161
Langmuir 1986,2, 161-165
Deformation of Droplets Suspended in Viscous Media in an Electric Field. 2. Burst Behavior Satoru Moriya,+Keiichiro Adachi, and Tadao Kotaka" Department of Macromolecular Science, Faculty of Science, Osaka University, Toyonaka, Osaka 560, J a p a n Received August 6, 1985. I n Final Form: October 24, 1985
A droplet of a slightly conducting liquid suspended in a dielectric medium becomes unstable and bursts under an electric field E above a certain critical strength E,. We investigated the burst behavior for droplets of water, a mixture of water and methanol, and ethylene glycol solutions of poly(vinylpyrrolidone), all suspended in di-n-butyl phthalate solutions of polystyrene. Two types of bursting were observed under the high field depending on the viscosity of the drop phase: a water drop whose viscosity is much lower than that of the medium bursted by ejecting a series of smaller droplets at its sharp pointed ends, while a drop of the viscous polymer solution was drawn into a fine thread. The experimental E, agreed approximately with the theoretical E , proposed by Garton and Krasucki. The initial rate of deformation under E > E, was characterized by the same characteristic time as that in the infinitesimal deformation from a sphere to an ellipsoid under a low field. The flow field inside the drop was found to be simple elongation.
Introduction The preceding paper' (part 1 of this series) described deformation of droplets suspended in dielectric media under an electric field of low strength. A simple theory was developed for describing the deformation behavior and predicted that it is approximately a single retardation time process. The characteristic times for such retardation processes were determined on the droplets of water and poly(vinylpyrro1idone) (PVP) solutions suspended in din-butyl phthalate (DBP) solutions of polystyrene (PS)and were found to be in accord with the theory. On the other hand, under an electric field of high strength, the deformation behavior was distinctly different from that in the low field: droplets become unstable under the field above a certain critical strength E, and burst.2 A number of authors studied the instability of a drop suspended in a nonpolar medium2-8 or a drop held at the end of a capillary tubes12 by applying a high electric field. Zelenyg found as early as in 1914 that a fine jet was drawn from a capillary tube when a high voltage was applied to the liquid contained in the tube. Wilson and TaylorlO further studied this phenomenon, and recently Larrondo and John Manley12applied this technique to fiber spinning of polymer melts. It is also known that droplets break up in a flow field of high shear However, all these works were concerned essentially with the instability of the suspended droplets, and little attention was directed to the rate of deformation of the bursting drops. In this study, we studied this problem by comparing the bursting of water and viscous PVP solutions under a high field. Experimental Section Pure water, a 16 wt % methanol in water mixture, and ethylene glycol solutions of PVP were used as the droplets and DBP solutions of PS as the media. Characteristics of these sample solutions except the water/methanol mixture were described in the preceding paper.' The literature values of dielectric constant K , viscosity 1,and surface free energy u of the water/methanol Pa, and 5.4 X lo4N (H,O/MeOH) mixture are 71.83, 1.6 X m-l, re~pectively.'~-'~ These solutions are coded as, for example, PS/DBP(30) for a 30 w t % solution of PS in DBP. For all cases the solution used as the drop phase has a higher electric conductivity than that of the medium, and hence we can assume that Present address: Research Center, Mitsui Petrochemical Industries, Ltd., Waki-cho, Kuga-gun, Yamaguchi 740, Japan.
the system is essentially of the type consisting of a conducting droplet suspended in an insulating medium. An alternating current (ac) field of 60 Hz was employed as in the preceding paper,' where the methods and materials were described in detail. For recording the motion of droplets we used a video camera (Ikegami,Model CTC-5600JS) and a video time
recorder (FOR-A Co. Ltd., Model VTG-55).
