Surfactant- and Capillary-Driven Instabilities along a Curved Interface

In a recent paper, we reported a particular class of dynamic oscillatory instabilities induced by the time-dependent adsorption of surfactant along th...
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Langmuir 1996, 12, 6632-6636

Surfactant- and Capillary-Driven Instabilities along a Curved Interface: The Case of the Convex (Oil-Water-Hydrophobic Solid) Interface H. Haidara,* L. Vonna, and J. Schultz Institut de Chimie des Surfaces et Interfaces (ICSI), CNRS, 15 rue Jean Starcky, B. P. 2488, 68057 Mulhouse Cedex, France Received March 26, 1996X In a recent paper, we reported a particular class of dynamic oscillatory instabilities induced by the time-dependent adsorption of surfactant along the wetting meniscus of the concave oil-water-solid interface. A rather phenomenological description of these instabilities was then proposed. In the present paper, a quite different configuration consisting of a convex wetting meniscus is used to check for the dependence of this oscillatory phenomenon on the geometry and direction of the triple phase line (TPL) motion as well. As for the concave wetting meniscus, it is found that the adsorption along the interfaces still results in oscillating instabilities as the meniscus readjusts its capillary parameters. These instabilities are essentially related and described through dynamic fluctuations of the surface concentration and hence surface pressure along the self-assembling film at the mobile oil-water interface. Based on a cyclic compression-relaxation process of the monolayer, a comprehensive picture is proposed for these surfactant-mediated instabilities. This involves both molecular exchange mechanisms between the metastable film and the adjacent subphases and molecular reorganization within the monolayer.

Introduction A great deal of attention has been paid recently to the specific class of surfactant mediated instabilities.1-12 Depending on the nature of the problem, the mechanisms which basically govern these instabilities appear to be quite different. This is so for (i) wetting instabilities of surfactant solutions,1,2 (ii) hydrodynamic and Marangoni instabilities within thin planar3-5 or soap films,6,7 and (iii) dynamic fluctuations associated with kinetics of surfactant adsorption8,9 or with the dynamic response of monolayers to mechanical stresses.10-12 In addition, we have presented in a recent paper oscillatory instabilities observed during adsorption of a nonionic poly(oxyethylene) surfactant along the ascending meniscus of an oil-water-hydrophilic solid interface.13 In the present work, we report the reversed and complementary case, i.e., a convex meniscus, descending toward the bulk aqueous phase (nonwetting case with θ > π/2). This configuration also leads to an inversion in the direction of the global motion of the triple phase line (TPL) * To whom correspondence should be addressed. Telephone: (33) 89.60.87.67. Fax: (33) 89.60.87.99. E-mail: [email protected]. X Abstract published in Advance ACS Abstracts, December 1, 1996. (1) Princen, H. M.; Cazabat, A. M.; Cohen-Stuart, M. A.; Heslot, F.; Nicolet, S. J. Colloid Interface Sci. 1988, 126, 84. (2) Franck, B.; Garoff, S. Langmuir 1995, 11, 87. (3) Tambe, D. E.; Sharma, M. M. J. Colloid Interface Sci. 1991, 147, 137. (4) Velev, O. D.; Gurkov, T. D.; Borwankar, R. P. J. Colloid. Interface Sci. 1993, 159, 497. (5) Velev, O. D.; Gurkov, T. D.; Ivanov, I. B.; Borwankar, R. P. Phys. Rev. Lett. 1995, 75, 264. (6) Lucassen, J. In Anionic Surfactants; Surfactant Series No. 11; Marcel Dekker, Inc.: New York, 1981; Chapter 6. (7) De Gennes, P.-G. C. R. Acad. Sci. Paris 1987, 305 II, 9. (8) Good, R. J.; Sun, C. J. J. Colloid Interface Sci. 1983, 91, 341. (9) Boury, F.; Ivanaova, Tz.; Proust, J. E. Langmuir 1995, 11, 1636. (10) Tabak, S. A.; Notter, R. H.; Ulman, J. S.; Dinh, S. M. J. Colloid Interface Sci. 1977, 60, 117. (11) Kwok, D. Y.; Tadros, B.; Deol, H.; Vollhardt, D.; Miller, R.; Cabrerizo-Vilchez, M. A.; Neumann, A. W. Langmuir 1996, 12, 1859. (12) Li, Z.; Zhao, W.; Quinn, J.; Rafailovich, M. H.; Sokolov, J.; Lennox, R. B.; Eisenberg, A.; Wu, X. Z.; Kim, M. W.; Sinha, S. K.; Tolan, M. Langmuir 1995, 11, 4785. (13) Haidara, H.; Vonna, L.; Schultz, J. Langmuir 1996, 12, 2478.

