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Liquid Ring Formation from Contacting, Nonmiscible Sessile Drops Hamidou Haidara* and Karine Mougin Institut de Chimie des Surfaces et Interfaces-ICSI-CNRS, 15 Rue Jean Starcky, B.P. 2488-68057 Mulhouse Cedex, France Received September 13, 2004. In Final Form: November 11, 2004 When two pure and nonmiscible liquid drops at rest on a rigid substrate come into close contact with a quasi-zero spreading velocity, one of them may be sucked around the second into a liquid ring, leading in some cases to the complete engulfment of the latter. We here show that the conditions for this amazing and unusual capillary effect to develop are defined by two sets of criteria: the “reciprocal” spreading of one drop with respect to the other and a “geometrical-wetting” criterion related to the opening of the groovelike channels along the base of the attracting drop. Despite the exceeding simplicity and roughness of liquid drops as compared to living cells, the phenomenon strangely recalls, at least in its mechanistic aspect, the fundamental biological process of phagocytosis. Besides these fundamental aspects, this effect may also have interesting implications for microstructuring techniques.
Introduction When two homophase drops or bubbles, either suspended in a bulk fluid or placed onto a substrate, come into close contact, they may remain stable or coalesce, depending on the pressure gradient across their interface (capillary and disjoining).1-3 The capture of small emulsion droplets by larger ones, driven by the capillary pressure difference (Ostwald ripening), and more generally the stability of foams and colloidal systems are well know examples of these phenomena.1-3 In case the contacting droplets are nonmiscible pure liquids that are initially brought in a “side-by-side” contact on a rigid substrate, what would be the evolution of the contact zone and the final equilibrium configuration of the system? Such liquid drop contact can be easily generalized to two dissimilar particles attached to a substrate, provided that one, at least, of the contacting particles is a soft, liquidlike droplet. In this respect, one may expect the underlying mechanism at work in this liquid drop contact to also apply to systems as diverse as the contact of a bubble (droplet) with a dust particle and the “vesicle/vesicle”, “cell/vesicle”, and dissimilar cells contacts. The experiments we here report show that, for liquid couples (l1, l2) presenting a high enough surface-tension difference (γ1 - γ2), it is the lowersurface-tension drop which is systematically “sucked” around the base of the second into a stable liquid ring. In some limiting cases where the sucked drop completely engulfs the second, the final configuration of the system amazingly recalls phagocytosis.4-6 Whereas most of the known liquid and drop motions are driven (in the absence of thermal gradients) by spatiotemporal variations of the surface tension, which invariably arise from compositional gradients within the system,7-11 the flow described here * Corresponding author. E-mail:
[email protected]. (1) Ivanov, I. B.; Kralchevsky, P. A. Colloids Surf., A 1997, 128, 155. (2) Churaev, N. V.; Starov, V. M. J. Colloid Interface Sci. 1985, 103, 301. (3) Bibette, J.; Morse, D. C.; Witten, T. A. Weitz, D. Phys. Rev. Lett. 1992, 69, 2439. (4) Shiratsuchi, A.; Nakanishi, Y. J. Biochem. 1999, 126, 1101. (5) Aderman, A.; Underhill, D. M. Annu. Rev. Immunol. 1999, 17, 593. (6) Shanahan, M. E. R. J. Adhes. 1995, 54, 67. (7) Chaudhury, M. K.; Whitesides, G. M. Science 1992, 256, 1539. (8) Daniel, S.; Chaudhury, M. K.; Chen, J. C. Science 2001, 291, 633. (9) Daniel, S.; Chaudhury, M. K. Langmuir 2002, 18, 3404.
