Article pubs.acs.org/Langmuir
Submerged (Under-Liquid) Floating of Light Objects Edward Bormashenko,*,† Roman Pogreb,† Roman Grynyov,† Yelena Bormashenko,† and Oleg Gendelman‡ †
Physics Faculty, Ariel University, Ariel, POB 3, 40700 Israel Faculty of Mechanical Engineering, Technion − Israel Institute of Technology, Haifa 32000, Israel
‡
ABSTRACT: A counterintuitive submerged floating of objects lighter than the supporting liquid was observed. Polymer plates with dimensions on the order of magnitude of the capillary length were hydrophilized with cold air plasma were floated in an “under-liquid” regime (totally covered by liquid) when immersed in water or glycerol. Profiles of liquid surfaces curved by polymer plates are measured. We propose a model explaining the phenomenon. The floating of Janus plates is reported.
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INTRODUCTION The floating of bodies with characteristic dimensions comparable to the capillary length lca = (γ/ρlg)1/2 (where γ and ρl are the surface tension and density of the liquid, respectively) results from the complicated interplay of surface tension and gravity.1−12 An understanding of floating is crucial for a variety of biological and engineering problems, including the behavior of particles attached to a liquid surface, the formation of lipid droplets and liquid lenses, and the motion of water striders.12−17 Much effort has been expended in the past decade for an understanding of how surface tension assists the floating of objects that are heavier than the supporting liquid.1,6,8 Our Article is devoted to the opposite situation, namely, the floating of bodies possessing a density that is lower than that of the liquid (i.e., “light” bodies). It is generally agreed and usually observed that the surface of a light floating body is only partially covered with liquid (Figure 1A). We revealed a somewhat paradoxical regime of floating, when a light body is completely coated with liquid, as schematically depicted in Figure 1B. This may occur when the energy gain due to the wetting of the high-energy surface of a light body over-
compensates for the increase in gravitational energy due to upward climbing of the liquid film.
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We studied the floating of various polymers, including low-density polyethylene (LDPE, Ipethene-810), polypropylene (PP), and polystyrene (PS) plates, in water and glycerol. Rectangular parallelepiped-shaped plates were manufactured from all studied polymers by injection molding. The length a of all of the plates was 15.35 mm; the widths b and thicknesses H were varied (their values are supplied in Table 1 with an accuracy of 0.01 mm). Densities ρp of the polymers are also supplied in Table 1. Consider that the dimensions of the plates were on the order of magnitude of the capillary length lca; that is about 2.5 mm for all polymers and liquids used in our study. To increase their surface energy, all polymer plates were treated by cold radio-frequency air plasma. Polymer plates were exposed to the inductive plasma discharge under the following conditions: frequency about 10 MHz, power 100 W, and pressure 6.7 × 10−2 Pa. The time span of irradiation was 1 min. (For the details of the experimental procedure, see refs 18 and 19.) The measurement of the liquid profile curved by the floating plate was based on the measurement of the electrical conductivity of the liquid (glycerol). The surface of the glycerol was scanned with a conducting tip (Figure 2). The tip was mounted on a micrometric precision XYZ stage, allowing the displacement of the tip with an accuracy of 1 μm. The tip was contacted to an ohmmeter (Keithley199), as shown in Figure 2. The second plane metallic contact was immersed in the liquid (Figure 2). The XYZ stage displaced the contact tip until it touched the surface of glycerol. Thus, closure of the electric circuit occurred, as registered by the ohmmeter. In this way,
Figure 1. (A) Conventional surface-tension-supported floating of a light object. (B) Under-liquid (submerged) floating of a light object; h is the maximal height of the liquid layer and l is the thickness of the liquid layer, coating the polymer. S(x) is the profile of the liquid coating the plate. © XXXX American Chemical Society
EXPERIMENTAL SECTION
Received: May 17, 2013 Revised: July 28, 2013
A
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Table 1. Thickness of the Coating Layer l and the Maximal Height h of the Liquid Layer Measured and Calcuated for Plates of Various Dimensions Manufactured from LDPE, PP, and PS h, maximal height of the liquid layer, mm polymer LDPE
PP
PS
dimensions, ± 0.05 mm b = 14.0 mm, H = 3.75 mm b = 12.0 mm, H = 3.75 mm b = 6.4 mm, H = 3.75 mm b = 14.0 mm, H = 1.55 mm b = 12.0 mm, H = 1.55 mm b = 6.38 mm, H = 1.55 mm b = 12.0 mm, H = 2.85 mm b = 6.0 mm, H = 2.85 mm
density, ρp g/cm3
experimental, ± 0.001 mm
calculated
0.918
0.5
0.63
0.918
0.45
0.6
0.918
0.44
0.5
0.946
0.239
0.239
0.946
0.29
0.23
0.946
0.19
0.193
1.043
0.305
0.293
1.043
0.305
0.24
Figure 3. Scheme of a laboratory-made goniometer used for the measurement of the thickness of the layer of liquid coating a polymer l. A d × d gold spot is sputtered onto the polymer plate with dimensions of a × b (top view).