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upon surfactant adsorption. To achieve this configuration, the solid plate which was treated to exhibit hydrophilic properties in the previous study has been replaced by a hydrophobic methyl-terminated self-assembled monolayer surface. This configuration should allow one to check for the dependence of these phenomena on both the geometry of the system and surface properties of the involved phases. These results, extended to those initially obtained with the concave (ascending) meniscus,13 are presented hereafter and discussed through the basic picture of the compression-relaxation process of that interfacial selfassembling film. Finally, another interesting aspect of this study concerns the way the instabilities take place within the monolayer. While the dynamics is externally induced in most of the previous investigations, these instabilities are naturally generated in this experiment through both adsorption kinetics and the reconformation process of the system. Therefore, these studies may bring some insight regarding the intrinsic parameters characterizing built-in instabilities related either to the formation or to transient events in self-assembling monolayers. Experiments and Materials The detail of the experiment has been presented in a previous paper.13 Basically, the Wilhelmy plate (tensiometric) method is used to record the time dependence of the oil-water interfacial force as surfactant diffuses and adsorbs at that interface. The tensiometer is the automatic contact angle analyzer DCA 322 from Cahn which actually measures a wetting force. The oilwater-solid interface is first stabilized in a thermostated working cell (T ) 22 °C) before surfactant is introduced in the working cell, just at the bottom of the solid plate. Before each series of experiments, both surface tensions at water-air and oil-water interfaces are systematically measured. Reference values of respectively 72.3 ( 0.5 and 49.8 ( 0.5 mN/m are obtained, indicating no significant contamination at the virgin interfaces. A given amount of surfactant is then taken from a stock solution using a syringe, and added to a constant volume of water through a capillary, to achieve the desired final bulk concentration. The system is zeroed at this point for both the resulting force on the plate and the time, so that the actual record reflects exclusively the time dependence of the wetting force upon adsorption. The solid plate, a silicon wafer, is first cleaned in a warm (70 °C) piranha solution (7/3 (v/v) H2SO4/H2O2) for about 30 min, rinsed with deionized and twice-distilled water and dried under nitrogen.

© 1996 American Chemical Society

Surfactant- and Capillary-Driven Instabilities

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Figure 1. Schematic representation of the system: (a) initial (equilibrium) state; (b) after adsorption as the meniscus reconforms its shape. The plates are then immediately immersed for about 10 h in a 10-3 M solution of hexamethyltrichlorosilane (HTS) in CCl4. The advancing and receding contact angles of water on these coated surfaces after solvent rinsing and N2 drying are respectively 114 and 105°. The nonionic surfactant hexaethyleneglycol dodecyl ether, the oil phase hexadecane 99%, and the silane were respectively from Fluka, Aldrich, and ABCR (Karlsruhe, Germany) and were used as supplied by the manufacturers.

Basic Approach The mechanical equilibrium of the meniscus in its initial state (Figure 1a) is either described by the Laplace capillary equation or the Young interfacial force balance which are both independently satisfied14 according to:

γ0ow/r0 ) (∆Fg)z0

(1)

γ0ow cos θ0 ) γ0so - γ0sw

(2)

