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 Nove mber 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 radiu s. List and Whelpdale '
observed that factors such as th e collision velocity,
the angle of impact, the s urface tension and th e
electric charges can affect the coalescence of colliding
water drops. Also, electric field s and charges enhance
the coli ision effic ienci es of cloud drops or particl es 2..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 rea r,
and a dro pl et Jllay then capture an even large r
overtaking drop by s uckin g it into it s wake . The
calc ulated linea r collision efficiency is substantially
higher th a n the geo metric coli is ion efficiency for
6
si milarl y sized drops because of the wake effect . The
wake effect behind the collector drops can produce
values o f colli sio n efficiency greater than uni ty 7. The
influ e nce of th e wake effect on the collision and
coalescence of eq ua l-sized drops was studied
experimentall/. The wake effect was noted as far
away as 11.5 c m (vertical se parati o n 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
JO
(Ref. 9). Model ex periments were also conducted · "
in which the fall of cloud droplets in air \vas
simulated by the fall of so lid spheres throug h liquid
viscous media . Faster collisional growth of graupel as
compared to ra in drops is o ne of th e Jllain points of
conceptual mode l of Rosenfeld and Woodley' 2 for
g laciogenic seed in g precipitation e nhancement 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
work ers J.1-' 6.
In thi s study th e labo ratory ex periments 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 lo ud a nd 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 c haracteri zed by the rati o of the inertial force s
to viscous fo rces, i.e. th e Rey nolds number. The
difficulti es in measurin g s izes a nd relati ve pos itions
of the cloud drops falling in air and detecting coll is ion
in the fall-path mi g ht be overcome by co ndu ct in g
16
IND IAN J RADIO & SPACE PHYS, FEB RUARY 1999
Table I-Details of experimental and simulated atmosphere
Experimental cond itions ( I)
Temperature
of oi l
°C
Density
of oil
g cm- J
Viscosity
of oil
poi se
Drop
radius
mm
Simul ated conditi ons (2) at 20°e. 900 mbar
Drop term i- Drag coefftnal velocity
cient
cm S- I
Drop
radi us
pm
Drop
terminal
ve locity
em S- I
C lou d drops fa llin g in ai r
Water drop s falling in mustard oil
0,9 10
28
0.63 19
1.61
Reynold s
Drag
Vert ica l
number for
coeffi- path length ( I) and (2)
cient of simu latcd
atmosphere
m
1. 13
t.3.00
34
33
48
12
0,52
( 134 0)
Water drops fa lling in kero se ne oil
27
0.78S
O.OIIS
1.7 1
Drizzle drops fall ing in air
13.07
0 .7 1
454
(485)
559
0.64
35
297
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; de termined experi mentall y and th ose 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 wa ter dro p radius in mm (!'rom meteorologica l glossery).
mea s ureme nts th at are eaS ier, fo r exa mpl e, by
performing the meas ure ments o n mu c h la rge r wa te r
d rops fal ling in a v isco us o il med ium . The principl e
of sim i larity a Il ows o ne to perform measure ments o n
mu ch larger dro ps a nd to apply th e res ults to c lo ud
drops by choos in g the size, density of drop and the
viscos ity and den s ity of med ium s uc h that Rey no ld s
num ber fo r th e experime nt is the same as th at for th e
I 6 17
atmospheric case . . The si mul ated drop size is
obta in ed as follows:
2
I .
2
D = J[ r - (DPnY
2
". (2)
." (3)
24
For Stoke ' s fl ow,
D,= 6mr V
... (4)
D\
97] V
PnJg
-'
w here, Ps is the de ns ity of dro p.
From Eqs (3 ) and (5),
... (7)
From Eq s (3) and (4),
D
CDR
Ds
24
... (8)
From Eqs (7) a nd (2) e limin at in g V, o ne gets
r
9
l/R
= 4 Pm(Ps -
( D)
... (9)
Pm)g Ds
l6
Us in g R from Eq . (2) a nd from the Co vs R curve ,
CIJ fo r si mul ated a tm osph ere is obtained. The ratio
DIDs for th e atmospheric case and , hence, the
s imul ated drop s ize a re ca lc ulated from Eqs (8) and
(9) . The te rmina l ve loc ity is give n by Eq . (2).
