Toward an Understanding of Magnetic Displacement of Floating

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Towards Understanding of Magnetic Displacement of Floating Diamagnetic Bodies, I: Experimental Findings Mark Frenkel, Viktor Danchuk, Victor Multanen, Irina Legchenkova, Yelena Bormashenko, Oleg Gendelman, and Edward Bormashenko Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b00424 • Publication Date (Web): 04 May 2018 Downloaded from http://pubs.acs.org on May 5, 2018

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Towards an Understanding of Magnetic Displacement of Floating Diamagnetic Bodies, I: Experimental Findings Mark Frenkel1, Viktor Danchuk2, Victor Multanen1, Irina Legchenkova1, Yelena Bormashenko1, Oleg Gendelman3, Edward Bormashenko1 1

Ariel University, Engineering Faculty, Chemical Engineering, Biotechnology and Materials Department, P.O.B. 3, 407000, Ariel, Israel 2

Ariel University, Exact Sciences Faculty, Physics Department, P.O.B. 3, 407000, Ariel, Israel

3

Faculty of Mechanical Engineering, Technion−Israel Institute of Technology, Haifa 3200003, Israel

Corresponding author: Edward Bormashenko E-Mail: [email protected] Phone: 972-3-074 7296863

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ABSTRACT Diamagnetic objects (polymer and metallic plates and spheres, ceramic beads and liquid marbles), floating on water and a variety of organic liquids may be driven by a steady magnetic field of

0.1 T, registered at the water-vapor surface.

Diamagnetic bodies are attracted to the magnet, when the apparent contact angle at the solid/liquid interface is obtuse and repelled from the magnet, when the angle is acute. Cold plasma treated polyolefin rafts and spheres, demonstrating underwater floating, are repelled by a permanent magnet. Addition of a surfactant to the water, as well as cold plasma treatment of the polyolefin bodies can turn the attraction into the repulsion. We conjecture that the observed effects are caused by the interplay of two main phenomena. The first is the gravity, which induces sliding of the particle on the deformed liquid/vapor interface (the Moses effect). The second cause is the hysteresis of the contact angle at the bodies' boundaries.

Keywords: diamagnetic body; diamagnetic liquid; floating; magnetic field; Moses effect; contact angle hysteresis.


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INTRODUCTION The influence of a magnetic field on wetting and capillarity events has been extensively addressed by researchers.1-8 A magnetic field was successfully used for the tuning of resonance frequencies of droplets1, DNA separation,2 self-assembly,3 remote-control of wetting properties of surfaces5 and remote displacement of droplets.6 The ferromagnetic properties of a fluid are usually exploited for magnetic control of wettability.4,6,8 Magneto-capillary effects (including self-assembly), attained with ferromagnetic

particles placed at the water-vapor interface were

addressed in Refs. 9-12. the use of paramagnetic HoCl3 solutions for controlled magnetically driven displacement of droplets and liquid marbles was reported recently in Ref. 13. The possibility to displace floating polymer rafts by moderate magnetic fields was reported in Ref. 14. The state-of-the-art in the field of magnetofluidics was reviewed in Refs. 15-16. We report the possibility to drive the diamagnetic objects (polymers, metals and liquid marbles17-21) floating on various diamagnetic liquids with a permanent magnetic field. The possible physical mechanism behind the reported effect is discussed. It is well known that the diamagnetic bodies are repelled by magnetic fields, enabling even levitation of heavy objects exposed to high magnetic fields (ca 10T) .2225

In contrast, we demonstrated that the diamagnetic bodies may be driven by the

permanent magnet, when they float on a liquid surface. The apparent attraction may be switched to repulsion by modifying the wetting regime. We suggest that the attraction is related to the interplay of buoyancy and magnetically induced deformation of the surface of the diamagnetic liquid, also known as the “Moses effect”.26-27 However, repulsion was also observed; this can be explained by the interplay of interfacial phenomena, involving the contact angle hysteresis28-33 , and direct diamagnetic repulsion. EXPERIMENTAL SECTION Diamagnetic bodies and liquids used in the experiments Diamagnetic floating bodies used in the experiments were: 1.

Сircular rafts manufactured with polymers, namely: lab-made extruded

polyethylene (PE) and polypropylene (PP); polytetrafluoroethylene (PTFE) supplied by Sigma-Aldrich, USA, and TPX polymethylpentene (PMP) was supplied by ACS Paragon Plus Environment

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Westlake Plastics Company, USA. TPX samples were loaded with a 0.6 g copper plummet. The geometrical parameters of all the samples are summarized in Table 1. 2.