Results and Discussion Deformation of Droplets. Under a low electric field, an initially spherical droplet of the radius b deformed into an ellipsoid. The behavior of deformation was described by eq 12-14 of ref 1. Under a high electric field, however, the degree of deformation D can no longer be described by these equation, since the shape deviates very rapidly from an ellipsoid. Figure 1 shows a series of photographs of a water/methanol (84/16) drop with b = 0.22 mm in (1)Moriya, S.; Adachi, K.; Kotaka, T. Langmuir, preceding paper in this issue. (2) Garton, C. G.; Krasucki, Z. Proc. R. SOC.London, Ser. A 1964,280, 211. (3) Allan, R. S.; Mason, S. G. Proc. R. SOC.London, Ser. A 1964,267, 45. (4) Tavlor. G. I. Proc. R. SOC.London. A 1964. A267. 45. (5) To;za,'S.; Cox, R. G.; Mason, S. G:Phil. Trans. R. SOC.London, Ser. A 1971, 269, 295. (6)Moriva, S.; Adachi, K.: Kotaka, T. Polym. Commun. 1985,26, 235. (7) Srivastava, B. C.; Pandya, T. P. J . Colloid. Interface Sci. 1981,83, 35. (8) Pandya, T. P.; Bali, L. M.; Jha, P. J . Colloid Interface Sci. 1984, 99, 278. (9) Zeleny, J. Phys. Reu. 1914, 3, 69; Ibid. 1917, 10, 1. (10) Wilson, C. R. T.; Taylor, G. I. Proc. Cambridge, Philos. SOC.1925, 22, 728. (11)Taylor, G. I.; Van Dyke, M. D. Proc. R. SOC.London, Ser. A 1969, 313, 453. (12) Larrondo, L.; John Manley, R. St. J . Polym. Sei., Polym. Phys. Ed. 1981, 19, 909, 921, 933. (13) Taylor, G. I. Proc. R. SOC.London, Ser. A 1934, 146, 501. (14) Rumscheidt, F. D.; Mason, S. G. J . Colloid Interface Sei. 1961, 16, 237. (15) Chin, H. B.; Han, C. D. J. Rheol. (N.Y.) 1979, 23, 557. (16) Torza, S.; Cox, R. G.; Mason, S. G. J . Colloid. Interface Sci. 1972, 38, 395. (17) Acrivos, A.; Lo, T. S. J . Fluid. Mech. 1978,86, 641. (18) Stroeve, P.; Varanasi, P. P. J. Colloid.Interface Sei. 1984,99, 360. (19) Albright, P. S.; Gosting, L. J. J . Am. Chem. SOC.1946,68, 1061. (20) Mikkail, S. 2.;Kimel, W. R. J. Chem. Eng. Data 1961, 6, 533. (21) "CRC Handbook of Chemistry and Physics"; West, R. C., Ed.; CRC Press: New York, 1979.
0743-7463/86/2402-0161$01.50/0 0 1986 American Chemical Society
162 Langmuir, Vol. 2, No.2,1986
Moriya el al.
O
l
p
~ I.-/"
L
/
3 0 H.01 PSmFi201 45 06 IC0 IWOBR~OI / PS/Ce440)
w
0
0
2
4
8
6 U'E'blV"'
Figure 3. Burst points (shown by arrows) and the equilibrium deformationD- for the drops of water/methmol mixture (84/16) and those of pure water suspended in di-n-butyl phthalate (DBP) solutions of polystyrene (PS). Here, b is the radius of the drop and E, the field strength.
Table 1. Comparison of Theoretical and Experimental b E 2 Figure I. Photographs of a water drop with the radius b = 0.22 mm suspended in di-n-butylphthalate solutions of polystyrene under the 60 Hz ac field E = 0.28 MV/m.
10VbE: 1 2
drop phase water/MeOH water/MeOH
3
water
4 5
water water
medium
ohsd
theory
PS/DBPC!O) PS/DBP(SO) PS/DBP(20) PS/DBP(SO) PS/DBP(40)
3.40
2.12 2.36 5.06 5.28
3.22 5.24 5.68 7.72
6.62
.Unit: v1 n i l .