implies only pure nonmiscible liquids, in interaction on substrates that are homogeneous, at least on a length scale comparable to the drop radius. In this respect, the capillary instability that we herein describe and the effective liquid motion which results are quite unusual. This liquid motion that develops in the absence of any surface-tension (energy) gradient is here discussed from a phenomenological standpoint and shown to result from the imbalance of the capillary forces around the contact. From our experiments, we show that the narrow space at the base of the immobile drop (the one which is encircled) actually acts as a “groove” that sucks around the liquid from the other drop, as already known from spreading and capillary rise studies on grooved substrates.12-14 Results and Discussion Basically, the experiment consisted of placing two droplets on a silicon plate, in such a way that they come into a side-by-side contact with a negligible kinetic energy (quasi-equilibrium contact of approximately zero spreading velocity). The silicon plate was previously cleaned by sonication in cyclohexane, dried under nitrogen, and immediately used. All the liquids were of analytical grade and used as received from the suppliers (Aldrich and ABCR GmbH Karlsruhe, Germany), except for the deionized and bidistilled water, prepared at the laboratory. The experiment was performed under ambient conditions (T ∼ 21°C), and the whole dynamic was recorded using a video-camera device (COHU CCD camera). A representative sequence of the drainage is given in Figure 1 for the “squalane (c30)/ water (w)” couple. In this specific case, the drainage of the squalane drop around water (w) was partial and completed within ∼3 min. The selected parts of Figure 2 represent the final (“quasi-equilibrium”) shape of a few studied liquid drop couples, which show at some degree the drainage of one drop (hereafter referred to as d1) in a liquid ring that surrounds the second (d2). The “fluorosilicon/hexadecane” oil couple here constitutes the unique exception to that observation of drainage and liquid ring formation. It is (10) Dos Santos, F. D.; Ondarc¸ uhu, T. Phys. Rev. Lett. 1995, 75, 2972. (11) Haidara, H.; Vonna, L.; Schultz, J. J. Chem. Phys. 1997, 107, 630. (12) Tang, L.-H.; Tang, Y. J. Phys. II 1994, 4, 881. (13) Darhuber, A. A.; Troian, S. Phys. Rev. E 2001, 64, 031603-1. (14) Bico, J.; Que´re´ D. J. Colloid Interface Sci. 2002, 247, 162.
10.1021/la047714y CCC: $30.25 © 2005 American Chemical Society Published on Web 01/28/2005
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Figure 3. Simplified drawing of the drop contact zone: (a) side-view of the early (initial) contact zone (time t0); (b) a zoom of the drop base, showing the emergence of the liquid ring from drop 1 (t0 + ); (c) top view showing liquid 1 being sucked along the base of d2 (in the groovelike channel).
Figure 1. Representative sequence of the drainage and ring formation for the squalane/water (c30/w) drop couple on a SiO2 substrate. Part a shows the contacting drops before instability. Parts b-f show the evolution of the contact from t ∼ 0 to about t ∼ 10 min. Note in part b the distortion of the contact zone in the very early stage and the formation of a neck that precedes the suction of squalane along the water drop. At longer time scales (part f), an enlargement of the ring may result from the evaporation of the surrounded water drop.
effects. For two contacting homophase drops or bubbles, it is essentially the balance between the capillary pressure difference across the contact, on one hand, and the disjoining pressure within the separating medium, on the other hand, that drives the fusion.1,3 For the two contacting drops in an air environment, such a mechanism would have simply resulted in the systematic drainage of the higher-curvature liquid phase (Pc ∼ 2γl/rd, with rd being the radius of curvature). This obviously is not the case here, as shown in Table 1 that reports the contact angle of the contacting liquid drops on SiO2, θliquid/SiO2, for an identical drop volume of 1 µL. Instead, it is the drop of higher θliquid/SiO2, and therefore of higher curvature, which systematically constitutes the attracting one, as shown in Figures 1 and 2. We show in the following that this peculiar capillary effect can be described by an ensemble of two criteria: a surface-tension-driven “spreading” of one of the contacting drops over the second and a “geometrical” criterion, which explicitly involves the contact angles between the drops and the substrate, on one hand, and the contact angle between the drops themselves, on the other. Both criteria must be satisfied simultaneously for the capillary instability to develop and the drainage and liquid ring formation to be observed as sketched out in Figure 3. The spreading condition of the contacting drop (d1) over the second (d2) is given by the spreading parameter
S1/2 ) (γ2 - γ1 - γ12)
(1)
S2/1 ) (γ1 - γ2 - γ12)
(2)
and inversely
Figure 2. Quasi-equilibrium shape of a few selected drop couples: (a) water sucked by mercury (left side droplet) (note the complete engulfment of the Hg droplet); (b) 0.01 Pa‚s silicon oil drop (left) that is completely sucked around ethylene glycol (note the initial spot of the “so” drop); (c) 10 Pa‚s silicon oil drop (right side)/ethylene glycol; (d) “stable” fluorosilicon (right side)/ hexadecane contact to drainage. All experiments are done on a clean SiO2 substrate, except for the silicon oil drop where a fluorinated surface was used.
