thermostated cold box and to impact these drops onto thin rods made to sweep through the cloud. Past studies have used this rotating-rod technique for collecting rime in order to understand secondary ice production (Hallett and Mossop, 1974: Foster and Hallett, 1982) and to investigate cloud electrification (Jayaratne et al., 1983). This experimental approach allows the cloud drops, here in equilibrium with the ambient SO,, to impact the simulated riming surface and freeze in a reasonably realistic manner.

The configuration used in these experiments is shown in Fig. 1. The primary flow of air containing the cloud drops and SO, was confined to the vicinity of the rotating rods by aluminum ducting (approximately I m long and 1Ocm in diameter) and a cylindrical plastic can (- 30 cm diameter) lined with aluminum foil. This arrangement was situated inside the sheet-metal liner of an environmental chamber (Bemco LA-N) which provided the primary temperature regulation (f 0.2’C) of the system by convoztive air flow around the liner. The temperature of the air in the duct within about 10 cm of its exit was measured continuously by means of a Type K thermocouple. Just past the exit of the duct was the surface for collecting the rime deposits. a set of six vertically oriented rods (12cm long by 1.5 mm diameter) which were made to rotate about a vertical rotation axis at 3.1 Hz yielding a relative impact speed of 2.0 + 0.3 m s- ‘.

Cloud drops were generated by ultrasonic nebulization of de-ionized water using a Monaghan 670 system. The nebulizer was modified to eliminate contact or the water with any neoprene surfaces, found in test runs to be a source of sulfates and nitrates. Contamination of the water was further reduced by providing an external reservoir of clean water which was allowed to flush through the nebulizer at a rate approximately 100 times that of cloud production. The system was consid- ered adequately clean when test analyses showed that the

concentration ofextraneoussulfate in the nebulizer water was less than about 5 ̂ /. of the concentration ofS(IV) expected in the cloud water after absorption of SO,.

The air used for cloud formation and dilution of the SO, was derived from commercial compressed air cylinders (Liquid Air, breathing quality). After two stages of pressure regulation, the air stream was split in two and the flows independently regulated and measured with rotometers. Each flow was set at lOOmI s-‘. The source of the SO, was a compressed-gas cylinder of approximately 200 ppm SO, in nitrogen (Scott-Marrin). The concentration 01‘ SO, in the isothermal chamber was controlled by adjusting the setting ol’ a calibrated metering valve while maintaining the pressure drop across the valve constant at 20 cm-H,O. This gas flow was cooled to about 5°C below the riming temperature prior to reunion with the room-temperature cloudy air by having it pass through an extra section of aluminum tubing inside the environmental chamber. The two flows were brought together at the top of the aluminum ducting to permit the liquid drops to contact the gaseous SO, and begin the absorption process. The mean residence time ofthe SO,-cloud mixture in the duct was 40 s.

A separate. heated tube allowed the cloudy air in the confinement vessel to be sampled before and after rime-ice formation on the rotating rods. The drops evaporated in this tube, allowing the dew point temperature (General Eastern 1200 APS) to be used as a measure of the liquid water content of the cloud. In this way the liquid water content was found to vary (with nebulizer fluid level and experimental temperature) between about 2 and 4 g m-‘. At the same time, the partial pressure of SO, was measured by a sulfur gas analyzer (Meloy).

The equilibrium concentration of S(IV) in the drops was calculated in the manner of fribarne et al. (1983) from the measured partial pressure of SO,, Psol, and the temperature T since

[H’] = [HSO;]+Z[SO:-1. (1)

For all conditions applicable to these experiments it can be shown that

Z[SO:-] $ [HSO;] = Hs;;;oa, (2)

Fig. 1. Schematic diagram of the experimental arrangement used to measure the entrapment ol’ SO1 during rime-ice formation.