182s
28.5s
Figure 2. Sketches of a drop of an ethylene glycol solution of poly(vinylpyrrolidone)suspended m the same medium as in Figure 1 under the ac field of 0.40 MV/m. PS/DBP(30) subjected to the field of E = 0.28 MV/m. At t = 121 s, a pole of the ellipsoid became suddenly a sharply pointed conical shape within about 1s. and the other pole also became c o n i d within the following few seconds. After this sudden change in the drop shape. small droplets of about 0.025" diameter were intermittently ejected from the sharply pointed ends. The size of the ejected droplets were usually smaller in a less viscous medium such as PS/DBP(20) in which the jet looked like smoke. On the other hand, in a very viscous medium such as PS/DBP(40), relatively large droplets of about 0.05-mm diameter were ejected in about every s and aligned like a pearl necklace along the direction of the field. Figure 2 shows sketches of a deforming PVP-I/EG(N) drop of initial radius b = 0.21 mm under the field of E = 0.40 MV/m. In the very early stage of deformation, the drop was ellipsoidal but soon assumed a shape intermediate between an ellipsoidal and conical shape. After 11 s, the drop became a top-pointed spindle shape and was drawn toward the electrodes. We define "bursting time" t , as the time a t which the pointed ends appear and length L and thickness or the fiber diameter d of the bursting
drop as shown in Figure 1and 2. The length L increased continuously and the top was soon out of the camels view. In contrast to bursting water drops, the ejection of smaller droplets at the ends was not observed for these viscous drops of the PVP solutions. Critical Field Strength. Figure 3 shows the equilibrium deformation D, vs. bE2 plot for drops of water and the water/methanol mixture suspended in PS/DBP solutions. In order to determine the critical field strength E. above which the droplet becomes unstable, we increased the field strength very slowly. The values of E, are indicated by the arrows in the figure. Garton and Krasucki* showed that above a certain critical field E, the drop exceeds a certain critical shape and becomes unstable, where the electric force is always larger than the restoring force due to the interfacial free energy. Therefore, the theoretical curves of D, vs. li? diverge at E:. Carton and Kurascki estimated that under such a situation the ratio of the major to minor axes should be 1.85, which corresponds to D, = 0.30. On the other hand, Taylor' evaluated, through an approach somewhat different from Carton et al., the critical ratio of the major to minor axes to be 1.9 (De = 0.31). According to Garton and Krasucki? E. is given by
E: = (2.4 X 10'o)y/K2b (in mks units) (1) where y,k,, and b were defined in the abstract of ref 1. The arrows fn Figure 3 indicate the minimum value of bE2 a t which the burst was observed. In Table I, we compared the experimentally determined values of E, with the theoretical values obtained by eq 1. We see that they are in fairly good agreement. Figure 4 shows the change of D with time for a water drop of b = 0.565 mm in PS/DBP(35). For this system, eq 1 predicts that E. = 0.34 MV/m. When the field corresponding to 0.99E. (=0.335 MV/m) was applied, D attained once a metastable state at about t = 300 sand then bursted as shown in Figure 4. If we assume the value of D a t this metastable state as D,, r was calculated by eq
~
Langmuir, Vol. 2, No. 2, 1986 163
Deformation of Droplets i n an Electric Field. 2 0.3
-1,2 02 0
0.1
It
-1.6 0
0
3
2
1
I og( t I
4
s)
Figure 4. Time dependence of the deformation D of a water LOP suspended in PS/DBP(BO) under various field strength E above or below the critical strength E,. The arrows indicate the characteristic time. I
\m
'
l
I
l
I
E,: 0 340'WIm Em13SEc
1
-
-
\O'O'
1
20 t/s Figure 6. Time dependence of the diameter of the equator of a bursting drop: PVP-I/EG(50) suspended in PS/DBP(BO). 0
IO
