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vapor) configurations. III. Dynamics of drop impaction, attachment, and spreading
Spreading and Wetting Phenomena in Four-Phase (Liq uid/Liquid/Substrate/Vapor) Configurations III. Dynamics of Drop Impaction, Attachment, and Spreading M. C. WILKINSON,* I. C. MATTISON,* A. C. ZETTLEMOYER,t J. W. V A N D E R H O F F , t AND M. P. ARONSON$ *Chemical Defence Establishment, Porton Down, Salisbury, Wiltshire, SP4 0JQ, England; tCenter for Surface and Coatings Research, Lehigh University, Bethlehem, Pennsylvania 18015; and ~-Lever Bros. Research Center, 45 River Road, Edgewater, New Jersey 07020 Received September 14, 1977; accepted August 23, 1978 The impaction, attachment, and spreading of oil drops on various substrates submerged under thin films o f water (<1 mm) has been shown to occur very rapidly (<10 -1 sec). Four-phase, substrate/oil/water/air configurations were formed during this short time interval and these rapidly approached an equilibrium state as the drop impaction energy was dissipated. The system either formed a stable configuration, split (if the water height was large), or disrupted (if the water height was small). In cases where the impaction energy was large, the dynamic advancing contact angle was in the region 150 to 170 °. The oil drops therefore spread in a similar manner to that recorded for very hydrophilic substrates such as glass and metal, and disruption did not immediately occur. Relaxation times of the advancing contact angles, perhaps to the advancing values for disruption were long in comparison to the impaction and spreading processes. Disruption of the configuration, or separation of the oil and water phases, occurred in less than 10-z sec. This process occurred when both oil/water/air and substrate/oil/water three-phase interfaces were separated by at least 2 x 10 -2 ram. INTRODUCTION
Despite the obvious importance of drop impaction and spreading processes, little attention has been devoted to their study, possibly due to the complexity of the processes occurring (3). These were described qualitatively as early as 1879 by Lord Rayleigh (4) and 1897 by Worthington (5), but a detailed study of the processes had to await the development of high-speed cinephotographic techniques. Recent studies using these particular techniques (3, 6-8) have confirmed the complex nature of the processes occurring and in addition the importance of the dynamic contact angle (9-12), as opposed to the equilibrium contact angle, in describing spreading and wetting processes. Impact, attachment, and spreading processes occurring in several different systems have been shown to be remarkably
Many important processes, such as the attachment of air bubbles to mineral ores during froth flotation (1, 2), the spreading of agricultural sprays on crop foliage (3), and the wetting-out of fabrics by rain drops depend for their action on processes occurring within very short time intervals. For example, in froth flotation, collector air bubbles spend only a short time (< 1 sec) within the mineral suspension and they must collect many grains on their way to the water surface to make the aeration profitable. Similarly, the quantity of agricultural spray required to effectively treat a crop depends on the extent of wetting and adhesion which can be achieved during drop impaction and attachment, i.e., if the droplets bounce off the leaf "in toto" then they are totally ineffective as an insecticide. 560 0021-9797/79/030560-15502.00/0 Copyright© 1979by AcademicPress, Ine. All rights of reproductionin any form reserved.
Journal of Colloid and Interface Science, Vol. 68, No. 3, March 1, 1979
SPREADING
AND
reproducible (9-12), and valuable information with regard to spreading and wetting processes has been obtained. These types of studies have provided a much clearer understanding of many naturally occurring and industrial processes despite the present lack of precise mathematical treatments to describe them. The purpose of the present study was to gain a better understanding of the rapid processes of oil-drop impaction at a wetted surface and the subsequent formation of partially submerged drops or fourphase configurations (13). The study was confined to substrate surfaces covered by very thin films of water, i.e., <1 mm. A study was also made of the rapid processes of disjoining or disruption and splitting (13, 14) which occur during the breakdown of these four-phase configurations. EXPERIMENTAL
All materials and general procedures are as described in Parts I and II (13, 14). One-hundred-foot reels of cine-negative film were used in high-speed cameras capable of speeds between 150 and 5000 frames/ sec; in most experiments the camera was run at 500 to 1200 frames/sec. Since the total filming time was only 1 to 8 sec, slow changes or relaxation phenomena of the type discussed in detail in Part II (14) could not be followed. The procedure was to allow an oil drop from an Agla microsyringe to fall a fixed distance (usually 100 to 120 ram) and impinge on a substrate surface covered with a thin film of water. The camera was started at
WETTING,
561
III
the instant the drop fell from the syringe so that the velocity of impact and processes of impaction and attachment could be recorded. The mass of the drop was within the range of 10 to 40 mg. One of the unavoidable difficulties with high-speed cinephotography of impaction and attachment processes is that no control can be exercised on the length of the induction period (see below). Fortunately in the present system all induction periods were <0.4 sec, and fell within the total filming time of the camera (1 to 8 sec, depending on speed). However, this meant that all drops were in their oscillatory mode of impaction when attachment occurred (see below) which tended to obscure the true forces acting on attachment (12). The cinefilms (Kodak High Contrast, Type 7457) were analyzed directly and the parameters as given in Fig. 1 were determined. RESULTS I.
OIL
AND
DISCUSSION
DROP
IMPACTION
Before impaction and attachment of the oil drop could occur at the wetted substrate surface, the "air cushion" formed between the drop and the water surface had to be displaced. "Induction periods," or times for this air cushion to be displaced, are generally very small for most systems where pure liquids are involved, and especially where the drop possesses some kinetic energy (11, 15). Induction periods in the present system were estimated to be < 10-~ sec,
SPREADING VELOCITY
AIR
-,,, /
/
/."
//
0, /
/
( 0R/
/~ ¢" / d," ," / i / I ~ SUBSTRATE - 7
F I G , 1. P a r a m e t e r s
measured
1 /
/
/
,"
/
,-
during spreading.
Journal ojColloid andlnterJace Science, Vol. 68, No. 3, March I, 1979
562
W I L K I N S O N ET AL.
PLATE 1. Approach of 8-mg oil drop at 4.8 m sec -1.
and were not a factor in the subsequent attachment at the substrate surface. Although most impacting oil drops with mass greater than 10 mg managed to form an oil/water interface during their residence time at the surface, some were reflected when the impaction energy was high (16). The work of adhesion (WA) of an oil to water is less than the work of cohesion of the oil (Wc), for oils which do not spread on water. However, WA can approach Wc during rapid dewetting (by the oil) since the dynamic receding contact angle (0dy, rec) between the oil and water approaches 0°, i.e., W A ( = ' ) / 0 (1 + cos 0dyr, re¢)) ~ We (=2T0), where 70 is the surface tension of the oil. In this case reflection of these oil drops in toto may not always occur. The drop may become encapsulated in an ejected column of water (Plates 1-3). It is not unknown for drops to be reflected in toto from thin layers of the same liquid on certain substrates (6, 7). However, it is usually found in these cases that it is some property of the underlying solid substrate which is responsible for this. For example, Hartley (7) found that a bean (Vicia) leaf accepted all incident water drops (within a Journal of Colloid and lnterjace Science, Vol. 68, No. 3, March 1, 1979
certain size range) when dry, but when uniformly wetted with a thin film of water it reflected all subsequent arrivals. This was ascribed to the microroughness of the leaf surface, whereby the impacting drop could not completely displace the air from the rough surface; thus being reflected. Thin films of water on a substrate are only successful in "reflecting" impacting drops if the drainage time for the water film between the drop and the substrate is larger than the impaction time, i.e., the induction period is greater than the residence time. The residence time is defined as the period which elapses while the oil drop is within sufficiently close proximity to the substrate surface such that an oil/substrate interface will be formed if the trapped water film between the drop and substrate is capable of being displaced. The water film is only capable of preventing impaction at the substrate surface if relatively deep, since penetration depths for impacting oil drops in bulk water can be very large (Plate 2, Fig. 2) even for small drops with densities less than unity. The residence time which the oil drop has at the substrate surface depends on the depth of the film. For example, a 3.5-rag
563
SPREADING AND WETTING, III
PLATE 2. Maximum penetration in bulk water after 2 × 10 2 sec.
oil drop at an impaction velocity of 0.7 m sec -1 penetrated 8.7 mm in 0.015 sec (Fig. 2), and therefore, if a substrate surface was interposed at this particular depth, then the residence time of the drop would be zero, i.e., attachment would be impossible. However,
for film depths less than this, residence times of 0.05 sec, or less, may be expected. Any secondary impaction process due to collapse of an ejected column of water, which may encapsulate the oil drop (Plate 3), results in significantly smaller penetra-
IO
12
I0
6~
E
T VELOCITY
2--
4~ INmAL
0
I0
N3.S~I
~
~
~31
PENETRATION X ~ffirCECTi0 N //p~ECEOTNDAARoYN "~
0.04
0-06 TIME [see)
0.1Z
0,16
Fz~. 2. Relationship between penetration and impact velocity for paraffin oil drops in bulk water. Journal of Colloid and lnterJace Science,
Vol. 68, No. 3, March 1, 1979
WILKINSON ET
564
AL.
