J. Phys. Chem. C 2007, 111, 14389-14393
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Effects of High Magnetic Field on Water Surface Phenomena Manabu Sueda,† Akio Katsuki,*,‡ Makiko Nonomura,† Ryo Kobayashi,† and Yoshifumi Tanimoto*,† Graduate School of Science, Hiroshima UniVersity, Higashi-Hiroshima 739-8526, Japan, and School of General Education, Shinshu UniVersity, Matsumoto 390-8621, Japan ReceiVed: April 6, 2007; In Final Form: July 18, 2007
We studied the magnetic field effect on surface phenomena of water with a vertical magnetic field (maximum fields: 15 T, 1500 T 2/m). The maximum diameter and mass of a pendant water droplet on the tip of a glass capillary are affected remarkably with response to the magnetic force and its direction. The height of a water droplet on a poly(vinylidene chloride) film is also affected by the field. A water thin film and a water bubble can be produced at a microgravity condition simulated by a high magnetic field, even though they cannot be prepared under earth surface gravity. All the results are interpreted in terms of the magnetic force acting on water: the force can control the effective gravitational acceleration. The results also indicate that surface tension can play an important role in a microgravity condition simulated by a high magnetic field.
1. Introduction Recently, astronaut Don Pettit performed unique experiments between his missions in the International Space Station:1 Under microgravity, with surfactant-free water, he made a large thin water film (φ ) ca. 53 mm) and a large water bubble (ca. φ ) 100 mm). Their preparations, if possible at all, are very difficult to achieve on the earth because these phenomena are controlled by the competing influences of gravitational energy and surface energy.1 The results of those experiments indicate that water shape is controlled by its surface tension in a microgravity condition. In 1991, Beaugnon and Tournier demonstrated for the first time that even diamagnetic materials such as water and plastics can be levitated magnetically using a vertical magnetic field.2 A uniform material can be regarded as placed under simulated microgravity if it is levitated by a uniform magnetic force. Therefore, magnetic fields are an application that can simulate microgravity on the earth. Since 1991, a few reports have described magnetic levitation,3-6 simulated microgravity,7 and related phenomena.8-13 However, little attention has been given to magnetic field effects (MFEs) on surface phenomena, despite the possibility of explaining MFEs on a chemical reaction at a surface or an interface in some other way. This paper describes results of our studies of MFEs on surface phenomena of water using a vertical superconducting magnet (15 T, 1500 T 2/m).14 Those results elucidate magnetic field influences on the phenomena and clarify their mechanisms. The MFEs on the shape and mass of a pendant water droplet, and MFEs on the height and shape of a water droplet on a substrate, are examined. Results show that a magnetic field remarkably affects the effective gravitational acceleration. Furthermore, we prepare a large water film and a bubble without surfactant under a magnetically simulated microgravity. To the best of our knowledge, they are the first such demonstrations. The MFEs can be explained mainly in terms of the magnetic force acting * To whom correspondence should be addressed. E-mail: tanimoto@ sci.hiroshima-u.ac.jp;
[email protected]. † Hiroshima University. ‡ Shinshu University.
on water. Effective gravitational change attributable to the magnetic force causes changes in the water surface phenomena. Magnetic fields are convenient tools to simulate microgravity in an earth-bound laboratory. 2. Experimental Section Magnetic fields were applied using a vertical superconducting magnet (maximum fields, 15 T and 1500 T 2/m; JMTDLH15T40; JASTEC). The inner diameter of the vertical roomtemperature bore tube was 40 mm. Distributions of the magnetic flux density and the product of magnetic flux density and its spatial gradient, which is called hereafter the magnetic force field for simplicity, in the tube are depicted schematically in Figure 1(a). The magnetic field and the magnetic force field were varied by changing the vertical position at which experiments were performed in the tube. Therefore, the magnetic field and the magnetic force used in this experiment were inhomogeneous. For example, the spatial homogeneity of the magnetic force field at z ) 346 mm from bottom, where the upward magnetic force to a diamagnetic material is maximum, is about 98% in a 5 mm sphere at most. All experiments were performed at room temperature (ca. 293 K). 2.1. MFE on a Dripping Water Droplet. Aerated distilled water (Wako Pure Chemical Industries, Ltd.) was used as received. Oxygen dissolved in aerated water did not significantly affect the results reported below, since its concentration was as low as 2.7 × 10-4 mol/dm3.15 The MFE on a pendant water droplet was studied using the experimental setup shown in Figure 1(b). Water droplets were made on the tip of a Pyrex glass capillary (outer diameter, 8.3 mm; inner diameter, 0.3 mm), which was cleaned by a neutral detergent solution, for surface tension measurements; it is known as the pendant drop method. Water was supplied to the tip with a flow rate of 0.5 g/min using a peristaltic pump. This flow rate was chosen so that a pendant water droplet fell without the influence of the flow rate at zero field. The droplets’ respective shapes were observed from the side and recorded on digital video with a bore scope (R100095-090-50; Olympus Optical Co. Ltd.)-CCD camera (OH411; Olympus Optical Co. Ltd.)-video recorder (GV-D1000;
10.1021/jp072713a CCC: $37.00 © 2007 American Chemical Society Published on Web 09/12/2007
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Figure 1. (a) Magnetic field intensity distributions in the bore of the magnet (JMTD-LH15T40). (b) Experimental setup for measurements of MFE on a pendant water droplet.
