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Stability of a Floating Water Droplet on an Oil Surface Chi M. Phan* Department of Chemical Engineering, Curtin University, GPO Box U1987, Perth WA 6845, Australia ABSTRACT: This article presents a new configuration of a water droplet floating on oil surface. The configuration is characterized by an acute contact angle (i.e., θ2 < π/2). In contrast, the previously identified droplet had an obtuse contact angle, which was easily sunk by a small disturbance. By employing a common surfactant, the new configuration was experimentally verified in a mineral oil with a density similar to that of crude oils. The new droplet is kinetically more stable than the previous configuration and can sustain strong disturbances. The results also highlight the significance of dynamic interfacial adsorption on the stability of the floating droplet. a previous study, attempts to float water on mineral oils have failed.7 Second, the water droplet was easily sunk by small disturbances. Such instability makes the phenomenon useless for practical purposes. Third, the droplet behavior with changing surface tension remains unknown. During oil decomposition, different organic compounds, many of which are surface-active, are continuously formed and/or consumed. Consequently, the tension forces might change dramatically during application. The stability of the floating droplet in the varying surface tensions will be vital to successful application, if any. This study addresses the above issues by modifying the theoretical model and applying it to a mineral oil.

1. INTRODUCTION Interfacial tensile forces are caused by asymmetric molecular arrangement in the interfacial zone, such as in air/liquid or liquid/liquid systems. The interfacial forces are limited to the vicinity around the interface and are fairly weak, typically less than 100 mN/m. Under special circumstances, these nanoscale effects can lead to interesting phenomena on the macroscale. Such physical observations have fascinated generations of curious minds. Around 350 B.C., Aristotle took notice of a heavy object floating on the surface of the water.1 In the 1490s, Leonardo da Vinci observed the capillary rise in small tubes, in which surface tension counterbalances gravity.2 In nature, striders can walk on water using similar phenomena. Mimicking this ability remains a formidable challenge, even with the latest advances in materials science.3 The floatability of spherical solid particles on liquid surfaces has been analyzed both experimentally4 and theoretically.5 By being wrapped in hydrophobic particles, a heavier liquid marble can also float on a lighter liquid.6 Previously, we reported that a heavy liquid droplet can float on a lighter liquid (e.g., water droplet on oil).7 The floating liquid droplet requires a delicate balance among three deformable interfaces. The phenomena can lead to a novel method of treating surface oil slicks, which can be catastrophic for the environment. In the literature, the decomposition of oil slicks by floating solid objects has been proposed, with embedded catalytic nanoparticles in either wood chips8 or hollow glass microbeads.9 Compared to solid floating objects, the floating water droplets are easier and cheaper to create. The floating droplet can contain catalytic nanoparticles, which would concentrate on the oil/water interface and decompose oils through photocatalytic reactions. Furthermore, the droplet can also contain bioreagents (such as enzymes, microorganisms, and nutrients) for the biochemical degradation of hydrocarbons. Nevertheless, the application needs to address some fundamental obstacles. First, the floating water droplet was observed only on canola oil, of which the density was substantially higher than those of crude oils. As mentioned in © 2014 American Chemical Society

2. THEORETICAL FRAMEWORK Modeling. The general equilibrium shape of a water droplet on an oil surface is shown in Figure 1. In this study, a droplet shape with an acute contact angle between the oil/water interface and the horizontal axis (i.e., θ2 < π/2) was analyzed. In contrast, the previous model was developed for θ2 > π/2 only.7 In summary, the model identifies the equilibrium configuration of the floating droplet based on predefined parameters: densities of air, water, and oil (ρa, ρw, and ρo, respectively), interfacial tensions of water/air, oil/water, and oil/air interfaces (γaw, γow, and γoa, respectively), and the droplet volume (Vb). The numerical model used four matching loops to obtain the configuration that satisfies the zero force balance, the interdependency among three contact angles, and the axisymmetric Young−Laplace equations along the three interfaces. It should be noted that the matching sequence (Figure 2) is slightly different from the previous model. In the previous model, the final loop was used for force balance. In contrast, the new model employs the volume balance in the final loop, which improves the robustness of the program. The floating condition requires a zero force balance Received: October 4, 2013 Revised: December 6, 2013 Published: January 7, 2014 768

dx.doi.org/10.1021/la403830k | Langmuir 2014, 30, 768−773

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Figure 1. Diagram of a water droplet on an oil surface.

Figure 2. Flowchart of the numerical model.

g[Vbρw + Vaρa − (Va + Vb)ρo ] = 0

where g is the gravitational constant and Va is the volume of the air pocket above the droplet.