PLATE3. Ejected water column and encapsulated oil drop after 6 × 10-2 sec. tion of the water (Fig. 2). If attachment occurs on secondary impaction then spreading may proceed since any residual energy within the drop at this stage is very much smaller than its original impaction energy (17) and possibly insufficient to cause a secondary recoil (Figs. 3 and 4). Failure to attach resulted in the formation of an oil lens on the water surface. Vibra-
tions within the drop were rapidly damped by the surface forces (<0.5 sec) and a stable contact angle (4~) of 157° formed. Contact with the substrate surface was then only possible by significant thinning of the water film, e.g., for a 40-mg drop (4~ of 157 °, and density 0.88 g m1-1) this would correspond to - 1 mm. Although attachment occurred during the
18c
~
~
f
fJff
DISRUPTITf/
E o lg
o
12C
I00 TIME {see)
FIG. 3. Drop impaction and spreading at graphite/water interface. Journal of Colloid and Interface Science,
Vol.68, No. 3, March1, 1979
565
SPREADING AND WETTING, III
, 0[
/I
160
~TION
--140
,,t
o
120
eAv
100
Ii~ 0.05
0.0
f
0.25 TIME (see)
0!50
I 0'75
I'0J
FIG. 4. Drop impaction and spreading at Teflon/water interface.
residence times of oil drops at the different surfaces considered, many of the drops still had sufficient residual energy after impact to bounce (Figs. 3 and 4). Drops not possessing sufficient residual energy to bounce off the surface oscillated and retarded the spreading process (Figs. 5 and 6). For ex-
ample, in the case of a low-energy impacting drop on polymethyl methacrylate very much faster spreading occurred than in the case of a drop exhibiting significantly larger kinetic energy (Fig. 7 and Table I). The faster spreading led to disruption after 0.3 sec, while the slower spreading drop disrupted after 3 sec.
180
160
E
8
TIME (sec)
Fro. 5. Drop impaction and spreading at Teflon/water interface. Journal of Colloid and lnter/~lce Science,
Vol.68,No.3,March1, 1979
566
WILKINSON
ET AL.
'B°I
eA,
~AV
E 4~
d
140
o
120
o.do4~o!,
o!s
TIME (see)
,.'o
,!s
FIG. 6. Drop impactionand spreading at graphite/waterinterface. Similar phenomena were noted with charcoal and polytetrafluoroethylene surfaces (Figs. 3 and 4), but in these cases sufficiently large amounts of the high impaction energies were dissipated on bouncing to allow rapid spreading on second impaction. It is the magnitude of 0oyn rec which de-
termines whether any part of the oil drop is left adhering to the substrate on recoil. Reflection in toto does not always occur, even when high surface energy drops impact on low surface energy solids. Pfeiffer (17), for example, found that 70-/zm-diameter water drops did not reflect in toto from a paraffin
180 ! OL~RLIPI'tON
AV
RUP'TION
/ / .,/
e,~v.~v, a'- t3,.goi,a,-op d
/
6 E E
z
r121
,
0'5
I!0
/~ TIME (~c)
FIG. 7, D r o p (13 a n d 25,6 m g - - T a b l e
,
2'0 ~'-
I) i m p a c t i o n a n d s p r e a d i n g at P l e x i g l a s / w a t e r i n t e r f a c e .
Journal of Colloid and Interface Science, Vol. 68, No. 3, March 1, 1979
SPREADING AND WETTING, III
567
TABLE I Impaction and Spreading of Oil Drops at Prewetted Surfaces
Reference
Fig. Fig. Fig. Fig. Fig.
3 4 5 6 7
Fig. 7 Fig. 9 Fig. 10
Substrate
Graphite Teflon Teflon Graphite Polyrnethyl methacrylate Polyrnethyl methacrylate Teflon Mercury
Waterfilm depth (ram)
Oil drop (rag)
Velocity of drop impact (m sec -1)
Spreading velocity (m sec -~)
0E~t
0EQ AD
0.9 0.7 0.5 0.5
33.0 25.6 13.0 25.6
2.08 -0,70 1.41
36.0 34.0 7.0 17.4
45 20 20 45
0.5
25.6
2.03
4.8
0.6 0.9 0.3
13.0 25.6 25.6
0.12 0.30 1.88
4.5 11.3 12.8
surface, a very small droplet was always left behind. High-speed photography showed that the dynamic receding contact angle dropped dramatically during recoil such that WA a p p r o a c h e d We. Simple analysis using the equilibrium contact angle (0~q) of 108 ° would, however, have predicted no adhesion s i n c e W A (0eq = 108 °, 0.05 Jm -z ~ We (0.144 Jm-2). The surface energy decrease (AE) for the impaction of an oil drop at a p r e w e t t e d surface, where an oil/substrate interface is formed is given to a first a p p r o x i m a t i o n by AE = (4~r2To + 7rRyw +
7rR23/s/w)
--
(TrR2y0
+ 7rRhTo/w + 7rR2y~/0),
[1]
where h is the depth of the w a t e r film, H R 2 is the area o f interface formed or lost, r is the radius of the impacting oil drop, and To, yw, ys/w, and ys/0 refer to the oil, water, substrate/water, and substrate/oil surface and interfacial tensions, respectively. F o r simplicity, it is a s s u m e d that the oil in w a t e r was of a cylindrical form with an oil/water contact angle o f 90 °. N o w using Y o u n g ' s relationship (18), i.e., Ys/w - Ys/0 = Yo/w cos 0eq.
[2]
Equation [1] can be rearranged to give
0DyN ADV
KE of impact (~J)
SE of impact (M)
120 29 29 120
165 160 160 170
70.4 -3.15 25.0
1.83 1.56 1.00 1.56
43
115
170
52.8
1.56
43 20 85
115 29 89
160 160 150
0.1 1.15 45.0
1.00 1.56 1.56
AE = 7rR2[yw + Y0/w X (COS 0eq - -
h/R) - Y0]
+ 4¢rr2y0 .
[31
It is apparent from Eq. [3] that AE depends on 0~q and the extent of spreading (Fig. 8). A large amount of the impact energy can be dissipated by the spreading process if the oil preferentially wets the substrate (e.g., polytetrafluoroethylene) but no energy can be dissipated in this m a n n e r with a very hydrophilic substrate such as glass. Energy decreases on spreading can only app r o a c h the kinetic energies of terminal velocity drops when the drops are very small (3) and within the range of aerosol droplets ( < 6 0 0 / z m in diameter). Thus, with the range of drop sizes used in this work, surface energy changes only b e c a m e p r e d o m i n a n t when the bulk of the kinetic energy had been dissipated by the impaction process itself (Figs. 3 and 4). Predicting whether a drop will either be reflected f r o m a wetted surface or adhere and spread is generally very difficult since the energy absorbing processes on impaction cannot be determined. H o w e v e r , for low impaction energies on substrates preferentially wet by oil, reflection b e c o m e s less likely since energy can be dissipated Journal of Colloid and Interface Science, Vol. 68, No. 3, March 1, 1979
568
WILKINSON
ET AL.