The γij are the interfacial tensions at oil-water (ow), solidoil (so) and solid-water (sw) interfaces, and r is the mean in-plane radius of curvature of the meniscus, the normal to plane one being infinite. ∆F, g, and z are respectively the difference in density between the two liquid phases, the gravitational constant, and the meniscus height, while θ is the contact angle (may be an equilibrium or a transient one) between the solid plate and the oil-water interface. In what follows, these indexed quantities will stand for initial equilibrium values while nonindexed ones will refer to transient values. After surfactant is introduced in the working cell, diffusion sets in toward the meniscus and molecules adsorb at both ow and sw interfaces as depicted in Figure 1b, resulting in the modification of the initial equilibrium. The sharp decrease in interfacial tensions (γow, γsw) and related unbalance of capillary and surface force equations (eqs 1 and 2) then result in an equivalent motion of the TPL which readjusts the meniscus parameters to the actual capillary forces. It’s noteworthy to mention that such an adjustment was observed in the Langmuir trough, where changes of the contact angle on the Wilhelmy slide over a compression-relaxation cycle can notably modify the measured surface pressure.10 Basically, the driving force for that motion is the unbalanced capillary force which is related to an excess gravitational pressure through the volume excess separating two adjacent positions of the meniscus (eq 1). Since the plate weight is zeroed at the beginning of the experiment, what is really measured upon adsorption is the force variation per unit length of contact line L: ∆F/L ≈ (γow cos θ - γ0ow cos θ0) + ∆(buoancy). Neglecting the operationally meaningless buoancy variation, any force variation in the course of the adsorption is then essentially related to that of γow cos θ, which actually corresponds to (14) Neumann, A. W.; Good, R. J. J. Colloid Interface Sci. 1972, 38, 341.

an equivalent fluctuation of the weight of the fluid in the meniscus. Because γow cos θ is related to the surface chemistry around the contact line through Young’s eq 2, the force fluctuation is basically relevant to the adsorption thermodynamics, no matter the surface chemistry around that contact line. In spite of this, the equation of Young may not be theoretically justified in a dynamic situation where the surface state is continuously changing due to adsorption. Nevertheless, the unique relation in the Wilhelmy plate method which gives the force actually measured in this experiment (and others like Langmuir troughs using Wilhelmy balance to measure ∆γ) is: ∆F/L ≈ γow cos θ - γ0ow cos θ0. On the other hand, the equation of Laplace is rather a mechanical equilibrium condition with no explicit reference to the local surface structure around the contact line. It relates all the relevant parameters of the meniscus to the experimental quantitysthe gravitational pressure of the meniscus fluid, the fluctuation of which is measured upon adsorption. Actually, the theoretical conditions leading to the application of both equations (Young and Laplace) might be equivalent, due to their straight linkage through γow. But since the equation of Laplace contains γow and adjustable meniscus parameters which determine the magnitude of the compressional process, one will discuss in the following the whole dynamic of the system through that equation. In doing so, one assumes that these relations apply at least around the extrema of the dynamic curves (Figure 2) where the system is locally pinned in a metastable state. Starting from that basic assumption and eq 1, one can relate the variations in the meniscus parameters (∆z and ∆r) to the magnitude of the adsorption ∆γ ) γ0 - γ according to

∆γow/γow ∼ ∆z/z + ∆r/r

(3)

The way the meniscus will readjust its parameters z, r, and θ upon adsorption (or desorption) can then be discussed through eq 3, which describes the interplay among the variations of these geometrical parameters and the surface pressure of the interfacial self-assembling film. Accordingly, one will discuss in what follows the stability of the meniscus, essentially from that macroscopic standpoint, using eqs 1 and 3. In adopting this macroscopic approach, no assumption is made regarding the existence of a thin wetting film (of oil) along the sw interface, ahead of the bulk meniscus. If such a film exists, it may either be dragged along with or rupture from the bulk meniscus during the reconformation of the system, depending on the relative importance of its cohesive to adhesive energies. Which of these mechanisms is actually involved is relatively unimportant regarding the initial reconformation process of the meniscus which governs the whole dynamic of the instabilities, as one aims to outline in the following. Because of the descending nature of the force dynamic, the overall analysis of the instabilities should involve a pinning process around the extremum, as well as a mechanism resulting in an inversion of the motion of the TPL. This is done by considering the force balance around an extremum where the triple line is locally pinned. Accordingly, around this extremum, the viscous forces which have contributed to the damping and pinning process of the triple line will vanish as the velocity of the meniscus goes to zero. Therefore, the condition for the local pinning of the meniscus can be described by the following transient equilibrium:

Pc - Pg + Πsteric - Πcomp ) 0

(4)

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Figure 2. Force dynamics of the oscillating process for both concave (central figure) and convex (inner figure) menisci; time interval between points ) 15 s. Left-hand ordinate: (a) Cb ∼ 4 × 10-3 cmc; (b) Cb ∼ cmc. Right-hand ordinate: (c) Cb ∼ 2 cmc. Inset: Cb ∼ cmc.

