Atmospheric Research, 22 (1988) 105-123 105 Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands

The Collect ion Eff ic iency of a Rime-Covered Target for Water Droplets

W.D. K E I T H and C.P.R. SAUNDERS

Physics Department, UMIST, Manchester M60 IQD (Great Britain)

(Received September 7, 1987; accepted after revision February 17, 1988)

ABSTRACT

Keith, W.D. and Saunders, C.P.R., 1988. The collection efficiency of a rime-covered target for water droplets. Atmos. IRes., 22: 105-123.

A laboratory investigation of the collection efficiency of a target riming by the collection of supercooled water droplets has shown that the target, which represents a soft-hailstone inside a thundercloud, collects more droplets than theory indicates. The additional growth is due to en- hanced collection on the "feathers of rime" that grow on the target surface. The effect is greatest when the rime density is low, which occurs with low droplet impact speeds and at cold temperatures.

By comparison of the results with collision efficiency theory for smooth targets, it is possible to determine an effective target size. For example, at an impact speed of 3 m s-1, a rough 5 mm diameter collector has an effective smooth diameter of 3.2 mm and at 5 m s - 1 the effective smooth diameter is 4.8 mm.

This work has relevance to the charging of soft-hail within thunderstorms where the charge transfer is highly sensitive to the surface conditions of the hail pellet.

R E S U M E

L'dtude en laboratoire du givrage d'une cible par collecte de gouttelettes d'eau surfondue montre que la cible, qui simule un gr~lon mou h l'intdrieur d'un orage, collecte davantage de gouttelettes que la thdorie ne le prdvoit. Le surplus de croissance est dfi h une augmentation de la collecte sur les "plumes de givre" qui poussent h la surface de la cible. L'effet est d'autant plus important que la densitd du givre est faible, ce qui arrive pour des faibles vitesses d'impact des gouttelettes et pour des basses tempdratures.

On peut d~terminer une dimension efficace de la cible en comparant les rdsultats expdrimentaux aux rdsultats thdoriques valables pour une cible lisse. Par exemple, un collecteur rugueux de 5 mm de diam~tre a un diam~tre efficace lisse de 3,2 mm pour une vitesse d' impact de 3 m s - 1, et de 4,8 mm pour une vitesse de 5 m s - 1.

Ce travail intdresse le probl~me de la charge des gr~lons h l'intdrieur des orages, off le transfert de charge est tr~s sensible aux conditions de surface des grains de grSsil.

0169-8095/88/$03.50 © 1988 Elsevier Science Publishers B.V.

106

INTRODUCTION

The accretion of supercooled water droplets upon cloud particles is known as riming and is the dominant growth process for large hydrometeors. Jayar- atne et al. (1983), Jayaratne and Saunders (1985) and Baker et al. (1987) showed that a likely thunderstorm electrification mechanism relies on charge transfer between soft-hailstones and colliding ice crystals and is crucially de- pendent upon the presence of liquid water droplets in the cloud. These droplets may accrete on the soft-hailstone surface and they also provide vapour for diffusional growth of the hailstone and the ice crystals in the cloud. The sign of the charge transferred to ice crystals bouncing off a soft-hailstone was found to be controlled by the cloud temperature, liquid water content and droplet size distribution and appears to be closely related to the precise conditions at the surfaces of the two interacting particles. It is therefore important to know the values of the collection efficiency of growing soft-hailstones for supercooled water droplets through which they fall.

Ranz and Wong (1952) modelled theoretically the collision efficiency of a smooth cylindrical target for smoke particles of a known diameter. Many work- ers, including Jayaratne et al. (1983), have used their results to determine the growth rate of a soft-hailstone when it moves through a cloud of supercooled water droplets of known drop size distribution and number concentration. The collision efficiency is assumed to be the same as the collection efficiency for this case because the droplets freeze and stick on impact with the collector. Jayaratne et al. simulated thunderstorm conditions in the laboratory and drew ice crystals and supercooled droplets past a rimed target which represented a soft-hailstone of 5 mm diameter falling at 3 m s - '; for this case, according to Ranz and Wong, the target does not collect any droplets smaller than 6 pm diameter.