2O
15,
g >.
g
S*l
s
0 GLASS(O [q- 16501
o
;:
,;
~
~,ASE RADIUSOFSPREAOINGOI~OP(mml
FIG. 8. S u r f a c e e n e r g y d e c r e a s e o n s p r e a d i n g o f d r o p s o n d i f f e r e n t s u r f a c e s .
by spreading and displacement of the water. For example, a 25.6-mg oil drop impacting at a polytetrafluoroethylene surface (water depth of 0.9 mm) with energy of 2.71 /xJ (1.15 /.LJ K E + 1.56 /zJ S E - - T a b l e I) showed very little oscillation during spreading (Fig. 9) and the surface energy decrease rapidly e x c e e d e d 25 ergs (Fig. 8), i.e., the spreading process rapidly led to a decrease in the total energy of the system. II. FOuR-PHASE
CONFIGURATIONS
1. A t t a c h m e n t at the Substrate
It is doubtful whether the initial contact of the oil with the substrate occurred at a single point, where the contact angle was just less than 180 ° . A t t a c h m e n t m o s t probably occurred across a liquid bridge which was at least 1 nm 2 in cross section (19). Watanabe, Higashitsuji, and Nishizawa (20) Journal of Colloid and Interface Science, Vol. 68, No. 3, March 1, 1979
found that a liquid bridge of ca. 2 x 10 -2 m m diameter was formed in < 5 x 10 -3 sec across a gap of 10 -1 m m during the coalescence of two drops of 10 -1 M KC1 in methylisobutyl ketone containing 5 x 10-3 M cetylpyridinium chloride. The actual process of a t t a c h m e n t was exceedingly difficult to observe in any of the present s y s t e m s since it not only occurred very rapidly ( < 10 -a sec) but the drop/substrate interface could not be clearly resolved photographically. Wilkinson and Elliott (12) have shown that initial a t t a c h m e n t of an oil to a m e r c u r y / w a t e r interface occurred in < 6 x 10 -4 sec and the initial contact angle appeared to depend on the difference in works of adhesion of the oil and w a t e r for the substrate. Certainly, incorrect contact angles can be measured from photographs unless clear resolution of the interface during time intervals < 10 .3 sec can be obtained.
SPREADING AND WETTING, III
/
I1~, /
/
v /
/
r-
/
r
569
-,
//
DISRUPTION
e~ v
-
d
..-
8
i
o.'ozs
o:~
TIME (see)
o.~T~
o.Ioo
F]6. 9. Drop impaction and spreading at Teflon/water interface. In many situations it is probable that complete wetting o f the substrate by the oil does not occur, especially if attachment is rapid (21-24). In this case droplets of water may be trapped in the attaching oil phase, or air may be carried through by the oil drop. These water droplets or air bubbles do not apparently affect the general spreading processes, which are controlled by the interfacial forces acting at the advancing front of the drop (12), but they may act to disrupt the oil film as it thins on spreading (13), thus causing the configuration as a whole to become unstable and disrupt. The rate of drainage of the trapped film of water depended on many factors (25), such as the impaction energy, surface tension, density difference between oil and water, drop size, viscosity of the water, nature of any adsorbed films, and magnitude of electrical double layer and electroviscous forces. Induction periods were several orders of magnitude smaller than those calculated on the basis of the approach of two fiat plates (26) and attachment almost certainly occurred on localized failure of the water film at relatively large water-film thicknesses (e.g., 10 -5 to 10 -3 cm).
The magnitude of the energy barrier to attachment o f the oil to the substrate surface and the displacement of water is given by [4]
E = Kyo/w h2,
where h is the film thickness, y0/w is the oil/water interfacial tension and the constant K, depends on the geometry of the liquid bridge, which for a cylindrical bridge is given by 1 cos Oeq + 1
(cos 0eq + 1)2 _
cos Oeq
]
(cos Oeq + 1)2 I ' where 0~q is the equilibrium contact angle in the oil/water/substrate system. This energy barrier is extremely small ( - 1 0 -4 ergs for h = 10 -3 cm) and cannot be a factor in attachment when impacting drops are being considered. 2. F o r m a t i o n
If the oil drop displaced the water film and made contact with the substrate surface a four-phase configuration was formed. The Journal o f Colloid and Interface Science, Vol. 68, No. 3, March 1, 1979
570
WILKINSON
subsequent stability of the configuration then depended on the magnitude of the residual energy in the drop (energy left after impaction and spreading) and the water film depth. When h < hspnt > hms, and the residual energy after impaction and spreading was insufficient to enable the drop to bounce, then a stable four-phase configuration was formed within 1 sec. This was also the case when the drop had sufficient kinetic energy to bounce, but attachment occurred on secondary impaction. Failure to attach resulted in the formation of an oil lens on the water surface. In this case, for the oil under consideration, formation of a four-phase configuration was then impossible since the water-film depths were always too great to allow oil/substrate attachment to occur (see above). When h > hspnt, and the induction period of the oil at the substrate/water interface was less than the residence time, then a transient configuration was formed which quickly split; part of the oil transferring to the water surface and part being left adhering to the substrate surface. In situations where h < hdis and the impaction energy was low, the configuration spread rapidly and disjoined (Fig. 7). However, with high impaction energies some drops bounced and failed to make contact on secondary impaction. In these cases an oil lens was formed and spreading and disruption did not occur.
3. Changes in Contact Angles There were very large fluctuations in the magnitude of the oil/water/air contact angle (4~--Fig. 1) during the first 10-1 sec, with values between 110 and 170° being recorded (Figs. 5 and 6). The extent of these fluctuations was much greater with the highenergy impacting drops than with the lowenergy ones. The degree of drop distortion occurring during these time intervals was reflected in the wide variation in qSLEVTand (~RIGHT(Fig. 1). Vibrations in the drop were rapidly Journal of Colloid and Interface Science, Vol. 68, No. 3, March 1, 1979
ET AL.
damped and ~ differed from ~beq (158°) by only a few degrees after ca. 0.3 sec. Similar short time intervals for the damping of induced oscillation on drop impaction have been noted for bubbles and drops attaching at a variety of surfaces (9-12). Spreading velocities had dropped from the very high initial values (Table 1) to <2 mm sec -1 during this time period. These results are in accord with those found earlier (14) where (h remained constant until the spreading velocity exceeded ca. 0.2 mm sec -~, whereupon it increased. Thus, the three-liquid system exhibited much smaller molecular reorientation times than liquid/ liquid/solid systems (as reflected in the magnitude of 0). The spreading velocities of drops at the various substrates were very much larger (Table I) than those recorded in Part II (14). The dynamic advancing contact angles (0oyn aov) were also greatly in excess of the equilibrium contact angles (0eq--Table 1) and very similar for all the different surfaces employed. This similarity in 0 d y n a d v was expected for rapidly spreading drops and is related to disorientation effects of molecules at the oil/water/substrate interface (14). The rate of spreading decreased rapidly as the impaction energy was dissipated, such that the oil-drop diameter became almost constant after ca. 0.2 sec (Figs. 4-6). The contact angle, 0, then gradually decreased. The contact angle at the mercury substrate, however, fell very rapidly (Fig. 10) since relaxation times of molecules in three-liquid systems are small. This system was also very unstable since it exhibited very little contact-angle hysteresis (13), and this instability was manifested in the very rapid spreading and disruption which followed attachment (i.e., -0.04 sec). This can be compared with the polymethyl methacrylate system (Fig. 7) where the impaction energy was similar (Table I), but the contact-angle hysteresis was very large (13, 14), in this case disruption occurred after 3 sec.
SPREADING
AND WETTING,
57 1
III
i
f
/"/f/"
"
DISRUPTION
S.\
d 10
-~ 140 z~
c::
12(1
IOC O' I
0'02 TIME (see)
0'03
0'04
FIG. 10. D r o p i m p a c t i o n a n d s p r e a d i n g at m e r c u r y / w a t e r i n t e r f a c e .
As long as the contact angle, oil-drop diameter, and water-film thickness remained within certain limits, the configuration was stable towards disruption or splitting (13). Although all of the present systems were basically unstable (since h < hdi~) for the particular oil volumes employed, disruption did not occur immediately since hd~s decreases with increasing contact angle (14) and most of the systems exhibited very high dynamic advancing contact angles during the initial stages of spreading. Thus, all the substrates behaved as if they were hydrophilic, such as glass or metal. Fourphase configurations on very hydrophilic surfaces are stable (to disruption) down to very thin water-film depths. Thus, it is of note that in all of the systems studied it was the magnitude of 0aynadv which was important and not 0e,, where 0dy~adv depended on the velocity of interface movement and the speed of the molecular reorientation processes occurring at this interface. The vibration of the oil drop diminished very quickly after the rapid processes of impaction and attachment. This involved a decrease in 0 (if the substrate was hydro-
philic) at almost constant or slowly increasing drop base diameter; a process which was relatively slow and in most cases outside the filming time of the camera (i.e., >5 sec). If the contact angle fell to that value corresponding to the advancing angle for disruption (for that particular water film depth and oil volume) then the oil drop respread and disruption followed. An example of this is shown in Fig. 4 for polytetrafluoroethylene, where 0 suddenly fell to 105° (after 0.9 sec) and the oil drop began to spread and disrupt, i.e., the advancing contact angle for disruption in the case of a 25-rag oil drop at a water-film depth of 0.7 mm was ca. 105°. Since the degree of instability of partially submerged oil drops in thin films of water depends on the magnitude of the contact angle hysteresis or, in the case of interface movement, on 0dynadv, as opposed to 0eq (or any other angle (13, 14)), then the time which elapses before disruption occurs is govered by the spreading velocity and the nature of the substrate surface. All the systems shown in Figs. 3 to 10 were basically unstable since the water film depths were all below hj~ for the respective systems. Journal of Colloid and Interlace Science, Vol. 68, No. 3, March 1, 1979
572
WILKINSON ET AL. I
X
/
Time 0.01 see
\
AIR / /
d: 1 . 8 5 mm
\ \
/
AIR
~OIL"/AIP~
\
~W A T E ~
/I/
,/
\"~
//
/
it. 0'4 mm V c o l : 3 . 6 ~ 1 V:25.6,ul
~"
OIL
. . . .
h:O,7 mm
/
/~//
/'
W;T?/
SUBSTRATE
TIME 0.20 •~" - - ~ .