M~surcment of the entmpment of sulfur dioxide by rime ice 1767

where H, is the Henry’s Law constant and K I is the first diiociation constant. Therefore, also taking fbe small amount of physically dissolved SO, into atiunt, we obtain

[S(IV)] + [HSO;] +{SOl.HtO]

= (H,K, PsQ,)“~ e H,Pso,. (3)

The temperature dependences of the equilibrium constants were taken from Maahs 119821 to be

1% K, +4.740 Thus, under ideal conditions, the equilibrium concen-

tration of S(1V) in liquid water is simply determined by the local temperature and the amount of gaseous SO, present, not on the sixes of the drops. It is at this point, however, that kinetic factors, which do depend on drop size, need to be considered to test the assumption of equilibrium. The size distribution of the cloud drops emanating from our nebulizer was not measured in this study, so we make use of measurc- ments made by DeMott et al. (1983) using a similar device. Correspondence between these two systems may not be exact, especially since the actual distribution can be expected to shift from run to run in response to variations in the liquid water flux coming from the ncbulizer and the temperature in the environment chamber. Nevertheless, it can be expected that the radii of the drops in the experiments will range between a few and about 10 pm, i.e. well within the ‘cloud-drop regime.’ Consideration of the Stokes number under our experimental conditions leads us to expect the collection efficiency of the riming rods to vary between a few hundredths and several tenths, favoring the largest drops in the distribution for collection.

Following the approaches taken by others (e.g. Schwartz and Freiberg. 1981; Seinfeld. 1986, Chapt. 6), we consider the characteristic times associated with each of the several serial processes occurring during the absorption of SO, by water drops of various radii a. The various steps and their respective characteristic times include gaseous diffusion

(6)

inlcrfLiaI transfer

(7)

aqueous-phase dissociation of SO,

Q= {kn+k,,t~H'la[HSOIJ))-', (8) and aqueous-phase dilTusion

a2 %a a----.

n2LJw (9)

Here, u is the drop radius, Ds and Dw are the diffusion coefficients in air and in the aqneous phase, respectively, R is the gas constant, H’ is the overall Henry’s Law ~lu~ity coeflkient (H’ = qH in Schwartzand F&erg, 1981f a is the gas sticking coe%cient, Pis the svera8e speed of gas mokcules, while kr, and k,, are the forward and reverse rate constants for dissociation of physically dissolved SO,. Using appropriate values for the various constants and applying the analysis to the largest drop sizes expected in our experiments, we calculate Ids = 5 x IO and T,,,

-7s.7 =4X10-*SIT~=3X10-‘4 = 5 x IO-’ s. The o&all transfer of SO, between the

gas and aqueous phases is controlled by the slowest step, which is here the aqueous-phase diffusion. Overall equilib- rium of solute between the two phases can therefore be expected to be achieved on time scales under 10ms for all drops in the population.

While it is clear thaat local solute equilibrium occurred on time scales which are short compared with the 40 s avaitable d&g transport in’ the duct, it is not immediately obvious that the temperature of the cloudy air was adequately equilibrated with the duct wall temperature. Errors here could potentially all&t the calculation of the SW’) solubility via Equations (4) and (S), so an analysis of heat transfer in a duct of constant wall temperature was performed according to the treatment of Birder al. (1960, Chapt. 13). Usinga linear speed v = 2.6 cm s - I of air in the duct, a Reynolds number of 180 and a Prandtl number of 0.7, we estimated the Nusselt number to be 5, from which an overall heat transfer coefficient of 3~ 10-5calcm-2 s-’ K-’ was calculated. An energy balance equation was then used to establish that a character- istic distance L, G 60 cm, or a characteristic time T,, = L&J & 20 s, was needed for the mean temperature ofair in the duct to ‘relax’ to the wall temperature. Thus, the air temperature at the end of the duct (100 cm long) was still a couple of degrees away from the temperature externally imposed by the en- vironmental chamber, a point which is consistent with measurements.

Fortunately, we do not need to rely rigorously on this heat transfer analysis or assumptions about equilibration with the duct walls since the air temperature was measured within about IOcm of the riming site. However, because the air temperature was still changing downstream of the ther- mocouple, the same heat transfer analysis implies that the actual riming temperature was about 0S”C lower than that measured. This difference was not taken into account in the reporting of the results, but affects the calculated S(IV) concentration by only about I %. Thus, we conclude that under the experimental conditions employed in this study it is appropriate to use the equilibrium relationships Equations (3~(5) to calculate the S(IV)concentration provided that the values of Tand PSO~ used are tjased on measurements close to the riming site.