surface energy of LDPE is on the order of 20 mJ/m2).20−22 Thus, it floats as depicted in Figure 1A. To increase the surface energy of LDPE plates, they were exposed to cold radiofrequency air plasma as described in the Experimental Section. Cold plasma treatment dramatically increases the surface energy of polymers and consequently influences their wettability.18,19,23−29 After plasma treatment, the floating regime of LDPE changed dramatically. The “underwater” floating of LDPE depicted in Figures 1B and 2 was observed; namely, water completely coated the LDPE plate. For the purpose of illustrating the submerged floating, we manufactured “Janus” LDPE plates composed of virgin and plasma-treated areas.30,31 The floating of such Janus plates in water is depicted in Figure 4. It is seen
Figure 2. Scheme of a laboratory-made goniometer used for the measurement of the curved profile of the liquid. the curved profile of the liquid was established with an accuracy of 1 μm. The thickness of the glycerol film coating the polymer plates l was established with the device depicted in Figure 3. For this purpose, a square gold spot with dimensions of 5 × 5 mm2 and a thickness of 1 μm was first sputtered in a vacuum onto the polymer plates. The gold spot served as an electrode, as will be explained below. The dimensions of the gold spot were much smaller than those of the polymer plates, thus the presence of the spot changed the floating regime only negligibly. The thickness of the layer was established with a twin-needle conducting probe mounted on the micrometric precision XYZ stage, as depicted in Figure 3. The XYZ stage displaced the twin-needle probe until it touched the surface of glycerol, achieving closure of the electrical circuit as recorded by the ohmmeter while fixing the level of the glycerol. Afterwards, the XYZ stage continued the vertical displacement of the twin-needle probe into the glycerol until it contacted the surface of the gold spot. When the needle’s tips touched the gold spot, the jump in resistance was registered by the ohmmeter. Thus, a precise measurement of the thickness of the glycerol layer l coating the polymer plate was accomplished with an accuracy of 10 μm.
Figure 4. Floating of a Janus LDPE plate: the plasma-treated area is submerged; the upper surface of the nontreated (virgin) area is not wetted.
that the plasma-treated section of the plate is submerged and completely coated with water, whereas the hydrophobic nontreated section stays partially above the water level. Submerged (under-liquid) floating was observed for all polymers and liquids used in our study; namely, the plasma treatment inspired submerged under-liquid floating of polymer plates. Intuitively, this regime could be easily explained: the energy gain achieved by the wetting of the high-energy plasma-
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RESULTS AND DISCUSSION Let us start with the floating of LDPE plates in water. LDPE as well as other polymers is a low-surface-energy material (the free B
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Figure 5. Profiles of glycerol surfaces S(x) as established for LDPE plates with a thickness of H = 3.75 mm and a length of a = 15.35 mm: plate widths are (A) b = 6.4 mm, (B) b = 12 mm, and (C) b = 14 mm.