Spheroid-like extruded PE pellets with a diameter of 5±0.2 mm, supplied by

Carmel-Olefins. 3.

Metallic circular rafts manufactured from gold (Au) and silver (Ag), supplied

by Testbourne Ltd, UK, 99,99 wt. % pure; and copper (Cu) foil, supplied by 3M, USA. 4.

Foamed polystyrene, abbreviated in the text as FPS.

5.

Liquid marbles with a volume of 10 µl, were prepared according to the protocol

reported in Ref. 6. Liquid marbles were coated with lycopodium, PTFE (supplied by Sigma-Aldrich, USA) and carbon black powder (supplied by Carbon Black Nederland B.V. Co.). 6.

Zirconia Ceramic beads (abbreviated as ZR) with a diameter of 3±0.05 mm

(supplied by Terio Co., China) were coated with Teflon (Poly(tetrafluoroethylene)) particles with a size of 1 µm (supplied by Sigma-Aldrich, USA). Diamagnetic liquids used in our experiments were: water (H2O); Ethanol (C2H5OH), supplied by Bio-Lab Ltd, Israel; Diiodomethane (CH2I2), supplied by Sigma-Aldrich, USA; Dichloromethane (CH2Cl2), supplied by Bio-Lab Ltd, Israel, and Dimethylformamide (C3H7NO), supplied by Bio-Lab Ltd, Israel. The physical properties and geometrical parameters of the floating objects and physical parameters of diamagnetic liquids are summarized in Tables 1, 2. Deionized water was prepared using the synergy UV water purification system from Millipore SAS (France). The specific resistivity of the water was ρˆ = 18.2 MΩ × cm at 25ºC. PE and FPS samples were exposed to a radiofrequency (13.56 MHz) inductive air plasma discharge with the power of 18W under the pressure of 133 Pa and ambient temperature, for 30 s. The surfactant used in the experiments was prepared as follows: 30 cm3 of oleic acid was mixed with 50 cm3 of distilled water. Added to the mixture were 73 cm3 of a 10% solution of tri-ethanolamine, 164 cm3 of pure glycerin and 47 cm3 of distilled water.34 All of these chemicals were supplied by Sigma-Aldrich, USA.


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Scheme of the experiment The scheme of the experimental unit is depicted in Figure 1. Diamagnetic bodies were placed at the initial lateral distance L = 20±1 mm from the axis of the cylindrical permanent magnet; the diameter of the magnet was 6mm. The clearance h between the magnet and the liquid level was h = 1.0±0.1mm. The motion of the floating objects driven by the permanent magnetic field was registered from above with a rapid camera (Casio EX-FH20). The experiments were carried out under ambient conditions. The stack of ten Cylindrical Neodymium permanent magnets producing the maximal magnetic field of B of 0.4±0.005T were placed above the water/vapor interface, as depicted in Figure 1. The magnetic field was measured by the magnetic field sensor Pasco-CI-6520A equipped with the PASCO-850 universal interface. The experiments were performed both with a bare magnet, and with the magnet placed in a shielding metallic cage (Figure 1). The shielding cage was manufactured as follows: the cylindrical hole was drilled coaxially in a massive steel (grade C10) cylinder (Z = 70 mm, Rc = 8 mm, the wall thickness was 4.75 mm). The experiments were performed under ambient conditions.

RESULTS AND DISCUSSION Study of the role of the wetting regime in the motion of floating of diamagnetic bodies All of the diamagnetic bodies, listed in Table 1, were displaced in some way by the permanent magnet, when placed on all of the diamagnetic liquids, listed in

Table 2. Both apparent repulsion and attraction of the floating bodies by the magnet were observed, depending on the regime of wetting. Generally, three main regimes were registered, as depicted in Figure 2 (A, B, C, D). The floating regime depicted in

Figure 2A is characterized by the obtuse apparent equilibrium contact angle θ (see Refs. 24-26). The interrelation between interfacial (i.e., the meniscus slope angle) and apparent contact angles in this situation is obvious: α = θ −

π 2

. When the apparent

equilibrium contact angles, inherent for a solid/liquid pairs were obtuse, the attraction was observed (see SI1). This was the case when PE, PP, PTFE, ZR, Cu, Au, Ag, and FPS bodies (see Figure 3) floated on water. Floating and attraction of the metallic bodies (demonstrated in supporting information SI2) to the magnet is possible due to the contact angle hysteresis.