An overall test ofthe equilibrium relationship was made in a special run. For this purpose a micro-pH probe (Microelectrodes MI-710) was mounted in a specially con- structed aspirating housing positioned in the confinement vessel near the exit of the ducting. As drops and SO2 were transported through the system under conditions similar to those employed in actual experiments, except that the tem- perature was about 25”C, the cloud was sucked through the pH probe. The relatively massive drops impinged onto the body of ihc pH electrode, coalc.sccd and drained onto ~hc sensitive tip. The indicated pli viituc was compared with that predicted from the measured value of Pso and found 10 agree within about 0.2 pH units at pH 4. This degree of agreement was considered adequate verification of the experimental arrangement given the technical difficulties of providing a sufficient supply of water to the pH probe in this configuration.

The procedure during an experimental run began by rinsing the surfaces of the rotating rod on which the rime would be collected with de-ionized water. The inner and outer chambers were then closed and the main airflow turned on, The SO1 flow was then turned on and the flows adjusted to yield the desired co~ntmtion of SO, in the coofinemen( V~SSCI. The nebulixer and its associated air flow were also turned on and the system allowed to attain steady-state. &X.X the indicated dew point temperature and SO2 concentration were constant, the sample tube was removed, and rotation of the riming rods was begun and allowed to continue for approximately 30 min.

During the course of an experimental run, a uniform- looking deposit of rime formed, which extended about 1 cm from the rod surfacc. After the rod rotation was stopped, but with the rest of the system still operating, the rime ice was Carefully scraped off the rod surface into a pre-chilled graduated vial. Typically. several tenths of a ml of sample were acquired from each run. A known volume of 0.001 M formaldehyde solution was added to the vial and the ice

1768 DENNIS LAMB and ROCHELLE BLUMENSTEIN

allowed to melt into the solution. formaldehyde serving IO stabilize the dissolved S(W) species (Kok er ai., 1983). The final volume of the solution was noted and the ice-water volume determined by differencing. The concentrations of S(IV) and WI) in this solution were determined bv ion chromatography (Dionex Model 14) using freshly prebared standard solutions containing comparable-concentrations of formaldehvde. The concentrations of SflV) and SIVI) in the , . I

rime-ice samples were calculated from the measured concen- trations and the appropriate dilution factors.

3. RESULTS AND DlSCUSSlON

a. Primuryfindinys

The conditions under which each experimental run was conducted and the results obtained are tabulated in Table 1. In all, 14 separate runs were made at five nominally distinct temperatures between about -2 and - 20°C. Except for one run (number 8) all experiments wereconducted at a single nominal partial pressure of SO, (0.7 x 10G6 atm). The equilibrium concentration of S(IV) in the supercoolet¶ drops was calculated for each run from the respective values of Pso, and temperature using Equations (3)-(5).

Various other parameters associated with the con- duct of these experiments are presented in the center grouping of columns in Table 1. The volume of rime collected was determined from the total volume of liquid after the rime ice had been melted into the known volume of diluent (which contained the for- maldehyde). The dilution factor, which was used to multiply the measured concentrations of S(IV) and S(VI) to obtain the corresponding values in the rime samples, was calculated as the ratio of the total solution volume to the rime volume. The maximum time that any entrapped S(IV) was in contact with the ice phase, i.e. from initial rime formation to melting in the formaldehyde solution, is given in the last column of this grouping.

The primary results of this investigation are shown in thelast threecolumnsofTable 1. Theconcentrations of S(lV) in the rime were found to vary greatly in relation to the temperature at which the rime formed. Generally, the colder the temperature the greater was the concentration of S(IV) that was entrapped. By

contrast, the amount of S(VI) found varied sporadi- cally with temperature and was unreproducible. A

background of about 0.8 FM SO:-, found in blank runs, has been accounted for in the data of Table I. but this may represent a lower limit given the technical dilhculties of controlling impurities from the nebulizer. It is not likely that any significant oxidation of S(IV) took place in the liquid drops prior to impact. but neither do these data provide any direct evidence for the oxidation (at least by air) ofS(IV) entrapped in the ice.

