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Levitation

March 27, 2017

Nearly everyone has heard the joke about the problem faced by the inventor of a universal solvent - He didn't have a bottle in which to keep it. Scientists have a similar problem when a container's materials can contaminate their sample, or when they need to heat a metal to a temperature higher than what a crucible can withstand. The solution is not to use a container at all, but to levitate the specimen.

Utopien 04 by Efthymios (Makis) Warlamis (1942-2016)Utopien 04, a painting by Efthymios (Makis) Warlamis (1942-2016).

Utopias are often depicted as levitated. The Star Trek episode, The Cloud Minders, has a floating Utopian city.

(Wikimedia Commons image.)

My first experience with levitation was very early in my career when I was part of a team doing experiments with an alloy of hafnium with vanadium, HfV2, a superconductor at 9.57 K that also absorbs hydrogen.[1] Hafnium, which is most commonly used as an additive to nickel alloys to promote protection from oxidation, has a very high melting point, 2,233 °C.

Vanadium likewise has a high melting point, 1500 °C, and hafnium is a very reactive metal. This leads to the problem of how to melt vanadium, alloy it with hafnium in a process that evolves quite a bit of heat, while not destroying the crucible or contaminating the alloy.

The solution was to levitate and heat the metals in a vacuum using a high power induction coil, as shown in the figure. Radio frequency currents in an induction coil induce eddy currents in metals contained within, and these currents heat the metals. Induction heating is a common industrial technique used to case harden items such as automobile crankshafts. The coils are formed from copper tubing so that they can be water cooled to not melt from radiant heat.
A levitation coilA levitation coil, commonly made from water-cooled copper tubing.

The arrows show the direction of an instantaneous current.

A nice example of levitation heating can be seen in this YouTube video.

(Created using Inkscape.)
The currents induced by the coil in the metals levitate them while also heating. The top coil turn is wound in an opposite direction to prevent the specimen from flying out of the coil. The conical shape concentrates the currents at the bottom to stabilize levitation, and the shape can hold the metal pieces before levitation. After solving the problem of tuning our particular coil to the frequency of the RF generator with some high voltage capacitors, we were able to levitate specimens of several tens of grams.

This method uses magnetism as the levitating force, since the induced currents produce a magnetic field in the specimen that opposes the magnetic field of the currents in the coil. Another magnetic effect, direct diamagnetic levitation, relies on the diamagnetism of many materials, including water, that opposes a magnetic field. Nobel Laureate, Andre Giem, and physicist, Michael Berry, famously levitated a frog in a 20 tesla magnetic field.[2]

Fig. 1 of US Patent No. 7,348,691, 'Magnetic levitation apparatus,' by Harold Davis and Lorne Whitehead, March 25, 2008It's all done with mirrors magnets.

(Fig. 1 of US Patent No. 7,348,691, "Magnetic levitation apparatus," by Harold Davis and Lorne Whitehead, March 25, 2008, via Google Patents[3].)

Winds generate considerable force, so it's not surprising that objects can be levitated by airflow. Vertical wind tunnels have been created as "indoor skydiving" simulators that levitate humans. A cute television commercial, found on YouTube, illustrates such a simulator. It's easy to levitate a light ball in an upwards airstream, and the ball remains in a stable position, since the Bernoulli effect will drag the ball back to center if it wanders away. Since sound is a pressure wave, sound can be used to levitate, also, as a 2016 demonstration of levitating a 50 mm diameter hollow polystyrene ball by 25 kHz ultrasonic transducers has shown.[4]

Most children have been taught the principle that "warm air rises, and cold air sinks," a short-form statement of convection. Convection allows movement of air without using a fan, all you need is a hot plate, so levitation is possible in that manner. Obviously, you need a lot of air for such levitation; or, do you? As a research team led by a pair of undergraduate students from the Department of Physics, The University of Chicago (Chicago, Illinois), has shown, it's possible to levitate lightweight objects in between a warm and cold plate in a partial vacuum.[5-6] The students are 3rd year Frankie Fung and 4th year Mykhaylo Usatyuk.[6]

This levitation is termed thermophoresis, and it's a phenomenon first observed in gas mixtures in 1870 by John Tyndall (1820-1893). It depends on the different response to a temperature gradient of different components in a mixture, and the mixture can be an aerosol of fine particles in a gas. In a 2009 study, dust aggregates of micrometer-sized particles were levitated over a hot plate as aggregates from 100 μm to 1 cm in size.[7] It was found that levitation occurred at pressures from 1-40 millibar when the temperature exceeded 400 K.[7] The advance made by the Chicago team is to transcend the simple case of levitation of small particles and their aggregates to stable levitation of larger objects for periods up to an hour.[6]

Thermophoretic levitation vacuum chamberThermophoretic levitation vacuum chamber.