Fo r Stoke's flow, DID, = I . The refore, from
Eq. (7), we have,
V= 2g,·2(Ps - PnJ
Fo r a c lo ud drop falling in air, pm is neg li g ibl e
compared to Ps. T herefore, th e terminal ve loc ity
becomes
2
V = 2gr Ps
balanced by th e net gravi tati o nal force.
So,
~m_3(ps -
2gr2(ps - PnJ
917
At terminal ve loc ity, th e drag o n the s phere is
=
D
3
rV
R = 2Pm
'7
C R
D = - D- 6m7Vr
... (6)
Fro m Eqs (4) and (5),
.,,(1)
w here, D is th e drag forc e actin g o n a spherica l drop
of radiu s r fa ll ing w ith te rminal ve loc ity V und er
grav ity. in a fluid of den s ity Pill and dynamic v iscos ity
11 , Co being the drag-coefficient. Us in g Reyno ld s
number (R), given by
D
16 2(
)
,
CD = :3 gr PI - Pm / VR 7]
... (5)
... ( 10)
9'7
Eq uatin g Reyn o ld s number for the fall of the
expe rime ntal wa.ter dro p in mustard o il/kerose ne oil to
that for th e fa 1,1 of a cloud dro p/dri zzle drop in air. the
s imulated dropsi ze is o btained .
PAUL: VELOCITIES OF WATER DROPS IN OIL MEDIA & WAKE EFFECT
3 Experimental set-up
The vertical motions of a single water drop of 3.22
mm diameter and of a pair of eq ual-sized water drops
of same dimension separated vertica ll y in the initi al
stage while falling through mustard oi l medium in a
perspex tank of size 17 x 17 x 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 depth s were computed. The
time of fall was measured by se nsitive stop watches
correct up to 0.05 s. Necessary illumination of the
tank was made and the temperature of oi I was
measured periodicall y with a sensitive thermom eter
correct up to 0. 10c. 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 catego ry
with five sets of observations was ±0.8°C. The sizes
were determined by weighing 100 drop s (correct up to
four decim a l places) released in th e oil medi ulll under
condition s similar to those inside th e experimental
chamber. The maximum variation in the di ameter of
equal size drops in th e experiments was estimated to
be 10%. A vertical scale and two hori zo ntal sca les.
graduated in centimetres, were fitted to th e 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 depth s of co lli sion and
coa lesce nce of a drop-pair were noted both visua ll y
and photographi ca ll y. Further details of the
experiments are given elsewhere 18. The experiments
in mustard o il were conducted in the prese nce of a
verti ca l electric fi eld of 230 Y cm- I and in absence of
a field . For th e purpose of the electric field , two
parallel copper plates were fitted-Dne at th e top and
th e ot her 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 re spect to the upper plate
which was gro und ed through the negat ive terminal o r
a variabl e 50 kV DC power supp ly. All the
measurem ents were repeated for a ing le and a pair of
water drops of 3.42 Illlll diameter, fall ing in kerosene
17
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 durin g th e 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 llin g in mu stard oil at ~28 ° C was
1. 13 cm s I, while that of the water drop of 3.42 mm
diam eter in kerosene o il at ~ 27°C was 13 .07 cm S- I in
absence of a fi eld . The sa id drops attain ed terminal
velocity at 10 cm and 25 cm of fall from the release
point (need le-t ip ), res pecti vely . While determining
termin al velocity, th e mea n va ri at ion of oil
temperature for six sets of obse rvati ons (each set
corresponding to a complete fall-path of a single
drop) was abo ut ± 0.6°C. Hence, the erro r in terminal
ve loc ity, due to change in viscos ity of oil ca used by ±
Table 2- Tcrlllinall'c locity (l11can of 6 scts or observat io ns) 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\·
Ran ge or fal
Mcan d.:ptil
of -rail
cm s· ! .