Although a trend with temperature is apparent in the S(IV) data, the equilibrium concentration in the super- cooled drops also varies in the same qualitative sense. Nevertheless, as indicated by the last column in Table 1. the fraction,

(10)

ofS(IV)originally present in the dropsalso increases as the temperature of rime formation decreases. This result is shown graphically in Fig. 2. Despite con- siderable scatter in the data, a distinct trend emerges. II the deviation of the air temperature T,,, from the thermodynamic freezing point of ice (To = 273.2 K) may be taken as the drop supercooling. i.e.

AT = T, - T,,,, (11)

then the linear regression shown in Fig. 1 takes the form

J&v, = a. AT+ b. (12)

When only the data pertaining to a nominal SO,

Table I. Mean values of experimental parameters and results

Equil. Rime Diluent Contact Rime Rime Run Temp. pso, [S(W)] vol. vol. Dil. time WV)1 Pw)l fsrrv, no. (‘C) (tOm6atm) (PM) (ml) (m)) factor (min) (PM) (PM) (%)

I - 10.1 0.70 341 0.4 0.80 3.0 40 27 18 7.9 2 - 15.6 0.77 441 0.7 0.80 2.1 40 42 I.7 9.5 3 - 20.3 0.76 528 0.7 0.80 2.1 38 74 3.8 14 4 - 10.3 0.77 361 0.6 0.80 2.3 38 I8 I.2 5.0 5 - IO.5 0.75 358 0.5 0.80 2.6 39 18 I2 5.0 6 - 10.2 0.73 350 0.4 0.80 3.0 39 13 6.0 7 - 10.9 0.7 I 354 0.4 0.80 3.0 41

:1 7.6 5.9

8 - 10.4 0.095 126 0.5 0.80 2.6 40 6.0 2.4 4.8 9 - 5.2 0.69 283 0.6 0.80 2.3 41 7.2 2.2* 2.5

10 -5.1 0.67 278 0.4 0.80 3.0 43 16 5.9 5.8 II - 15.2 0.69 411 0.9 0.80 1.9 40 49 5.1 12 I2 - .I.7 0.71 254 0.2 1.00 6.0 40 9.6 7.5 3.8 I3 - 19.3 0.68 479 0.9 1.00 2.1 38 68 1.9 14 14 - 2.0 0.69 253 0.5 1.00 3.0 37 IO 7.8 4.0

l This value is uncertain by about + 20% due to technical difficulties midway through the ion chromato- graphic analysis of this sample.

Measurement of the entrapment of sulfur dioxide by rime ice 1169

20 ’ I I I

O-’

Fig. 2. Plot of the fraction of S(W) entrapped in the rime ice as a function of the air temperature. The solid circles pertain to experimentsconducted with a partial pressure of

SQ2. ho2 = 0.7 x 10m6 atm; the single open circle near - 10°C corresponds to a lower value, Pso, = 0.1

x IO-‘atm.

partial pressure of 0.7 x lo-’ atm are considered, a correlation coefficient of0.79 results, the slope a = (5.8 &0.5)x 10e3 K-‘, and the intercept b = (1.2 AO.6) x lo-‘. The departure of the intercept from zero is probably not significant. Although no conclusion should be based solely on one point (Run 8) the entrapped fraction does not appear to vary strongly with SO, partial pressure.

These experimental findings show that the fraction of dissolved SO, which remains with the drop after freezing is proportional to the drop supercooling. This trend suggests that the primary mechanism of gaseous entrapment may be linked to the growth of ice during the initial, adiabatic phase, during which the latent heat of fusion, L, = 80 cal g- ‘, is expended in warming the drop up to 0°C. The fraction A of the drop mass m,, which freezes rapidly during this phase of growth is also known to be proportional to the supercooling

where mi is the mass of ice and C, = 1 cal g-’ K-’ is the heat capacity of the liquid (Pruppacher and Klett, 1978, p. 549). The magnitude of this proportionality constant, C,/L, + 1.25 x lo-’ K-l, is about twice that for S(IV) entrapment.