/
d- 2.75mm h -l~0-7mm Vca I " B.B,ul V.ZS.6~ul
~
/ /
""
\
/
/ ~ / /
// / / / / / / / /
III TIME 0.90 see d= 3.55 mm h= I =0"7 mm Veal z 13,?ul V=25.6,pl
TIME= 0.95 s¢c h ~ l = 0 "7 mm
V= 25-6~I
Vc a l = ~ . 6 , u l / / / / / /
/
//
/
/
/
TIME= 1.00 sec d = 6.ZO mm h =1= 0"7 mm V e a l = 31.7~JI V ' 2 5 . 6 ) J I
/
/
/
/
/ / / /
/
/
/
/
//
/
/
/
TIME > 1 . 0 0 stc dest = 8 mm h = I ~ 0"7 mm
/
Vcal = 49,6JJI V 25-6)11
\ -
-
.
-
/ / / / / ' /
/ / / /
/
/
/
/
/
/
/
/
/
/
/
/
/
FIG. 11. Spreading and disruption of the Teflon/oil/water/air configuration. (a) Oil drop receding-prior to breaking substrate contact. (b) Second impact--drop spreading. (c) Drop spreading. (d) Prior to disruption. (e) Disruption occurs. (f) Hypothetical state of spread. Journal of Colloid and Interface Science, Vol. 68, No. 3, March 1, 1979
SPREADING
AND WETTING,
was contained below the free water surface. It was found that most drops advanced across the substrate surface at about the same contact angle (150 to 170°) and further, that the oil/water meniscus could be described reasonably accurately as a straight line joining the oil/water/air intersection to the substrate/oil/water intersection; calculation shows that the radius of curvature of the oil/water meniscus was approximately 19 ram. It was therefore possible to draw the drop profile during spreading and calculate the volume of the oil drop contained below the free water surface (from simple cylinder of height h, Fig. 1); these are given in Figs. i 1 and 12 for two different systems (drawn to scale of 20:1). The remainder of the drop profile (i.e., the difference between actual and calculated volumes) has been drawn on this basis.
However, several systems were stable for many seconds before disruption finally occurred, and it was during this time period that 0 decreased towards its value for disruption. Thus, it is apparent that highenergy impacting oil drops may be reflected or bounce before disjoining can occur, whereas with low-energy impacting drops disjoining may be very rapid, although considerations based on "equilibrium" data would have predicted disruption in both cases. III. DISRUPTION Although the complete profile of the impacting and spreading drop could not be clearly distinguished (i.e., the oil/air meniscus could not be observed), it was possible to estimate what proportion of the drop
i// AIR
t\ \
/ /
.~'~0"0 ILl AIR WATER/AIR/ OIL
o)
"x, AIR ., ~
~
/
Time 0.t0 sec d= 3'55mm h= 0-6 mm i = 0 . 5 mm V celt= 6.3)JI V : 12)JI
"
//
\
/
\\
,..
b)
Time 0.20sec d= 4,95 rnm k=0'6 mm L=O.S mm V cal=ll,Sul V=12~l
7 / / 7 / ' / - / f
. ~
Time 0.005 sic d: Z'15mm h: O.6mm l= O'5mm 2"51,11 V=121ul
SUBSTRATE /
(:)
573
III
/
~/"
/
7
/
/
/" ~
Time d: I~= I.= Vca.L :
/
/"
6.275 s i c 6-25 mm 0.6 mm 0.35 mm 12"5 ,ul V:12/ul
\____,..
.f.. ,) Fz~. 12. S p r e a d i n g a n d d i s r u p t i o n o f t h e P l e x i g l a s / o i l / w a t e r / a i r c o n f i g u r a t i o n . (a) Oil s p r e a d i n g . (b) Oil s p r e a d i n g . (c) P r i o r to d i s r u p t i o n . (d) D i s r u p t i o n o c c u r s . Journal of Colloid and lnterjace Science, Vol. 68, NO. 3, March 1, 1979
574
WILKINSON ET AL.
It is obvious from the system of interfacial forces acting that some form of breakdown has to occur if the drop spreads beyond a certain s t a g e - - r e f e r to Figs. 1 le and 12d. This stage was reached when the oil/air interfacial tension could no longer act at an angle of 93 ° (calculated from interfacial tensions) to that of the oil/water interfacial tension, and occurred when the oil/ air meniscus dropped below the water level, or more specifically oil/water/air intersection. Disruption was in fact found to occur when this stage was reached. The actual process o f disruption could not be observed, partly since the process occurred in less than 10 -3 sec, but mainly because there was a sudden change in refractive indices in the system on disruption of the oil/water interface. Although it is clear that disruption occurs at some positive value o f / (13), there is no experimental p r o o f that this occurred when the balances of forces acting at the interfaces (oil/air/water and oil/water/substrate) and the Laplacian equations describing the curvatures of the liquid interfaces (28) could not simultaneously be maintained. It was not possible to achieve attachment of a very wide range of oil-drop sizes (even at very small water depths) at any of the very hydrophilic substrates such as glass and metal surfaces, since the induction periods were very much longer than the residence times. Maintaining even a very thin film of water (<10 -4 mm) over the substrate, such as by use of gum arabic in the water solution of the lithographic process (this absorbs strongly on hydrophilic surfaces and " h o l d s " large amounts of water in its molecular structure), ensures that attachment cannot occur, thus preventing any problems associated with disruption (29). REFERENCES 1. Philipott, W., Mining Eng. 4, 386 (1932). 2. Sven-Nilsson, I., Kolloid Z. 69, 230 (1934). 3. Ford, R. E., and Furmidge, C. E. L., Wetting S.C.I. Monograph No. 25, P. 417, 1967. Journal of Colloidand lnterjaceScience, Vol.68, No. 3, March 1, 1979
4. Lord Rayleigh, "The Theory of Sound," Vol. II, 2nd ed., Dover, New York, 1945. 5. Worthington, A. M., " A Study of Splashes," MacMillan, New York, 1963. 6. Hartley, G. S., and Bronskill, R. T., in "Surface Phenomena in Chemistry and Biology" (J. F. Danielli, Ed.), p. 214, Pergamon, New York, 1958. 7. Hartley, G. S., Wetting S.C.I. Monograph No. 25, p. 433, 1967. 8. Schulman, J. H., and Leja, J., in "Surface Phenomena in Chemistry and Biology" (J. F. Danielli, Ed.), p. 236, Pergamon, New York, 1958. 9. Elliott, T. A., and Leese, L., J. Chem. Soc. 2230. (1957); 1466 (1959). 10. Elliott, T. A., and Morgan, M., J. Chem. Soc. A 558, 563,567, 570 (1966). 11. Elliott, T. A., and Ford, O. M., Trans. Faraday Soc. I, 1814 (1972). 12. Wilkinson, M. C., and Elliott, T. A., J. Colloid Interface Sci. 48(2), I87, 209, 225 (1974). 13. Wilkinson, M. C., Ze~ttlemoyer, A. C., Aronson, M. P., and Vanderhoff, J. W., J. Colloid Interface Sci. 68, 508 (1979). 14, Wilkinson, M. C., Ellis, R., Aronson, M. P., Vanderhoff, J. W., and Zettlemoyer, A. C., J. Colloid Interface Sci. 68, 545 (1979). 15, Schotland, R. M., Discuss. Faraday Soc. 29, 72 (1960). 16. Gillespie, T., and Rideal, E. K., J. Colloid Sci. 10, 281 (1955). 17. Pfeiffer, A., U. S. Army Chem. Res. & Dev. Labs., CRDLR 3220, 1964, Unclassified. 18. Young, T., Phil. Trans. Roy. Soc. London 95, 65, 82 (1805). 19. Picknett, R., Ph.D. Thesis, London University, 1957. 20. Watanabe, A., Higashitsuji, K., and Nishizawa, K., J. Colloid Interface Sci. 64, 278 (1978). 21. Wark, I. N., J. Phys. Chem. 37, 637 (1933). 22. Frumkin, A., and Gorodetzkaja, A., Acta Physiochim. USSR 9, 327 (1938). 23. Frumkin, A., Gorodetzkaja, A., and Nekrassow, N., Soy. Phys. 1,255 (1932). 24. Smolders, C. A., and Duyvis, E. M., Rec. Tray. Chim. Pays Bas 80, 699 (1961). 25. Bikerman, J. J., "Surface Chemistry," Academic Press, New York, 1958. 26. Reynolds, Phil. Trans. Roy. Soc. London, 177, 157 (1886), 27. Stott, R., Ph.D. Thesis, London University, 1971. 28. de Laplace, P. S., Theorie MOcanique de la Chaleur, 369 (1869). 29. Wilkinson, M. C., Aronson, M. P., Vanderhoff, J. W., and Zettlemoyer, A. C., in "Adhesion Science and Technology" (L.-H. Lee, Ed.), Vol. 9B, p. 725, Plenum, New York, 1975.