treated polymer surface prevails over the energy loss due to the upward climbing of the liquid film. It may be mistakenly assumed that the cold plasma treatment led to the total wetting of polymer plates (total wetting occurs when the spreading parameter ψ = γSA − (γSL + γ) > 0,where γSA, γSL, and γ are a triad of interface tensions at the solid/air, solid/liquid, and liquid/air interfaces, respectively). Actually, we have a partial wetting of plasma-treated polymers by water and glycerol, namely, ψ < 0, and a nonzero contact angle is observed.20 The quantitative theory of the phenomenon will be proposed below. We observed submerged floating of polymer plates with both liquids: water (ρw = 1.0 g/cm3,γw = 72 mJ/m2) and glycerol (ρgl = 1.261 g/cm3, γgl = 63 mJ/m2). However, quantitative measurements of the profile of the liquid surface, curved by polymer plates of various dimensions, were performed with glycerol only. The high viscosity of glycerol, ηgl = 1.5 Pa·s (when compared to that of water, ηw = 9 × 10−4Pa·s, where both values are supplied for ambient conditions), allowed a stable floating of polymer plates and made possible an accurate measurement of the curved profile of the liquid coating the plasma-treated polymer plate. It should be emphasized that a traditional goniometry measurement does not allow for the establishment of this profile. Hence, the measurements were carried out with a laboratory-constructed device, as depicted in Figure 2 (details in Experimental Section). Typical profiles of the liquid surfaces established with the aforementioned device are depicted in Figure 5A−C (the dashed line in these Figures is supplied for visual guidance). The excellent repeatability of the measurement of the profiles is noteworthy. (Plates of the same dimensions gave rise to the same profile with an accuracy of 0.5%.) We also measured the thickness of glycerol coating the polymer plates with the laboratory-constructed device depicted in Figure 3, as explained in detail in the Experimental Section. Experimental data summarizing the values of h and l established with polymer plates of different dimensions are supplied in Tables 1 and 2. A theoretical analysis of the phenomenon is based on a simplified model presented below. Let us consider the situation of the submerged floating presented in Figure 1B more closely. The horizontal axis is denoted as x, and S(x) is the height of the liquid surface as a function of the horizontal coordinate. We will
Table 2. Thickness of the Layer Covering the Polymer Plate lexp vs the Equilibrium Thickness of Glycerol Puddles (Estimated with Expression 5 lest and Measured lpuddle) polymer
dimensions, ±0.01 mm
LDPE
b = 14 mm, H = 3.75 mm b = 12 mm, H = 3.75 mm b = 6.4 mm, H = 3.75 mm b = 14 mm, H = 1.55 mm b = 12 mm, H = 1.55 mm b = 6.38 mm, H = 1.55 mm b = 12 mm, H = 2.85 mm b = 6 mm, H = 2.85 mm
PP
PS
lexp, ±0.01 mm
lest, mm
lpuddle, ±0.025 mm
0.20
0.68
0.9
0.17
0.68
0.9
0.15
0.68
0.9
0.19
0.79
0.9
0.16
0.79
0.9
0.12
0.79
0.9
0.16
0.38
0.17
0.09
0.38
0.17
adopt that for some characteristic point X0 close to the edge of the plate we have S(X0) ≈ h. The capillary length of the glycerol is close to lca ≈ 2.25 mm, and under the current experimental conditions h, l ≪ lca. At the same time, the length and the width of the plates essentially exceed the capillary length; hence, in the lowest-order approximation, one can disregard the corner effects and estimate the profile of the liquid while considering the plate to be a wall with infinite length. Therefore, one can assume that the shape of the surface outside the plate obeys the exponential decay law (ref 32): ⎛X − x⎞ S(x) ≈ S(X 0) exp⎜ 0 ⎟ ⎝ lca ⎠
(1)
Then, the vertical component of the force exerted by the lifted surface on the plate and the liquid layer above the plate Fs can be estimated as Fs ≈ 2γ(a + b)
d S(x ) dx
= x = X0
2γ(a + b)h lca
(2)
This component, together with the weights of the plate and the liquid layer above the plate, is balanced by the Archimedean force acting on the plate. If one neglects the edge effects related C
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the long-range van der Waals forces in the case of the polymer/ glycerol interaction, as shown in refs 37−39. We come to the conclusion that the paradoxical under-liquid floating of light objects is governed to a greater extent by interfacial phenomena, as studied experimentally and theoretically first in this Article.
to the corners of the plate, this balance can be approximately expressed as follows: 2γ(a + b)h + abρl gl + abρp gH = abρl g (H − h + l) lca (3)
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Here, ρp is the density of the plate material and H is the height (thickness) of the plate. It should be stressed that the Archimedean force acts only on the part of the plate submerged under the initial level of liquid. The pressure exerted by the elevated part of the liquid is balanced by the surface tension forces (the Laplace pressure) and thus should be omitted when evaluating the Archimedean force. From eq 3, it is easy to derive an expression for the general height of the liquid “hump”: ρp l (a + b) μH h≈ ; μ = 1 − ; ξ = ca 2ξ + 1 ρl ab (4)
CONCLUSIONS The submerged (under-liquid) floating of polymer plates (made from polyethylene, polypropylene, and polystyrene) was observed in liquids possessing densities larger than those of polymers. Polymers were hydrophilized with cold air radiofrequency plasma treatment. Plates, hydrophilized with plasma, were completely coated with liquids (water and glycerol). Profiles of the liquid surfaces curved by polymer plates were established precisely with a specially constructed device. The model explaining the paradoxical submerged floating of objects with dimensions comparable to the capillary length and lighter than the supporting liquid is proposed. The floating of Janus polyethylene-based plates illustrating the effect is reported.