A time-scaling argument may also be used to demonstrate an expectation of gaseous entrapment during the adiabatic freezing stage. An estimate of the time ?r, required for freezing a drop of radius (I and supercooling AT may be obtained from

where G(AT) is the linear growth rates of the ice dendrites (Pruppacher and Klett, 1978. p. 550). At least up to a supercooling of lO’C, a variety of growth rate data (Pruppacher and Klett. p. 559) may be reasonably

well approximated by a parabolic growth law:

G(AT) = kr, . AT’, (15)

where k,., z 0.05 cm s-’ K-‘. Thus, for drops on the order of 10 pm radius. the characteristic times for freezing the fraction_&. of the drop mass will vary from on the order of 1 to 0.1 ms as the supercooling changes from 5 to 15°C. From the mass transfer analysis provided earlier, we can expect the characteristic time for gaseous expulsion, z,r, to bc dominated by aqueous phase dill‘usion. given by Equation (9). Thus. the ratio of the expulsion and freezing time constants, which provides a measure of the potential for gaseous entrapment, is

h = a.kr,.AT’ (16) \ ,

5 + 9, This shows that gaseous entrapment is favored by large droplets and large supercoolings. Evaluation of Equation (16) with the stipulation that T_,, = T,., en- ables calculation of a ‘threshold’ supercooling AT, for each drop size; for radii between 5 and IOpm, AT, varies from about 2.7 to 1.9”C. Thus, for all greater supercoolings Texp > T,., and gaseous entrapment is feasible during the initial adiabatic stage of drop freezing.

During the second stage of freezing, once the drop temperature has reached 0°C further growth of ice is possible only to the extent that the latent heat of fusion

can be transferred to the environment. As shown by Hobbs (1974, p. 619) the preferred path for this heat transfer is through the ice substrate, so an estimate 01 the heat flux is given by

I! AT

= nk,a’.-_, Ax

07)

where kj A 4 x lo-‘cal cm-‘s-l K-’ is the thermal conductivity of ice, and AT is actually the difference in temperature between the growing ice (-0°C) and the ambient temperature, but will be very close to the original drop supercooling. The characteristic distance Ax for heat transfer can be approximated by the drop radius (Brownscombe and Hallett, 1967). so to first approximation

0 = nkiaAT. (18)

Balancing this heat flux away from the drop with that released by latent heat, we estimate the characteristic time for freezing during the second stage to be given by

(1%

Again, for gaseous expulsion limited by aqueous diffusion, we may contrast this freezing time with the expulsion time:

h _ %AT 51.2 - 4z=pL,. Dq ’ (20)

Now, in contrast to Equation (16) we see no depen- dence on drop size and a weaker dependence on AT.

I770 DENNIS LAME and ROCHELLE BLUMENSTE~N

This ratio is on the order of unity at an ambient temperature of -SC, so we accept the fact that the rates of gaseous expulsion are comparable with the freezing rates of the drops during the second stage. The major portion of the dissolved SO, should nevertheless experience little difficulty in escaping from the individ- ual drops as long as freezing is from the ‘inside out,’ which does happen when the latent heat is dissipated preferentially through the riming substrate.

Overah, both the data and the analysis suggest that the conditions most favorable for gaseous entrapment occur at relatively targe supercoolings (low ambient temperatures) during the adiabatic freezing stage. However, it should also be realized that the mechanism of entrapment during this early stage must provide some physical barrier to prevent their subsequent escape when greater time is available for diffusion. Whether this barrier arises through the formation of isolated pockets of brine or air bubbles or through molecular incorporation into the ice lattice cannot be determined without further investigation.

Laboratory m~surements of specific phenomena of nature are only as good as the quality of the measure- ment process itself. Uncertainties of both random and systematic nature are necessarily a part of all measure- ments. In this subsection we attempt to identify the dominant sources of error in our data set and to establish quantitative bounds on the range of entrap- ment fractions.

