Revisiting the surface tension of liquid marbles: Measurement of the effective surface tension of liquid marbles with the pendant marble method

Colloids and Surfaces A: Physicochem. Eng. Aspects 425 (2013) 15–23

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Colloids and Surfaces A: Physicochemical and Engineering Aspects journal homepage: www.elsevier.com/locate/colsurfa

Revisiting the surface tension of liquid marbles: Measurement of the effective surface tension of liquid marbles with the pendant marble method Edward Bormashenko a,∗ , Albina Musin a , Gene Whyman a , Zahava Barkay b , Anton Starostin c , Viktor Valtsifer c , Vladimir Strelnikov c a

Ariel University Center of Samaria, Physics Faculty, P.O.B. 3, 40700 Ariel, Israel Wolfson Applied Materials Research Center, Tel-Aviv University, 69978 Tel-Aviv, Israel c Institute of Technical Chemistry of Ural Division of Russian Academy of Science, Russia b

h i g h l i g h t s

g r a p h i c a l

 Effective surface tension of marbles was measured with the pendant droplet method.  The effective surface tensions demonstrated pronounced hysteresis.  The effective surface tensions under inflating and evaporation were different.  The effective surface tensions depend on the volume and surface of marbles.  Phenomenological model describing the effective surface tension is presented.

Measurement of the effective surface tension with the “pendant marble” method.

a r t i c l e

a b s t r a c t

i n f o

Article history: Received 13 December 2012 Received in revised form 30 January 2013 Accepted 6 February 2013 Available online 28 February 2013 Keywords: Liquid marbles Effective surface tension Pendant droplet Hysteresis of surface tension Colloidal particles Surface phase

a b s t r a c t

The effective surface tension of liquid marbles coated with polyvinylidene fluoride, polytetrafluoroethylene, lycopodium, carbon black and hydrophobized SiO2 powder particles is discussed. It was established with the pendant-droplet method under inflation and deflation (evaporation) of liquid marbles. The effective surface tension depends strongly on the marble volume and demonstrates the pronounced hysteretic behavior. The phenomenological model predicting the linear dependence of the effective surface tension of marbles on their inverse surface area is proposed. The model is validated experimentally. Three “surface phases” are distinguished under inflation and deflation of marbles, some of which are featured by the predicted linear dependence of the effective surface tension on the inverse surface area of marbles. It turned out that the notion of the effective surface tension of a surface covered with solid particles is ambiguous, since this quantity depends on the pathway of its measurement and on the marble size. © 2013 Elsevier B.V. All rights reserved.

1. Introduction

∗ Corresponding author. Tel.: +972 3 906 6134; fax: +972 3 906 6621. E-mail address: [email protected] (E. Bormashenko). 0927-7757/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.colsurfa.2013.02.043

Interest in colloidal particles attached to liquid surfaces increased during the past decade for both scientific and technological reasons. Colloidal particles deposited on the liquid/vapor interface give rise to abundant and technologically important products including foams, emulsions, and so-called “dry” water [1–4].

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Fig. 1. SEM images of the powders: (a) lycopodium; scale bar is 100 ␮m (b) PE; scale bar is 10 ␮m (c) PTFE; scale bar is 1 ␮m (d) SiO2 ; scale bar is 1 ␮m.

Hydrophobic particles enwrapping liquid droplets allowed the manufacture of so-called “liquid marbles” introduced in the pioneering works of Quèrè and Mahadevan and exerted to intensive research by various groups recently [5–29]. Liquid marbles are non-stick droplets encapsulated with microor nano-scaled solid particles [1–4]. A variety of media including organic and ionic liquids and liquid metals could be converted into liquid marbles [22,25–28]. An interest to liquid marbles arises from both their very unusual physical properties and their promising applications for gas sensing, blood typing, water pollution revealing, and others [16,24,28–30]. Liquid marbles present an alternative approach to superhydrophobicity, i.e. creating a nonstick situation for a liquid/solid pair. Usually, superhydrophobicity is achieved by surface modification of a solid substrate. In the case of liquid marbles, the approach is opposite: the surface of a liquid is coated by particles, which may be more or less hydrophobic (marbles coated by graphite and carbon black, which are not strongly hydrophobic, were reported [20,31]). It should be stressed that liquid marbles retain non-stick properties on a broad diversity of solid and liquid supports [5,14,15]. Actually, liquid marbles are separated from the support by air cushions in a way similar to Leidenfrost droplets [32]. One of the most intriguing questions is: what is the effective surface tension of liquid marbles? Only several works have discussed this problem [12,13,30,31,33,34]. The experimental data are few and contradictory. Various experimental techniques have been applied for the establishment of the effective surface tension of liquid marbles: (1) the puddle height method, (2) the analysis of marble shape and (3) the analysis of eigenfrequencies of vibrated marbles. The values of the effective surface tension in a range from 40 to 75 mJ/m2 were reported [33,34]. Arbatan et al. in their recent work measured the effective surface tension of liquid marbles coated by polytetrafluoroethylene (PTFE) via two different methods: the capillary rise and the Wilhelmy plate method [34]. They introduced a capillary tube directly into the marble and