Here, μ is a buoyancy parameter of the plate material, and ξ is a dimensionless parameter characterizing the relationship between the geometry of the plate and the capillary properties of the liquid. The results of the calculations according to eq 4 are presented in Table 1 in comparison with the experimental findings. One can see that the correlation is reasonable and in some cases very good. Now let us discuss the thickness of the liquid layer coating the polymer l; the values of the thickness lexp, which were established experimentally with the device depicted in Figure 3, are supplied in Table 2. It is recognized that they are much smaller than the capillary length lca. The problem of the prediction of the layer thickness l is complicated because the latter as it seems cannot be determined from the force balance considerations. It looks reasonable to compare this thickness with the equilibrium thickness of the glycerol “puddle”, namely, the liquid layer flattened by gravity. This estimated thickness lest is predicted by the expression lest = lca sin
θY 2
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We are thankful to Mrs. A. Musin for her kind help in preparing this Article.
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REFERENCES
(1) Liu, J.-L.; Feng, X.-Q.; Wang, G.-F. Buoyant force and sinking conditions of a hydrophobic thin rod floating on water. Phys. Rev. E 2007, 76, 066103. (2) Singh, P.; Joseph, D. D. Fluid dynamics of floating particles. J. Fluid Mech. 2005, 530, 31−40. (3) Neumann, A. W.; Economopoulos, O.; Boruvka, L.; Rapacchietta, A. V. Free energy analysis of heterogeneous cylindrical particles at fluid interfaces. J. Colloid Interface Sci. 1979, 71, 293−300. (4) Vella, D.; Lee, D. G.; Kim, H. Y. The load supported by small floating objects. Langmuir 2006, 22, 5979−5981. (5) Lee, D. G.; Kim, H. Y. Impact of a superhydrophobic sphere onto water. Langmuir 2008, 24, 142−145. (6) Vella, D. Floating objects with finite resistance to bending. Langmuir 2008, 24, 8701−8706. (7) Vella, D.; Metcalfe, P. D. Surface tension dominated impact. Phys. Fluids 2007, 19, 072108. (8) Keller, J. B. Surface tension force on a partly submerged body. Phys. Fluids 1998, 10, 3009. (9) Mansfield, E. H.; Sepangi, H. R.; Eastwood, E. A. Equilibrium and mutual attraction or repulsion of objects supported by surface tension. Philos. Trans. R. Soc. London, Ser. A 1997, 355, 869−919. (10) Wagner, T. J. W.; Vella, D. Floating carpets and the delamination of elastic sheets. Phys. Rev. Lett. 2011, 107, 044301. (11) Bormashenko, E.; Bormashenko, Y.; Musin, A. Water rolling and floating upon water: marbles supported by a water/marble interface. J. Colloid Interface Sci. 2009, 333, 419−421. (12) Phan, C. M.; Allen, B.; Peters, L. B.; Le, Th. N.; Tade, M. O. Can water float on oil? Langmuir 2012, 28, 4609−4613. (13) Binks, B. P.; Horozov, T. S. Colloidal Particles at Liquid Interfaces; Cambridge University Press: Cambridge, U.K., 2006. (14) Bormashenko, E. Liquid marbles: properties and applications. Curr. Opin. Colloid Interface Sci. 2011, 16, 266−271.