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Contrary to the experimental finding reported in Ref. 14, not only attraction but also repulsion of floating diamagnetic bodies by a permanent magnet was observed. The repulsion was observed when the apparent contact angles were acute. The wetting regime shown in Figure 2B is typical for the acute apparent contact గ

angles θ (note that in this case the interrelation ߠ = − ߙ takes place). This was the ଶ

situation when all of the polymer bodies floated on the organic liquids, listed in Table

2. The apparent contact angles were acute, when plasma treated polymers floated on water, and also in the situation when the polymer bodies floated on the water coated by molecules of surfactant (see Section 2.1). In all these cases, we observed that the permanent magnet repelled the floating diamagnetic bodies. One encounters an additional possible scenario of “underwater (submerged) floating,” depicted in Figure 2C35,36. This floating regime is typical for cold plasma treated polyolefin bodies.35,36 The underwater (submerged) regime of floating becomes possible when the energy gain achieved by the wetting of the high-energy plasma-treated polyolefin surface prevails over the energy loss due to the upward climbing of the liquid film.35,36 We propose the following qualitative explanation for the observed phenomena. Obviously, the wetting regime of floating bodies plays a crucial role in their displacement, strongly affecting their apparent attraction and repelling by the magnet. Let us start from the analysis of the wetting regime depicted in Figures 3-

4(A, B) (i.e. the apparent contact angle θ which is obtuse). Physical reasons giving rise to the displacement of diamagnetic bodies in this specific case were suggested in Ref. 10, in which magnetically driven motion of hydrophobic polyolefin rafts floating on water was reported. In Ref 10, it was conjectured that the effect arises from the interplay of magnetic deformation of the water surface, gravity and contact angle hysteresis. We suggested that the permanent magnet deformed the liquid/vapor interface, as shown in Figure 1. The inclination angle was established by shadowgraph technique as ߮ ≅ 0.1଴ . This deformation spread to the surface of the floating object, where the so-called contact (or triple) line is pinned to its surface.37-39 Pinning of the triple line may be accompanied by the contact angle hysteresis28-33, 42-46; in other words the apparent interfacial contact angles (denoted as α and β in Figure

4B) along the circumference of a floating object47-49 become different, as shown in Figure 4B. This change gave rise to the attraction of the floating body to the magnet.


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This inhomogeneity in the contact angle might create net forces sufficient to displace the body. Consider magnetically inspired driving of floating bodies possessing an acute apparent contact angle θ, illustrated in Figure 2B, 5A and Figure 6. In this case, the interfacial contact angle α is decreased due to the Moses effect (as shown in Figure

5A); thus, the horizontal component of the interfacial tension at the liquid/vapor surface is diminished, and the body is repelled by the magnet. Similar physical reasoning explains repulsion of submerged bodies by a permanent magnet, as illustrated in Figure 5B. The Moses effect in different ways impacts the interfacial contact angles α at the “front” and “back” sides of the submerged raft; thus, giving rise to the non-compensated horizontal component of the surface tension γ at the water/vapor interface, repelling the raft from the magnet (the contact angle α is decreased due to the Moses effect, as shown in Figure 5B). The driving of floating magnetic bodies inspired by the Moses effect is to some extent similar to the effect of capillary interaction addressed in much detail in Refs. 50-51. Indeed, the water/vapor interface, deformed by the magnet, may be seen as a “capillary charge”, introduced in Refs. 50-51, interacting with a floating object. It should be emphasized that the nature of motion of the studied bodies was practically insensitive to exact values of their magnetic susceptibilities (see Table 1), hinting at the pure magneto-capillary nature of the entire effect. Consider that the volume magnetic susceptibilities of floating bodies have been varied within three orders of magnitude, whereas the volume magnetic susceptibilities of the underlying liquids were relatively close to each other. In this context, the experiments carried out with foamed polystyrene (FPS) are of special interest, due to the very low value of the volume magnetic susceptibilities, inherent for the FPS beads. The apparent attraction of pristine FPS, and repulsion of plasma-treated FPS beads, by the magnet constitute rather compelling evidence of the crucial role played by the Moses effect and the capillarity in the observed phenomenon.