Cill
cm
s
Fo r mu s tard o il
0-20
0-] 2
0-86
20-32
32-8f)
10
I II
--I]
21l
5')
17.775
2R .-11<J
76. 156
10.6--1 ·1
--17 .737
I . ! 25
1.126
I I~ <J
127
13 1
For kerosene oi l
0-20
0-48
0-72
2()---I X
--18- 72
10
2"1
]()
J·I
60
1.53 7
3.678
5.5 10
2. 1·11
I .X32
13 .0 12
13.051
13 .067
13 .0 78
iJ . IOO
18
IND IAN 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 wate r 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 se paration for
Table 3-Dbservation s (mean of 5 sets) of different parameters
fu r water drops of 3.22 mm diameter falling in musta rd oi l in
absence of an electric field (oi l temp. 27-29°C. max. dep th of
fall 86 cm)
Range of
fall
cm
Mean depth
0-32
O-X6
32-X(,
16
43
59
1.001'\: r Upper
drop
drop
(d)
cm
Av. velocity at d
cm S- I
Accelerati on
x 10-' cm S- 2
Category I
1.1 252
1.121 4
1. 11 92
Upper
Lower
drop
drop
- 16
- 15
LJpper
Lower
drop
drop
Ca tegory II
0-32
0-62
32-62
16
31
,,\ 7
16
31
47
1.1197
1.1 4 1X
1.1664
1.1 307
I IX59
1.2510
+ 172
+ 172
+460
+460
16
43
59
16
43
59
1.2044
1.1 073
1.1931
1.2181
1.2344
1.2442
(iii) The drops were accele rated or retarded durin g
the fa ll-path. The acce lerations or retardations
were fair ly uniform at different depths durin g 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 du e 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 th e fall-pat h could
overcome the initial vertical separat ion between
the drops, coli ision of th e drops wou ld occ ur.
(iv) The relative acce leration of the upper drop with
respect to the lower drop dec reased graduall y
from Category II to Category IV showing th at
th e wake effect decreases as the initia l separation
of the drops increases . Also, the relati ve
acce lerati ons at different depths of fa ll were
nea rl y th e same for.e ach cateogory.
(v) The wake effect for the experimenta l water drops
in musta rd oi L in abse nce 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 slight approach (towards each other) at the
end of a fall of 86 cm.
J
4.3 Observations in mustard oil in prese nce of a fie ld
Ca tegory III
0-32
0-X6
32 -X6
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 th eir
termina l velocities. The ve locity of the following
drop was greater (at higher depths) or a little
greater (at lower depths) than that of the
preceding drop.
-3 I
-32
+75
+75
Category IV
I. !985
1.1 985
16
{J-32
16
- 30
-3
1.1 9 16 1.1 9n
43
0-X6
43
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 se paration 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: slight
1ll00'clllcnt of th e drops towards each other.
The details of the observatio ns for water drops of
3.22 111111 diameter falling in Illu stard oil in prese nce
of an e lectri c 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 Illu stard oil , the termin al ve loc ity of a single
drop in th e electri c fie ld ( 1.15 Clll s 1) is slightly
greater th an that in absence of the fi eld ( 1.1 3 cm
s 1).
(ii ) In mu stard o il, th e ve loc ities of either of the
drops in the prese nce of the field were grea ter or
sli ghtl y greater at lower initial separations
(Category 1/ and 1/ I) an d sl ightl y sma lI er at
hi gher initi al se parations (Category IV) than
th ose in th e absence of th e field (Table 3). This
( '.:' <
I.