deduced the effective surface tension from the capillary rise [34]. The measurements demonstrated that the effective surface tension is independent of the size of PTFE particles coating the marble and is close to that of pure water [34]. However, values of effective surface tensions which were different from those of the liquid filling the marbles were reported by other groups [12,29,30,33,35]. Actual experimental situation is challenging, because physical properties of surfaces stabilized with solid particles depend on the density and nature of the covering. Such surfaces behave as two-dimensional elastic solids (and not liquids) when compressed [36]. Stretching modulus and bending stiffness of such surfaces were reported recently [36]. Here we discuss the effective surface tension of liquid marbles established with the pendant-marble method, which allows one also to clear up its dependence on the marble size. 2. Experimental 2.1. Materials Six kinds of powders were used for manufacturing marbles. Five kinds of powders were hydrophobic. Polyvinylidene fluoride (PVDF) nanobeads with the average diameter of particles equal to 130 nm, polytetrafluoroethylene (PTFE) powder (100–200 nm), and polyethylene (PE) spectrophotometric grade powder (10 ␮m) were supplied by Aldrich. Lycopodium (the diameter of particles of about 30 ␮m) was supplied by Fluka. Hydrophobized SiO2 powder (the diameter of particles of about 100 nm) was supplied by Nanotech Ltd (Perm, Russia). The silicon-oxide powder has been produced under the multistage process including three main stages. At the first stage, the preliminary preparation of the powder, namely powdering and drying, has been carried out. The second stage included treatment of the powder particles with the polyalkylhydrosiloxane compound, resulting in the grafting of functional hydrophobic groups onto the powder surface. The third stage was the final heat

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Fig. 2. Pendant marbles: (a) lycopodium and (b) carbon black. Sessile marbles: (c) PVDF and (d) SiO2 . The volumes are 10 ␮l.

treatment of the powder at 120–200 ◦ C resulting in formation of a stable hydrophobic coating. The hydrophobic-coating content on the surface of silicon oxide was established as 5 wt%. Liquid marbles were also manufactured with the hydrophilic powder of carbon black supplied by Cabot Corporation. The average diameter of particles was established with SEM imaging. SEM images of the powders are presented in Fig. 1. 2.2. Methods The syringe filled with de-ionized water was fixed vertically, and a water droplet of the necessary volume was suspended to the needle. Superhydrophobic substrate covered with a thin layer of powder was carefully brought in a contact with a water droplet and moved gently relative to a droplet. Powder covered a water droplet so that it turned to a marble. Fig. 2 presents pictures of various marbles taken by the Exilim camera. Volume, surface area and effective surface tension of marbles were measured with the Rame-Hart goniometer (Model 500) according to the pendant- drop method. Fig. 3 presents shadowgraph pictures of the 8 ␮l droplet and marbles taken by the goniometer.

When a marble was formed its surface was covered with a very thin layer of powder that was not monolayer. Increasing the volume by adding water from the syringe may result in the rearrangement of powder on the water surface giving rise to the changes in the effective surface tension of a marble. During subsequent evaporation of water the volume of a marble decreased that may lead again to the changes in a powder coverage and accordingly to the change in the effective surface tension. 3. Results and discussion 3.1. Structure of the powder coating enwrapping marbles Environmental scanning electron microscopy (ESEM) study of the surface supplied valuable information about the structure of a powder layer enwrapping marble depicted in Fig. 4. Two observations are noteworthy: (1) the powder layer coating a marble is not homogeneous and hermetic; water clearings separating particles of lycopodium are clearly seen; (2) the powder coating is multi-layer: lycopodium particles which are partially buried beneath water are clearly seen. The later observation is important for understanding and interpretation of the effective surface tension of liquid marbles. Schematically, the multi-layer structure of a coating layer is shown in Fig. 5. When marbles of 10 ␮l volume were deflated under evaporation in the ESEM, the surface area of water clearings decreased as shown in Figs. 6 and 7. The sequence of images in these figures show the effect of variation of relative humidity from 100% down to 75% under conditions of 2 ◦ C and pressure variation from 5.4 to 4.1 torr. 3.2. What is the effective surface tension of a liquid marble?