As was pointed out earlier, the liquid water content LWC of the cloud flowing down the duct was found to vary by a factor of about two from run to run. The difficulty of controlfing this variable experimentally. coupled with the likelihood that both thedrop number concentration and the drop size therefore varied, gives reason for discussing the possible errors introduced into the determination of the entrapped fraction f&v,. Potentially the worst cast arises when all of‘ the

observed variation in LWC resulted from variations m drop radius a since the characteristic time scale to achieve diffusive equilibrium of solute in the drops 1s proportional to u2 [via Equation (9)]. However, even in this case, D a: LWC”3, implying TV ‘3~ LWC2’3 and a weaker than linear dependence on LWC. Moreover. since everywhere in the cloud-drop regime (up to a 2 50 pm) the time constant for diffusive equilibrium is at least two orders of magnitude smaller than other time constants of the system, most notably the time for air in theduct toequ~librate with the walls, weconclude that the uncontrolled variations in LWC cannot be used to account for any uncer~jntjes in the compu- tation of [S(lV)J in the drops prior to impact.

Once the drops collided with the riming rods, however, the amount of S(N) held-up was conceivably afTected by the variations in LWC. This follows from the analysis leading up to Equation (16) which shows that the threshold supercooling AT, required for gaseous entrapment varies as u’ I2 and has values within the experimental range of supercoolings studied. While the dependence of AT, on LWC is weak (- I/6 power). uncontrolled variations in LWC could affect the entrapped fraction f, at lower supercoolings, Future experimental studies should therefore place greater control over the cloud liquid water content and. particularly, measure the distribution of drop sizes collected.

In Table 2 we indicate our best estimates of the ranges over which the different experimental par- ameters that enter directly into the computation of

/ s,,v, varied. Each line of Table 2 corresponds to the respective run number of Table 1, and each pair of coiumns in Table 2 gives the low and high values about the respective means of Table 1. Using extrema in this way provides a worst-case error analysis, but is necessi- tated here by the manner in which some of the parameters varied. Temperature, for instance. exhi- bited a distinctive trend with time due to the periodic opening ;tntl closing ot‘ the snvironmcntal chamber IO

Table 2. Ranges of experimental parameters and results

Equil. Rime fsw Temperature pso,

%G fstw.eq. Dilution dil. fact.

Run (“(3 (top6 atm) (%) factor %T (%) no. Low High Low High Low High Low High Low High Low High Low High

: - - 10.7 17.4 - - 14.9 8.8 0.68 0.7 1 0.73 0.88 411 32f 357 506 7.6 8.4 10 8.5 2.6 3.7 23 40 24 46 33 6.9 9.1 to 9.7

3 -20.9 - 19.4 0.68 0.83 482 567 13 16 ::: 2‘3 71 82 14 15 4 - 10.7 - 10.1 0.71 0.81 345 376 4.7 5.1 2:l 2:6 f6 20 4.3 5.6 5 -11.8 -10.1 0.74 0.76 351 379 4.6 5.0 2.3 3.0 16 20 4.6 6.0 6 - 10.7 - 9.8 0.68 0.79 333 372 5.7 6.4 2.6 3.7 18 26 5.3 7.5 7 - 11.4 - 10.1 0.64 0.77 326 377 5.6 6.5 2.6 3.7 18 26 5.2 7.4 8 - 12.0 - 9.8 0.077 0.1 I 112 146 4.1 5.4 2.3 3.0 5.3 6.9 4.2 5.5 9 - 5.2 - 5.1 0.69 0.70 282 285 2.5 2.6 2.1 2.6 6.6 8.1 2.3 2.9

10 - 5.5 - 4.4 0.61 0.71 259 292 5.3 6.0 2.6 3.7 14 19 4.8 6.9 II -15.5 - 14.7 0.52 0.72 393 426 II 12 1.8 2.0 46 51 II 12 12 - 1.8 - 1.7 0.70 0.73 252 259 3.7 3.8 4.3 11 6.9 I8 2.7 6.9 13 -20.9 - 17.9 0.66 0.70 448 518 13 I.5 2.0 2.3 65 74 14 16 14 - 2.2 - 1.8 0.68 0.70 250 256 4.0 4.1 2.1 3.5 9.3 12 3.7 4.7