Sony Corp.). Droplets that had fallen down from the tip were collected, and the mass was measured using a conventional microbalance. 2.2. MFE on a Water Droplet on Poly(vinylidene chloride) Film. A poly(vinylidene chloride) (PVDC) thin film (Asahi Kasei, Saran Wrap) was cleaned with a neutral detergent solution before use. The shape of a semispherical water droplet on the film was observed and recorded on digital video similarly from the side, and the droplet height was calculated from the video images. 2.3. Preparation of a Water Thin Film and a Water Bubble in Magnetic Field. 2.3.1. Water Thin Film. A tin-coated copper ring (φ ) 25 mm) was made from a tin-coated copper wire (φ ) 1 mm). A water thin film was prepared by scooping up small amount of water from a magnetically levitated water sphere (φ ) ca. 20 mm) with the ring. The film on the ring was observed from the top, the direction along the magnet bore, using a bore scope-CCD camera-video recorder. No water thin film could be prepared on the ring under earth surface gravity in a zero field. 2.3.2. Water Bubble. A water bubble was prepared by an air injection into a water droplet on a tip of a Pasteur pipet (φ ) 1.6 mm; Fisher Scientific International) in a simulated microgravity with a similar setup shown in Figure 1(b). A water bubble was observed and recorded from the side similarly to the method described in 2.1. No bubble could be prepared under earth surface gravity in a zero field. 3. Results and Discussion 3.1. MFE on a Pendant Water Droplet. Figure 2 shows sequential photographs of a pendant water droplet on the tip. At zero field (0 T and 0 T 2/m), the maximum diameter of a droplet, i.e., the droplet immediately before leaving down from the tip, is about 6.5 mm and the drop rate is 3-4 droplets per
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Figure 2. Sequential photographs of pendant water droplet at various magnetic fields: (a) 0 T, ca. 0 T 2/m outside of the bore; (b) 11.5 T, +1230 T 2/m under a simulated hypergravity of 1.8 G. See text; (c) 9.9 T, -1500 T 2/m at a simulated microgravity of ca. 0 G; (d) 15 T, ca. 0 T 2/m. The time at the upper right corner of each photograph is the time at the start of a water flow. The double arrow indicates ca. 5 mm in the photograph.
minute (Figure 2(a)). At 11.5 T and +1230 T 2/m, the droplet diameter is about 5.2 mm, which is about 80% of that in a zero field. The rate is about 8-9 droplets per minute (Figure 2(b)). At 9.9 T and -1500 T 2/m, the maximum diameter of a droplet is about 11.5 mm, which is about 1.8 times that in a zero field; the drop rate is about 0.5-0.6 droplets per minute (Figure 2(c)). For purposes of comparison, the size and droplet rate are also examined at 15 T and ca. 0 T 2/m. Under this condition, the size and drop rate of a pendant droplet are about 6.3 mm and 4-5 droplets per minute, which are similar to those in a zero field (Figure 2(d)). The size and the drop rate of a water droplet are apparently affected strongly not by the magnetic flux density but by the magnetic force field. The mass magnetic susceptibility of water is -7.20 × 10-3 J T-2/kg.16 It is a diamagnetic material, so the upward magnetic force on water is equivalent, but opposite, to that of gravity at -1360 T 2/m. This is considered to be a simulated microgravity condition (0 G). At +1230 T 2/ m, the downward magnetic force operates in addition to that of gravity, so water is under a simulated hypergravity of about 1.8 G. Measurements of the droplet mass are suitable to examine the magnetic force field dependence of the droplet in detail because fluctuation in mass of water can be small compared to fluctuation in the drop rate. Figure 3 shows the magnetic force field dependence of the water droplet mass. At 0 T 2/m, no magnetic force field acts on water droplets; the earth gravity at sea level is 1 G. With a decreasing magnetic force field from 0 T 2/m, the mass increases dramatically; at -1500 T 2/m it becomes six times greater than that at 0 T 2/m. In stark contrast to that observation, with increasing magnetic force from 0 T 2/ m, the mass decreases gradually. At +1200 T 2/m it is about 55% of the value at 0 T 2/m. The experimental setup shown in Figure 1(b) resembles the setup for measuring surface tension of liquids: the pendant drop
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Figure 3. Dependence of a droplet mass on B∂B/∂z. The mass is an average of 10 droplets.