Despite the obvious importance of drop impaction and spreading processes, little attention has been devoted to their study, possibly due to the complexity of the processes occurring (3). These were described qualitatively as early as 1879 by Lord Rayleigh (4) and 1897 by Worthington (5), but a detailed study of the processes had to await the development of high-speed cinephotographic techniques. Recent studies using these particular techniques (3, 6-8) have confirmed the complex nature of the processes occurring and in addition the importance of the dynamic contact angle (9-12), as opposed to the equilibrium contact angle, in describing spreading and wetting processes. Impact, attachment, and spreading processes occurring in several different systems have been shown to be remarkably
Many important processes, such as the attachment of air bubbles to mineral ores during froth flotation (1, 2), the spreading of agricultural sprays on crop foliage (3), and the wetting-out of fabrics by rain drops depend for their action on processes occurring within very short time intervals. For example, in froth flotation, collector air bubbles spend only a short time (< 1 sec) within the mineral suspension and they must collect many grains on their way to the water surface to make the aeration profitable. Similarly, the quantity of agricultural spray required to effectively treat a crop depends on the extent of wetting and adhesion which can be achieved during drop impaction and attachment, i.e., if the droplets bounce off the leaf "in toto" then they are totally ineffective as an insecticide. 560 0021-9797/79/030560-15502.00/0 Copyright© 1979by AcademicPress, Ine. All rights of reproductionin any form reserved.
Journal of Colloid and Interface Science, Vol. 68, No. 3, March 1, 1979
SPREADING
AND
reproducible (9-12), and valuable information with regard to spreading and wetting processes has been obtained. These types of studies have provided a much clearer understanding of many naturally occurring and industrial processes despite the present lack of precise mathematical treatments to describe them. The purpose of the present study was to gain a better understanding of the rapid processes of oil-drop impaction at a wetted surface and the subsequent formation of partially submerged drops or fourphase configurations (13). The study was confined to substrate surfaces covered by very thin films of water, i.e., <1 mm. A study was also made of the rapid processes of disjoining or disruption and splitting (13, 14) which occur during the breakdown of these four-phase configurations. EXPERIMENTAL
All materials and general procedures are as described in Parts I and II (13, 14). One-hundred-foot reels of cine-negative film were used in high-speed cameras capable of speeds between 150 and 5000 frames/ sec; in most experiments the camera was run at 500 to 1200 frames/sec. Since the total filming time was only 1 to 8 sec, slow changes or relaxation phenomena of the type discussed in detail in Part II (14) could not be followed. The procedure was to allow an oil drop from an Agla microsyringe to fall a fixed distance (usually 100 to 120 ram) and impinge on a substrate surface covered with a thin film of water. The camera was started at
WETTING,
561
III
the instant the drop fell from the syringe so that the velocity of impact and processes of impaction and attachment could be recorded. The mass of the drop was within the range of 10 to 40 mg. One of the unavoidable difficulties with high-speed cinephotography of impaction and attachment processes is that no control can be exercised on the length of the induction period (see below). Fortunately in the present system all induction periods were <0.4 sec, and fell within the total filming time of the camera (1 to 8 sec, depending on speed). However, this meant that all drops were in their oscillatory mode of impaction when attachment occurred (see below) which tended to obscure the true forces acting on attachment (12). The cinefilms (Kodak High Contrast, Type 7457) were analyzed directly and the parameters as given in Fig. 1 were determined. RESULTS I.
OIL
AND
DISCUSSION
DROP
IMPACTION
Before impaction and attachment of the oil drop could occur at the wetted substrate surface, the "air cushion" formed between the drop and the water surface had to be displaced. "Induction periods," or times for this air cushion to be displaced, are generally very small for most systems where pure liquids are involved, and especially where the drop possesses some kinetic energy (11, 15). Induction periods in the present system were estimated to be < 10-~ sec,
SPREADING VELOCITY
AIR
-,,, /
/
/."
//
0, /
/
( 0R/
/~ ¢" / d," ," / i / I ~ SUBSTRATE - 7
F I G , 1. P a r a m e t e r s
measured
1 /
/
/
,"
/
,-
during spreading.
Journal ojColloid andlnterJace Science, Vol. 68, No. 3, March I, 1979
562
W I L K I N S O N ET AL.
PLATE 1. Approach of 8-mg oil drop at 4.8 m sec -1.
and were not a factor in the subsequent attachment at the substrate surface. Although most impacting oil drops with mass greater than 10 mg managed to form an oil/water interface during their residence time at the surface, some were reflected when the impaction energy was high (16). The work of adhesion (WA) of an oil to water is less than the work of cohesion of the oil (Wc), for oils which do not spread on water. However, WA can approach Wc during rapid dewetting (by the oil) since the dynamic receding contact angle (0dy, rec) between the oil and water approaches 0°, i.e., W A ( = ' ) / 0 (1 + cos 0dyr, re¢)) ~ We (=2T0), where 70 is the surface tension of the oil. In this case reflection of these oil drops in toto may not always occur. The drop may become encapsulated in an ejected column of water (Plates 1-3). It is not unknown for drops to be reflected in toto from thin layers of the same liquid on certain substrates (6, 7). However, it is usually found in these cases that it is some property of the underlying solid substrate which is responsible for this. For example, Hartley (7) found that a bean (Vicia) leaf accepted all incident water drops (within a Journal of Colloid and lnterjace Science, Vol. 68, No. 3, March 1, 1979
certain size range) when dry, but when uniformly wetted with a thin film of water it reflected all subsequent arrivals. This was ascribed to the microroughness of the leaf surface, whereby the impacting drop could not completely displace the air from the rough surface; thus being reflected. Thin films of water on a substrate are only successful in "reflecting" impacting drops if the drainage time for the water film between the drop and the substrate is larger than the impaction time, i.e., the induction period is greater than the residence time. The residence time is defined as the period which elapses while the oil drop is within sufficiently close proximity to the substrate surface such that an oil/substrate interface will be formed if the trapped water film between the drop and substrate is capable of being displaced. The water film is only capable of preventing impaction at the substrate surface if relatively deep, since penetration depths for impacting oil drops in bulk water can be very large (Plate 2, Fig. 2) even for small drops with densities less than unity. The residence time which the oil drop has at the substrate surface depends on the depth of the film. For example, a 3.5-rag
563
SPREADING AND WETTING, III
PLATE 2. Maximum penetration in bulk water after 2 × 10 2 sec.
oil drop at an impaction velocity of 0.7 m sec -1 penetrated 8.7 mm in 0.015 sec (Fig. 2), and therefore, if a substrate surface was interposed at this particular depth, then the residence time of the drop would be zero, i.e., attachment would be impossible. However,
for film depths less than this, residence times of 0.05 sec, or less, may be expected. Any secondary impaction process due to collapse of an ejected column of water, which may encapsulate the oil drop (Plate 3), results in significantly smaller penetra-
IO
12
I0
6~
E
T VELOCITY
2--
4~ INmAL
0
I0
N3.S~I
~
~
~31
PENETRATION X ~ffirCECTi0 N //p~ECEOTNDAARoYN "~
0.04
0-06 TIME [see)
0.1Z
0,16
Fz~. 2. Relationship between penetration and impact velocity for paraffin oil drops in bulk water. Journal of Colloid and lnterJace Science,
Vol. 68, No. 3, March 1, 1979
WILKINSON ET
564
AL.
