Indian Journal of Radio & Space Physics Vol. 28, February 1999, pp. 15-21

Velocities of water drops falling in oil media and the wake effect

S K Paul

Indian Institute of Tropical Meteorology, Pune 411008

Received 14 January 1998: revised 10 November 1998: accepted 2 December 1998

Laboratory experiments were conducted on the velocities of pairs of equal-sized water drops of 3.3 mm di­ameter, falling with an initial vertical separation in undisturbed oil media (in presence and in absence of an electric field in mustard oil, and in absence of a field in kerosene oil). During the fall from the initial point, the position where a drop attained terminal velocity while falling ' alone, the following (upper) drop got accelerated with respect to the preceding (lower) drop due to the wake effect. The wake effect in mustard oil existed up to an initial vertical 3eparation of 2 em and 2.4 cm for a pair of drops, respectively, in absence and in presence of an electric field of 230 V cm' l for their collision at the end of the 86-cm fall. The wake effect in kerosene oil existed up to an initial vertical separation of 4.5 cm in absence of a field for collision of a pair of drops at the end of a 72-cm fall.

1 Introduction ·

Collision-coalescence is the principal process for the growth of warm cloud drops of unequal size

greater than 18 ~lIn radius. List and Whelpdale ' observed that factors such as the collision velocity, the angle of impact, the surface tension and the electric charges can affect the coalescence of colliding water drops. Also, electric field s and charges enhance the coli is ion effic iencies of cloud drops or particl es2..l.

Beard and Ochs4 observed that the coalescence efficiency decreases with both increasing collector drops and collected cloud droplet sizes. For equal­sized cloud drops falling in air with the same terminal velocity and with an initial vertical separation, collision is possible when one drop is brought under the wake of the othe r. According to Mason s, the

ai rflow around water droplets of radius > 30 ~lm

becomes asymmetrical as a wake develops in the rear, and a dro pl et Jllay then capture an even large r overtaking drop by sucking it into it s wake . The calculated linea r collision efficiency is substantially higher than the geometric coli is ion efficiency for si milarly sized drops because of the wake effect

6. The

wake effect behind the collector drops can produce values o f colli sion efficiency greater than uni ty7. The influence of the wake effect on the collision and coalescence of eq ual-sized drops was studied experimentall/. The wake effect was noted as far away as 11.5 cm (vertical separati on of the droplets)

for water droplets of 700 ~111 diameter falling in air.

The distance decreases directly with droplet size, and

for 115 ~m droplets the di stance was 1.15 cm (Ref. 9). Model ex periments were also conducted JO

·"

in which the fall of cloud droplets in air \vas simulated by the fall of so lid spheres through liquid viscous media . Faster collisional growth of graupel as

compared to ra in drops is one of the Jllain points of conceptual mode l of Rosenfeld and Woodley' 2 for g laciogenic seed ing precipitation enhancement in clouds with active coalescence process. FlIIther, drag coefficients and terminal velocities of water drops/ ice particl es, falling in air, were determined by Jllany workers J.1-' 6 .

In thi s study the laboratory experiments on the velocities and collision-coalescence of a pair of eq ual­s ized water drops of 3.3 mm diameter falling in Jllustard o il (in presence and in absence of an e lectric fi e ld) and in kerosene oil (in absence of a field) were conducted in order to s imulate qualitatively the behaviour of c loud and drizzle drops. The detail s of experimental and s imulated conditions are g iven in Table I .

2 Design of the experiment

The motion of a cloud droplet falling freely in air may be characterized by the rati o of the inertial forces to viscous forces, i.e. the Rey nolds number. The difficulties in measurin g s izes and relati ve pos itions of the cloud drops falling in air and detecting coll is ion in the fall-path might be overcome by conduct in g

16 INDIAN J RADIO & SPACE PHYS, FEBRUARY 1999

Table I-Details of experimental and simulated atmosphere

Experimental cond itions ( I) Simulated conditi ons (2) at 20°e. 900 mbar Reynolds

Temperature of oi l

°C

Density Viscosity Drop Drop term i- Drag coefft- Drop Drop Drag Vert ica l number for of oil of oil radius nal velocity cient radi us terminal coeffi- path length ( I) and (2)

g cm-J poi se mm cm S- I pm ve locity cient of simu latcd em S- I atmosphere

m

Water drops falling in mustard oil C lou d drops fa llin g in ai r

28 0,9 10 0.63 19 1.61 1. 13 33 34 t.3.00 48 12 0,52 ( 1340)