Fig. 3. Shadowgraph pictures of (a) water droplet, (b) PE, (c) lycopodium, and (d) SiO2 marbles. All volumes are 8 ␮l.

First of all let us clarify the notion of the “effective surface tension of a liquid marble”. The surface tension is usually identified

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clearings depicted in Figs. 4–7. This pathway is illustrated with Fig. 8b. Obviously, in this case the surface tension of the surface will be equal to that of pure liquid; (3) by adding a solid particle to the surface as shown in Fig. 8c; (4) by adding liquid and solid particles simultaneously (in other words the suspension of liquid and particles) to the surface as depicted in Fig. 8d (pathways 2–4 occur under transfer of solid particle and/or liquid “from liquid”). Thus, it is seen that the notion of “effective” surface tension of liquid surface containing solid particles is at least ambiguous. Now let us estimate the “eventual” surface energy of a liquid surface containing solid particles. When the water droplet is covered with a powder, its total interface energy G can phenomenologically be written as G = (SL + SA )S0 + (S − S0 ), where (S − S0 ) is the contribution due to the bare liquid/air interface and (SL + SA )S0 is the contribution due to solid particles (it is latently supposed for the sake of rough estimation that 50% of a solid-particle surface is wetted). Here SL , SA and  are the surface tensions at the powder–liquid, powder–air, and liquid–air interfaces, respectively; S is the total surface of a liquid marble, and S0 is the area of a marble occupied by powder. We define the effective surface tension as a ratio of the total interface energy and the total area of the coated droplet: eff =

1 (S − S0 ) + (SL + SA )S0 =  + (SL + SA − )S0 . S S

(1)

When ratio S0 /S remains constants under the conditions of experiment, the effective surface tension will be independent on the total surface of a marble. This means that the portion of the surface coated by solid particles remains constant. Such a situation may occur, when a suspension of water and particles is added to (or removed from) the surface, as shown in Fig. 8d. When pure water is added under “inflation” of a marble (as shown in Fig. 8b), the ratio S0 /S decreases, and, as it is seen from Eq. (1), eff tends to that of pure water. It should be noted that phenomenological Eq. (1) neglects the capillary interaction between solid particles. 3.3. Measurement of the “effective surface tension” of liquid marbles with the pendant-marble method

Fig. 4. ESEM images of the surface of lycopodium-coated marble (2 ◦ C, 5.4 torr). (a) Scale bar is 100 ␮m, (b) scale bar is 50 ␮m. Multilayer structure of the coating is clearly seen.

with the energy (work) supplied to increase the surface area by one unit. Consider liquid surface covered with solid particles, depicted in Fig. 8. It is seen that the energy of the surface may be increased within very different pathways: (1) by transferring solid particles to the surface “from air” (see Fig. 8a); (2) by transferring molecules from the bulk of the liquid to its surface, i.e. increasing area of water

Solid particles

The pendant-drop method is one of the most precise and commonly used methods of the measurement of the surface tension of liquids [37,38]. When liquid is suspended at the tip of a thin tube with the inner radius R, as shown in Fig. 9, its shape results from the balance between the capillary and gravitational forces. Equalizing the pressures yields: 

Fig. 5. Scheme illustrating multi-layer structure of a coating layer.

R1

+

1 R2



= gz,

(2)

where  is the density of liquid, g is the gravity acceleration, R1 and R2 are the main radii of curvature of the pendant droplet surface. Defining r = r(z), r  = dr/dz, r  = d2 r/dz 2 , we obtain the following equation (see [37,38] and Fig. 9):





Liquid

1

1 r(1 + r  2 )

1/2

+



r  (1 + r  2 )

3/2

= gz

(3)

which could be solved numerically. The pendant drop is imaged and  is considered as a fitting parameter. The surface tension  is adjusted until the solution of Eq. (3) agrees with experimental results obtained with the droplet imaging [37,38]. We applied the pendant drop method for the establishment of the effective surface tension of liquid marbles eff . Pendant liquid marbles were imaged with goniometer as described in Section 2.2, and eff was considered as a fitting parameter for the certain kind of a marble coating. We established eff under inflating liquid marbles with micro-syringe (in this situation liquid and solid particles come to

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Fig. 6. “Shrinking” of water clearings under evaporation of the lycopodium-coated marble in the ESEM at 2 ◦ C for (a) 5.4 torr, (b) 4.9 torr, (c) 4.7 torr, and (d) 4.1 torr.