PLATE3. Ejected water column and encapsulated oil drop after 6 × 10-2 sec. tion of the water (Fig. 2). If attachment occurs on secondary impaction then spreading may proceed since any residual energy within the drop at this stage is very much smaller than its original impaction energy (17) and possibly insufficient to cause a secondary recoil (Figs. 3 and 4). Failure to attach resulted in the formation of an oil lens on the water surface. Vibra-
tions within the drop were rapidly damped by the surface forces (<0.5 sec) and a stable contact angle (4~) of 157° formed. Contact with the substrate surface was then only possible by significant thinning of the water film, e.g., for a 40-mg drop (4~ of 157 °, and density 0.88 g m1-1) this would correspond to - 1 mm. Although attachment occurred during the
18c
~
~
f
fJff
DISRUPTITf/
E o lg
o
12C
I00 TIME {see)
FIG. 3. Drop impaction and spreading at graphite/water interface. Journal of Colloid and Interface Science,
Vol.68, No. 3, March1, 1979
565
SPREADING AND WETTING, III
, 0[
/I
160
~TION
--140
,,t
o
120
eAv
100
Ii~ 0.05
0.0
f
0.25 TIME (see)
0!50
I 0'75
I'0J
FIG. 4. Drop impaction and spreading at Teflon/water interface.
residence times of oil drops at the different surfaces considered, many of the drops still had sufficient residual energy after impact to bounce (Figs. 3 and 4). Drops not possessing sufficient residual energy to bounce off the surface oscillated and retarded the spreading process (Figs. 5 and 6). For ex-
ample, in the case of a low-energy impacting drop on polymethyl methacrylate very much faster spreading occurred than in the case of a drop exhibiting significantly larger kinetic energy (Fig. 7 and Table I). The faster spreading led to disruption after 0.3 sec, while the slower spreading drop disrupted after 3 sec.
180
160
E
8
TIME (sec)
Fro. 5. Drop impaction and spreading at Teflon/water interface. Journal of Colloid and lnter/~lce Science,
Vol.68,No.3,March1, 1979
566
WILKINSON
ET AL.
'B°I
eA,
~AV
E 4~
d
140
o
120
o.do4~o!,
o!s
TIME (see)
,.'o
,!s
FIG. 6. Drop impactionand spreading at graphite/waterinterface. Similar phenomena were noted with charcoal and polytetrafluoroethylene surfaces (Figs. 3 and 4), but in these cases sufficiently large amounts of the high impaction energies were dissipated on bouncing to allow rapid spreading on second impaction. It is the magnitude of 0oyn rec which de-
termines whether any part of the oil drop is left adhering to the substrate on recoil. Reflection in toto does not always occur, even when high surface energy drops impact on low surface energy solids. Pfeiffer (17), for example, found that 70-/zm-diameter water drops did not reflect in toto from a paraffin
180 ! OL~RLIPI'tON
AV
RUP'TION
/ / .,/
e,~v.~v, a'- t3,.goi,a,-op d
/
6 E E
z
r121
,
0'5
I!0
/~ TIME (~c)
FIG. 7, D r o p (13 a n d 25,6 m g - - T a b l e
,
2'0 ~'-
I) i m p a c t i o n a n d s p r e a d i n g at P l e x i g l a s / w a t e r i n t e r f a c e .
Journal of Colloid and Interface Science, Vol. 68, No. 3, March 1, 1979
SPREADING AND WETTING, III
567
TABLE I Impaction and Spreading of Oil Drops at Prewetted Surfaces
Reference
Fig. Fig. Fig. Fig. Fig.
3 4 5 6 7
Fig. 7 Fig. 9 Fig. 10
Substrate
Graphite Teflon Teflon Graphite Polyrnethyl methacrylate Polyrnethyl methacrylate Teflon Mercury
Waterfilm depth (ram)
Oil drop (rag)
Velocity of drop impact (m sec -1)
Spreading velocity (m sec -~)
0E~t
0EQ AD
0.9 0.7 0.5 0.5
33.0 25.6 13.0 25.6
2.08 -0,70 1.41
36.0 34.0 7.0 17.4
45 20 20 45
0.5
25.6
2.03
4.8
0.6 0.9 0.3
13.0 25.6 25.6
0.12 0.30 1.88
4.5 11.3 12.8
surface, a very small droplet was always left behind. High-speed photography showed that the dynamic receding contact angle dropped dramatically during recoil such that WA a p p r o a c h e d We. Simple analysis using the equilibrium contact angle (0~q) of 108 ° would, however, have predicted no adhesion s i n c e W A (0eq = 108 °, 0.05 Jm -z ~ We (0.144 Jm-2). The surface energy decrease (AE) for the impaction of an oil drop at a p r e w e t t e d surface, where an oil/substrate interface is formed is given to a first a p p r o x i m a t i o n by AE = (4~r2To + 7rRyw +
7rR23/s/w)
--
(TrR2y0
+ 7rRhTo/w + 7rR2y~/0),
[1]
where h is the depth of the w a t e r film, H R 2 is the area o f interface formed or lost, r is the radius of the impacting oil drop, and To, yw, ys/w, and ys/0 refer to the oil, water, substrate/water, and substrate/oil surface and interfacial tensions, respectively. F o r simplicity, it is a s s u m e d that the oil in w a t e r was of a cylindrical form with an oil/water contact angle o f 90 °. N o w using Y o u n g ' s relationship (18), i.e., Ys/w - Ys/0 = Yo/w cos 0eq.
[2]
Equation [1] can be rearranged to give
0DyN ADV
KE of impact (~J)
SE of impact (M)
120 29 29 120
165 160 160 170
70.4 -3.15 25.0
1.83 1.56 1.00 1.56
43
115
170
52.8
1.56
43 20 85
115 29 89
160 160 150
0.1 1.15 45.0
1.00 1.56 1.56
AE = 7rR2[yw + Y0/w X (COS 0eq - -
h/R) - Y0]
+ 4¢rr2y0 .
[31
It is apparent from Eq. [3] that AE depends on 0~q and the extent of spreading (Fig. 8). A large amount of the impact energy can be dissipated by the spreading process if the oil preferentially wets the substrate (e.g., polytetrafluoroethylene) but no energy can be dissipated in this m a n n e r with a very hydrophilic substrate such as glass. Energy decreases on spreading can only app r o a c h the kinetic energies of terminal velocity drops when the drops are very small (3) and within the range of aerosol droplets ( < 6 0 0 / z m in diameter). Thus, with the range of drop sizes used in this work, surface energy changes only b e c a m e p r e d o m i n a n t when the bulk of the kinetic energy had been dissipated by the impaction process itself (Figs. 3 and 4). Predicting whether a drop will either be reflected f r o m a wetted surface or adhere and spread is generally very difficult since the energy absorbing processes on impaction cannot be determined. H o w e v e r , for low impaction energies on substrates preferentially wet by oil, reflection b e c o m e s less likely since energy can be dissipated Journal of Colloid and Interface Science, Vol. 68, No. 3, March 1, 1979
568
WILKINSON
ET AL.