Results and Discussion

Figure 3. Local detail of the meniscus tip around the triple point line (TPL). The detail shows the transition from the compressed state as the film goes toward areal expansion (respectively maximum to minimum peak in Figure 2).

where Pc and Pg are the capillary and gravitational pressures as defined in eq 1 and Πsteric is a steric pressure arising from the local excess concentration (∆Fexc) of surfactant in the confined space around the meniscus tip (Πsteric ∼ kT∆Fexc). One can notice that this term is effective only from the first cycle of the force dynamic where both adsorbed and bulk surfactant in the immediate vicinity of the triple line can sterically hinder the motion of the meniscus. Actually, Πsteric should be dominant along the descending branch where the motion of the TPL contributes in that case to accumulate surfactant ahead of the moving line (see Figure 3). The last term arises from the compressional rigidity of the film due to the repulsive hard-sphere interaction within the film. Aside from the basic contribution of viscous frictions, the resisting pressure Πcomp may be the dominant pinning mechanism of the meniscus in the compression mode (rising branch in central Figure 2).

The central plots of Figure 2 represent the timedependent records of the wetting force corresponding to three different bulk concentrations c (in units of the critical micelle concentration, cmc): c ∼ 4 × 10-3 cmc, c ∼ cmc ∼40 mg/L, and c ∼ 2 cmc. As a reference to the previous study concerning the ascending meniscus, an equivalent plot corresponding to c ) cmc is given in the inset of Figure 2. It’s noteworthy to stress that the characteristic oscillatory instabilities observed in these studies are effectively mediated by the adsorption process, since benchmark experiments which have been performed in both static and dynamic (withdrawing) modes did not show any noticeable stick-slip or background noise. Actually, as surfactant adsorbs, the excess gravitational pressure generated by the jump in the interfacial tension ∆γow will drive the meniscus toward new geometrical parameters, according to eq 3. An estimation of the magnitude of the initial reconformation can be made, based on an average instantaneous jump of the interfacial tension ∆γow ∼ 25-30 mN/m, as indicated in central Figure 2. Since ∆z is comparable to the initial height of the macroscopic meniscus z0 ∼ 7 mm and r . z, one can assume |∆r/r| , |∆z/z|. Using these conditions together with the reference value γow ∼ 50 mN/m results in a ∆z ∼ 4 mm which is almost identical to what we measured experimentally. Due to the initial adsorption whose amplitude ∆γow determines both the magnitude and the rate of the areal compression (∆A/A) along the (ow) interface (see Figure 3), the system will move to the first maximum of the force dynamic (central Figure 2). As the interfacial film is compressed up to the maximum, the relaxation process followed by a new adsorption sets in along the descending