(1) 769

dx.doi.org/10.1021/la403830k | Langmuir 2014, 30, 768−773

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In eq 1, the first term is the weight of the water droplet, the second term is the weight of the air volume above the water droplet, and the last term is the weight of the displaced oil volume (which corresponds to buoyancy). As shown in Figure 1, Vb can be divided into two parts: above the contact line (V1) and under the contact line (V2). The volume of the air pocket above the droplet is given by

Va = πr 2h3 − V1

(2)

where r is the contact line radius and h3 is the height of the submerged meridian. Hence, eq 1 can be rearranged as (V1 + V2)ρw + (πr 2h3 − V1)ρa − (πr 2h3 + V2)ρo = 0

(3)

The interdependency among the three contact angles follows the Neumann triangle of surface tension:10 ⎡γ 2 + γ 2 − γ 2⎤ ow oa ⎥ θ1 + θ2 = π − arccos⎢ aw ⎢⎣ ⎥⎦ 2γawγow

(4)

⎡γ 2 + γ 2 − γ 2⎤ aw ow ⎥ θ1 + θ3 = arccos⎢ oa ⎢⎣ ⎥⎦ 2γoaγaw

(5)

Figure 3. Theoretical predictions of a floating droplet with (a) obtuse θ2 and (b) acute θ2.

Table 1. Parameters for Theoretical Configurations

It is noteworthy that the line tension is neglected in the above equations.10 The reported line tension for the liquid/ liquid/air contact line is ∼10−9 N.11 With a contact radius of ∼1 mm, the line tension force is around 10−6 N/m, which is negligible in comparison to the interfacial forces (∼10−3 to 10−4 N/m). The air/water, oil/water, and oil/air interfaces resemble sessile, pendant, and submerged meridians,12 respectively. Each interfacial profile can be solved routinely by a system of first ODEs as shown previously.7 The mathematical system (i.e., eqs 3−5) and three systems of first ODEs was solved using the algorithm in Figure 2 to determine the configuration of the droplet. Interfacial Tensions. One can expect to obtain the new equilibrium configuration by varying densities and/or interfacial tensions. Generally, a smaller θ2 would require a smaller sum of θ2 and θ1, which can be obtained by lowering both the water/ air and water/oil interfacial tensions (as given in eq 4). Examples of the two equilibrium shapes, at Vb = 3 μL, are shown in Figure 3. In Figure 3a, the original configuration was generated using the interfacial tensions (Table 1) without additional surfactant.7 The theoretical configuration in Figure 3b was obtained using literature values of γwa13 and γow14 with a common anionic surfactant, sodium dodecyl sulfate. With a larger base-to-volume ratio, the second configuration is expectedly more resilient to disturbance than the previous one. The practical method of reducing γaw and γwo is by employing surfactants. A wide range of surfactants have been shown to reduce γaw,15 which can be as low as 15m N/m.16 Similarly, surfactant systems can reduce γwo to less than 1 mN/m.17 In enhanced recovery in the petroleum industry, aqueous solutions with extremely low γwo values ( γoa, lowering γwo increases the instability of the droplet. For γaw < γoa, lowering γwo has the opposite effect (i.e., it increases the stability of the droplet). The uniqueness of the theoretical curve can also lead to a new method of determining γwo, which is valuable for oil/water interfacial studies. Currently, the most reliable method of oil/ water interfacial tension is the spinning drop method using Vonnegut’s approximation.30 The spinning drop method is impractical when oil and water phases have similar densities (i.e., ρo ≈ ρw). In contrast, such systems would be easier to test with the floating droplet. If one can precisely determine and control γaw and Vb, then the theoretical model can be employed to relate γow to r directly. The practicality and accuracy of such a method will be tested in future work. From the modeling, the required combinations of γaw and γow are matched to the dynamic values in Figure 5. Hence, the transient values of γaw and γow are plotted in Figure 7. The data indicated that γaw reached equilibrium, ∼26 mN/m, within 10 s whereas γow was reduced at a slower rate. The relative reducing rates are physically consistent with the adsorption kinetics,16 which is slower at the water/oil interface. It can be concluded that the driving force for the droplet reshaping process was the dynamic adsorption at the two interfaces of the water droplet. The modeled γow was similar to the reported values of water/ hexadecane interfacial tension, ∼8 mN/m.14 It should be noted that if γow is reduced to 4.5 mN/m then the required condition for Neumann’s triangle is no longer valid. In such an instance,

5. CONCLUSION The study theoretically identified a second configuration of a floating droplet, which is characterized by an acute contact angle. The configuration was successfully verified with a surfactant solution and paraffin oil. There were three significant findings with the new configuration: (i) it varies with the dynamic reduction of oil/water and air/water interfacial tension; (ii) it is more stable than the previous configuration; and (iii) it is applicable to crude oils. The new floating configuration has greater applicability to the treatment of oil spills than does the previous configuration. The floating droplet can be obtained with a wide range of combinations between γwo and γaw. The flexibility is an advantage for applications in which the droplet is loaded with oil-decomposing materials and surfactants. For successful applications, the surfactant system should be selected for the dynamic tensions, both γwo and γaw, rather than the equilibrium values. It should be noted that the droplet volume in this study was very small, ∼ 2% of the previous droplet. Nevertheless, such volume ranges can be easily created through spraying nozzles, which are widely used in agriculture. An investigation of the phenomenon on crude oils is underway.



AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] Notes

The authors declare no competing financial interest.



REFERENCES

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dx.doi.org/10.1021/la403830k | Langmuir 2014, 30, 768−773

Stability of a floating water droplet on an oil surface.

This article presents a new configuration of a water droplet floating on oil surface. The configuration is characterized by an acute contact angle (i...
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