2O
15,
g >.
g
S*l
s
0 GLASS(O [q- 16501
o
;:
,;
~
~,ASE RADIUSOFSPREAOINGOI~OP(mml
FIG. 8. S u r f a c e e n e r g y d e c r e a s e o n s p r e a d i n g o f d r o p s o n d i f f e r e n t s u r f a c e s .
by spreading and displacement of the water. For example, a 25.6-mg oil drop impacting at a polytetrafluoroethylene surface (water depth of 0.9 mm) with energy of 2.71 /xJ (1.15 /.LJ K E + 1.56 /zJ S E - - T a b l e I) showed very little oscillation during spreading (Fig. 9) and the surface energy decrease rapidly e x c e e d e d 25 ergs (Fig. 8), i.e., the spreading process rapidly led to a decrease in the total energy of the system. II. FOuR-PHASE
CONFIGURATIONS
1. A t t a c h m e n t at the Substrate
It is doubtful whether the initial contact of the oil with the substrate occurred at a single point, where the contact angle was just less than 180 ° . A t t a c h m e n t m o s t probably occurred across a liquid bridge which was at least 1 nm 2 in cross section (19). Watanabe, Higashitsuji, and Nishizawa (20) Journal of Colloid and Interface Science, Vol. 68, No. 3, March 1, 1979
found that a liquid bridge of ca. 2 x 10 -2 m m diameter was formed in < 5 x 10 -3 sec across a gap of 10 -1 m m during the coalescence of two drops of 10 -1 M KC1 in methylisobutyl ketone containing 5 x 10-3 M cetylpyridinium chloride. The actual process of a t t a c h m e n t was exceedingly difficult to observe in any of the present s y s t e m s since it not only occurred very rapidly ( < 10 -a sec) but the drop/substrate interface could not be clearly resolved photographically. Wilkinson and Elliott (12) have shown that initial a t t a c h m e n t of an oil to a m e r c u r y / w a t e r interface occurred in < 6 x 10 -4 sec and the initial contact angle appeared to depend on the difference in works of adhesion of the oil and w a t e r for the substrate. Certainly, incorrect contact angles can be measured from photographs unless clear resolution of the interface during time intervals < 10 .3 sec can be obtained.
SPREADING AND WETTING, III
/
I1~, /
/
v /
/
r-
/
r
569
-,
//
DISRUPTION
e~ v
-
d
..-
8
i
o.'ozs
o:~
TIME (see)
o.~T~
o.Ioo
F]6. 9. Drop impaction and spreading at Teflon/water interface. In many situations it is probable that complete wetting o f the substrate by the oil does not occur, especially if attachment is rapid (21-24). In this case droplets of water may be trapped in the attaching oil phase, or air may be carried through by the oil drop. These water droplets or air bubbles do not apparently affect the general spreading processes, which are controlled by the interfacial forces acting at the advancing front of the drop (12), but they may act to disrupt the oil film as it thins on spreading (13), thus causing the configuration as a whole to become unstable and disrupt. The rate of drainage of the trapped film of water depended on many factors (25), such as the impaction energy, surface tension, density difference between oil and water, drop size, viscosity of the water, nature of any adsorbed films, and magnitude of electrical double layer and electroviscous forces. Induction periods were several orders of magnitude smaller than those calculated on the basis of the approach of two fiat plates (26) and attachment almost certainly occurred on localized failure of the water film at relatively large water-film thicknesses (e.g., 10 -5 to 10 -3 cm).
The magnitude of the energy barrier to attachment o f the oil to the substrate surface and the displacement of water is given by [4]
E = Kyo/w h2,
where h is the film thickness, y0/w is the oil/water interfacial tension and the constant K, depends on the geometry of the liquid bridge, which for a cylindrical bridge is given by 1 cos Oeq + 1
(cos 0eq + 1)2 _
cos Oeq
]
(cos Oeq + 1)2 I ' where 0~q is the equilibrium contact angle in the oil/water/substrate system. This energy barrier is extremely small ( - 1 0 -4 ergs for h = 10 -3 cm) and cannot be a factor in attachment when impacting drops are being considered. 2. F o r m a t i o n
If the oil drop displaced the water film and made contact with the substrate surface a four-phase configuration was formed. The Journal o f Colloid and Interface Science, Vol. 68, No. 3, March 1, 1979
570
WILKINSON
subsequent stability of the configuration then depended on the magnitude of the residual energy in the drop (energy left after impaction and spreading) and the water film depth. When h < hspnt > hms, and the residual energy after impaction and spreading was insufficient to enable the drop to bounce, then a stable four-phase configuration was formed within 1 sec. This was also the case when the drop had sufficient kinetic energy to bounce, but attachment occurred on secondary impaction. Failure to attach resulted in the formation of an oil lens on the water surface. In this case, for the oil under consideration, formation of a four-phase configuration was then impossible since the water-film depths were always too great to allow oil/substrate attachment to occur (see above). When h > hspnt, and the induction period of the oil at the substrate/water interface was less than the residence time, then a transient configuration was formed which quickly split; part of the oil transferring to the water surface and part being left adhering to the substrate surface. In situations where h < hdis and the impaction energy was low, the configuration spread rapidly and disjoined (Fig. 7). However, with high impaction energies some drops bounced and failed to make contact on secondary impaction. In these cases an oil lens was formed and spreading and disruption did not occur.
3. Changes in Contact Angles There were very large fluctuations in the magnitude of the oil/water/air contact angle (4~--Fig. 1) during the first 10-1 sec, with values between 110 and 170° being recorded (Figs. 5 and 6). The extent of these fluctuations was much greater with the highenergy impacting drops than with the lowenergy ones. The degree of drop distortion occurring during these time intervals was reflected in the wide variation in qSLEVTand (~RIGHT(Fig. 1). Vibrations in the drop were rapidly Journal of Colloid and Interface Science, Vol. 68, No. 3, March 1, 1979
ET AL.
damped and ~ differed from ~beq (158°) by only a few degrees after ca. 0.3 sec. Similar short time intervals for the damping of induced oscillation on drop impaction have been noted for bubbles and drops attaching at a variety of surfaces (9-12). Spreading velocities had dropped from the very high initial values (Table 1) to <2 mm sec -1 during this time period. These results are in accord with those found earlier (14) where (h remained constant until the spreading velocity exceeded ca. 0.2 mm sec -~, whereupon it increased. Thus, the three-liquid system exhibited much smaller molecular reorientation times than liquid/ liquid/solid systems (as reflected in the magnitude of 0). The spreading velocities of drops at the various substrates were very much larger (Table I) than those recorded in Part II (14). The dynamic advancing contact angles (0oyn aov) were also greatly in excess of the equilibrium contact angles (0eq--Table 1) and very similar for all the different surfaces employed. This similarity in 0 d y n a d v was expected for rapidly spreading drops and is related to disorientation effects of molecules at the oil/water/substrate interface (14). The rate of spreading decreased rapidly as the impaction energy was dissipated, such that the oil-drop diameter became almost constant after ca. 0.2 sec (Figs. 4-6). The contact angle, 0, then gradually decreased. The contact angle at the mercury substrate, however, fell very rapidly (Fig. 10) since relaxation times of molecules in three-liquid systems are small. This system was also very unstable since it exhibited very little contact-angle hysteresis (13), and this instability was manifested in the very rapid spreading and disruption which followed attachment (i.e., -0.04 sec). This can be compared with the polymethyl methacrylate system (Fig. 7) where the impaction energy was similar (Table I), but the contact-angle hysteresis was very large (13, 14), in this case disruption occurred after 3 sec.
SPREADING
AND WETTING,
57 1
III
i
f
/"/f/"
"
DISRUPTION
S.\
d 10
-~ 140 z~
c::
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0'02 TIME (see)
0'03
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FIG. 10. D r o p i m p a c t i o n a n d s p r e a d i n g at m e r c u r y / w a t e r i n t e r f a c e .