method. In a zero field, when a droplet just leaves the tip, the downward force on the droplet, mg, is equal to the upward force, 2πrγ, m, g, r, and γ being the mass of a droplet, the gravitational acceleration of earth, the outer radius of the capillary, and the surface tension of a liquid:17
2πrγ ) mgf
Figure 4. Plots of reciprocals of a water droplet mass 1/m vs g′, where g′ is the effective gravitational acceleration acting on the water droplet. See text.
(1)
where f is the empirical correction factor related to the droplet volume and the capillary outer radius.18 Therefore, from eq 1, the results described above suggest that water droplets’ weight can be controlled by the magnetic force to act on the droplets. To understand the magnetic force effect on water droplets, the additional force to act on a water droplet must be taken into account. In a magnetic field, magnetic force, Fmag, acts on the droplet,19 as
Fmag )
1 ∂B mχ B µ0 m ∂z
(2)
where χm is the mass magnetic susceptibility of a droplet, µ0 is the magnetic permeability of vacuum, B is the magnetic flux density, and ∂B/∂z is the gradient of B at position z, z being taken upward. Therefore, g in eq 1 is replaced by an effective gravitational acceleration, g′ because an upward or downward magnetic force acts on the droplet in a magnetic field.
g′ ) g +
∂B 1 χ B µ0 m ∂z
(3)
Then, the relationship between g′ and m is given as the following equation.
1/m ) g′f/(2πrγ)
(4)
If γ is assumed as magnetic-field independent, 1/m will be proportional to g′ because f is approximately constant in the present experimental condition and is magnetic-field independent. Figure 4 shows plots of 1/m vs g′. As expected, a good linear relation is apparent between 1/m and g′. Taking f ) 1.6,18 γ is obtained to be about 9.0 × 10-4 N/cm from the slope, which is qualitatively in agreement of the reported value (7.3 × 10-4 N/cm at 293 K).16 According to eq 4, m is expected to be infinite at g′ ≈ 0 G, though experimentally it is about 6 times larger than that at g′ ≈ 1 G. This discrepancy happens mainly because the space for g′ ≈ 0 G condition is small (approximately, a 5 mm sphere) compared to the water droplet size due to spatial inhomogeneity of the force field (Figure 1(a)). Therefore, the water droplet mass is controlled mainly by a magnetic force field; the magnetic force can control the gravitational acceleration affecting the water droplet.
Figure 5. Photographs of a water droplet (102 mg) on PVDC film at various positions in the magnet: (a) 10.3T, -1380 T 2/m, (b) 14.7T, ∼0T 2/m; (c) 11.0T, +1120 T 2/m.
3.2. MFE on a Water Droplet on a Poly(vinylidene chloride) Film. The MFE on the shape of a water droplet on a PVDC thin film is also studied. Figure 5 shows photographs of a water droplet (102 mg) on the film at various magnetic fields. Compared to the height at 0 T 2/m, the droplet height increases in the negative magnetic force fields, whereas it decreases in the positive force fields. Figure 6 shows magnetic field dependence of the height of 102 and 86 mg droplets. The height changes are +8 to +10% at -1000 T 2/m and -2 to -9% at +1000 T 2/m. Similar MFE is also observed for a water droplet on polystyrene and poly(ethylene terephthalate) plates. A model of motion and evaporation of a droplet of a solute with precipitation has been reported.20 According to the model, the transport equation of an incompressible solution under the lubrication approximation to a viscous-liquid flow is written as
∂h/∂t ) (1/3η) ∇‚{h3∇(δF/δh)}
(5)
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Figure 6. Droplet height changes induced by magnetic force field, B∂B/∂z. h(B∂B/∂z) and h(0) are the height in the presence and absence of the magnetic force field. [ and 9 are the ratio for 102 and 86 mg droplet, respectively. A broken line is the ratio obtained by simulation. See text.