(5)
where θY is the equilibrium (Young) contact angle. The experimental establishment of the Young contact angle is not a trivial task because of the phenomenon of contact angle hysteresis.20,33,34 For the purpose of a very rough estimation, we suggested that the Young contact angle is equal to the socalled static or “as-placed” contact angle, established with the traditional goniometry procedure.35 Static contact angles measured for plasma treated LDPE, PP, and PS/glycerol pairs are equal to 35 ± 1, 41.5 ± 1, and 19 ± 1°, respectively. (As already mentioned, we have the partial wetting of polymers.) The thicknesses of the liquid puddles, lest, predicted by eq 5 for the polymers used in our study are supplied in Table 2. We also established the equilibrium thickness of liquid puddles experimentally; the measured values of the thickness, labeled lpuddle, are also presented in Table 2. One can see that eq 5 could be involved only for the qualitative interpretation of the puddles’ thickness. The discrepancy is due to the effect of contact angle hysteresis, as has been demonstrated explicitly in ref 36. However, it is also seen that both estimated and measured values of the thickness of the equilibrium puddles are much larger (especially for LDPE and PP) than those established experimentally and supplied in Table 2. It is reasonable to suggest that the value of l is actually dictated by D
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(15) Brown, D. A. Lipid droplets: proteins floating on a pool of fat. Curr. Biol. 2001, 11, R446−R449. (16) Shi, F.; Niu, J.; Liu, J.; Liu, F.; Wang, Zh.; Feng, X.-Q.; Zhang, X. Towards understanding why a superhydrophobic coating is needed by water striders. Adv. Mater. 2007, 19, 2257−2261. (17) Gao, X.; Jiang, L. Biophysics: water-repellent legs of water striders. Nature 2004, 432, 36. (18) Bormashenko, Ed.; Grynyov, R.; Bormashenko, Ye.; Drori, El. Cold radiofrequency plasma treatment modifies wettability and germination speed of plant Seeds. Sci. Rep. 2012, 2, 741. (19) Bormashenko, E.; Chaniel, G.; Grynyov, R. Towards understanding hydrophobic recovery of plasma treated polymers: storing in high polarity liquids suppresses hydrophobic recovery. Appl. Surf. Sci. 2013, 273, 549−553. (20) de Gennes, P. G.; Brochard-Wyart, F.; Quéré, D. Capillarity and Wetting Phenomena; Springer: Berlin, 2003. (21) van Krevelen, D. W. Properties of Polymers; Elsevier: Amsterdam, 1997. (22) Chibowski, E.; Perea-Carpio, R. Problems of contact angle and solid surface free energy determination. Adv. Colloid Interface Sci. 2002, 98, 245−264. (23) Yasuda, H. J. Plasma for modification of polymers. J. Macromol. Sci. A 1976, 10, 383−420. (24) France, R. M.; Short, R. D. Plasma treatment of polymers: effects of energy transfer from an argon plasma on the surface chemistry of poly(styrene), low density poly(ethylene), poly(propylene)and poly(ethylene terephthalate). Faraday Trans. 1997, 93, 3173−3178. (25) Hegemann, D.; Brunner, H.; Oehr, Ch. Plasma treatment of polymers for surface and adhesion improvement. Nuclear Instr. Methods Phys. B 2003, 208, 281−286. (26) Morra, M.; Occhiello, E.; Garbassi, F. Contact angle hysteresis in oxygen plasma treated poly(tetrafluoroethylene). Langmuir 1989, 5, 872−876. (27) Morra, M.; Occhiello, E.; Marola, R.; Garbassi, F.; Humphrey, P.; Johnson, D. On the aging of oxygen plasma-treated polydimethylsiloxane surfaces. J. Colloid Interface Sci. 1990, 137, 11−24. (28) Kaminska, A.; Kaczmarek, H.; Kowalonek, J. The influence of side groups and polarity of polymers on the kind and effectiveness of their surface modification by air plasma action. Eur. Polym. J. 2002, 38, 1915−1919. (29) Mortazavi, M.; Nosonovsky, M. A model for diffusion-driven hydrophobic recovery in plasma treated polymers. Appl. Surf. Sci. 2012, 258, 6876−6883. (30) Walther, A.; Müller, A. H. E. Janus particles: synthesis, selfassembly, physical properties, and applications. Chem. Rev. 2013, 113, 5194−5264. (31) Bormashenko, Ed.; Bormashenko, Ye.; Pogreb, R.; Gendelman, O. Janus droplets: liquid marbles coated with dielectric/semiconductor particles. Langmuir 2011, 27, 7−10. (32) Landau, L. D.; Lifshits, E. M. Fluid Mechanics; ButterworthHeinemann: Oxford, U.K., 1987. (33) Joanny, J. F.; de Gennes, P. G. A model for contact angle hysteresis. J. Chem. Phys. 1984, 81, 552−562. (34) Bormashenko, E. Wetting of Real Surfaces; De Gruyter: Berlin, 2013. (35) Tadmor, R.; Yadav, P. S. As-placed contact angles for sessile drops. J. Colloid Interface Sci. 2008, 317, 241−246. (36) Bormashenko, Ed.; Musin, A.; Pogreb, R.; Luz, E.; Zinigrad, M. Thickness of gravity-flattened water layers (“puddles”) deposited on the polymer substrates and the hysteresis of the contact angle. Colloids Surf., A 2010, 372, 135−138. (37) Starov, V. M.; Velarde, M. G. Surface forces and wetting phenomena. J. Phys: Condens. Matter 2009, 21, 464121. (38) Israelichvili, J. N. Intermolecular and Surface Forces, 3rd ed.; Elsevier: Amsterdam, 2011. (39) Erbil, H. Y. Solid and Liquid Interfaces; Blackwell Publishing: Oxford, U.K., 2006.
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