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Spreading involving the marangoni effect: Some preliminary results
Colloids and Surfaces,
41 (1989)
Elsevier Science Publishers
97-105 B.V., Amsterdam
97
-
Printed
in The Netherlands
Spreading Involving the Marangoni Effect: Some Preliminary Results P. CARLES* and A.M. CAZABAT Physique
de la Mat&e
Condensde,
Colkge
de France,
11 Place Marcelin-Berthelot,
75231 Paris
Cedex 05 (France)
(Received 27 September
1988; accepted
16 January
1989 1
ABSTRACT We have studied the spreading of an oil drop under an atmosphere saturated with a volatile compound that could mix with the oil. We observed that the usual laws for spreading were not valid any longer: the spreading was strongly accelerated and instabilities developed at the edge of the drop. We also observed the retraction of some drops after a fast initial spreading. All these phenomena are linked with the Marangoni effect, i.e. the presence of surface tension gradients in the drop.
INTRODUCTION
The spreading of liquids on solid surfaces is a phenomenon that has been known for a long time. In spite of its great practical interest, it is not yet fully understood, but recent progress, both from theoretical and experimental points of view, has been achieved [ 1,2]. The parameters controlling the dynamics of spreading in ideal situations (pure liquids on perfectly smooth surfaces) have been clearly recognized, and besides verifying and refining the theoretical predictions, current studies can now deal with more complex situations, involving rough surfaces [ 3,4] or complex liquids [5-l 11. This last field is of great practical importance, because most liquids are not pure and contamination often plays an important role (e.g. the effect of water in Hardy’s experiments [ 121). Spreading in inhomogeneous situations has already been the subject of various studies, some involving instabilities of the contact line [5-B] or surface tension gradients [5,6,9,10] (Marangoni effect
ill1 1.
We have undertaken the study of the spreading of a non-volatile silicone oil interacting with an atmosphere saturated with a volatile solvent of the oil. This system exhibits both the Marangoni effect and instabilities of the contact line, *On leave from Direction
0166-6622/89/$03.50
des Recherches,
Etudes et Techniques,
0 1989 Elsevier Science Publishers
Paris, France.
B.V.
98
and can be quantitatively studied. Besides, as the disjoining pressure of the oil is low, the normal precursor film [l] is not developed during our experiments, which allows us to discuss the observed effects on a macroscopic scale. EXPERIMENTAL
We have used a polydimethylsiloxane oil (PDMS) with terminal methyl groups which is available with various viscosities (typically between lop3 and lo3 Pa s). It is not volatile, not very reactive and has already been used for various studies. It also has a great practical use in that it is a well-known lubricant and a basic compound for adhesives. The volatile solvent we have used is trans-decaline, a saturated hydrocarbon made of two 6-membered saturated, fused rings. Its viscosity is roughly that of water, and its volatility is high. An important parameter is the surface tension y of these compounds. The measured values, using the du Noiiy ring method, were for PDMS, y= 20.0. lo-” N m-l and, for trans-decaline, ~=26.3*10-~ N m-l. PDMS wets glass, but trans-decaline does not, this may seem odd, but is probably due to structural effects. For instance, cyclohexane, which is made of one saturated 6-membered ring, does not wet glass either (see for instance Ref. [ 51)) although its surface tension is only 25.5~10~” N m-l. We measured the surface tension of mixtures of these two components, and found that it varied roughly linearly with the composition of the mixture (Fig. 1). The spreading of the oil drops was studied on glass microscope slides, cleaned with boiling sulfochromic acid for one hour, rinsed with triply distilled water and then dried with methanol. With this cleaning procedure, which had already been used for other studies, the observed phenomena were reproducible. As it is almost impossible to remove PDMS when it has adsorbed on a surface [ 61, we chose microscope slides instead of better defined silica plates because,
T
y(10-3N.m-1)
26-
Fig. 1. Surface tension caline in the mixture).