The liquid water content, w, of a supercooled cloud can be measured from the amount of rime which is accreted on a moving target in a given time (Brun et al., 1955; Rogers et al., 1983; Saunders et al., 1985; Keith et al., 1986). The density of rime grown in this way was investigated by Macklin (1962) and Saunders and Zhang (1987). In both cases the targets were exposed to a stream of water droplets which froze on impact and formed the rime. From the geo- metrical dimensions and weight, the rime density was calculated. This method provided a measure of the effective liquid water content in the cloud, Ew, where E is the collection efficiency. Measurements of the density of rime are only concerned with the amount of water that collides with the target and so this method removes the need to calculate E accurately. The results of Saunders and Zhang compared favourably with those of Macklin. At low impact speeds and temperatures the growth of rime 'feathers' is enhanced. The term 'feath- ers' was used by Macklin to describe the rime appearance following the freezing of individual droplets on top of one another so that the rime deposit grew out

107

from the ice surface. Under these conditions, a riming target will not be of uniform cross-section and the collision efficiency theory of Ranz and Wong may not be strictly applicable.

It is the purpose of this study to investigate whether soft-hailstones have an increased collection efficiency for water droplets due to the presence of rime feathers. The study also investigates the dependence of the collection effi- ciency on temperature and impact velocity.

EXPERIMENTAL METHOD

The experiments were performed in a cloud chamber situated within a large cold room. The temperature of the cloud environment could be controlled to within 0.5 ° C. The aim of the experiments was to determine whether small droplets are collected by rime feathers. In order to achieve this the droplets were formed from a strong salt solution and then drawn past a previously rimed target of length 53 mm. The target diameter was 5 mm which is the same size as that used in the charging experiments of Jayara tne et al. (1983) and Keith (1987). A plastic target was used in preference to a metal one because rime scraped from a metal target contained t iny metal shavings which subsequently contaminated the rime solution. Comparisons with various types of target showed that the target material did not affect the nature of the riming.

The presence of the salt droplets in the rime was detected by a Kent con- ductivity meter. If the droplets hit the rime feathers then the pre-existing pure rime became contaminated with the salt solution. As contamination increased due to increasing exposure to the salt droplet cloud or increasing collection efficiency with feather development, the rime conductivity also increased. The conductivity meter was first calibrated with known concentrations of NaC1 solution. The results, presented in Fig. 1, show that the meter has a linear response with increasing salt solution concentration. This linearity continues up to 100 g 1-1 at which point the solution starts to become supersaturated with salt. The response of the instrument was 0.05 ~S c m - 1 which corresponds to a change of 0.006 zl in the amount collected. The salt solutions were made up with NaC1 and deionised distilled water so as to minimise the effect of any impurities and to ensure that the solutions were of a consistent conductivity. New standard salt solutions were used every day because the concentration of the solution increased due to evaporation of the water. The concentration used was 10 g l - 1; a concentration of 1 g l - ~ was tried but the contamination of the rime was below the detectability threshold of the conductivity meter. The me- ter was checked periodically, however, there was no change in the calibration. The presence of the salt in the solution will cause a depression in the freezing point of about 0.6 ° C. As the experiments were performed at or below - 5 °C this depression could be ignored as it is small compared with the air temperature.

The pure water droplet cloud was produced using the method of Jayara tne

108

28

16

12

Conductlvlty (mS/cm)

/

J J J i ; ,

2 % 6 8 18

Conc. (g /L)

Fig. 1. Calibration of the conductivity meter. Variation of the conductivity with the salt solution concentration.

et al. (1983), Mossop (1984), and others. A boiler introduced water vapour into the cloud chamber at a constant rate to produce droplets which subse- quently cooled to the ambient temperature. The cloud had a modal drop size of 12/~m and the liquid water content was typically between 1 and 2 g m -;~. The experiments were performed at temperatures in the range - 5 ° C to - 20 ° C with impact speeds of 3 and 5 m s - 1. The cloud was drawn past the target at a constant rate for 5 min which was found to be sufficient time for the rime feathers to grow. The rimed target was then exposed to the salt droplet cloud produced by a small Unicorn Nebuliser. This cloud was drawn past the target for 5 min at the same velocity as that used in the pure riming par t of the ex-

109

periment. All the contaminated rime was then removed from the target and diluted with 20 ml of deionised distilled water.