Water drops fa lling in kerosene oil Drizzle drops fall ing in air

27 0.78S O.OIIS 1.7 1 13.07 0 .7 1 559 454 0.64 35 297 (485)

otc: Simulated drop radii wcre computed using the method described by 8eard & Pruppaehcr l 6 The termin al \'cloci ty values for (I ) WI:n; determined experimentally and those for (2) werc computed using Eq, (2), The termina l ve l oeiti '~s in brackets were computed

using Eq. ( 10) for cloud drops and the rel ation . / ' = 650;;' . for dri zzle drops. where r is water dro p radius in mm (!'rom meteorologi­ca l glossery).

measurements that are eaS ier, fo r exa mpl e, by performing the meas urements o n much la rge r wa te r drops fal ling in a v iscous o il med ium . The principle of sim i larity a Il ows one to perform measurements o n much larger drops and to apply the results to c loud drops by choos ing the size, density of drop and the viscos ity and dens ity of med ium such that Reyno lds num ber for th e experiment is the same as that for the atmospheric case I6

.17

. The si mul ated drop size is obta ined as follows:

2 I . 2 D = J[ r - (DPnY .,,(1)

2

w here, D is the drag forc e actin g o n a spherica l drop of radius r fa ll ing w ith te rminal ve locity V under

grav ity. in a fluid of dens ity Pill and dynamic v iscos ity

11 , Co being the drag-coefficient. Us ing Reyno lds number (R), given by

R = 2PmrV ". (2) '7

C R D = - D- 6m7Vr ." (3)

24

For Stoke ' s fl ow,

D,=6mr V ... (4)

At terminal ve loc ity, the drag on the sphere is balanced by the net gravi tational force.

So,

D = ~m_3(ps - PnJg ... (5) -'

w here, Ps is the dens ity of drop. From Eqs (3 ) and (5),

, 16 2( ) CD = :3 gr PI - Pm / V R 7] ... (6)

From Eqs (4) and (5),

D 2gr2(ps - PnJ ... (7) D\ 97] V

From Eqs (3) and (4),

D CDR ... (8) Ds 24

From Eqs (7) and (2) e liminat ing V, o ne gets

3 9 l/R ( D) r = 4 Pm(Ps - Pm)g Ds

... (9)

Us in g R from Eq . (2) and from the Co vs R curvel 6

,

CIJ fo r si mulated a tmosphere is obtained. The ratio DIDs for the atmospheric case and , hence, the s imulated drop s ize a re calculated from Eqs (8) and (9) . The te rmina l ve loc ity is given by Eq . (2).

For Stoke's flow, DID, = I . Therefore, from

Eq. (7), we have,

V = 2g,·2 (Ps - PnJ 917

For a c lo ud drop falling in air, pm is negli gibl e

compared to Ps. T herefore, the terminal ve loc ity

becomes 2

V = 2gr Ps ... ( 10)

9'7 Eq uating Reyno lds number for the fall of the

experimental wa.ter dro p in mustard o il/kerosene oil to

that for the fa 1,1 of a cloud drop/drizzle drop in air. the s imulated dropsize is obtained .

PAUL: VELOCITIES OF WATER DROPS IN OIL MEDIA & WAKE EFFECT 17

3 Experimental set-up

The vertical motions of a single water drop of 3.22 mm diameter and of a pair of equal-sized water drops of same dimension separated vertica lly in the initi al stage while falling through mustard oi l medium in a perspex tank of size 17x 17x 100 cm', were observed photographically and the trajectories of the' fall-path were obtained. The time intervals of fall of the single and the pair of drops for known depths were measured from the initial point. Here, the initial point means that position in the tank where a drop, whi le falling alone, attained the terminal velocity . The average ve locities at the mean depths were computed. The time of fall was measured by sensitive stop watches correct up to 0.05 s. Necessary illumination of the tank was made and the temperature of oi I was measured periodically with a sensitive thermometer correct up to 0.1 0c. Water drops of same size were released from a suitable drop-release device through a hypodermic needle dipped inside the oil , at a des ired rate, giv ing no jerk to the drops and no disturbance to the oi l medium. Drop sizes were measured at fixed intervals at known oil temperature. The maximum variation in the oil temperature for a given category with five sets of observations was ±0.8°C. The sizes were determined by weighing 100 drops (correct up to four decimal places) released in the oil medi ulll under conditions similar to those inside the experimental chamber. The maximum variation in the di ameter of equal size drops in th e experiments was est imated to be 10%. A vertical scale and two hori zontal sca les. graduated in centimetres, were fitted to the front wa ll of the chamber for measuring the depth of fall and vertica l and lateral separations of th e pair of drops at different pos iti ons. The initial and final vertical and lateral separations and the depths of co lli sion and coa lescence of a drop-pair were noted both visua lly and photographica lly. Further details of the experiments are given elsewhere 18. The experiments in mustard o il were conducted in the presence of a