of PDMS-trans-decaline
mixtures
(c is the volume fraction of trans-de-
99
thanks to their low cost, each slide could be used just once and then disposed of. The drops were observed with a simple video assembly: they were lit by a parallel beam and their image was formed directly onto a video camera, connected to a video tape recorder. The records of each experiments could thus be analysed. Contrast was often enhanced using the strioscopy technique. The whole set-up was calibrated by imaging known grid systems. Preliminary study: interaction of two droplets Apart from our main series of experiments, which we will discuss later, we repeated a few classical observations reported for instance in Refs [ 61 and [ 71, which give some insight into the physical processes involved during spreading in the presence of volatile compounds. We placed two drops, one of PDMS and one of trans-decaline, each a few millimeters wide, on a glass slide with a few millimeters between them. After some seconds, the (spreading) PDMS drop begins to move towards the (motionless) trans-decaline drop (Fig. 2). When the PDMS reaches it, the solvent drop begins to move away, and a kind of pursuit begins. This can be easily explained. The solvent, which is volatile, evaporates and penetrates the oil drop. AS ysolvent> Ysilicone,the surface tension of the oil drop
a
b
C
Fig. 2. Interaction of two droplets: the PDMS drop lies on the left, the trans-decaline drop on the right. (a) Principle of the interaction: the solvent evaporates (wide arrows) and the oil spreads with different rates at different points of its edge (thin arrows). (b) (early stage) and (c) (later stage): typical deformation of the drops (the dotted lines show their initial locations).
100
rises, mainly in the direction from which the solvent comes. This induces a stream of liquid in the bulk of the drop, and thus the observed movement. A similar phenomenon occurs when the PDMS drop reaches the solvent, the surface tension of the solvent decreases at the point where it mixes with the oil, which induces the flight of the solvent drop. In this experiment, the spreading liquid is not volatile and its precursor is not developed, which makes the interpretation easier. We were able to prove that the interaction actually took place via the atmosphere and not via an invisible film because the early stages of the pursuit were still observed if the drops were placed on two different slides, close together. When the drops were under draughts, we also observed periodic increases and decreases of rolls of liquid at the edge of the oil drop. They seemed to be associated with alternate evaporation or condensation processes. These experiments are easily understood, at least in their general trends, and show that a difference of surface tension can induce dramatic phenomena on a macroscopic scale. This is an example of the well-known Marangoni effect. This effect is also involved in our main experiments, which we shall now discuss. RESULTS
We studied the spreading of a PDMS droplet under an atmosphere saturated with solvent. A PDMS drop was placed with a calibrated pipette on a glass slide, and then covered with a box presaturated with the solvent vapour by means of a filter paper impregnated with the solvent (we checked that the paper was still impregnated at the end of the experiments). Before covering the drop the box was first equilibrated at room temperature, which remained constant ( 2 1 ‘C ) during the time of the experiments. However, we did not measure the temperature variations due to evaporation/condensation of the solvent, in the drop itself. Acceleration of spreading We first plotted the radius R of the wetted spot (Fig. 3 ), as measured on the video screen, versus the time t (both in logarithmic scale). Usual laws for spreading of pure liquids are R K t “lo or R CKt ‘j8, depending on whether gravity is negligible or not. We still observed asymptotic laws of the kind Rat”, but with IZbetween roughly 0.25 and 0.5 (Fig. 4). These limits were not strict, and n increased with the initial size of the drop. It can be shown that the radius of a drop, spreading under a constant driving force per unit length of perimeter, follows a law Ra t0.25 or Ra t0.5,depending on whether its volume is constant or not (this last case corresponds to the
101
Solvent PDMS
Fig. 3. Principle
bgR(mm)
vapour
drop
of the experiments.
PDMS /TRANSDECALINE
Fig. 4. Example of spreading vapour.