worth noting here that, even after the suction of d1 and its collection in a liquid ring surrounding the “attracting” drop (d2), the two nonmiscible liquids remain distinctly separated. In other words, this “drop/drop” interaction has features that basically differ from the classical coalescence of homophase droplets or bubbles (Ostwald ripening), although both are chiefly driven by capillary
for the spreading of d2 over d1. The difference between these two quantities amounts to
(S1/2 - S2/1) ) 2(γ2 - γ1)
(3)
the sign of which defines the “thermodynamic” direction of the liquid flow, regardless of the way this will kinetically develop, with the latter depending on both the magnitude of (γ2 - γ1) and the rate-determining friction of the moving liquid (of viscosity η) along the substrate. Taking water (γw ∼ 73 mN/m) or ethylene glycol (γeg ∼ 58 mN/m) for droplet d2 and either of the investigated oils (silicon oil and hydrocarbons, γoil ∼ 25 ( 5 mN/m) for droplet d1, one is led to typical values of (Soil/w - Sw/oil) ranging between 66 ( 5 and 96 ( 5 mN/m. From this simple thermodynamic estimate, one effectively expects any of the oil drops to spread over both water (w) and ethylene glycol (eg) drops
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Langmuir, Vol. 21, No. 5, 2005 1897 Table 1. Contact Angle Values and Related “Geometrical-Wetting” Criterion for the Contacting Drop Couples contacting drop couple
Figure 4. Schematic of the relevant geometrical-wetting parameters and the profile of the moving liquid ring (from drop 1), in the narrow groovelike channel at the basis of the immobile drop (d2).
and the water drop to also spread around the mercury (Hg) drop, as shown in Figures 1 and 2. For the “hexadecane (c16)/fluorosilicon (fs)” couple, which is stable with respect to drainage and liquid ring formation (Figure 2c), the droplets essentially evolve after the early contact, through an expansion of their contact area within the plane perpendicular to the substrate, with the unique consequence that both drops have to relax the increased capillary pressure that results from this frontal perturbation by a slight and quite uniform spreading. As determined from both measured and quoted surface-tension values for hexadecane (27.5 mN/m) and the fluorosilicon oil used herein (25.7 mN/m), the reciprocal spreading parameter for this liquid oil couple (Sc16/fs - Sfs/c16) is only ∼3 mN/m. This weak, but finite difference of surface tension satisfies the reciprocal spreading criterion and should therefore be enough to drive the drainage, although the kinetics in that case would be considerably reduced by viscous friction forces, which resist the flow. As shown in the following, the complete lack of flow in this system (Figure 2d) rather arises from the second “geometricalwetting” criterion, which at the difference of the reciprocal one is not satisfied by this “hexadecane/fluorosilicon” couple. Whenever the systems satisfy the thermodynamic criterion of reciprocal spreading, an additional requirement (this one geometrical), related to the opening of the “groovelike” space at the base of the immobile sucking drop, has to be equally satisfied for the flow to develop. This condition is achieved for values of the opening angle equal or less than a critical one,12-14 Rc < π - 2θ, where θ represents the equilibrium contact angle of the flowing liquid with the substrate (groove’s walls). The opening of the groove space is here determined uniquely by the contact angle θ2/S of the immobile drop (d2) on the substrate (see Figure 4), and is equal to (π - θ2/S), whereas the interface of drop d2 along the triple contact line constitutes with the substrate the groove’s walls. For our system and, more specifically, for drop d1, the contact angle of which with the substrate is θ1/S, the flow condition in the groove of the opening angle (π - θ2/S) thus reads