Levitation is between an upper cold plate and a lower warm plate.

(University of Chicago image by Jean Lachat.)

In the Chicago experiments, the air pressure was 1-10 torr, and the size of the levitated particles were between 10 μm and 1 mm.[5] The bottom plate, made of copper, was kept at room temperature (about 300 K) while a stainless steel cylinder filled with liquid nitrogen served as the top plate with a constant temperature of 77 K.[6] The particles could be suspended indefinitely with a proper plate geometry that included an ideal ratio of the plate sizes, spacing, and parallel alignment.[6] A misalignment of just a degree severely reduced the levitation stability.[6] Says Cheng Chin, professor and leader of the ultracold atomic and molecular physics group at the University of Chicago,

"Only within a narrow range of pressure, temperature gradient and plate geometric factors can we reach stable and long levitation... Different particles also require fine adjustment of the parameters."[6]

The levitated particles were stable both radially and vertically, radial stability achieved by the increasing temperature field, and vertical stability achieved by the transition to hydrodynamic behavior as the particles ascend.[5] The research team levitated polyethylene spheres under various conditions to examine the limits of the levitation process.[5] While magnetic levitation will only work if the particles are magnetic, and optical levitation requires that objects can be polarized by light, the thermophoretic levitation will work on any material.[6]

Thermophoretic levitation of lintThermophoretic levitation of lint.

(University of Chicago/Chin Lab video.)

This levitation mechanism will be especially useful in a microgravity environment, where larger particles can be manipulated.[6] The research team speculates that the process could facilitate assembly of small micro-electro-mechanical (MEMS) devices.[6] Chin's laboratory is pursuing levitation of objects larger than a centimeter in size.[6] Funding for this research was provided by the National Science Foundation, the Grainger Foundation and the Enrico Fermi Institute.[6]

References:

  1. P. Duffer, D.M. Gualtieri, and V.U.S. Rao, "Pronounced Isotope Effect in the Superconductivity of HfV2 Containing Hydrogen (Deuterium)," Phys. Rev. Lett., vol. 37, no. 21 (November 22, 1976), pp. 1410-1413.
  2. Andrey Geim, "Everyone's Magnetism," Physics Today, vol. 51, no. 9 (September, 1998), pp. 36-39, doi: http://dx.doi.org/10.1063/1.882437. A PDF file can be found here.
  3. Harold Davis and Lorne Whitehead, "Magnetic levitation apparatus," US Patent No. 7,348,691, March 25, 2008 (Google Patents).
  4. Marco A. B. Andrade, Anne L. Bernassau, and Julio C. Adamowski, "Acoustic levitation of a large solid sphere," Appl. Phys. Lett., vol. 109, no, 4 (July 25, 2016), Article No. 044101,doi: http://dx.doi.org/10.1063/1.4959862 .
  5. Frankie Fung, Mykhaylo Usatyuk, B. J. DeSalvo, and Cheng Chin, "Stable thermophoretic trapping of generic particles at low pressures," Applied Physics Letters, vol. 110, no. 3 (January 16, 2017), Article No. 034102, doi: http://dx.doi.org/10.1063/1.4974489.
  6. Greg Borzo, "New method uses heat flow to levitate variety of objects," University of Chicago Press Release, February 14, 2017.
  7. Thorben Kelling and Gerhard Wurm, "Self-Sustained Levitation of Dust Aggregate Ensembles by Temperature-Gradient-Induced Overpressures," Phys. Rev. Lett., vol. 103, no. 21 (November 20, 2009), Article No. 215502, https://doi.org/10.1103/PhysRevLett.103.215502.

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