The drop size distribution of the salt cloud was analysed by a Knollenberg Forward Scattering Spectrometer Probe (FSSP) . The modal diameter was about 10 ,um and a typical drop size distribution is shown in Fig. 2. As can be seen there were some droplets larger than 20/~m which were not desirable but were unavoidable. The presence of these droplets was accounted for in the analysis of the data.

The theoretical collection efficiencies, shown in Fig. 3, were calculated from the equations of Loftier and Muhr (1972) for a smooth collector of 5 mm di- ameter, cloud temperature of - 10°C with air velocities of 3 and 5 m s -1. The Ranz and Wong efficiencies used by Jayara tne et al. over-estimated the collec-

2eB

108

160

lh.0

120

180

N/cc

y 8O

60 ,

28 .

10 20 30 ~-0

Droplet Diameter (Nm)

Fig. 2. The drop size distribution of the nebuliser cloud.

50

110

lOO 7 C, E, /

i

60

(~.)

5 m/'5

3 m/s

~o-

20 i

20 ~0 60 80 100

d (pro)

Fig. 3. The collection efficiency of a 5-mm target at 3 and 5 m/s ; from Loftier and Muhr, 1972.

tion efficiency for small droplets by about 10% compared with the Loffler and Muhr equations. The collection efficiency increases slightly with decreasing temperature due to the lower viscosity of air at lower temperatures. For the 3 m s- ~ air velocity it can be seen that the collection efficiency for droplets of diameters between 5 and 8/~m is less than 1.0%. These theoretical collection efficiencies are for smooth collectors and do not take into account any turbu- lence due to the roughness of the surface.

The total volume of salt water droplets collected by the soft-hailstone target can be calculated from the following formula:

V~= (X L)(Vc + Vd + 2 0 X 1 0 - 3 ) / ( X N ) (1)

where XN is the concentration of salt solution in the nebuliser (g 1--1); Xt, is

111

the concentration of salt solution in the rime plus 20 ml of water (g l- 1 ); Vd is the total volume of salt solution droplets which collide with the target (1); and Vc is the volume of pure rime on the target (1).

Now, Vc + Vd is much less than 20 ml so from eq. 1 it follows:

Vd = 2 0 × IO-3XL/XN (2)

Thus from the salt concentration of the rime liquid and the initial salt solution concentration, the volume of salt cloud which hits the rime target can be cal- culated. From the Loftier and Muhr formula and the measured droplet size distribution, the total volume of salt droplets that can collide with the target can be calculated and will be called VD. So if Vd > VD then the difference is

37, @

36,6

36.2

35,8

35.~-

V o L , CoLLected (wL)

i i i i i

lg 2e 30 ;g s8

Conc, (~a/l)

Fig. 4. The volume of salt droplets collected using different concentrations of salt solution.

112

38

37

3 B

3 5

33

32.

31

30

29

2B

V o L , CoL Lected (p L ) T

/ / / ] i

-5 - lO -15 -2B -25

T e m p . (de 9 C)

Fig. 5. The variation of salt droplet volume collected with cloud temperature at 3 m/s.

made up from the extra droplets that collide which are not accounted for by the collection efficiency formula for smooth targets.

RESULTS

A i r v e l o c i t y = 3 m s -~

The experiments were performed at different temperatures between - 5 ° and - 20 ° C at a constant air velocity of 3 m s - 1. The pure droplet cloud was drawn past the target for 5 min before being exposed to the salt droplets for 5 min. The validity of the equations described in the previous section was con- firmed by varying the concentration, XN, of the nebuliser solution. Fig. 4 shows

37.8

36,8

3 6 , 6

36, h-

36.2

3 6 . 0

3 5 , 8

35 .6

35,~

35.2

VoL. CoLLected (pt)

O

O

O _ _

113

i i

2 % 6 8 18

Ex, Time (mln)

Fig. 6. The variation of salt droplet volume collected in 5 min with the exposure time of clean rime at 3 m/s.

that the volume collected is approximately the same for all values of XN. The only limits on the solution concentrat ion were of detectability at low values and of supersaturation at high values.