Rc ) (π - θ2/S) < π - (θ1/S + θ1/2)
(4)
or equivalently
(θ1/S + θ1/2) < θ2/S
(5)
with θ1/S and θ1/2 representing the contact angles of liquid drop d1 on the substrate and liquid drop d2, respectively. Let’s notice that the fulfilment of this condition for a contacting drop couple does not assume anything a priori on the direction of the flow (drainage) that can be of d1 toward d2, or vice versa. For the flow to be characterized, this “geometrical-wetting” condition, (θ1/S + θ1/2) < θ2/S, should thus be completed by the reciprocal spreading criterion, |S1/2 - S2/1| ) 2|γ2 - γ1| > 0, which locally gives both the thermodynamic direction and the magnitude of
water (w)/squalane (c30) on SiO2 mercury (Hg)/water (w) on SiO2 ethylene glycol (eg)/ silicon oil (so) on fluorinated (CF3-terminated) surface hexadecane (c16)/ fluorosilicon (fs) on SiO2
contact angle (θ)/deg θw/SiO2 ∼ 65
θc30/SiO2 ∼ 15 θc30/w ∼ 25
θHg/SiO2 ∼ 132 θw/SiO2 ∼ 65
θw/Hg ∼ 39
θeg/CF3 ∼ 96
θso/CF3 ∼ 55
θso/eg ∼ 25
θc16/SiO2 ∼ 0
θfs/SiO2 ∼ 10
θfs/c16 ∼ 45
a Note that the geometrical-wetting criterion is fully satisfied for all of the liquid ring forming couples: (θc30/SiO2 + θc30/w) ∼ 35° < θw/SiO2 ∼ 65°, (θw/SiO2 + θw/Hg) ∼ 104° < θHg/SiO2 ∼ 132°, and (θso/CF3 + θso/eg) ∼ 80° < θeg/CF3 ∼ 96°. On the other hand, the stable “hexadecane/fluorosilicon” couple does not satisfy this criterion, since (θfs/SiO2 + θfs/c16) ∼ 55° . θc16/SiO2 ∼ 0.
the flow. For the drainage of drop d1 into a liquid ring surrounding the base of d2, these two conditions together lead to
(θ1/S + θ1/2) < θ2/S and γ2 > γ1
(6)
For all the studied liquid couples, for which the capillary instability and resulting drainage were observed, these two criteria were simultaneously satisfied as shown in Table 1. For the stable “hexadecane/fluorosilicon” drop couple (Figure 2d) for which, a low but finite reciprocal spreading parameter 2(γc16 - γfs) ∼ 3 mN/m was found, an estimate of the geometrical-wetting parameter for this couple (see Table 1) definitely shows that the lack of flow arises from the fact that this second criterion is not satisfied for this system. To further test the effectiveness of this geometrical-wetting criterion, we need a substrate that can significantly alter the required wetting conditions, at least for one of the above liquid couples, which already develops the capillary instability in the above experimental conditions (Table 1). For the c30/w liquid drops (Figure 1), which we selected for this test experiment, such alteration requires that (θc30/subst + θc30/w) be θw/(SiOx-OH) ∼ 3°. As expected from this alteration, we did not observe any capillary instability with the c30/w couple in this case (Figure 5), showing that the substrate constitutes an effective parameter for tuning this capillary effect. We can summarize this on a twodimensional diagram, which displays the stable/unstable domains for the development of the capillary effect, as a function of the two criteria (reciprocal spreading and geometrical wetting). This is done in Figure 6 where the upper-half quadrant of the chart represents, with respect to the “zero” reciprocal spreading line, the instability and drainage of drop d1 around drop d2 and the lower-half quadrant represents the instability and drainage of d2 around d1. If the above reciprocal spreading and geometrical-wetting criteria well account for the emergence (15) Haidara, H.; Mougin, K. Langmuir 2002, 18, 9566.