the plots of In (1- D/D,)against t for the infinitesimal deformation was also 22 f 2 s. This suggests that as long as the drop has an ellipsoidal shape, the T is the same regardless of the field strength E either below or above E,. From the intercept of the plot and the ordinate, we determined the value of D, to be 0.21 for E = 1.38EC (=0.468 MV/m). This value is smaller than the critical value D, (=0.3)of the drop instability.2 However, this is not surprising because D , thus determined corresponds to the degree of deformation at a hypothetical equilibrium obtained by extrapolating the linear portion of the D , vs. bE2 relation to E = 1.38EC,(see Figure 3). Since D is approximately linear against bE2 only in the range D < 0.1, the rate of deformation under E > E, can be described by eq 12-14 of ref 1 only up to the time when D reaches 0.1. Rate of Deformation of Bursting Drops. The change in the size and shape of bursting drops was followed by a video camera. In the case of bursting water drops, the original drop volume decreased as it ejected smaller droplets. The drop length L defined in Figure 1 decreased in proportion to time t during the ejection, but the diameter d of the elongated drop (see Figure 2) remained almost unchanged. We observed that the bursting drop has a spindle shape as if the drop is pulled a t the two poles of the ellipsoid. Since the charge induced in such a spindle shape drop is concentrated at the poles, the electric forces F, may act dominantly around the poles. This force, considered to be independent of the drop size L, should be counteracted by the interfacial free energy and the pressure difference A p between the inside and outside of the drop. Therefore, the force balance around the equator is given by
F, = ayd - ( a d 2 / 4 ) A p
(3)
Taylor showed that the second term is about 1 order of magnitude smaller than F, for a drop held at the end of a tube under E, (see Table I11 in ref 11). Therefore, the second term in the right-hand side of eq 3 may be negligible in our systems for the rough estimation of the force balance of the bursting drop. Thus, d may remain approximately constant during the bursting. For the drop shown in Figure 1, the value of a-yd was calculated to be 0.47 dyn. Here, y was evaluated to be 5.3 X Pa from the slope of D , vs. bE2 shown in Figure 3. Van Dyke1' calculated the electric force acting on conducting needles having various shapes. We attempted to explain the experimentally obtained F, (=0.47 dyn) by the theory. However, his theory indicates that F , is very sensitive to the shape of the end of needles, and, therefore,
-
161 Langmuir, Vol. 2, No. 2, 1986
a
Moriya et 01. 1
b
Figure 7. Abnormal behavior of a deformation at the top of bursting drop of PVP/EG: (a) ejection of mist; (b) coiling.
we could not give a meaningful explanation of the F. value unless the electrical force for a spindle-shaped needle was calculated. Unfortunately, we cannot calculate it at present. In contrast to the water drops, drops of the PVP/EG solutions were spun continuously as sketched in Figure 2, being accompanied by a decrease in the fiber diameter d. In such a case, we should assume that F, given by eq 3 is counteracted not only by the interfacial free energy but also by the viscous drags against elongation. Neglecting the pressure difference term, we obtain the force balance around the equator:
F. = r y d
+ (3/4)m&dA/dt)
(4)
where 1) and A denote shear viscosity and the elongation ratio, respectively. For the viscous drop, the first term in the rhs of eq 4 should be negligible. Thus, we obtain an expression for the change in d with t by solving eq 4 with the relation d.2 = Ad2: In ( d / d J = -(2Fe/3r1)d:)(t
- t,)
(5)
where d, is d a t t = t , when pointed ends appear at the poles of the drop. Figure 6 shows the plot of In d vs. t for the drop shown in Figure 2. The plot obeys eq 5 fairly well. Evidently eq 5 should be valid a t any point of the drop surface except a t the pointed ends. Equation 5 in which d and d. are replaced by the thickness of the drop 2fb) and Zf&) defined by the insertion in Figure 6 also holds. Since the thickness tends t o zero a t the tips of the drop, eq 5 diverges. Thus, other deformation mechanisms must operate around the poles. We define this region by AL as shown by the insertion in Figure 6. In fact, we often observed the tips of the drop vibrating and ejecting mists or continuously coiling and uncoiling as shown in Figure 7. From these observation, we estimate AL is about 5-10% of L,, the value of L a t t = t,. Returning to the steadystate elongation of the drop under the high field, we can calculate the rate of spinning in the following manner, provided the profile fc(y) of the drop at t = t, is known. We define the coordinate and fJy) as shown in Figure 6. If we assume that the force acting on the poles is constant during further elongation of the spindle-shaped drop, its length L(t) a t time t should be given by
U t ) = 2 10' exp[F.(t - t.)/(3rnf.W2)1 dr + 2AL
Figure 8. Observation of the flow profile inside the drop with a video camera for a drop of PVP-l/EG(SO) containing a small amount of a carbon black.