Fig. 5 shows the volume of salt droplets collected by the rime against cloud temperature. At - 5 ° C the volume collected is around 28.9/A increasing to 37.1 /11 at a temperature of - 20 ° C.

The time of exposure of the target to the pure droplet cloud was varied from 2 to 7 min at a temperature of - 10 ° C while keeping the salt droplet exposure to 5 min. The subsequent increase in the collection efficiency of the target for the salt droplets is reflected in the larger volume of salt droplets collected at longer exposure times (Fig. 6). As the exposure time to pure droplets increased,

114

79

78

77

76

75

VoL. Collected (pl)

/

/

/

-5

, i i , i i ~ i

-18 -15 -20 - 2 5

Tem p , (deQ C)

Fig. 7. The variation of salt droplet volume collected with cloud temperature at 5 m/s.

the number and size of the rime feathers was observed to increase for the first 6 min of collection. Beyond this time the collection efficiency remained ap- proximately constant indicating no further increase in feather concentration.

A i r v e l o c i t y = 5 m s -~

In these experiments, performed under the same conditions as above, the pure droplet cloud was drawn past the target at a velocity of 5 m s- l for 5 min. The rime acquired the kernel appearance described by Macklin ( 1962 ) and the rime feathers were not as pronounced as in the above case. Fig. 7 shows the salt droplet volume collected in 5 min against temperature. At this higher im- pact velocity the increase in the amount collected with decreasing temperature

1 1 5

is less than at 3 m s-~. The reasons for this will be discussed in the following section.

DISCUSSION

It has been hypothesised by previous workers, Macklin (1962) and Dong and Hallett (1986), that as a hailstone grows due to the accretion of water droplets, the collection efficiency for those droplets increases due to the for- mation of rime feathers. Mossop (1984) showed that in the production of lab- oratory clouds the drop size distribution is affected by the size of the water vapour inlet nozzle. It can be seen from Fig. 8 that as the nozzle size decreases the drop size distribution shifts to a higher concentration of smaller droplets. This was confirmed by Jayaratne and Saunders (1985), Fig. 9, when they showed that the charging of a hailstone due to the collision and separation of ice crystals is dramatically affected by the drop size distribution present in the cloud. Fig. 10a shows the charging which occurs with a large nozzle of diameter 32 mm at - 10 o C whereas Fig. 10b shows the charging under similar conditions but with the small droplet cloud produced by the small nozzle of 5 mm diam- eter. In the second case when negative charging occurs, the ice crystals have

I I I ] I ~ _ )rifice WateP 3rops L.W.C

z x " -x-~ . . x ~ x dia .(cm: temp(~Cl (era "3} ( g m -3)

/ / ~ 1 100 1890 1.57 102 2 X / ~ ~ 2 100 990 133

~ ~ - ~ - - o . ~ , 5 lOO 3so 1.oo / / \~ lo 91 12o 0.6o

x' ? 25 82 7o

g 5 *',\

10_1r +~25 cm ORIFICE ~ \ ' \\ i ' \ i i~i~÷

10 -2 / J I I i I i 1 i l 0 10 ;O 30 40 50

DROP DIAMETER (p rn )

F ig . 8. T h e e f f e c t o f n o z z l e d i a m e t e r o n t h e c l o u d drop size distribution; from Mossop, 1984.

116

300

200

o

u

%

E

2 o o L C3

100

- - - - 4

Large Nozzle

i

S.'6 814 1112 14.0 16.819.6 22.4 25228.0 30,8 Droplet DiQmeter (~m)

120001

80001 I

, ooot _ -

I I Smat[ Nozz{e

5.6 8.4 11.2 14.0 Droplet Diameter (pro)

Fig. 9. The effect of nozzle diameter on the cloud drop size distribution; from Jayaratne and Saunders, 1985.

grown at the expense of the droplets which have a maximum size of 6 pm and so are too small to strike the target according to the theory of Ranz and Wong (1952). Jayaratne and Saunders (1985) and Baker et al. (1987) concluded from these experiments that it is the surface properties of the interactants which are important in controlling the sign of the charge transfer. Charging is positive if the hailstone is growing faster than the ice crystals and negative if growing more slowly. The results of the present study show that some riming due to the small droplets may occur due to the presence of rime feathers on the target and this brings the charge sign hypothesis into question. It can be shown, however, by using the formulae of Baker et al. that the amount of water ac- creted by the hailstone is insufficient to increase the hailstone growth rate above that of the ice crystals and so the sign of the charging is unaffected. A detailed account of the relative growth rates of the cloud particles is given in Appendix A.