Effect of the spatial distribution of the magnetic field on the motion of floating diamagnetic bodies We performed two series of experiments, to clarify the role of the spatial (radial) distribution of the field of the magnet B(x) in the reported phenomena. In the first series, the bare magnet was used, and in the second one, the magnet was


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surrounded by a metallic cage, described in detail in Section 2.2 and depicted in

Figure 1. The radial distribution of magnetic field produced by the bare magnet is

 x satisfactorily approximated by the exponential fitting: B(x) = B0 exp  −  , with λ =  λ 5.1 mm, and B0 = 0.4±0.005 mT (the exact expression for the radial distribution of the magnetic field is obviously more complicated,52 however the implemented exponential fitting enabled the rough estimation of the characteristic length λ. The suggested decrease law of the near magnetic field is justified by fact that the used stack of magnets has rather complicated internal structure). When the magnet was placed into the shielding cage the magnetic field outside the cage decreased by two orders of magnitude at the lateral distance of 20 mm from the magnet, where floating bodies were initially placed. We established that the character of motion of all the floating bodies was virtually unaffected by the shielding cage. This finding sheds light on the physical mechanism behind the modification of the interfacial angles, that drives floating diamagnetic bodies. Generally, two main scenarios are possible, the change is due to the direct influence of the magnetic field, occurring at the circumference of a floating body; or perhaps,the interfacial angle was changed following the deformation of the liquid/vapor interface in the vicinity of the magnet, due to the Moses effect occurring nearby (see Figure 1).26-27 The shielding, depicted in Figure 1, completely blocked the magnetic field in the vicinity of the floating bodies, yet in spite of this, they were displaced by the magnet. We necessarily conclude that the interfacial angles followed the Moses-effect-inspired deformation of the liquid surface,26-27 which took place beneath the magnet. Consider that the interrelations: L>>lca , L>λ, took place, where ݈௖௔ ≅ 2.7 mm is the so-called water capillary length (note, that the values of the capillary length are close for a diversity of liquids).29,30 It means that the initial displacement of rafts is due to the effect of contact angle hysteresis, and not due the direct capillary and magnetic interactions between the magnet and a floating raft. Note that rafts with the characteristic lateral dimensions close to lca and λ, and also those which were much larger than lca and λ have been driven by the magnetic field (see Table 1). In the present work, we demonstrated the universal nature of the effect, namely that a broad variety of diamagnetic objects (polymer and metallic rafts, and liquid marbles) may be driven by relatively weak permanent magnetic fields, when placed on organic and non-organic diamagnetic liquids (see Tables 1-2 and Figures ACS Paragon Plus Environment

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7A-C). It is noteworthy that the velocity of all the bodies attracted by the magnet increased dramatically in the course of their approach to the magnet (see Figures 7A-

C). Theoretical explanation of this effect will be addressed in the second part of our paper. The typical time dependencies of the velocity of the center mass for the polymer bodies repelled by the magnet are presented in Figure 8. One might assume that the effect of surface deformation of diamagnetic liquids by the moderate magnetic fields inherent for our study (ca 0.1T, as established at the water/vapor interface) is weak, and that consequently the displacement of floating diamagnetic bodies, is expected to be negligible. However, the experimental findings and theoretical analysis (to be presented in the next part of our manuscript) demonstrate the opposite (see Figures 7A-C and Supplementary Material).

Displacement of floating liquid marbles by the magnet. Displacement of liquid marbles by the permanent magnet, illustrated with

Figure 7B, is of particular interest from both practical and theoretical points of view. From the theoretical point of view, liquid marbles represent floating objects, for which the diamagnetic contrast between them and the liquid support is minimal (marbles absorb less than 5% of mass for their polymer coating). Thus, the displacement of liquid marbles definitely cannot be related to the variations in the magnetic susceptibility. From the practical point of view, remote displacement of the liquid marbles opens broad possibilities for micro-fluidics and bio-medical applications.53-56

The role of plasma treatment and surfactant on reversing the motion regime Both plasma treatment of polymer bodies and addition of surfactant decreased the apparent contact angles for the studied diamagnetic objects. Plasma treatment increases the specific surface energy of the organic surfaces; thus promoting their pronounced hydrophilization.57 Neither the added surfactant nor the plasma treatment influenced the bulk properties of the studied bodies; this was an additional hint to the primarily interfacial nature of the reported effects. Submerged plasma-treated spheroid-like PE pellets, and FPS bodies were also repelled by the magnet (see

Figure 9 and Supporting Information SI3).