PAUL: VELOCITIES OF WATER DROPS IN OIL MEDIA & WAKE EFFECT
\\\
\\
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
fall
cm
Mean depth
(d)
cm
Av. velocity at d
cm S· I
Acceleration
x 10. 5 cm
S· 2
16
43
59
Lower
drop
water drops of 3.42 mm diameter falling in kerosene oil in absence of an electric field (oil temp. 26-28°C, max. depth of fall
72 cm)
Range of
fall
cm
Mean depth
(d)
cm
16
25
41
16
25
41
1.1896
1.3077
1.5702
Upper
drop
Lower
drop
Upper
drop
Lower Upper
drop
drop
16
39
55
16
39
55
1.2062
1.2223
1.2336
1.2214
1.3600
1.6814
+ 1952
+ 1952
+2453
+2453
0-36
0-50
36-50
18
25
43
18
25
43
1.2261
1.2687
1.2994
Lower
drop
Upper
drop
+22
+27
Lower
drop
Upper
drop
13 .043
13 .055
13 .084
12.996
13.405
14.583
+224
+210
+8521
+8505
-476
-487
+1073
+1077
0.0
0.0
+634
+642
Category III
+85
+85
+236
+235
0-48
0-72
48-72
24
36
60
24
36
60
Category IV
)
Acceleration
x 10-4 cm S· 2
Category II
Category III
0-32
0-79
32-79
A v. velocity at d
cm S·I
13.065
13.067
13.072
24
36
60
0-48
0-72
48-72
+26
+26
Category II
0-32
0-51
32-51
'
0-32
16
16
1.1586 1.1586
43
43
+28
1.1513 1.1650
-31
0-86
1.1470 1.1688
-31
+28
32-86
59
59
Note : Category I-Single drop falling alone.
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 III-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
. t... /
~/
' ~
IT
~
Table 5-0bservations (mean of 5 sets) of differen't'-Paraf!!c:!~
Category I
1.1436
1.1497
1.1534
Lower Upper
drop
drop
j
~ < .:"
Category I
0-32
0-86
32-86
. rt:-t~ ~~
.
crf7l,T;;~ 0 .(~) .~: ~:)\
.. f .))h !d9?~:·;, ,-.
12.834
12.789
12.698
13 .115
13 .211
13.408
Category IV
0-48
0-72
48-72
24
36
60
24
36
60
12.903
12.903
12.903
12.938
12.996
13 . 115
/
Note: Category I-Single drop falling alone.
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
I
of 230 V cm- 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
I
vertical field of 230 V cm- 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
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 mu stard 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 a bout 4.5 cm
and 6.5 cm o f 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 equa l-sized water drops from th e initial po int ,
the following (upper) drop got acc lerated w ith
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, overco me th e
initial separation, de pending o n the relative
acce leration o f th e two drops and the length of the
fall. The wake effect in kerosene o il wa greater than
that in mu stard 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 th e
drops at the end o f the fall o f 72 cm and 86 cm,
respect ive ly. In mustard o il , the rel ative acce lerati on
of the upper drop, with respect to the lower, was little
g rea ter in th e presence of a vcrtical e lectr ic field of
50 kV
+
DC
1
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 th c angh.: bct\\'cc n the:
linc joini ng ce ntre or the drop s or the pai r and direction Il l' th ..:
c::h.:c tric lic::ld n.
23 0 V C Ill- than in absence o f a fi e ld (causing the
co llidin g drops to coa lesce), overcomin g an in iti a l
vertica l separatio n of2.4 Clll and 2.0 Clll , res pective ly.
for th e co llis ion at the end of the 86 c m fa ll. Th e
grea ter acce lerati on was ca used by the e lectrostatic
force under th e e lec tri c field and thi s res ulted in the
coa lesce nce of the co llidin g dro ps. T wo col li d in g
PA UL: VELOCITIES OF WATER DROPS IN OIL MEDIA & WAKE EFFECT
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 di stance of separation where
the potential difference between two droplets is
larger l 7 . 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
2l
the paper. The author is also thankful to Dr A S R
Murty for encouragement and help.
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