verti ca l electric fi eld of 230 Y cm- I and in absence of a field . For the purpose of the electr ic field , two parallel copper plates were fitted-Dne at th e top and the other at the bottom of the tank whi ch was \\ e ll in sulated, and the bottom plate was maintained at a pos iti ve potential wi th respect to the upper plate which was grounded through the negat ive terminal or a variable 50 kV DC power supp ly. All the measurem ents were repeated for a ingle and a pair of water drops of 3.42 Illlll diameter, fall ing in kerosene

oil in a separate identical perspex tank (I m high) in absence of a field .

4 Results and discussion

[n Tables 2-5 , each set of observations corresponds to the whole trajectory of a drop or a drop-pair. The depths of fa ll/initial vertical and lateral separations of the drops were measured from , or, at the initial point, defined earlier. [n Tables 2-5, the acceleration of a drop at a given depth was taken as the change in average velocity (positive or negative) of the drop at that depth with respect to the average velocity at a lower depth divided by the time interval of fall of the drop between the two depths.

4.1 Determination of terminal ve locity

Table 2 gives the fall ve locity of a single water drop in oil media at different depths of the experimental chamber. The velocity of a drop remained constant during the fall and was approximately equa l to its terminal velocity. The experimenta l terminal velocity of the water drops of 3.22 mm diameter fa lling in mustard oil at ~28 °C was 1.13 cm s I, while that of the water drop of 3.42 mm diameter in kerosene o il at ~ 27°C was 13 .07 cm S- I in absence of a fi e ld . The sa id drops attained terminal velocity at 10 cm and 25 cm of fall from the release point (need le-t ip), respecti vely . While determining termin al velocity, the mea n va ri at ion of oil temperature for six sets of observati ons (each set corresponding to a complete fall-path of a single drop) was about ± 0.6°C. Hence, the erro r in terminal ve loc ity, due to change in viscos ity of oil caused by ±

Table 2- Tcrlllinall'c locity (l11can of 6 scts or observat ions) in I11l1 stard oil (wate r dror ciiamct.:r 3.22 mm. 111':<1n t.:mp . 27. 7"(' )

and Keroscne oil (water drop diameter 3.42 111m. n1l' l1n tcmp. 26 .R°C)

Mean period A\' . \ .:IOl.:it\· of -rail cm s· ! .

Range or fal Mcan d.:ptil cm Cill

s Fo r mu stard o il

0-20 10 17.775 I . ! 25 0-] 2 I II 2R .-11<J 1.126 0-86 --I] 76.156 I I~ <J

20-32 21l 10.6--1 ·1 127 32-8f) 5') --17 .737 13 1

For kerosene oi l

0-20 10 1.53 7 13 .0 12 0-48 2"1 3.678 13.051 0-72 ]() 5.510 13 .067

2()---I X J·I 2. 1·11 13 .078 --18-72 60 I .X32 iJ . IOO

18 INDIAN J RAD IO & SPACE PHYS, FEBRUARY 1999

0.6°C change in temperature during the experiment in either oils, was very small. The parallax error was avoided as far as possible. However, the parallax errors, while recording depths of fall of a drop, were about ± 0.1 cm in mustard oil and about ± 0.5 cm in kerosene oi l leading to an error in terminal velocity by ± 0.5% and ± 2.5%, respectively.

4.2 Observations in mUistard oil in absence of a field

The details of the observations for water drops of 3.22 mm diameter falling in mustard oil in absence of :} field are given in Table 3.

The inferences drawn from Tab le 3 are as follows:

(i) The ve locity of a single drop at different depths was constant and was approximately equa l to its terminal ve locity.