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The role of gravity in the motion As we observed, the permanent magnet caused no displacement of thin polymer films (PP, PE, and TPX thickness 10-20 µm). This lack of effect was presumably related to the extremely small deformation of the liquid surface caused by the deposed thin film. Thus, the imbalance of the contact angles was negligible. In addition, hydrodynamic resistance presumably has been rather significant due to the large spatial extent of the film, compared to its thickness. It should be emphasized that thin polyolefin film rafts were attracted to the magnet when loaded with a plummet of 0.6 g, giving rise to the deformation of the water/vapor interface accompanied by obtuse apparent contact angles. Thus, the role of gravity (buoyancy) in the apparent attraction of floating diamagnetic bodies by a permanent magnet is not negligible, as it takes place for the “cheerios effect”.58 The quantitative analysis of the role of gravity in the displacement of floating diamagnetic bodies by static magnetic fields will be addressed in the second part of our manuscript.

Conclusions We demonstrated that the diamagnetic bodies floating on the diamagnetic liquids can be displaced by a permanent magnet with a characteristic near field of about about 0.1 T, as measured at the water/vapor interface. The effect presumably occurred due to the interplay between deformation of the liquid/vapor interface by the magnetic field, known as the “Moses effect”, buoyancy and the interfacial phenomena related to the hysteresis of the contact angle. A pronounced Moses effect commonly arises when strong magnetic fields are applied to the liquid/vapor interface. In our experiments, the magnetic field was moderate, and the deformation of the diamagnetic liquid surface was small. However, it turned out to be sufficient for the apparent attraction and repulsion of floating millimetrically-scaled bodies (polymer, metallic and ceramic diamagnetic objects and liquid marbles9,19-21) by the common permanent magnet. We can also hypothesize that the contact angle hysteresis is due to the Moses effect and the pinning of the triple (three-phase) line.37-41 The objects demonstrating obtuse apparent contact angles are attracted by the magnet; on the contrary, the bodies characterized by the acute apparent contact angles are repelled by the magnet. The attraction may be switched to repulsion by an appropriate surface treatment of the floating diamagnetic bodies, increasing their wettability. Alternately, a similar result


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was achieved by the addition of surfactant. Cold plasma treated polyolefin rafts (demonstrating submerged floating35-36) were repelled by the magnet.


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Acknowledgements Acknowledgement is made to the donors of the Israel Ministry of Absorption for the partial support of the scientific activity of Dr. Mark Frenkel. The authors are indebted to anonymous reviewers for their fruitful and useful remarks.

Supprorting Information 3 movies


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(29) Bormashenko, E. Physics of Wetting. Phenomena and Applications of Fluids on Surfaces, De Gruyter: Berlin, Germany, 2017. (30) de Gennes, P. G. Wetting: statics and dynamics. Rev. Mod. Phys. 1985, 57, 827– 863. (31) Louge, M. Y. Statistical mechanics of the triple contact line. Phys. Rev. E 2017, 95, 032804-1–032804-12. (32) Dubov, A. L.; Mourran, A.; Möller, M.; Vinogradova, O. I. Regimes of wetting transitions on superhydrophobic textures conditioned by energy of receding contact line. Appl. Phys. Lett. 2015, 106, 241601-1–241601-4. (33) Tadmor, R. Line energy, line tension and drop size. Surf. Sci. 2008, 602, L108L111. (34) Bragg, L.; Nye, J. F. A dynamical model of a crystal structure. Proc. Royal Soc. A 1947, 190, 474–481. (35) Bormashenko, Ed.; Pogreb, R.; Grynyov, R.; Bormashenko, E.; Gendelman O. Submerged (under-liquid) floating of light objects. Langmuir, 2013, 29 (34), 10700– 10704. (36) Multanen, V.; Pogreb, R.; Bormashenko, Ye.; Shulzinger, E.; Whyman, G.; Frenkel, M, Bormashenko Ed. Under-liquid self-assembly of submerged buoyant polymer particles. Langmuir, 2016, 23, 5714–5720. (37) Liu, J. L.; Mei, Y.; Xia, R. A new wetting mechanism based upon triple contact line pinning. Langmuir 2011, 27, 196–200. (38) Liu, J. L.; Xia, R.; Zhou, X. H. A new look on wetting models: continuum analysis. Sci. China: Phys., Mech. Astron. 2012, 55, 2158–2166. (39) Dubov, A. L.; Mourran, A.; Möller, M.; Vinogradova, O. I. Contact angle hysteresis on superhydrophobic stripes. J. Chem. Phys. 2014, 141, 074710-1–0747107. (40) Bormashenko, Ed. Wetting of Real Surfaces; De Gruyter: Berlin, Germany, 2013. (41) Bormashenko, E.; Musin, A.; Zinigrad, M. Evaporation of droplets on strongly and weakly pinning surfaces and dynamics of the triple line. Colloids Surf., A 2011, 385, 235–240. (42) Hejazi, B.; Nosonovsky, M. Contact angle hysteresis in multiphase systems. Colloid Polym. Sci. 2013, 291, 329–338. (43) Erbil, Y. Surface chemistry of solid and liquid interfaces; Blackwell Publishing: Oxford, 2006.