the surface “from water”) and deflating of evaporated marbles, as described in Section 2.2. 3.4. The dependence of the effective surface tension on the volume of a marble Thus, the dependencies eff (V ) were obtained, where V is the volume of a marble. The typical dependencies are depicted in Fig. 10. It is seen that these dependencies are different for different kinds of marbles. However, some mutual features inherent to the curves eff (V ) are recognized. First of all, the effective surface tensions vary within a broad range and this is true for all kinds of powders used in our investigation. Secondly, the presented curves eff (V ) are obviously hysteretic, i.e. the effective surface tensions corresponding to the same volume and obtained under inflation and deflation of pendant marbles do not coincide (this is also true for all kinds of studied powders). It turns out that the effective surface tension depends on the pathway of the experiment and thus on the rearrangement of particles illustrated with Figs. 5–7. Thirdly, effective surface tensions tend to the saturation value of eff ≈ 71 − 72 mJ/m2 when the volume of a marble is increased. This observation calls for explanation. As it was shown experimentally in Section 3.1, liquid marbles are coated by multi-layer particles’ coatings, as shown in Fig. 4 and depicted schematically in Fig. 5. When water is added solid

particles from inner layers constituting the coating migrate to the surface (see Figs. 5 and 8c and d). At a certain stage all solid particles are spread at the liquid surface and distanced one from another, thus the capillary interaction between them is negligible. From this moment, the further inflation of the marble (adding water, as shown in Fig. 8b) leads to the increase in the liquid/air surface only. Naturally the effective surface tension of the marble tends to that of pure water (see discussion in Section 3.2). 3.5. The dependence of the effective surface tension on the surface of a marble Eq. (1) predicts the linear dependence of the effective surface tension on the inverse area of the pendant marble when S0 is constant. This prediction has been validated by our experiments. The evaporation data were chosen, since the inflation data were less smooth, seemingly due to perturbation introduced by adding water to the pending marble. Indeed, we observed broad intervals of the linear dependence of eff on the inverse area for all kinds of powders (see Figs. 11 and 12). In the course of evaporation, the slope of the dependences abruptly changes, as shown in Figs. 11 and 12. This may be attributed to the change in the effective surface of a covering S0 or to the formation of different two-dimensional quasi-solid phases on a droplet surface in the course of evaporation, as was argued in Refs. [36,39], that may induce the changes in SL and/or SA in Eq. (1).

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Fig. 7. “Shrinking” of water clearings under evaporation of PVDF-coated marbles in the ESEM at 2 ◦ C for (a) 5.4 torr, (b) 4.9 torr, (c) 4.7 torr, and (d) 4.1 torr.

Three domains are seen distinctly at all curves eff (1/S) (see Figs. 11–13). The first domain corresponding to small values of 1/S was registered on the first stage of evaporation (remember that evaporation in Figs. 11–13 proceeds from the left to the right). At this stage solid particles do not cover all the surface of a marble and marbles’ surfaces contain distinct water clearings (see Figs. 4, 6–7). At the second (intermediate) stage solid particles cover uniformly the marble surface. At the third (final) stage buckling of marbles’ coatings was observed. The values of effective surface tensions corresponding to this stage and presented in Figs. 11 and 12 should not

be taken seriously. Eq. (3) exploited for calculation of the effective surface tension is obviously inapplicable at the final stage of evaporation. It is reasonable to suggest that the aforementioned domains correspond to three surface phases, discussed in detail in [39]. It is also seen that in spite of the presence of common features the dependencies eff (1/S) are different for various coating particles. Let us interpret these dissimilarities. We start the discussion from the PTFE coated marbles. The intermediate stage of evaporation (covering a span of inverse area from 0.051 to 0.063 mm−2 ) is described by the linear dependence with the

Fig. 8. Various pathways of increasing the liquid surface coated with solid particles: (a) transferring a solid particle from air, (b) transferring a molecule from a liquid bulk to the surface, (c) adding solid particle, (d) simultaneous adding of a solid particle and a molecule of liquid. Particles and molecules coming to the surface are highlighted with red. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article).

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Fig. 9. Scheme illustrating the pendant-drop method of the surface-tension measurement.

Fig. 11. Dependence of the effective surface tension on the inverse marble surface in the course of evaporation for (a) PTFE and (b) lycopodium marbles.