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Figure 5. Contacting water (w)/squalane (c30) drops on a silanol-rich silicon wafer (SiOx-OH). The alteration of the surface properties and therefore of the geometrical-wetting criteria has tuned the capillary effect from unstable (on simple solvent (cyclohexane) cleaned wafers, Figures 1 and 2) to stable on the highly hydrophilic silanol-rich substrates. The contact still remains stable even after an increase in the volume of the droplets to “force the instability”.
Figure 6. Stability diagram for two contacting drops, d1 and d2, as a function of the reciprocal spreading and geometricalwetting criteria. The upper-half quadrant (I) is the stability (instability) domains of drop d1 with respect to drop d2, and the lower-half quadrant (II) is for the stability of d2 with respect to d1.
of the capillary instability, they give no information on the other hand on the kinetics and dynamics of the drainage which results. The kinetics was found to strongly depend on both the nature (viscosity) and shape (curvature and radius) of the contacting drops, which together determine the balance between the driving and resisting forces, as well as the volume (size of the ring) of the moving drop (say d1) that can be transferred around the attracting one (say d2). Although the video-microscopy observations fail to account for the exact profile of the liquid ring d1 that surrounds d2, a reasonable estimate of this profile (curvature, especially) can be obtained from the boundary conditions on the interface of this liquid ring, which are given by the contact angles θ1/S and θ1/2 (see Figure 4). We here assume, from the few investigated cases, this curvature of the liquid ring to be close to zero. The driving force of the flow thus essentially arises from the capillary pressure within drop d1, Pc/d1 ∼ (2γl/rd1), right before it starts flowing around d2. Assuming the “no-slip” boundary condition at the substrate and neglecting gravity (small fluid size + lateral flow), the flow kinetics is given, at first order, by the balance between the above capillary pressure and the resisting viscous friction at the substrate, 2γl/rd1 ) -ηv/h. Once the geometrical-wetting and reciprocal spreading criteria are satisfied, the normal-to-plane averaged velocity (v), along the rectilinear flow direction, finally results from this simple balance, v ∼ (γlh/ηrd1), with h being the average height of the moving fluid ring. With a simple estimate
based on γl ∼ 0.025 N/m, η ∼ 0.01 Pa‚s, h ∼ 10-5 m, and rd1 ∼ 3 × 10-3 m, all values that are on average typical of our systems (either measured, given by providers, or taken from the literature), a flow velocity on the order of v ∼ 1 cm/s was found, which for a rectilinear length of the ring of 2πRd2 ∼ 2 cm (Rd2 of 3 mm) gives a time scale on the order of ∼2 s. This time scale is effectively that of the early-stage flow which immediately follows the instability of the drop/drop contact and leads to the quite instantaneous formation of the liquid ring in our experiments (see Figure 1c). The velocity of this early-stage flow, where almost all the “transferable” liquid is entrained, was such that the corresponding sequence with our standard video camera (25 fps/s) could not be reasonably exploited for the less viscous liquid drops (d1). As we demonstrated in complementary experiments (not shown here), for a fixed size of the “reservoir” drop (d1), both the extent and total time involved in the flow depend significantly on the size of drop d2 (∼2πRd2). We varied the radius Rd2 of the drop contact area for the “eg(d2)/so(d1)” couple on a fluorosilanecoated substrate (see below), so as to have Reg < Rso, Reg ∼ Rso, and Reg > Rso. In doing so, we could increase (in the same order) the amount of “so” sucked around the “eg” drop, from very tiny amounts (Reg < Rso) to almost complete drainage (Reg > Rso). In the same way, the influence of the initial profile of drop d1 on the drainage, which directly determines both Pc and viscous dissipation, was also shown for two “so” drops of viscosity η ) 0.01 and 10 Pa‚s, respectively, still against an “eg” drop. These oils almost completely wet the clean, bare silicon wafer, leading to a quasi-equilibrium drop height (film) of ∼15 µm. With such low drop thickness (t) and related capillary pressure Pc(γ/rd), one expects the flow velocity (∼t/ηrd) experienced by these high viscosity “so” drops to be negligible. As a result, no significant drainage of the silicon oil drops was observed on the clean bare SiO2, within experimental time scales. If one now substitutes a nonattaching fluorinated surface (CF3 terminated) for this clean, bare silicon wafer, a higher-curvature spherical “so” drop is formed, which is entirely drained around the “eg” drop (Figure 2). This result well accounts for the intrinsic influence and relative importance of viscous effects on the phenomenon. The negligible resisting friction arising from the use of the nonsticking CF3-terminated surface has resulted in the complete suction of both “so” drops (though on different time scales), as shown by the initial spots (Figure 2, parts b and c) that are free of any macroscopic size residual film. These results thus show how the intrinsic properties (surface tension, viscosity, and wetting) of the triplet “d1/ d2/substrate”, on one hand, and the drop size, on the other hand, can be adjusted to tune the magnitude and extent of the drainage and ring formation. Finally, the Hg/w couple (see Figure 2) that involves both polar and metallic
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interactions (γHg ∼ 0.2 N/m)16 was originally introduced to generalize the observations and to show the nondependence of the phenomenon on the nature of the contact liquids, once the nonmiscibility and the combined geometrical-wetting and reciprocal spreading criteria were satisfied. Beyond the amazing consequence of this capillary effect at the macroscopic scale (liquid ring formation driven by the suction of a droplet by a second one), the phenomenon also appears, at least in its mechanistic aspect, to show some analogy with phagocytosis4-6 (see the engulfment of the rigid “particle-like” Hg droplet by water in Figure 2a). Because this biological process involves the physical contact between defending cells (phagocytic) and unwanted pathogens (apoptotic) which generally present significant differences in their shell (membrane) structures,4,5 one may expect both the nonmiscibility and the combined geometrical-wetting and reciprocal spreading criteria to apply to these contacts. Whenever satisfied locally, these criteria may drive the encirclement and eventually the engulfment of the infectious agent. Although phagocytosis is an exceedingly more complex biological process involving the reorganization of the cytoskeleton, the amazing observation that arises from this mechanistic analogy with the above drop/drop interaction is that the engulfed particle actually mediates its own “ingestion”, irremediably driven in that by its higher surface tension (see the engulfment of the rigid particle-like Hg droplet by water in Figure 2a)! On a more practical viewpoint, we have shown that the liquid ring (16) Fowkes, F. M. Ind. Eng. Chem. 1964, 56, 40.
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formed in this way could be frozen to give millimeter size free-standing objects. Potentially, the use of such curable polymeric materials in conjunction with structured substrates may lead to the fabrication of micron to millimeter size three-dimensional surface patterns, based on the use of these specific capillary effects. Conclusion We studied the contact of two nonmiscible sessile drops which meet each other under quasi-equilibrium conditions with respect to spreading. Under certain conditions, it is shown that these contacting drop couples can enter a capillary instability, leading to the formation of a liquid ring surrounding the second droplet. The conditions for this instability to emerge were shown to resume in two criteria. The first is a geometrical-wetting condition related to the opening of the groovelike channels along the drop base, while the second defines the direction of the thermodynamic instability of one drop with respect to the other to spreading. Together, these two criteria well describe the experimental observations for both stable and unstable drop couples to suction and liquid ring formation. In some limited cases, our results (mercury/ water) show an amazing mechanistic analogy to the complex biological phenomenon of phacocytosis. To this regard, and to many others (microstructuring techniques), this surprising consequence of capillary effects could be of both fundamental and practical interest. LA047714Y