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(58) Vella, D.; Mahadevan, L. The “Cheerios effect”. Am. J. Phys. 2005, 73(9), 817825.


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Table 1. Physical properties and parameters of floating bodies. Material Density, ρ Volume Diameter Thickness kg/m3

Mass

magnetic

of rafts,

of rafts,

of rafts,

suscepti-

mm

mm

g

bility, χv ×10-6 Gold (Au)

19300

-85.96

57± 0.5

0.1± 0.01

4.98835± 0.0001

Silver(Ag)

10490

-54.69

57± 0.5

0.1± 0.01

1.8199±0.0001

840

-8.64*

50± 0.5

0.25± 0.01

1.188± 0.0001**

Teflon (PTFE)

2200

-10.28

5.6 ± 0.1

0.4 ± 0.01

0.0075± 0.0001

Polyethylene

941

-9.67

5.6 ± 0.1

0.6 ± 0.01

0.0134 ± 0.0001

8920

-21.20

5.6 ± 0.1

0.02 ±

0.0223± 0.0001

Polymethylpentene (PMP)

(HDPE) Copper (Cu)

0.01 Polypropylene

946

-9.57

5.6 ± 0.1

0.9 ± 0.01

0.0172 ± 0.0001

17

-0.15

5.6 ± 0.1

3.3 ± 0.05

0.0045 ± 0.0001

5680

-19.31

3± 0.05

(PP) Foamed Polystyrene, FPS Zirconium ceramic

0.095± 0.001

bead

(ZR) * Calculated according to Van Krevelen D., Klaas te Nijenhuis K. Properties of Polymers, 4th edition, chapter 12. ** Including the mass of a 0.6 g copper plummet.


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Table 2. Physical properties of liquids used in the investigation. Liquid

Density, ρ, kg/m

3

Surface

Viscosity, η

Volume magnetic

tension, γ,

-3

susceptibility,

×10 Pa·s

-3

χv ×10-6

×10 N/m

Water (H2O)

998.2

72.75

1.005

-9.035

Ethanol (C2H5OH)

789.3

22.27

1.2

-7.233

Diiodomethane (CH2I2)

3325

50.8

2.6

-14.52

1326.6

27.12

0.413

-9.147

948

34.4

0.92

-6.78

Dichloromethane (CH2Cl2) Dimethylformamide (C3H7NO) Dimethyl sulfoxide

1100.4

(C2H6OS)


-7.95

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Z permanent magnet shielding cage

diamagnetic body H l

Rc L

h

ϕ

diamagnetic liquid

x Figure 1. Scheme of the experimental unit is depicted.


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α

α

θ=α+π/2

liquid

A

α

α liquid

θ

B

α

α liquid C

D Figure 2. The possible wetting regimes are depicted schematically. A. The apparent contact angle θ is obtuse. B. The apparent contact angle θ is acute. C-D. Submerged floating of the cold plasma treated polyolefin rafts.


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magnet

6 mm

Figure 3. Zirconium ceramic bead (ZR), coated with Teflon powder, attracted by the permanent magnet is depicted. The deformation of the water/vapor interface by the bead is clearly seen. The apparent contact angle is obtuse.


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h

A

α

magnet

β

h

α

diamagnetic body

α

water

β

L B

Figure 4. Floating diamagnetic object is depicted (the apparent contact angle θ is obtuse); α and β are the interfacial contact angles. The green dashed line shows the water level far from the raft. The interfacial contact angle α corresponds to the zero magnetic field; the interfacial contact angle β

Toward an Understanding of Magnetic Displacement of Floating

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