(ii) Withi n the li mits of initial vertical separation for

Table 3-Dbservations (mean of 5 sets) of different parameters fu r water drops of 3.22 mm diameter falling in mustard oi l in absence of an electric field (oi l temp. 27-29°C. max. dep th of

fall 86 cm)

Range of Mean depth

fall (d)

cm cm

0-32 16 O-X6 43 32-X(, 59

1.001'\: r Upper drop drop

0-32 16 16 0-62 3 1 31

32-62 ,,\ 7 47

0-32 16 16 0-X6 43 43 32 -X6 59 59

{J-32 16 16 0-X6 43 43

Av. velocity at d cm S- I

Category I

1.1 252 1.121 4 1. 11 92

Lower Upper drop drop

Ca tegory II

1.1197 1.1 307 1.1 4 1X I IX59 1.1664 1.2510

Ca tegory III

1.2044 1.2181 1.1 073 1.2344 1.1931 1.2442

Category IV

1.1 985 I . !985 1.1 9 16 1.1 9n

Accelerati on x 10-' cm S- 2

- 16 - 15

Lower drop

+ 172 + 172

-3 I -32

- 30

LJpper drop

+460 +460

+75 +75

- 3 32-X6 59 59 1.1 xn 1.1 973 - 2X - 4

Note : Category I- Single drop fallin g alone . Category· II - A pair of drops falling one abo ve the other: in itial \ ertical separatioll 1.6 cm: initial lateral separation 0.0 cm: co lli sion at (,2 cm. Category Ill- A pair of drops: initial vertica l separation 2.0.em : initial lateral separation (J.05 cm: co lli sion at 86 em . Category IV- A pair of drops : initi al ve rt ical scparatioll 2.6 cm: fina l vcrtica l separation 2. 1 cm at X6 em: in itial lateral separation () I cm : fi na l lateral se raration 0.2 cm: sl ight 1ll00'clllcnt of th e drops towards each other.

wh ich the two drops of a given pair gradually approached each other, the velocities of the pair of drops were, in genera l, greater than their termina l velocities. The velocity of the following drop was greater (at higher depths) or a little greater (at lower depths) than that of the preceding drop.

(iii) The drops were accelerated or retarded during the fa ll -path. The acce lerations or retardations were fair ly uniform at different depths during the fall . In all the cases, at each depth, the following (upper) drop got acce lerated \~ ith respect to the preceding (lower) drop. This is due to the wake effect. The following drop suffers less resistance of the fluid in the wake of the preceding drop and, therefore, gets acce lerated relative to it. If this relative acce leration in the fall-path could overcome the initial vertical separat ion between the drops, coli ision of the drops wou ld occur.

(iv) The relative acce leration of the upper drop with respect to the lower drop dec reased gradually from Category II to Category IV showing that the wake effect decreases as the initia l separation of the drops increases . Also, the relative acce lerati ons at different depths of fa ll were nea rly the same for.each cateogory.

(v) The wake effect for the experimenta l water drops in musta rd oi L in absence of a fielel , existed up to an initial' vert ica l separation of abou t 2 cm and 2.6 cm, respective ly, of the drops for collision and sl ight approach (towards each other) at the end of a fall of 86 cm.

4.3 Observations in mustard oil in prese nce of a fie ld

The details of the observations for water drops of 3.22 111111 diameter falling in Illustard oil in presence of an e lectric field of 230 V cm 1 are given in Table 4.

The in fere nces (i)-(iv) drawn in Sec. 4.2 are app licable to thi , case as we ll. Bes ides th ese, the following points are noti ced: (i) In Illustard oil , the terminal ve loc ity of a s ingle

drop in th e electri c fie ld ( 1.15 Clll s 1) is sl ightly greater than that in absence of the fi eld ( 1.1 3 cm s 1).

( ii ) In mustard o il, the ve loc ities of either of the drops in the presence of the field were greater or s li ghtly greater at lower initial separations (Category 1/ and 1/ I) and sl ightl y sma lI er at hi gher initi al separations (Category IV) than those in the absence of the field (Table 3). This

J

)

(' .:' < . . rt:-t~ ~~

I . crf7l,T;;~ 0 .(~) . ~: ~:)\ PAUL: VELOCITIES OF WATER DROPS IN OIL MEDIA & WAKE EFFECT \\\ .. f .))h !d9?~:·;, ,-.