The appearance of the rimed surface under varying conditions has been de- scribed in detail by Macklin (1962), Stallabrass (1978) and Lowaski et al. ( 1983 ). At low temperatures and low impact velocities the droplets freeze with-

"8

l(Pa)

.6

*L.,

"2-

0 1 2 3 t (mins)

(a) Large Nozzle

+10-

117

.,8.

l(pa)

+2-

0 t(mins)

-i1 b) Srnol[ Nozzle

Fig. 10. The effect of the nozzle diameter on the hailstone charging current; from Jayaratne and Saunders, 1985.

out significant flattening which enhances the growth of the rime feathers. At higher temperatures, the rime appears as smooth clear ice. As the droplets freeze they release latent heat of fusion which warms the rime surface above the ambient cloud temperature. Using the results of Ludlam (1951) it can be shown tha t if a cloud of temperature - 5 ° C and liquid water content 1 g m -3 is drawn past a 5 mm diameter target at 5 m s - 1 then the surface temperature

118

of the rime increases to - 2 . 9 ° C. Under similar conditions but with a cloud temperature of - 8 ° C the rime surface temperature will be - 5 . 9 °C. Thus, conditions of wet growth are not achieved in these experiments. However, the droplet freezing time is temperature-dependent with longer freezing times at higher temperatures giving time for the freezing droplets to flow over the sur- face leading to a smooth ice surface. The effect of the thermal mass of the target may influence the rime surface when the rime thickness is small. However, these experiments were performed over a period of 5 min which was considered large enough to minimise any effect due to the target. Loftier and Muhr ( 1972 ) assumed that the collector is smooth and thus their theory and the present experimental results agree, with a near zero target collection efficiency at tem- peratures above - 8 ° C. In the case of a smooth collector, the theoretical col- lection efficiency increases with increasing air velocity. However, if the collector is rough then the experiments show tha t the increase in the volume collected due to the roughness, decreases with increasing air velocity as indicated in Fig. 11. The volume collected at - 5 ° C (3 m s - 1 ) and - 8 ° C (5 m s ~ 1 ) is taken as zero and the relative increase in volume collected due to the presence of the rime feathers is shown as a function of temperature. It can be seen that at low speeds where feather growth is enhanced, the volume collected increases sub- stantially at lower temperatures. At a flow speed of 5 m s - 1 the feather growth is inhibited and thus the collector surface is essentially smooth. Macklin ( 1962 ) noted that with an increase in impact velocity the rime surface appearance changed from a 'feathery' to a 'kernal' type due to gaps in the rime being filled- in by subsequent droplets impacting at the higher velocity. This change will occur at lower temperatures for higher values of liquid water content. For in- stance, at a temperature of - 1 5 ° C where rime feather growth is prominent the surface temperature would rise to - 10~C if the liquid water content was increased to :3 g m-:~; the growth of rime feathers would then be inhibited and the collection efficiency of the target would decrease. As the exposure time of the target to the pure droplet cloud increases the appearance of the rime sur- face changes from a frost-like surface to a feather-like surface. This change is due to a positive feedback mechanism which causes certain leathers to grow preferentially. Thus, as the exposure time increases from 2 to 7 min the feather concentration falls because some feathers grew from the rime surface into the flow and therefore captured more droplets. Fig. 6 shows that the amount of salt water collected by the rime increases in the first 6 min of pure water riming after which time the amount does not change significantly. If the data is ex- trapolated from the short exposure region to longer times the relationship be- tween salt volume collected is roughly linear. This reduction in the actual amount collected to the extrapolated amount cannot be explained by the re- moval of rime feathers by the airflow. At t = 7 min, the amount collected is 30% lower than the extrapolated value. There was no evidence of gaps in the target rime indicating such break-off by the airflow. The majority of the experiments