Measurement of the entrapment of sulfur dioxide by rime tee 1771

insert and remove the heated sample tube. Typically, the temperature at the beginning of each run would be at the minimum value (shown in Table 2) but would increase rapidly (within a few minutes) to the maxi- mum value. Thereafter, the temperature would de- crease gradually until the end of the run. The mean value (indicated in Table 1) was taken to be the value from a stripchart recording which represented by eye the best time-weighty average.

Since the con~ntration of SO, was measured only before and after rime formation, the extrema shown in Table 2 are the same as these two measured values. The mean was taken as the simple arithmetic average of the extrema. The range shown for the equilibrium S(W) concentration was calculated from Equations (3b(5) using, respectively, the minimum Pso and maximum temperature for the minimum [S(IV)j. and the maxi- mum P,, and minimum temperature for the maxi- mum [S(lV)]. Again. this method of computing the bounds provides a worst-case estimate of the un- certainty in the equilibrium concentration.

Uncertainty in the calculated fraction of S(W) held up by the riming process can, according to Equation (IO), arise both from uncertainties in the measured concentration of S(W) in the rime and from un- certainties in the calculated concentration in the super- cooled drops. Thus, Table 2 shows two estimates of fs,,v, based on the assumption that errors in each of the S(IV) concentrations are independent of each other. The range shown for /s,,vLeq was derived from Equation (10) using the mean value of [SW)] rime and the appropriate extrema for [S(W)],,,,,. The other range forfs,,v, is given in the last column pair of-fable 2 and was obtained using the range indicated for rime [SilV)] and the mean equilibrium drop concentration. Uncertainty in [SCIV)],,, stems almost entirely from the relatively large percentage uncertainty in the di- lution factor, which in turn arises from the difficulty of reading the total sample volume (rime plus diluent) to no better than 0. I ml. Clearly gravimetric methods for determining sample volume should be considered in future investigations in order to reduce the overall measurement uncertainty.

Bein dominant. the range offS,tVLd,, iacl. were plotted on Fig 2 for most of the experimental runs. Although the estimated un~rtainties are relativety large in some

cases. the trend ofj..,,vt with temperature is nevertheless preserved. However, the fact that the uncertainty

intervals do not always span the regression line, nor do they always overlap replicate runs. suggests that still

other factors. not yet taken into account, are contribut- ing to some of the scatter in the data.

4. CONCLUSlONS

From this series of laboratory experiments we find that a measurable fraction of the SO, originally dissolved in supercooled cloud drops is trapped in the ice as a result 01‘ the riming process. The magnitude of

this fraction varies from about 1% near 0°C to more than 12 % at - 20°C. To a reasonable first approxi- mation the entrapped fraction is proportional to the drop supercooling, suggesting that most of the entrap ment probably occurs during the adiabatic portion of the phase transition.

In atmospheric clouds undergoing precipitation formation by the accretional sweepout of supercooled cloud water, which commonly occurs near the - 10°C IeveI, we expect something like 7 or 8 % of the dissoived SO, to remain with the ice particle until it melts or experiences metamorphism in snowpacks on the earth’s surface. This degree of entrapment is less than a third that measured by Iribarne et al. (1983). but is nonetheless substantial when integrated over large volumes of cloud or snowpack.

Future efforts should be devoted to measuring the entrapped fraction of other trace gases. Such measure- ments would have value in themselves, but also could contribute to our understanding of the mechanism of entrapment, perhaps by relating the magnitudes of entrapment to the diffusivities of the various species in solution. Also, consideration should be given to the possible oxidation 0f‘S0, in the ice when other trace gases, such as 0, or H,O,, are present simultaneously.

,&knowledgemenr--This work was sponsored in part by the U.S. Forest Service under Contract No. 40-82FT-S-811. Discussions with Richard Sommerfeld are also gratefully acknowledged.

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