Fig. 10. Dependence of the effective surface tension on the volume during inflation (open circles) and evaporation (solid circles) for the (a) lycopodium and (b) PVDF coated marbles.

intercept 72 mJ/m2 corresponding to pure water (when S0 /S → 0); that may be interpreted as the absence of interaction between powder particles (see Sections 3.1–3.3). In this case, the slope in Eq. (1) gives  SL + SA − = −7 mJ/m2 and  SL + SA = 65 mJ/m2 that agrees approximately with the value of 78 mJ/m2 following from independent data related to PTFE:  SA = 26 mJ/m2 , Y = 112◦ , SL = SA −  cos Y = 52mJ/m2 [40]. In the dilute and quasi-solid phases the strong interaction between particles occurs that may lead to the substantial change in the powder surface tension SL + SA (see Fig. 11a). The similar, although less expressed, behavior is revealed for lycopodium coated marbles depicted in Fig. 11b. (Surfaces of lycopodium-coated marbles imaged with ESEM are shown in Figs. 4, 6). For the intermediate phase (from 0.067 to 0.076 mm−2 ) the intercept is exactly 72 mN/m and SL + SA = 49mJ/m2 . The lack of independent experimental data for lycopodium does not allow the comparison with independent experimental data. In some cases presented in Fig. 12, the positive slope is observed; that means that SL + SA −  is positive (see Eq. (1)), and the sum of interactions of powder with other phases is higher than water interaction with air for the dilute surface phase around 0.04 mm−2 . Indeed, for PE the independent calculation like that was done above for PTFE gives SL + SA = 81mJ/m2 > 72mJ/m2 (see Ref. [40]). An interesting example is given by the marbles covered with carbon-black powder (Fig. 13), which almost does not change the surface tension of pure water under sufficient dilution. This also explains why carbon black coated marbles could be shaved as demonstrated in Ref. [31]: carbon black coating may be partially removed from the surface leaving the marble stable [31]. This is possible due to proximity of the surface tension of carbon black coated liquid surface to that of the pure water. On the other hand, carbon-black marbles give a rare example the of “correct” behavior of the effective surface tension under the size change: it remains constant at the initial and final measured stages of evaporation that means the constancy of the ratio S0 /S

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in Eq. (1), i.e. particles of carbon black leave the marble surface in the course of evaporation. The abrupt jump in the middle of the graph corresponds to the surface-phase transition [36,39] already mentioned above. In conclusion, three or two surface marble phases are distinctly observed in the course of evaporation. PTFE and lycopodium marbles demonstrate a gradual decrease in their effective surface tensions under evaporation tending for one of the powder phases to the value 72 mJ/m2 inherent to pure water. For these phases, no interaction between powder particles takes place under sufficient dilution. Unlike these, under infinite dilution, the PVDF, SiO2 , and PE marbles are characterized by effective surface tensions, which are much lower than that of pure water that may be explained by strong interaction of powder particles. An exception is the carbonblack powder (Fig. 13), which does not change the water surface tension for large marbles. Thus, we conclude that the notion of the “effective surface tension” of a liquid covered with colloidal particles is ambiguous. It depends on the marble size and on the way in which the surface area is changed. This explains a high scattering in experimental values of the “effective surface tension” of liquid marbles, reported recently by various groups [12,13,30,31,33,34]. 4. Conclusions The notion of the effective surface tension of a liquid surface coated with solid particles is ambiguous. The experiments performed with inflated and deflated (evaporated) liquid marbles show that the effective surface tension (calculated from the marbles’ shapes) depends on the volume of a marble and varies within a broad range of values. Moreover, the effective surface tension demonstrates pronounced hysteretic behavior. At the same time the linear dependence of the effective surface tension on the inverse area of the marble surface demonstrates common features for various solid coatings of marbles. Three “surfaces phases” are distinguished, the first of which corresponds to the dilute distribution of solid particles on the surface of the marble. The second phase corresponds to the uniform distribution of solid particles on the marble surface. And during the third stage, the buckling of the solid coating is observed, as demonstrated in Ref. [39]. The reported results are validated by ESEM study of surfaces of the evaporated marbles. Acknowledgements Fig. 12. Dependence of the effective surface tension on the inverse marble surface in the course of evaporation for (a) PVDF, (b) PE and (c) SiO2 marbles.

The work was financially supported by the Russian Foundation for Basic Research (grant Nr. 12-03-31881) and of Ministry of Education of Perm Region (Agreement No. C-26/203 of 09.12.2011). The authors are grateful to Mrs. Revital Balter and Mrs. Yelena Bormashenko for their kind help in preparing this manuscript. We thank Dr. Roman Grinyov for the SEM images. References

Fig. 13. Dependence of the effective surface tension on the inverse marble surface in the course of evaporation for carbon-black marbles.

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