VAPOUR
of a PDMS drop (of viscosity
lOO*lO-” Pa s) under trans-decaline
presence of a reservoir) [3]. Besides, in a recent work [9], Joanny showed that, in a somewhat analogous situation (the spreading of a drop covered by an insoluble surfactant ) , a surface tension gradient between the center and the edge gives rise to a constant driving force per unit length of contact line. Our case is of course different, but a surface tension gradient seems to be a good reason for explaining what we observed. The surface tension of the drop depends mainly on the composition of a superficial layer with a thickness of the order of one micrometer (the range of
102
Van der Waals interactions). To account for the sign of our effect (acceleration of spreading), we need a higher surface tension at the edge of the drop than in its center, i.e. a higher concentration of solvent at the edge. We can imagine at least two hypotheses for the origin of this difference. First, if the diffusion of the solvent in the drop is slow, this layer is not in equilibrium with the vapour phase, i.e. its composition is not homogeneous. The concentration of solvent is higher where the thickness of the drop is smaller, i.e. near the edge. Second [ 131, if the diffusion of the solvent in the atmosphere is slow, the spreading drop creates a depletion zone, low in solvent, in the atmosphere. The concentration of solvent in the layer is nearly homogeneous, except in the very foot of the drop, where it is higher because this foot arrives first in solvent rich regions of the atmosphere. We have not yet been able to choose between these two possible origins. A last possibility might have been the adsorption of solvent on the glass plate. Indirect ar~ments against this hypothesis were provided by contact angle measurements on glass slides previously exposed to the solvent atmosphere, no changes were observed. A more direct argument has been obtained by following the thickness of films on oxidized silicon wafers by ellipsometry [ 141, the adsorbed trans-decaline layer was less than 0.6 A (averaged value over 0.2 mm”) and disappeared rapidly when the saturated atmosphere was taken off. Instabilities The fast spreading we have just described only lasts for a while, because after a few minutes instabilities appear at the edge of the drop. From this moment, it is very difficult to give an accurate measurement of the radius of the drop. The instabilities grew rather regularly, and divided into smaller ones when they got too large. They had rather regular, though not exactly reproducible, shapes and wavelengths (Fig. 5 ) . Their origin can be at least qualitatively understood. First, there is a destabilizing effect. Whatever the exact origin of this inhomogeneity (see above), an instability has a higher surface tension than the bulk of the drop. Due to the Marangoni effect, it tends to spread faster than the bulk of the drop, which still increases its surface tension, and so on. Second, there is of course a stabilizing phenomenon, creating an instability costs surface energy. But it seems that after a while the destabilizing effect prevails, whether it be a matter of critical size or maybe of critical curvature of the edge of the drop. As for the size of the instabilities, it is a problem of selection of wavelength that has not been resolved yet.
103
Amm 1.5 I 1.0,
.
0.5 -
2
* 0
Fig. 5. Typical shapes of instabilities of their size versus time.
1
I
I
I,
tinie(mn1
I,
0123456
(in dotted lines initial size of the drop) and typical evolution
C
1
10
100
Log t (9
Fig. 6. Spreading of small droplets: the lower curve shows the retraction of a drop. The upper one corresponds to a drop, probably of some critical size, which showed a curious behaviour: the instabilities appeared and disappeared several times.
Small droplets If the drop was very small (roughly if its volume was less than 2. lo-” mm”), the description above remained valid only for a moment. After some time the instabilities seemed to become too large for the drop, and the drop divided into several irregular smaller ones, which did not spread any longer (Fig. 6 ) .
104
The retraction and breaking up of the drop might be a de-wetting phenomenon, which occurs when the surface tension has increased so much that its edges become non-wetting. The resulting smaller drops are probably in equilibrium with the gas phase and do not evolve further. A final curious effect
The last surprising feature we observed appeared when, after the end of the experiments, we removed the saturated atmosphere off. Then, in less than a second, the drop divided into a very large number of very small drops, which attracted each other (probably much like the way the solvent drop attracted the PDMS) and then spread again. This comes from the inverse Marangoni effect, due to evaporation of the solvent from the drop, which acts against spreading and causes the retraction of the drops. Later, the solvent has entirely evaporated, and the spreading of the oil may start again. CONCLUSIONS
The results we have reported are still limited and not yet fully understood, but they seem to be interesting and worth further study, which is currently under way. We shall especially concentrate on the problem of the surface tension gradients, and on the instabilities we have observed. From a theoretical point of view, the problems do not seem easy either, since the surface tension, the concentration of solvent and the shape of the drop are closely linked. ACKNOWLEDGEMENTS
The authors are pleased to acknowledge very fruitful discussions with P.G. de Gennes. The ellipsometric test is due to the courtesy of F. Heslot and the surface tension measurements to the courtesy of J.M. di Meglio. The constructive criticism of the referees is also acknowledged.