Surfactant- and Capillary-Driven Instabilities

branch, restoring the meniscus in a position equivalent to the initial one. This restoring step thus depends on the characteristics of the compression-relaxation process, especially their respective time scales τcompr and τrelax. As long as τrelax is > τcompr, the actual molecular area σa within the compressed film will be a nonrelaxed one which we will note as σ*a. Molecular relaxation times available from the literature appear to be characterized by quite a large scatter. Depending on the experimental method, the solubility and the nature of the film, the initial surface coverage, and the magnitude of the compression, relaxation times going from 10 s up to 105 s are determined.9,10,12 For instance,10 dynamic Π-A curves of unsoluble DPL films (dipalmitoylphosphatidyl chlorine) successively compressed at ∼0.5 Å2/s from 100 to 68 Å2 and from 68 to 49 Å2 exhibit relaxation times of 50 and 100 s, respectively. These relaxation times are about 850 s close to the collapse limit (40 Å2) before they drastically approach 12 × 103 s beyond that limit. For soluble films, the only systematic attempt to study and relate the real-time dynamic response of a monolayer to combined diffusion-adsorption kinetics was developed by Boury et al.,9 using the pendant drop technique. A characteristic relaxation time of ∼10 s was obtained by this method upon applying a compression-relaxation cycle to the BSA (bovine serum albumin) monolayer adsorbing at the DCM (dichloromethane)water interface. One should emphasize here that the intrinsic relaxation time following a compression is quite independent of the bulk diffusion time as this might essentially involve the expulsion of molecules from the film or their conformational reorganization within the monolayer. Nevertheless, both these mechanisms can be hindered by the subphase concentration for steric reasons as one will see later for our system. On the other hand, the relaxation time of a soluble monolayer submitted to areal expansion (creation of new adsorption areas) depends essentially on the characteristic time scales of bulk diffusion and incorporation of subsurface molecules to the film. For the experiment we are concerned with, the compressed film can relax either by conformational rearrangement within the film at constant mole number or by expulsion of small size aggregates in adjacent phases, depending on both compression rate and magnitude. In order to compare our relaxation data to those taken from literature and given above, one will consider the following characteristics for the initial decaying branch of the dynamic curve (central Figure 2): the compression time (from less than 15 to 60 s), the magnitude of surface pressure Π ) ∆γ (from ∼ 25 to above 30 mN/m), and the relaxation time (∼150 s). In defining the relaxation time, we considered the linear part of the decaying branch, with a time origin located at the top of the compression. This is, of course, lower than the total time along the decaying branch but is still significantly high compared to the time scale of the compression. It also appears that this relaxation time is notably higher than that given in ref 9 (∼10 s), for the soluble BSA film. Several reasons may explain this difference: (i) the higher magnitude of the compression in our case (Π ∼ 30 mN/m) which contributes to lengthen the relaxation of the film,10 (ii) the confined excess concentration around the meniscus which hinder mobility and conformational reorganization of molecules in the film, (iii) the compression time, the bulk, and initial surface concentrations which may differ. Based on the above discussions, a phenomenological picture of the basic mechanisms involved in these instabilities is proposed through the following virtual Langmuir pressure-area (Π-A) isotherm as shown in parts a-c of

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Figure 4. Virtual Langmuir Π-σ isotherm for analogy with the compression process of the monolayer film along the ow interface. (a) Possible transition paths (1, 2, and 3) for the unrelaxed film. (b) Arbitrary initial area A0 of the monolayer in the gaseous state. (c) Equilibrium compression path (A0 f A) ) relaxed film with σa ) σ0a. (d) Nonequilibrium compression path (A0 f A) simultaneous to adsorption w unrelaxed film with σa ) σ*a > σ0a.

Figure 4. One will first introduce two distinct quantities which are all changing with the compression ratio: the usual average molecular area σav ∼ A/N, where N is the mole number at the interface, and the actual area σa, which corresponds to the real spatial extension (3D) of the adsorbed molecules at the interface. For standard Langmuir isotherms, σav/σa will roughly go from ∞ to 1 when the system goes from a gaseous to a solid-like state. If one applies a compression ratio (∆A/A) through a thermodynamic route (infinitely slow process), the molecules will continuously rearrange within the film and relax toward some equilibrium values (σav/σa). By increasing ∆A/A, σa will tend toward σav with the corresponding surface pressures Π(σa) ∼ Π(σav) located on the equilibrium (Π-σ) isotherm. In the experiment we are concerned with, two determining differences exist with the equilibrium (Π-σ) isotherm which results in the observed instabilities: the magnitude and characteristic time scale of compression and the concomitance of that compressional process with the adsorption along the compressed film. If one applies instantaneously a high compression ratio to the film, one expects the monolayer response to depend on the surface concentration, the surface pressure, and the relative time scales of compression and molecular relaxation processes as discussed above.9-12 Comparatively, an equivalent compression ratio applied through an equilibrated route would have continuously resulted in quite a relaxed monolayer, with an actual equilibrium molecular area σ0a < σ*a (σ*a being the actual nonrelaxed molecular area within the compressed film). Because of these differences between the two compression paths, an additional free energy term due to the unfavorable packing state of crowded and interpenetrated molecules (steric repulsion) may appear within the metastable film. If f(σa) is the free energy per molecule of the film, a second order expansion15 around the average molecular area σav which minimizes this free energy gives

f(σa) ∼ f(σav) + f′(σav) dσ + f′′(σav) dσ2

(5)

For a film which has been compressed up to the collapse limit through an equilibrated path, σa ) σ0a ) σav and f(σa) (15) Samuel, A. S. In Statistical Thermodynamics of Surfaces, Interfaces, and Membranes; Addison-Wesley Publishing Co.: New York, 1994; Chapter 6.