\\ j ' . t... /

Table 4--Observations (mean of 5 ~ets) of different parameters for water drops of 3.22 mm diameter falling in mustard oil in

presence ofan electric field of230 Vern- I (oil temp. 27-29°C, max. depth of fall 86 cm)

Range of Mean depth Av. velocity at d Acceleration fall (d) cm S· I x 10. 5 cm S· 2

cm cm

Category I

0-32 16 1.1436 0-86 43 1.1497

32-86 59 1.1534

Lower Upper Lower Upper drop drop drop drop

Category II

0-32 16 16 1.1896 1.2214 0-51 25 25 1.3077 1.3600

32-51 41 41 1.5702 1.6814

Category III

0-32 16 16 1.2062 1.2261 0-79 39 39 1.2223 1.2687 32-79 55 55 1.2336 1.2994

Category IV

0-32 16 16 1.1586 1.1586 0-86 43 43 1.1513 1.1650

32-86 59 59 1.1470 1.1688

Note : Category I-Single drop falling alone.

+26 +26

Lower drop

+ 1952 + 1952

+85 +85

-31 -31

Upper drop

+2453 +2453

+236 +235

+28 +28

Category II-A pair of drops falling one above the other ; ini­tial vertical separation 1.5 cm; initial lateral separation 0.0 cm; collision and coalescence at 51 cm. Category I II-A pair of drops; initial vertical separation 2.4 cm; initial lateral separation 0.05 cm; collision and coales­cence at 86 cm. Category IV-A pair of drops; initial vertical separation 3. 1 cm; final vertical separation 2.6 cm at 86 cm; initial lateral separation 0.1 cm; final lateral separation 0.3 cm; slight movement of the drops towards each other.

suggests that, for Category II and III , the attractive force between the dipoles formed on a pair of water drops in presence of the vertical field was greater than the repulsive force between the same, and the net attractive force due to the field decreased with the increase in initial vertical separation of the' drops. For Category IV, the attractive force was a little smaller than the repulsive force. These might be due to the difference in relative positions of the drops and the orientation of the pair of drops (with dipoles formed on them in presence of the electric field) with the direction of the field along the fall-path (Fig. I). At initial stage and along the fall-path, the lateral separations between the drops of the pairs were a little greater for

~ " ~~/ < .: ' IT ~ Table 5-0bservations (mean of 5 sets) of differen't'-Paraf!!c:!~

water drops of 3.42 mm diameter falling in kerosene oil in ab-sence of an electric field (oil temp. 26-28°C, max. depth of fall

Range of Mean depth fall (d) cm cm

0-48 24 0-72 36 48-72 60

Lower Upper drop drop

0-36 18 18 0-50 25 25

36-50 43 43

0-48 24 24 0-72 36 36

48-72 60 60

72 cm)

A v. velocity at d cm S·I

Category I

13.065 13.067 13.072

Lower Upper drop drop

Category II

13 .043 12.996 13 .055 13.405 13 .084 14.583

Category III

12.834 13 .115 12.789 13 .211 12.698 13.408

Category IV

0-48 24 24 12.903 12.938

/

0-72 36 36 12.903 12.996 48-72 60 60 12.903 13 .115

Note: Category I-Single drop falling alone.

Acceleration x 10-4 cm S· 2

+22 +27

Lower drop

+224 +210

Upper drop

+8521 +8505

-476 +1073 -487 +1077

0.0 0.0

+634 +642

Category II-A pair of drops falling one above the other ; initial vertical separation 3 cm; initial lateral separation 0.0 cm; collision at 50 cm. Category II1-A pair of drops; initial vertical separation 4.5 cm; initial lateral separation 0. 1 cm; collision at 72 cm. Category IV-A pair of drops; initial vertical separation 6.5 cm; final vertical separation 6.0 cm at 72 cm; initial lateral separation 0.2 cm; final lateral separation 0.5 cm; slight movement of the drops towards each other.

Category IV than those for Categories II and III. The force of attraction between the dipoles of the pair of drops is maximum when 8 = 0° and the force of repulsion between the same is maximum when 8 = 90°, where 8 is the angle between the electric field direction and th'~ line joining the centres of the drops. For 68° < 8 < 112°, the drops experience mutual repulsion due to polarization charges l8

.

(iii) The accelerations in presence of the electric field were greater than those without the field , causing the colliding drops to coalesce. In absence of a field, two colliding drops never coalesced, and this might be due to the presence of a thin oil film preventing them from coalescence.

(iv) The wake effect for the experimental water drops in mustard oil in the presence of an electric field

20 INDIAN J RADIO & SPACE PHYS, FEBRUARY 1999

of 230 V cm- I was observed up to an initial vertical separation of about 2.4 cm and 3.1 cm of the drops of the pair for collision, resulting in coalescence and slight approach, respectively, at the end of a fall of 86 cm (Table 4).