REFERENCES 1 2 3 4 5
P.G. de Gennes, Rev. Mod. Phys., 57 (1985) 827. G.F. Teletzke, Thesis, University of Minnesota, 1983. B.V. Derjaguin, N.V. Churaev and V.M. Muller, Surface Forces, Consultants Bureau, New York, 1987,440 pp. B.V. Derjaguin, Langmuir, 3 (1987) 601. A.M. Cazabat and M.A. Cohen Stuart, Prog. Colloid Polym. Sci., 74 (1987) 69. J.F. Olivier, C. Huh and S.G. Mason, Colloids Surfaces, I (1980) 79. E. Bayramli, T.G.M. Van de Ven and S.G. Mason, Colloids Surfaces, 3 (1981) 131. D. Pesach and A. Marmur, Langmuir, 3 (1987) 519.
105 6 7 8 9 10
11 12 13 14
R.L. Cottington, CM. Murphy and CR. Singleterry, Adv. Chem. Ser., 43 (1964) 341. D.H. Bangham and Z. Saweris, Trans. Faraday Sot., 34 (1938) 554. A. Marmur and M.D. Lelah, Chem. Eng. Commun., 13 (1981) 133. J.F. Joanny, to be published. S. Troian, X.L. Wu and S.A. Safran, Phys. Rev. Lett., 62 (1989) 1496. W.D. Bascom, R.L. Cottington and C.R. Singleterry, Adv. Chem. Ser., 43 (1964) 355. M.K. Bernett and W.A. Zisman, Adv. Chem. Ser., 43 (1964) 332. C. Marangoni, Nuovo Cimento, 5 (1871) 239. W.B. Hardy, Philos. Mag., 38 (1919) 49. P.G. de Gennes, personal communication, 1988. F. Heslot, unpublished results.
41 (1989)
Elsevier Science Publishers
97-105 B.V., Amsterdam
97
-
Printed
in The Netherlands
Spreading Involving the Marangoni Effect: Some Preliminary Results P. CARLES* and A.M. CAZABAT Physique
de la Mat&e
Condensde,
Colkge
de France,
11 Place Marcelin-Berthelot,
75231 Paris
Cedex 05 (France)
(Received 27 September
1988; accepted
16 January
1989 1
ABSTRACT We have studied the spreading of an oil drop under an atmosphere saturated with a volatile compound that could mix with the oil. We observed that the usual laws for spreading were not valid any longer: the spreading was strongly accelerated and instabilities developed at the edge of the drop. We also observed the retraction of some drops after a fast initial spreading. All these phenomena are linked with the Marangoni effect, i.e. the presence of surface tension gradients in the drop.
INTRODUCTION
The spreading of liquids on solid surfaces is a phenomenon that has been known for a long time. In spite of its great practical interest, it is not yet fully understood, but recent progress, both from theoretical and experimental points of view, has been achieved [ 1,2]. The parameters controlling the dynamics of spreading in ideal situations (pure liquids on perfectly smooth surfaces) have been clearly recognized, and besides verifying and refining the theoretical predictions, current studies can now deal with more complex situations, involving rough surfaces [ 3,4] or complex liquids [5-l 11. This last field is of great practical importance, because most liquids are not pure and contamination often plays an important role (e.g. the effect of water in Hardy’s experiments [ 121). Spreading in inhomogeneous situations has already been the subject of various studies, some involving instabilities of the contact line [5-B] or surface tension gradients [5,6,9,10] (Marangoni effect
ill1 1.
We have undertaken the study of the spreading of a non-volatile silicone oil interacting with an atmosphere saturated with a volatile solvent of the oil. This system exhibits both the Marangoni effect and instabilities of the contact line, *On leave from Direction
0166-6622/89/$03.50
des Recherches,
Etudes et Techniques,
0 1989 Elsevier Science Publishers
Paris, France.