(6)
where a = L,/2 - AL. In eq 6, we assumed that AL is roughly independent of time. Since AL is relatively small, this approximation does not cause a serious error. So far, we are unable t o express the profile f,(y) by a simple analytical function. However, if necessary, we can roughly estimate U t ) and also the rate of spinning &/dt by nu-
- 1
I
1.2
1.4
A
1.6
0.6
0.8
I
/Jx
I
Figure 9. Plot of the cwrdinate y and x for the points A and B sham in Figure 8 with respect to the elongation ratio A. A slight distortion of the video image seen in Figure 8 was corrected.
merical integration of eq 6, using the profile f,(y) determined at t = t, of the drop about to burst. Observation of Flow Patterns. In the preceding paper' and here, we assumed that the flow inside the drop is approximately a simple elongation flow hy a constant tensile force. Here, we attempt to analyze the flow pattern recorded by using a video camera to check this assumption. To do this, we observed the flow field inside the drop of the PVP/EGsolution, adding a small amount of carbon black as the marker. Figure 8 shows typical photographs of the drop. We recognized that the movement of the carbon black was approximately of the type induced by a simple elongation of the liquid thread. T o confirm this, we followed the motion of two arbitrarily chosen markers (A and B in Figure 8) in a series of the video stills and determined their coordinates ( x y ) as a function of time t. Here, they and x axes are taken in the direction of the field and that perpendicular to it, respectively, as shown
Langmuir 1986, 2, 165-169 in Figure 6. Then, we plotted y / y o against X and x / x o against X-lI2, where X is the overall extension ratio equal to Y/2b (see Figure 1)and xo and yo are the initial coordinates. The results are shown in Figure 9. We see that
165
the y coordinates of the markers are proportional to X, while the x coordinates are proportional X-lI2, as we have anticipated for the flow inside the drop being a simple elongation under a constant tensile force.
Synthesis and Characterization of Aqueous Tris(2,2'-bipyridine)ruthenium(11)-Zirconium Phosphate Suspensions Dominique P. Vliers,? Dirk Collin,t Robert A. Schoonheydt,*t and Frans C. De Schryved Laboratorium uoor Opperulaktechemie, K . U. Leuuen, Kard. Mercierlaan 92, B-3030 Leuuen (Heverlee),Belgium, and Departement Scheikunde, K . U.Leuuen, Celestijnenlaan 200F, B-3030 Leuuen (Heuerlee),Belgium Receiued August 14, 1985. I n Final Form: October 30, 1985 Tris(2,2'-bipyridine)ruthenium(II) (R~(bpy),~+) is ion-exchanged on stable suspensions of hydrogen zirconium phosphate (HZrP) and hexylammonium zirconium phosphate (HexA-ZrP) to a maximum extent of 1.20 mmol/g of solid. In the former case, the particles are almost completely disordered and there is no intercalate with R ~ ( b p y ) , ~ + In. the latter case, both interlamellar adsorption and adsorption on the external surface occur, because the material is only partially disordered. The adsorption and emission bands of adsorbed R ~ ( b p y )are ~ ~red-shifted + with respect to their aqueous solution values by 5 nm, and the extinction coefficient of the 458-nm band strongly decreases with loading. By quenching with Fe(CN):it is possible to distinguish between R~(bpy)~'+ on the external surface and in the interlamellar space: in the former case the Stern-Volmer constant is 11500 M-', in the latter case 7200 M-'.