Figure 7. A photograph of a water thin film on a tin-coated copper ring (φ ) ca. 25 mm) prepared under simulated microgravity. Light reflecting glitter in the film is indicated by an arrow. The film cannot be prepared under earth surface gravity.
where h is the droplet height, t is the time, η is the viscosity of liquid, ∇ is the nabla operator with respect to r ) (x, y), and F[h] is a free energy functional. By taking the surface energy, the gravity, and the magnetic energy into account, we set the form of F[h] to be
F[h] )
∫ dr [γl {(1 + (∇h)2)1/2 - cos θ}χ(h) + (Fg′/2)h2]
(6)
where F is the liquid density, g′ is the effective gravitational acceleration, γl is the surface energy of a liquid at the liquid/ vapor interface, and θ is the contact angle of liquid. The function χ(h) is set to one at the wet region and zero at the dry region. Simulations are carried out for the equation obtained by substituting eq 6 into eq 5 with polar coordinates. In the simulation, χ(h) is approximated by the function
χδ(h) ) tanh (h/δ) )0 he0
h>0 (7)
where δ is a small positive number and fixed to the value δ ) 0.05. Parameters, γl ) 72.75 × 10-3 kg s-2 and θ ) 80°,16 are used in simulation. The equilibrium droplet height is obtained after a sufficiently long evolution. As shown in Figure 6, the height changes of a droplet due to the magnetic force are estimated to be about 17% at -1000 T 2/m and about -12% at +1000 T 2/m. The observed height change is parallel to the theoretical estimation, though the experimental data points are deviated slightly from the simulated line. This might be partly due to contamination of the film and partly due to inhomogeneity of the force field. Thus the MFE on a water droplet height is qualitatively interpreted in terms of the magnetic force. 3.3. Preparation of a Water Thin Film and a Water Bubble in Magnetic Field. As described in the preceding sections, the shape of water is sensitively affected by a magnetic force field. It is greatest under the simulated microgravity condition, in which the effective gravitational acceleration is nearly 0 G. Consequently, based on these results, it is inferred to be possible to make a water thin film and a bubble without surfactants under simulated microgravity in the magnet, similarly to the space laboratory experiments mentioned in the Introduction. 3.3.1. Water Thin Film. First, a water thin film is prepared using a tin-coated copper ring of ca. 25 mm diameter. At this diameter, it is impossible to prepare a water thin film under
Figure 8. Sequential photographs of a water bubble preparation under simulated microgravity. The bubble is indicated by an arrow. Water bubbles cannot be prepared under earth surface gravity. (a) Before preparation, the capillary tip. (b) A water droplet pending on the tip. (c) After injection of a little air. (d) After further air injection. (e) After more air injection; the bubble is almost maximum in size. (f) After too much air injection; the broken bubble immediately after bursting.
earth surface gravity in a zero field. Figure 7 shows a photograph of a water thin film prepared under simulated microgravity conditions in the magnet bore. The film’s formation can be recognized from the light-reflecting glitter inside of the ring. This film is sufficiently stable against shaking of the ring. It is stable even when it is moved a few centimeters upward in the bore. The film thickness is smaller than the diameter of the wire (φ ) 1 mm), though it cannot be measured because of a small bore diameter (φ ) 40 mm). An analogous thin water film is also prepared using a copper ring. 3.3.2. Water Bubble. Second, a water bubble is prepared by injecting air into a small pendant water droplet on the tip of a glass capillary under nearly simulated microgravity in the bore. Figure 8 shows sequential photographs of water bubble preparation. A water droplet is prepared on a tip of a Pasteur pipet (a, b). By injecting air into a water droplet, a water bubble is generated and inflated (c-e). Finally it is disrupted (f). The maximum bubble diameter is about 15 mm. As described briefly above, formations of a water thin film and a bubble strongly suggest that high magnetic fields can simulate microgravity sufficiently as a substitute of space