B.V.
98
and can be quantitatively studied. Besides, as the disjoining pressure of the oil is low, the normal precursor film [l] is not developed during our experiments, which allows us to discuss the observed effects on a macroscopic scale. EXPERIMENTAL
We have used a polydimethylsiloxane oil (PDMS) with terminal methyl groups which is available with various viscosities (typically between lop3 and lo3 Pa s). It is not volatile, not very reactive and has already been used for various studies. It also has a great practical use in that it is a well-known lubricant and a basic compound for adhesives. The volatile solvent we have used is trans-decaline, a saturated hydrocarbon made of two 6-membered saturated, fused rings. Its viscosity is roughly that of water, and its volatility is high. An important parameter is the surface tension y of these compounds. The measured values, using the du Noiiy ring method, were for PDMS, y= 20.0. lo-” N m-l and, for trans-decaline, ~=26.3*10-~ N m-l. PDMS wets glass, but trans-decaline does not, this may seem odd, but is probably due to structural effects. For instance, cyclohexane, which is made of one saturated 6-membered ring, does not wet glass either (see for instance Ref. [ 51)) although its surface tension is only 25.5~10~” N m-l. We measured the surface tension of mixtures of these two components, and found that it varied roughly linearly with the composition of the mixture (Fig. 1). The spreading of the oil drops was studied on glass microscope slides, cleaned with boiling sulfochromic acid for one hour, rinsed with triply distilled water and then dried with methanol. With this cleaning procedure, which had already been used for other studies, the observed phenomena were reproducible. As it is almost impossible to remove PDMS when it has adsorbed on a surface [ 61, we chose microscope slides instead of better defined silica plates because,
T
y(10-3N.m-1)
26-
Fig. 1. Surface tension caline in the mixture).
of PDMS-trans-decaline
mixtures
(c is the volume fraction of trans-de-
99
thanks to their low cost, each slide could be used just once and then disposed of. The drops were observed with a simple video assembly: they were lit by a parallel beam and their image was formed directly onto a video camera, connected to a video tape recorder. The records of each experiments could thus be analysed. Contrast was often enhanced using the strioscopy technique. The whole set-up was calibrated by imaging known grid systems. Preliminary study: interaction of two droplets Apart from our main series of experiments, which we will discuss later, we repeated a few classical observations reported for instance in Refs [ 61 and [ 71, which give some insight into the physical processes involved during spreading in the presence of volatile compounds. We placed two drops, one of PDMS and one of trans-decaline, each a few millimeters wide, on a glass slide with a few millimeters between them. After some seconds, the (spreading) PDMS drop begins to move towards the (motionless) trans-decaline drop (Fig. 2). When the PDMS reaches it, the solvent drop begins to move away, and a kind of pursuit begins. This can be easily explained. The solvent, which is volatile, evaporates and penetrates the oil drop. AS ysolvent> Ysilicone,the surface tension of the oil drop
a
b
C
Fig. 2. Interaction of two droplets: the PDMS drop lies on the left, the trans-decaline drop on the right. (a) Principle of the interaction: the solvent evaporates (wide arrows) and the oil spreads with different rates at different points of its edge (thin arrows). (b) (early stage) and (c) (later stage): typical deformation of the drops (the dotted lines show their initial locations).