119

le dV ( tJL)

5 m/s

-5 -18 -15 -20 Temp, ( d e g C)

-25

Fig. 11. The relative increase in volume collected at 3 and 5 m/s ; see text for explanation.

were conducted outside the accepted ice multiplication regime (Mossop et al., 1974; Hallet t and Saunders, 1979; Mossop, 1985, 1986), and so losses due to droplet shattering were minimal.

The equivalent collector diameter is defined as tha t smooth collector diam- eter which would theoretically (Loftier and Muhr, 1972) collect the same vol- ume of droplets as in the experiment. At low air speeds (3 m s-1 ) where feather growth occurs, this diameter is 3.2 mm whereas at 5 m s -1 the equivalent col- lector diameter is 4.8 mm. The presence of rime on the collector increases the collection efficiency for all droplet sizes. At 3 m s-1 the collection efficiency for 5/2m droplets has increased from 0.06% for a smooth 5 mm collector to 0.21% for a rough surface with an equivalent collector diameter of 3.2 mm. Table I shows the collection efficiency for a 5 mm and a 3.2 mm diameter

12(}

TABLE I

Collection efficiency ( % ) given by Loftier and Muhr { 1972 ) for a collector diameter of 5 and 3.2 mm at a flow speed of 3 m s-

Droplet Collector diameter: diameter (zm) 5 mm 3.2 mm

2.5 0.00 0.00 5.0 0.06 0.21 7.5 0.66 2.37

10.0 3.56 10.94 12.5 11.28 26.16 15.0 23.38 40.94 17.5 35.84 51.92 20.0 46.05 59.81 22.5 53.87 65.72 25.{) 59.91 70.36 27.5 64.73 74.11 30.0 68.68 77.21 32.5 74.81 82.00

TABLE II

The ratio of number of droplets caught to the number in the airflow for smooth and rough collectors

Temp. 3ms-~ 5 m s t { :C)

smooth rough smooth rough

- 5 0.300 0.369 - 8 0.303 0.430 0.447 0.450

- 10 0.304 0.463 0.448 0.452 -- 12 0.306 0.468 0.451 0.455 - 15 0.308 0.474 0.453 0.460 - 20 0.313 0.482 0.457 0.468

c o l l e c t o r a t a i r s p e e d s o f 3 a n d 5 m s - 1. A s s h o w n in A p p e n d i x A t h i s i n c r e a s e

is i n s u f f i c i e n t to h a v e a n y e f f ec t o n t h e s i g n i f i c a n c e o f t h e s m a l l d r o p l e t c h a r g - ing e x p e r i m e n t s b y J a y a r a t n e a n d S a u n d e r s ( 1985 ) .

T h e r e s u l t s p r e s e n t e d h e r e a r e for a c e r t a i n se t o f e x p e r i m e n t a l p a r a m e t e r s

s u c h as c o l l e c t o r d i a m e t e r , c l o u d d r o p l e t s p e c t r u m a n d i m p a c t spe e ds . T h e n e t c o n t r i b u t i o n o f t h e r i m e f e a t h e r s to t h e i n c r e a s e in c o l l e c t i o n e f f i c i e n c y m u s t be o b t a i n e d in o r d e r t h a t t h e r e s u l t s c a n be a p p l i e d to a d i f f e r e n t e x p e r i m e n t a l s i t u a t i o n . T a b l e II s h o w s t h e p r o p o r t i o n o f t h e d r o p l e t s c a u g h t to t h e t o t a l n u m b e r in t h e a i r f low for b o t h t h e s m o o t h a n d t h e r o u g h c o l l e c t o r s . A t a f low s p e e d of 3 m s - 1 t h e r a t i o i n c r e a s e s a s t h e t e m p e r a t u r e fa l l s due to t h e en-

121

hanced growth of the rime feathers at lower temperatures. Thus the volume of droplets collected by a rimed collector may be increased by 50% above that predicted by the Loftier and Muhr equations for a smooth collector. However, at 5 m s -1, the ratio for the rough collector is about the same as that of the smooth collector. This is due to the feather growth being inhibited at higher impact speeds as discussed earlier.