As long as the contact angle, oil-drop diameter, and water-film thickness remained within certain limits, the configuration was stable towards disruption or splitting (13). Although all of the present systems were basically unstable (since h < hdi~) for the particular oil volumes employed, disruption did not occur immediately since hd~s decreases with increasing contact angle (14) and most of the systems exhibited very high dynamic advancing contact angles during the initial stages of spreading. Thus, all the substrates behaved as if they were hydrophilic, such as glass or metal. Fourphase configurations on very hydrophilic surfaces are stable (to disruption) down to very thin water-film depths. Thus, it is of note that in all of the systems studied it was the magnitude of 0aynadv which was important and not 0e,, where 0dy~adv depended on the velocity of interface movement and the speed of the molecular reorientation processes occurring at this interface. The vibration of the oil drop diminished very quickly after the rapid processes of impaction and attachment. This involved a decrease in 0 (if the substrate was hydro-
philic) at almost constant or slowly increasing drop base diameter; a process which was relatively slow and in most cases outside the filming time of the camera (i.e., >5 sec). If the contact angle fell to that value corresponding to the advancing angle for disruption (for that particular water film depth and oil volume) then the oil drop respread and disruption followed. An example of this is shown in Fig. 4 for polytetrafluoroethylene, where 0 suddenly fell to 105° (after 0.9 sec) and the oil drop began to spread and disrupt, i.e., the advancing contact angle for disruption in the case of a 25-rag oil drop at a water-film depth of 0.7 mm was ca. 105°. Since the degree of instability of partially submerged oil drops in thin films of water depends on the magnitude of the contact angle hysteresis or, in the case of interface movement, on 0dynadv, as opposed to 0eq (or any other angle (13, 14)), then the time which elapses before disruption occurs is govered by the spreading velocity and the nature of the substrate surface. All the systems shown in Figs. 3 to 10 were basically unstable since the water film depths were all below hj~ for the respective systems. Journal of Colloid and Interlace Science, Vol. 68, No. 3, March 1, 1979
572
WILKINSON ET AL. I
X
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Time 0.01 see
\
AIR / /
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III TIME 0.90 see d= 3.55 mm h= I =0"7 mm Veal z 13,?ul V=25.6,pl
TIME= 0.95 s¢c h ~ l = 0 "7 mm
V= 25-6~I
Vc a l = ~ . 6 , u l / / / / / /
/
//
/
/
/
TIME= 1.00 sec d = 6.ZO mm h =1= 0"7 mm V e a l = 31.7~JI V ' 2 5 . 6 ) J I
/
/
/
/
/ / / /
/
/
/
/
//
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TIME > 1 . 0 0 stc dest = 8 mm h = I ~ 0"7 mm
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\ -
-
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FIG. 11. Spreading and disruption of the Teflon/oil/water/air configuration. (a) Oil drop receding-prior to breaking substrate contact. (b) Second impact--drop spreading. (c) Drop spreading. (d) Prior to disruption. (e) Disruption occurs. (f) Hypothetical state of spread. Journal of Colloid and Interface Science, Vol. 68, No. 3, March 1, 1979
SPREADING
AND WETTING,
was contained below the free water surface. It was found that most drops advanced across the substrate surface at about the same contact angle (150 to 170°) and further, that the oil/water meniscus could be described reasonably accurately as a straight line joining the oil/water/air intersection to the substrate/oil/water intersection; calculation shows that the radius of curvature of the oil/water meniscus was approximately 19 ram. It was therefore possible to draw the drop profile during spreading and calculate the volume of the oil drop contained below the free water surface (from simple cylinder of height h, Fig. 1); these are given in Figs. i 1 and 12 for two different systems (drawn to scale of 20:1). The remainder of the drop profile (i.e., the difference between actual and calculated volumes) has been drawn on this basis.
However, several systems were stable for many seconds before disruption finally occurred, and it was during this time period that 0 decreased towards its value for disruption. Thus, it is apparent that highenergy impacting oil drops may be reflected or bounce before disjoining can occur, whereas with low-energy impacting drops disjoining may be very rapid, although considerations based on "equilibrium" data would have predicted disruption in both cases. III. DISRUPTION Although the complete profile of the impacting and spreading drop could not be clearly distinguished (i.e., the oil/air meniscus could not be observed), it was possible to estimate what proportion of the drop
i// AIR
t\ \
/ /
.~'~0"0 ILl AIR WATER/AIR/ OIL
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"x, AIR ., ~
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Time 0.20sec d= 4,95 rnm k=0'6 mm L=O.S mm V cal=ll,Sul V=12~l
7 / / 7 / ' / - / f
. ~
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SUBSTRATE /
(:)
573
III
/
~/"
/
7
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/
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\____,..
.f.. ,) Fz~. 12. S p r e a d i n g a n d d i s r u p t i o n o f t h e P l e x i g l a s / o i l / w a t e r / a i r c o n f i g u r a t i o n . (a) Oil s p r e a d i n g . (b) Oil s p r e a d i n g . (c) P r i o r to d i s r u p t i o n . (d) D i s r u p t i o n o c c u r s . Journal of Colloid and lnterjace Science, Vol. 68, NO. 3, March 1, 1979
574
WILKINSON ET AL.
It is obvious from the system of interfacial forces acting that some form of breakdown has to occur if the drop spreads beyond a certain s t a g e - - r e f e r to Figs. 1 le and 12d. This stage was reached when the oil/air interfacial tension could no longer act at an angle of 93 ° (calculated from interfacial tensions) to that of the oil/water interfacial tension, and occurred when the oil/ air meniscus dropped below the water level, or more specifically oil/water/air intersection. Disruption was in fact found to occur when this stage was reached. The actual process o f disruption could not be observed, partly since the process occurred in less than 10 -3 sec, but mainly because there was a sudden change in refractive indices in the system on disruption of the oil/water interface. Although it is clear that disruption occurs at some positive value o f / (13), there is no experimental p r o o f that this occurred when the balances of forces acting at the interfaces (oil/air/water and oil/water/substrate) and the Laplacian equations describing the curvatures of the liquid interfaces (28) could not simultaneously be maintained. It was not possible to achieve attachment of a very wide range of oil-drop sizes (even at very small water depths) at any of the very hydrophilic substrates such as glass and metal surfaces, since the induction periods were very much longer than the residence times. Maintaining even a very thin film of water (<10 -4 mm) over the substrate, such as by use of gum arabic in the water solution of the lithographic process (this absorbs strongly on hydrophilic surfaces and " h o l d s " large amounts of water in its molecular structure), ensures that attachment cannot occur, thus preventing any problems associated with disruption (29). REFERENCES 1. Philipott, W., Mining Eng. 4, 386 (1932). 2. Sven-Nilsson, I., Kolloid Z. 69, 230 (1934). 3. Ford, R. E., and Furmidge, C. E. L., Wetting S.C.I. Monograph No. 25, P. 417, 1967. Journal of Colloidand lnterjaceScience, Vol.68, No. 3, March 1, 1979
4. Lord Rayleigh, "The Theory of Sound," Vol. II, 2nd ed., Dover, New York, 1945. 5. Worthington, A. M., " A Study of Splashes," MacMillan, New York, 1963. 6. Hartley, G. S., and Bronskill, R. T., in "Surface Phenomena in Chemistry and Biology" (J. F. Danielli, Ed.), p. 214, Pergamon, New York, 1958. 7. Hartley, G. S., Wetting S.C.I. Monograph No. 25, p. 433, 1967. 8. Schulman, J. H., and Leja, J., in "Surface Phenomena in Chemistry and Biology" (J. F. Danielli, Ed.), p. 236, Pergamon, New York, 1958. 9. Elliott, T. A., and Leese, L., J. Chem. Soc. 2230. (1957); 1466 (1959). 10. Elliott, T. A., and Morgan, M., J. Chem. Soc. A 558, 563,567, 570 (1966). 11. Elliott, T. A., and Ford, O. M., Trans. Faraday Soc. I, 1814 (1972). 12. Wilkinson, M. C., and Elliott, T. A., J. Colloid Interface Sci. 48(2), I87, 209, 225 (1974). 13. Wilkinson, M. C., Ze~ttlemoyer, A. C., Aronson, M. P., and Vanderhoff, J. W., J. Colloid Interface Sci. 68, 508 (1979). 14, Wilkinson, M. C., Ellis, R., Aronson, M. P., Vanderhoff, J. W., and Zettlemoyer, A. C., J. Colloid Interface Sci. 68, 545 (1979). 15, Schotland, R. M., Discuss. Faraday Soc. 29, 72 (1960). 16. Gillespie, T., and Rideal, E. K., J. Colloid Sci. 10, 281 (1955). 17. Pfeiffer, A., U. S. Army Chem. Res. & Dev. Labs., CRDLR 3220, 1964, Unclassified. 18. Young, T., Phil. Trans. Roy. Soc. London 95, 65, 82 (1805). 19. Picknett, R., Ph.D. Thesis, London University, 1957. 20. Watanabe, A., Higashitsuji, K., and Nishizawa, K., J. Colloid Interface Sci. 64, 278 (1978). 21. Wark, I. N., J. Phys. Chem. 37, 637 (1933). 22. Frumkin, A., and Gorodetzkaja, A., Acta Physiochim. USSR 9, 327 (1938). 23. Frumkin, A., Gorodetzkaja, A., and Nekrassow, N., Soy. Phys. 1,255 (1932). 24. Smolders, C. A., and Duyvis, E. M., Rec. Tray. Chim. Pays Bas 80, 699 (1961). 25. Bikerman, J. J., "Surface Chemistry," Academic Press, New York, 1958. 26. Reynolds, Phil. Trans. Roy. Soc. London, 177, 157 (1886), 27. Stott, R., Ph.D. Thesis, London University, 1971. 28. de Laplace, P. S., Theorie MOcanique de la Chaleur, 369 (1869). 29. Wilkinson, M. C., Aronson, M. P., Vanderhoff, J. W., and Zettlemoyer, A. C., in "Adhesion Science and Technology" (L.-H. Lee, Ed.), Vol. 9B, p. 725, Plenum, New York, 1975.