100
rises, mainly in the direction from which the solvent comes. This induces a stream of liquid in the bulk of the drop, and thus the observed movement. A similar phenomenon occurs when the PDMS drop reaches the solvent, the surface tension of the solvent decreases at the point where it mixes with the oil, which induces the flight of the solvent drop. In this experiment, the spreading liquid is not volatile and its precursor is not developed, which makes the interpretation easier. We were able to prove that the interaction actually took place via the atmosphere and not via an invisible film because the early stages of the pursuit were still observed if the drops were placed on two different slides, close together. When the drops were under draughts, we also observed periodic increases and decreases of rolls of liquid at the edge of the oil drop. They seemed to be associated with alternate evaporation or condensation processes. These experiments are easily understood, at least in their general trends, and show that a difference of surface tension can induce dramatic phenomena on a macroscopic scale. This is an example of the well-known Marangoni effect. This effect is also involved in our main experiments, which we shall now discuss. RESULTS
We studied the spreading of a PDMS droplet under an atmosphere saturated with solvent. A PDMS drop was placed with a calibrated pipette on a glass slide, and then covered with a box presaturated with the solvent vapour by means of a filter paper impregnated with the solvent (we checked that the paper was still impregnated at the end of the experiments). Before covering the drop the box was first equilibrated at room temperature, which remained constant ( 2 1 ‘C ) during the time of the experiments. However, we did not measure the temperature variations due to evaporation/condensation of the solvent, in the drop itself. Acceleration of spreading We first plotted the radius R of the wetted spot (Fig. 3 ), as measured on the video screen, versus the time t (both in logarithmic scale). Usual laws for spreading of pure liquids are R K t “lo or R CKt ‘j8, depending on whether gravity is negligible or not. We still observed asymptotic laws of the kind Rat”, but with IZbetween roughly 0.25 and 0.5 (Fig. 4). These limits were not strict, and n increased with the initial size of the drop. It can be shown that the radius of a drop, spreading under a constant driving force per unit length of perimeter, follows a law Ra t0.25 or Ra t0.5,depending on whether its volume is constant or not (this last case corresponds to the
101
Solvent PDMS
Fig. 3. Principle
bgR(mm)
vapour
drop
of the experiments.
PDMS /TRANSDECALINE
Fig. 4. Example of spreading vapour.
VAPOUR
of a PDMS drop (of viscosity
lOO*lO-” Pa s) under trans-decaline
presence of a reservoir) [3]. Besides, in a recent work [9], Joanny showed that, in a somewhat analogous situation (the spreading of a drop covered by an insoluble surfactant ) , a surface tension gradient between the center and the edge gives rise to a constant driving force per unit length of contact line. Our case is of course different, but a surface tension gradient seems to be a good reason for explaining what we observed. The surface tension of the drop depends mainly on the composition of a superficial layer with a thickness of the order of one micrometer (the range of
102
Van der Waals interactions). To account for the sign of our effect (acceleration of spreading), we need a higher surface tension at the edge of the drop than in its center, i.e. a higher concentration of solvent at the edge. We can imagine at least two hypotheses for the origin of this difference. First, if the diffusion of the solvent in the drop is slow, this layer is not in equilibrium with the vapour phase, i.e. its composition is not homogeneous. The concentration of solvent is higher where the thickness of the drop is smaller, i.e. near the edge. Second [ 131, if the diffusion of the solvent in the atmosphere is slow, the spreading drop creates a depletion zone, low in solvent, in the atmosphere. The concentration of solvent in the layer is nearly homogeneous, except in the very foot of the drop, where it is higher because this foot arrives first in solvent rich regions of the atmosphere. We have not yet been able to choose between these two possible origins. A last possibility might have been the adsorption of solvent on the glass plate. Indirect ar~ments against this hypothesis were provided by contact angle measurements on glass slides previously exposed to the solvent atmosphere, no changes were observed. A more direct argument has been obtained by following the thickness of films on oxidized silicon wafers by ellipsometry [ 141, the adsorbed trans-decaline layer was less than 0.6 A (averaged value over 0.2 mm”) and disappeared rapidly when the saturated atmosphere was taken off. Instabilities The fast spreading we have just described only lasts for a while, because after a few minutes instabilities appear at the edge of the drop. From this moment, it is very difficult to give an accurate measurement of the radius of the drop. The instabilities grew rather regularly, and divided into smaller ones when they got too large. They had rather regular, though not exactly reproducible, shapes and wavelengths (Fig. 5 ) . Their origin can be at least qualitatively understood. First, there is a destabilizing effect. Whatever the exact origin of this inhomogeneity (see above), an instability has a higher surface tension than the bulk of the drop. Due to the Marangoni effect, it tends to spread faster than the bulk of the drop, which still increases its surface tension, and so on. Second, there is of course a stabilizing phenomenon, creating an instability costs surface energy. But it seems that after a while the destabilizing effect prevails, whether it be a matter of critical size or maybe of critical curvature of the edge of the drop. As for the size of the instabilities, it is a problem of selection of wavelength that has not been resolved yet.