Introduction The adsorption of the photosensitizer tris(2,2'-bipyridine)ruthenium(II), R ~ ( b p y ) ~on ~ +inorganic , colloids has currently obtained a large interest in the field of heterogeneous photochemistry, especially the water splitting.'r2 Among the colloidal systems, clay suspensions, especially smectite clays, are attractive supports?-* These are layered aluminosilicates with swelling behavior, a large surface area (700-800 m2/g), and a cation-exchange capacity of 1 mequivfg. The luminescence of R~(bpy),~+-claysuspensions is sensitive to the chemical composition and loading of the clays.g The wavelength of the emission maximum increases linearly with the negative charge of the lattice. The quantum yield is independent of the loading up to 40% and the quenching by structural Fe(II1) follows Perrin's law of quenching in the absence of diffusion. Quenching studies using neutral organic molecules or potassium ferricyanide differentiate Ru(bpy)? adsorbed on the external surface of kaolin clay and Ru(bpy)gl+intercalated between montmorillonite clay layers.6 The structure of zirconium phosphate is similar to that of smectite clays. Layers of zirconium octahedra are separated by phosphate tetrahedra like the aluminum octahedra and silicium tetrahedra in clays. The attractive features of zirconium phosphates are (i) the lack of iron and (ii) the very high cation exchange capacity (CEC) (6.64 mequiv/g). Three types of Ru(bpy):+ adducts of zirconium phosphates (ZrP) can be synthesized.ll (i) A crystalline intercalate is formed when Ru(bpy)z+is incorported during the synthesis of zirconium phosphate in the presence of HF. Its emission maximum is at 615 nm. (ii) By t Laboratorium voor Oppervlaktechemie.
* Department Scheikunde.
ion exchange or impregnation of R ~ ( b p y ) , ~the + complex is adsorbed only on the external surface. These materials have their emission maximum at 640-645 nm. (iii) When Ru(bpy),Cl,, ZrOC12,and are refluxed, less crystalline materials are formed. Two Ru(bpy),2+ species are distinguished. One which emits at 615 nm and another which emits at 590 nm. The latter is predominantly visible with excitation at 420 nm. The chemical species is believed to be ( R u ( b p ~ ) ~ ( b p y H ) ) ~ + . ~ ~ Although inorganic cations larger than K+ cannot be intercalated at room temperature into Zr(03POH)2.H20, a-HZrP,'O amines,12-14pyridine,', and amino acids15 are easily taken up in the interlamellar space. With vigorous stirring a-HZrP crystals, exchanged with alkylammonium (1)Duonghong, D.; Borgarello, E.; Gratzel, M. J. Am. Chem. Soc 1981, 103,4685. (2)Nijs, H.; Fripiat, J. J.; Van Damme, H. J . Phys. Chem. 1983,87, 1279. (3)Krenske, D.; Abdo, S.; Van Damme, H.; Cruz, M.; Fripiat, J. J. J . Phys. Chem. 1980,84,2447. (4)Abdo, S.;Canesson, P.; Cruz, M.; Fripiat, J. J.;Van Damme, H. J. Phvs. Chem. 1981.85. 797. 15) Nijs, H.; Cruz, M.;Fripiat, J. J.; Van Damme, H. J . Chem. SOC., Chem. Commun. 1981,1026. (6)Della Guardia, R.A.; Thomas, J. K. J. Phys. Chem. 1983,87,990. (7)Schoonhevdt, R. A.; Pelarims, J.; Heroes, Y.; Uytterhoeven, J. B. Clay Miner. 1978,13,435. (8) Ghosh, P. K.; Bard, A. J. J . Phys. Chem. 1984,88, 5519. (9)Schoonheydt, R.A,; De Pauw, P.; Vliers, D.; De Schryver, F. C. J . Phys. Chem. 1984,88,5113. (10)Clearfield, A,; Hagiwara, M. J . Inorg. Nucl. Chem. 1978,40,907. (11)Vliers, D. P.;Schoonheydt, R. A.; De Schryver, F. C. J. Chem. SOC.,Faraday Trans I , 1985,81,2009. (12)Clearfield, A.; Tindwa, R. H. J . Inorg. Nucl. Chem. 1979,41,871. (13)Yamanaka, S.;Haribe, Y.; Tanaka, M. J . Inorg. Nucl. Chem. 1976, 38,323. (14)Tindwa, R.W.; Ellis, D. K.; Peng, G.; Clearfield, A. J. Chem. SOC., Faraday Trans. 1, 1985,81, 545. (15)Kijima, T.;Ueno, S.; Gab, M. J. Chem. Soc., Dalton Trans. 1982, 2499.
0743-7463/86/2402-Ol65$01.50/0 0 1986 American Chemical Society