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) f(σ0a) ∼ f(σav). Since this corresponds to a minimum in the packing free energy of the film, the second term representing the surface energy variation around σa ) σ0a ∼ σav is zero, while the quadratic term related to the compression energy remains unchanged. For the nonequilibrated path (σa ) σ*a) the film is compressed simultaneously to adsorption, and the molecules are taken from their disordered state (large σ*a) to quite close to σav at the collapse limit. Actually, the newly incorporated molecules in the metastable film are quenched in their initial disordered state. The molecular free energy f(σ*a) is therefore intrinsically different from f(σ0a) as it contains a drastic steric repulsive component. In the local expansion of f(σ*a), one can assume the surface energy variation term f′(σav) to be negligible compared to the compression energy f′′(σav), though it is not identically zero (∂f/∂σ*a * 0 for σ*a ) σav). This may result from the presence of trapped alkyl tails (Figure 4c) among polar heads as the compression rate may not allow the newly incorporated molecules to rearrange in the ordered state (fully stretched molecules) corresponding to a minimum interfacial tension (Figure 4b). A consequence of the higher free energy of the unrelaxed film is that this will cost much energy to maintain such a film in this state or to compress it further. Since the difference ∆ ) f(σ*a) - f(σ0a) is >0, the unrelaxed film should reconform toward a stable equilibrium state. This may be achieved either by in situ relaxation of sterically constrained molecules in the disordered film or by a partial expulsion of small aggregates into adjacent phases, due to local undulations along the film. As shown in Figure 4a, the instantaneous surface pressure Π(σ*a) upon compression is located above the equilibrium isotherm as expected from the dynamic response of the compression-relaxation behavior of monolayer films.9-11 Because adsorbed molecules cannot relax instantaneously and simultaneously to the compression (τrelax g τcompr), it then results that σ*a > σ0a at the collapse limit, while both relaxed and unrelaxed states have an identical average molecular area σav. The different relaxation paths (Figure 3a) of the compressed film can then be analyzed as follows. From the unrelaxed state Π(σ*a), the system may relax along path 1, 2, or 3 toward some local equilibrium state Πe(σe) located on the isotherm. In relation to the experimental results, the only physical ways for the monolayer to do so are those resulting in the descending branch of the force dynamics (Figure 2) consecutive to the maximum, so that ∂Π/∂σ ∼ ∂∆γ/∂σ < 0. As sketched out in Figure 4a, path 1 which restructures

Haidara et al.

the film toward Π1 ) Π(σ0a) at constant mole number is performed at quite constant surface pressure (∂Π/∂σ ∼ 0). Path 2 is physically unrealistic since the monolayer cannot relax toward Π2 as it continues to retain the same actual and average molecular areas σ*a and σav. The only way left for the monolayer to relax is path 3 (Π ) Π3) which results in both higher actual and average molecular areas. This may be achieved as already discussed by in situ molecular reorganization within the film or by transferring a fraction of these molecules to the adjacent bulk phases. As the film relaxes from the metastable maximum position, the interfacial tension γow will increase (dγow > 0). The meniscus then expands its interfacial area as it reconforms along the descending branch toward a transient minimum (θ, r, z) where both forces resulting from the inversion of the surface pressure (Π ) dγow > 0) are locally balanced. As the meniscus goes to that adjacent minimum and probably during its finite residence time around that position, further adsorption from the bulk phase sets in at the expanding interfacial area. This may thereby result in a position equivalent to the initial one. Equivalently, the system will transit to the next adjacent maximum through the cycle described above, with an increasing damping proportional to the decrease in the magnitude of the compression-depletion process within the monolayer film. Conclusion We have described in this paper dynamic instabilities which develop along the wetting meniscus of a liquidliquid-solid system as surfactant self-assembles at these interfaces. It is shown that these built-in oscillatory instabilities do not depend on whether the meniscus is concave or convex. The dynamic seems to be essentially governed by the capillary instability of the meniscus in the gravitational field and the relaxation (restructuration) of the newly self-assembling film. It is likely that the magnitude, frequency and duration of these instabilities depend on the nature and size of the amphiphilic molecule. To that respect, further investigations are planned toward higher molecular weight polymeric amphiphiles of both linear and branched structure. This may contribute to the better understanding of the relation between the molecular structure and the stabilizing process of selforganizing films in complex fluids. LA960290Q