CONCLUSION

The collection efficiencies given by Loftier and Muhr (1972) are only valid for smooth collectors. When the target is covered with rime the collection ef- ficiency of the target for small droplets does increase particularly at low tem- peratures. It does not, however, increase with velocity because feather growth is inhibited when the rime density increases with increase in the droplet impact velocity. The collection efficiency also increases, up to a certain limit, with increasing amounts of rime on the target. The collection of small droplets is insufficient to modify the soft-hailstone growth rate enough to influence the conclusions of Jayaratne and Saunders (1985) concerning the sign of the charge transferred when ice crystals bounce off a soft-hailstone.

A P P E N D I X A - - T H E G R O W T H RATE OF CLOUD H Y D R O M E T E O R S

Mason (1974) s tates t h a t the general equat ion for the rate of increase in ice crystal mass by vapour diffusion takes the form:

drn dt - 4uCD (p~o -p~ ) (A. 1 )

where the cons tan t C depends on the shape of the crystal, D is the diffusion coefficient of water vapour in air and fli and poj are the vapour densities at the crystal surface and the cloud, respectively.

For a hexagonal plate, C has the value of 2 r / ~ if it is considered to be a circular disc. At - 10 ° C, (P~o-Pi) is 0.21 g m - '~ and the rate of increase in mass of a 30/ lm diameter plate is approximately 10-s g s - '. The rate of increase of mass per un i t area may be calculated from the original area if dr << r and is approximately 4.10 -5 g cm -~ s - ~.

There are two contr ibut ions to the growth rate of the hailstone; firstly the vapour flux to the surface from the deep field vapour supply and secondly the vapour flux from a single droplet freezing on the hai ls tone surface. These two contr ibut ions can be calculated from the equations given by Baker et al. (1987).

( 1 ) The deep field vapour flux to the surface is given by:

fD ~',=--ff(Po~-P~) [gm-2s -']

where f is the vent i la t ion coefficient. Thus i f / = 1 5 , D = 2 " 1 0 -~ m 2 s - ' , R = 2 . 5 - 1 0 -3 m and (P,,~-PO =0.2 g m -3 then ~, =2 .4-10 -3 mg cm -2 s - '

(2) The mass growth rate due to the vapour arr iving at the surface from a single freezing droplet is given by:

122

~t=37~fDa(po-Pi) [gs 1]

The mass of droplet lost as vapour is all assumed to deposit on the hailstone surface and is given by:

M=3~fDa(po-p,)tf [g]

where t~ is the freezing time. Typically [ = 15, D = 2 - 1 0 ~' m ~ s l (Po-P~)=4 g in ~, a = 5 ~tm, t~=l ms and so M=5.6 .10 - ~ g.

The target used by Jayaratne et al. was rotated at 3 in s " ~ in a cloud of droplets of diameter 5 /~m and concentration 1000 cc- 1. From the present work the collection efficiency of the target for this droplet diameter is 0.2% and the number of droplets swept out per unit area per second is 300 X 1000 × 0.002 = 600 c m - 2 s - 1. Thus the available mass flux, ~2, is:

~ = 5 . 6 " 1 0 ~1×6"102=3.36"10 ~ [gcm ~s ~]

The total rate of increase of mass per unit area of the hailstone is just the sum of ~ and ~ . Thus,

dm -2.43"10 -~ [gcm ~s-~]

dt

The ratio of the rate of increase of crystal mass to that of the hailstone is:

4.10 16.44

2.43" 10 ' ~ -

that is, the ice crystals are growing some sixteen times ihster than the hailstone in this stiuation. In any case the collection of droplets in the range 5-8 ttm due to the rime feathers still does not provide as much vapour as from the droplets in the cloud. Therefore, the conclusions of Jayaratne et al. ( 1983 ) that the charge transfer in these experiments is controlled by the vapour diffusion to the target surface from droplets in the cloud still stands.

R E F E R E N C E S

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