Effects of High Magnetic Field on Water Surface microgravity, though homogeneity of the magnetically simulated microgravity generated is about 98% in a 5 mm sphere at most, and, therefore, its quality is currently not as good as those in the space laboratory and its volume is very small. The advantage of magnetically simulated microgravity is the duration for producing the microgravity condition. A superconducting magnet can provide a simulated microgravity condition of over 1 month’s duration, whereas other simulated microgravity generation techniques on the earth, for example, a freefalling container or a free-falling airplane, can only provide less than a 1 min duration. Therefore, the magnetically simulated microgravity is very useful in many cases. It must be mentioned that in a high magnetic field, some additional MEFs attributable to other mechanisms19 might intervene because of the high field. Therefore, magnetically simulated microgravity might not always be useful for simulation of microgravity. In a preliminary work,21 we reported the MFE on the photocatalytic reaction of TiO2 particles suspended in a solution in vertical magnetic fields. The yield of hydrogen gas production from the particles changed by application of high magnetic fields (10-15 T), though its mechanism was unraveled. In such a reaction, there is a possibility that the effective gravitational acceleration change induced by a magnetic force will affect somewhat its reaction rate and chemical yield, since a contact pressure at an interface or a surface will be affected by the change. 4. Conclusion The MFEs on surface phenomena of water were studied using vertical magnetic fields (maximum field: 15 T, 1500 T 2/m). The maximum mass and diameter of a dripped water droplet on the tip of a glass capillary are affected strongly by magnetic fields. The height of a water droplet on a PVDC film is also affected by the fields. These results, which show that water droplet shape is affected dramatically, are interpreted mainly in terms of magnetic force acting on the droplet. The effective gravitational acceleration, which is the sum of gravitational acceleration and the magnetic force field, changes greatly according to the intensity and direction of magnetic force field. A thin water film and water bubble were prepared in this study, to the best of our knowledge, for the first time with a
J. Phys. Chem. C, Vol. 111, No. 39, 2007 14393 simulated microgravity generated by a magnetic field, even though they cannot be prepared without the field. This technique might be applicable to produce films without a substrate or might be applicable to new material synthesis. Acknowledgment. The work was supported in part by a Grant-in-Aid for Scientific Research on Priority Area ‘Innovative utilization of strong magnetic fields’ (Area 767, No. 15085208) from MEXT and a Grant-in-Aid for Scientific Research (B), 16350007, 2004 from JSPS of Japan. References and Notes (1) Pettit, D. Saturday Morning Science Videos, February 25, 2003, http://science.nasa.gov/headlines/y2003/25feb_nosoap.htm. (2) Beaugnon, E.; Tournier, R. Nature 1991, 349, 470. (3) Berry, M. V.; Geim, A. K. Eur. J. Phys. 1997, 18, 307. (4) Brooks, J. S.; Cothern, J. A. Phys. B (Amsterdam, Neth) 2001, 294295, 721. (5) Motokawa, M.; Watanabe, K.; Awaji, S. Curr. Appl. Phys. 2003, 3, 367. (6) Tanimoto, Y.; Fujiwara, M.; Sueda, M.; Inoue, K.; Akita, M. Jpn. J. Appl. Phys. 2005, 44, 6801. (7) Yin, D. C.; Wakayama, N. I.; Harata, K.; Fujiwara, M.; Kiyoshi, T.; Wada, H.; Niimura, N.; Arai, S.; Huang, H. D.; Tanimoto, Y. J. Cryst. Growth 2004, 270, 184. (8) Mogi, I.; Umeki, C.; Takahashi, K.; Awaji, S.; Watanabe, K.; Motokawa, M. Jpn. J. Appl. Phys. 2003, 42, L715. (9) Kitamura, N.; Makihara, M.; Hamai, M.; Sato, T.; Mogi, I.; Awaji, S.; Watanabe, K.; Motokawa, M. Jpn. J. Appl. Phys. 2000, 39, L324. (10) Weilert, M. A.; Whitaker, D. L.; Maris, H. J.; Seidel, G. M. Phys. ReV. Lett. 1996, 77, 4840. (11) Duan, W.; Fujiwara, M.; Tanimoto, Y. Jpn. J. Appl. Phys. 2004, 43, 8213. (12) Koyama, F.; Tanimoto, Y. Mol. Phys. 2006, 104, 1703. (13) Tanimoto, Y.; Sueda, K.; Irie, M. Bull. Chem. Soc. Jpn. 2007, 80, 491. (14) Preliminary results have appeared: Katsuki, A.; Kaji, K.; Sueda, M.; Tanimoto, Y. Chem. Lett. 2007, 36, 306. (15) Murov, S. L.; Carmichael, I.; Hug, G. L. Handbook of Photochemistry; Marcel Dekker: New York, 1993; p 293. (16) Chemical Society of Japan, Ed. Kagakubinran; Maruzen: Tokyo, 1966; p 529, p 542, p 1080. (17) Chihara, H., Ed. Buturikagakujikkenhou; Tokyokagakudojin: Tokyo, 1988; p 205. (18) Harkins, W. D.; Brown, F. E. J. Am. Chem. Soc. 1919, 41, 499. (19) Yamaguchi, M.; Tanimoto, Y. Eds. Magneto-Science; Kodansha/ Springer: Tokyo, 2006. (20) Nonomura, M.; Kobayashi, R.; Nishimura, Y.; Shimomura, M. J. Phys. Soc. Jpn. 2003, 72, 2468. (21) Wakasa, N.; Tanimoto, Y. Syokubai 2004, 46, 224.