From inferences (v) of Sec. 4 .2 and (iv) of Sec. 4.3, h appears that the effect of electrostatic force in a vertical field of 230 V cm- I was to overcome a vertical separation of about 5 mm of the two drops of 3.22 mm diameter each, falling in the mustard oil within the depth of 86 cm. It is stated here that Cataneo e/ 01.9 did not observe the effect of

F

50 kV

+ DC

E 7"

I:ig. 1- /\ pair or wat er drops Ihlling in an oi l mediul11 un der a \\.Ttieal ckct ric licld (I' - ) a di poic. 0-)0 thc angh.: bct\\'cc n the: linc joining centre or the drops or the pai r and direction Il l' th ..: c::h.:c tric li c::ld n.

electrostatic charges on the vertical separation of a pair of equal-sized water drops falling in air.

4.4 Observations in kerosene oil in absence of a field

The details of the observations of water drops of 3.42 mm diameter each, falling in kerosene oil in absence of a field are given in Table 5.

In addition to the inferences (i)-(iv) drawn in Sec. 4.2 (which are applicable to tbis case also) the following findings are noted :

(i) The magnitudes of the acce lerations and retardations of the drops in kerosene oil were much greater than those in mustard oil , the terminal velocity of a drop in kerosene being one order more than that in mustard oil.

(ii) The wake effect for the experimenta l water drops in kerosene oil in the absence of a field existed up to an initial vertical separation of about 4.5 cm and 6.5 cm of the drops of a pa ir for co llision and slight approach, respectively, at the end of a fall of72 cm.

The experimental apparatus permitted the drops to be observed for the wake effect · at a maximum distance of 86 cm and 72 cm be low the po int at which the drops attain the term inal ve locity in mustard oi l and kerosene oil , respective ly.

5 Conclusions

During the fa ll ( in the undi sturbed o il medium) of a pair of equal-sized water drops from the initial point , the following (upper) drop got acc lerated with respect to the preceding (lower) drop due to wake effect. T he upper drop co uld oveltake the lower drop under the wake of the latter and , thus, overcome the initial separation, depending on the relative acce leration of the two drops and the length of the fall. The wake effect in kerosene o il wa greater than that in mustard oil, exi sting up to an initia l vertica l separation of 4.5 cm and 2 Clll , respectively, in absence of a field , leadi ng t the colli s ions of the drops at the end of the fall o f 72 cm and 86 cm, respect ive ly. In mustard o il , the relative acce leration of the upper drop, with respect to the lower, was little g rea ter in the presence of a vcrtical e lectr ic field of

23 0 V CIll-1 than in absence o f a fi e ld (causing the

co lliding drops to coa lesce), overcoming an in iti a l vertica l separation of2.4 Clll and 2.0 Clll , respective ly. for the co llis ion at the end of the 86 cm fa ll. The grea ter acce leration was ca used by the e lectrostatic force under the e lec tric field and thi s resulted in the coa lescence of the co lliding drops. Two col li d ing

PA UL: VELOCITIES OF WATER DROPS IN OIL MEDIA & WAKE EFFECT 2l

drops never coalesced in the absence of a field. Further, the wake effects were observed up to an initial vertical separation of 2.6 cm/3 . l em in the absence/presence of the field in mustard oil , and 6.5 cm in absence of a field in kerosene oil , leading to slight approach of the drops of the pair towards each other at the end of the fall.

The trend of these results may be applied qualitatively and approximately to the atmospheric cases, the experimental water drops in mustard oil and kerosene oil simulating a cloud drop of radius 34 11m and a drizzle drop of radius 0.559 mm, respectively, falling in air, the Reynolds number being 0 .52 and 297, respectively. However, the simulated conditions in the present experiments differ from the natural conditions existing in the atmosphere. The differences in the ratios of the densities of water drops to oil and to air, the difference in the dielectric constants of oil and air and the differences in surface conditions of the drops for the experimental and the simulated environments are the major sources of error. Although electrostatically the case of cloud droplets in air and that of water drops in mineral oil are similar, discharge will occur more readily between cloud droplets and at a greater distance of separation where the potential difference between two droplets is larger l7

. Droplet motion and electrical effects , produced by lightning within the clouds may cause a rapid and effective drop coalescence process 14.

Further, the inertia of drops falling within a turbulent flow leads to the format ion of significant velocity deviations from the surrounding ai r '9.

Acknowledgements

The author is thankful to the anonymous referees for their valuable suggestions for the improvement of

the paper. The author is also thankful to Dr A S R Murty for encouragement and help.

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