103
Amm 1.5 I 1.0,
.
0.5 -
2
* 0
Fig. 5. Typical shapes of instabilities of their size versus time.
1
I
I
I,
tinie(mn1
I,
0123456
(in dotted lines initial size of the drop) and typical evolution
C
1
10
100
Log t (9
Fig. 6. Spreading of small droplets: the lower curve shows the retraction of a drop. The upper one corresponds to a drop, probably of some critical size, which showed a curious behaviour: the instabilities appeared and disappeared several times.
Small droplets If the drop was very small (roughly if its volume was less than 2. lo-” mm”), the description above remained valid only for a moment. After some time the instabilities seemed to become too large for the drop, and the drop divided into several irregular smaller ones, which did not spread any longer (Fig. 6 ) .
104
The retraction and breaking up of the drop might be a de-wetting phenomenon, which occurs when the surface tension has increased so much that its edges become non-wetting. The resulting smaller drops are probably in equilibrium with the gas phase and do not evolve further. A final curious effect
The last surprising feature we observed appeared when, after the end of the experiments, we removed the saturated atmosphere off. Then, in less than a second, the drop divided into a very large number of very small drops, which attracted each other (probably much like the way the solvent drop attracted the PDMS) and then spread again. This comes from the inverse Marangoni effect, due to evaporation of the solvent from the drop, which acts against spreading and causes the retraction of the drops. Later, the solvent has entirely evaporated, and the spreading of the oil may start again. CONCLUSIONS
The results we have reported are still limited and not yet fully understood, but they seem to be interesting and worth further study, which is currently under way. We shall especially concentrate on the problem of the surface tension gradients, and on the instabilities we have observed. From a theoretical point of view, the problems do not seem easy either, since the surface tension, the concentration of solvent and the shape of the drop are closely linked. ACKNOWLEDGEMENTS
The authors are pleased to acknowledge very fruitful discussions with P.G. de Gennes. The ellipsometric test is due to the courtesy of F. Heslot and the surface tension measurements to the courtesy of J.M. di Meglio. The constructive criticism of the referees is also acknowledged.
REFERENCES 1 2 3 4 5
P.G. de Gennes, Rev. Mod. Phys., 57 (1985) 827. G.F. Teletzke, Thesis, University of Minnesota, 1983. B.V. Derjaguin, N.V. Churaev and V.M. Muller, Surface Forces, Consultants Bureau, New York, 1987,440 pp. B.V. Derjaguin, Langmuir, 3 (1987) 601. A.M. Cazabat and M.A. Cohen Stuart, Prog. Colloid Polym. Sci., 74 (1987) 69. J.F. Olivier, C. Huh and S.G. Mason, Colloids Surfaces, I (1980) 79. E. Bayramli, T.G.M. Van de Ven and S.G. Mason, Colloids Surfaces, 3 (1981) 131. D. Pesach and A. Marmur, Langmuir, 3 (1987) 519.
105 6 7 8 9 10
11 12 13 14
R.L. Cottington, CM. Murphy and CR. Singleterry, Adv. Chem. Ser., 43 (1964) 341. D.H. Bangham and Z. Saweris, Trans. Faraday Sot., 34 (1938) 554. A. Marmur and M.D. Lelah, Chem. Eng. Commun., 13 (1981) 133. J.F. Joanny, to be published. S. Troian, X.L. Wu and S.A. Safran, Phys. Rev. Lett., 62 (1989) 1496. W.D. Bascom, R.L. Cottington and C.R. Singleterry, Adv. Chem. Ser., 43 (1964) 355. M.K. Bernett and W.A. Zisman, Adv. Chem. Ser., 43 (1964) 332. C. Marangoni, Nuovo Cimento, 5 (1871) 239. W.B. Hardy, Philos. Mag., 38 (1919) 49. P.G. de Gennes, personal communication, 1988. F. Heslot, unpublished results.