Faraday waves, also known as Faraday ripples, named after

Michael Faraday Michael Faraday (; 22 September 1791 – 25 August 1867) was an English chemist and physicist who contributed to the study of electrochemistry and electromagnetism. His main discoveries include the principles underlying electromagnetic inducti ...

(1791–1867), are

nonlinear In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathe ...

standing wave In physics, a standing wave, also known as a stationary wave, is a wave that oscillates in time but whose peak amplitude profile does not move in space. The peak amplitude of the wave oscillations at any point in space is constant with respect t ...

s that appear on liquids enclosed by a vibrating receptacle. When the vibration frequency exceeds a critical value, the flat hydrostatic surface becomes unstable. This is known as the Faraday

instability In dynamical systems instability means that some of the outputs or internal states increase with time, without bounds. Not all systems that are not stable are unstable; systems can also be marginally stable or exhibit limit cycle behavior. ...

. Faraday first described them in an appendix to an article in the ''

Philosophical Transactions ''Philosophical Transactions of the Royal Society'' is a scientific journal published by the Royal Society. In its earliest days, it was a private venture of the Royal Society's secretary. It was established in 1665, making it the second journ ...

'' of the

Royal Society of London The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, r ...

in 1831. If a layer of liquid is placed on top of a vertically oscillating piston, a pattern of

s appears which oscillates at half the driving frequency, given certain criteria of

. This relates to the problem of parametric resonance. The waves can take the form of stripes, close-packed

hexagon In geometry, a hexagon (from Greek , , meaning "six", and , , meaning "corner, angle") is a six-sided polygon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°. Regular hexagon A regular hexagon is de ...

s, or even

squares In geometry, a square is a regular polygon, regular quadrilateral. It has four straight sides of equal length and four equal angles. Squares are special cases of rectangles, which have four equal angles, and of rhombuses, which have four equal si ...

or quasiperiodic patterns. Faraday waves are commonly observed as fine stripes on the surface of wine in a

wine glass A wine glass is a type of Glass (drinkware), glass that is used for drinking or wine tasting, tasting wine. Most wine glasses are stemware (goblets), composed of three parts: the bowl, stem, and foot. There are a wide variety of slightly differe ...

that is ringing like a bell. Faraday waves also explain the 'fountain' phenomenon on a

singing bowl A standing bell or resting bell is an inverted bell, supported from below with the rim uppermost. Such bells are normally bowl-shaped, and exist in a wide range of sizes, from a few centimetres to a metre in diameter. They are often played by st ...

. The Faraday wave and its

wavelength In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...

is analogous to the de Broglie wave with the de Broglie wavelength in

de Broglie–Bohm theory The de Broglie–Bohm theory is an interpretation of quantum mechanics which postulates that, in addition to the wavefunction, an actual configuration of particles exists, even when unobserved. The evolution over time of the configuration of all ...

in the field of

quantum mechanics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...

Application

Assembly of microscale beads on Faraday waves

Faraday waves are used as a liquid-based template for directed assembly of microscale materials including

soft matter Soft matter or soft condensed matter is a type of matter that can be deformed or structurally altered by thermal or mechanical stress which is of similar magnitude to thermal fluctuations. The science of soft matter is a subfield of condensed ...

, rigid bodies, biological entities (''e.g.'', individual cells, cell spheroids and cell-seeded microcarrier beads).P. Chen, Z. Luo, S. Guven, S. Tasoglu, A. Weng, A. V. Ganesan, U. Demirci, Advanced Materials 2014, 10.1002/adma.201402079. http://onlinelibrary.wiley.com/doi/10.1002/adma.201402079/abstract Unlike solid-based template, this liquid-based template can be dynamically changed by tuning vibrational frequency and acceleration and generate diverse sets of symmetrical and periodic patterns. This phenomenon is also used by alligators to call mates. They vibrate their lungs at low frequencies slightly below the surface, causing their spikes to move and induce surface waves. These surface waves are basically Faraday waves and one can observe the splashing effect characteristic of certain resonances. This effect can also be used for mixing two liquids acoustically. Faraday waves form on the interface between the two liquids, which increases the surface area between the two, rapidly and thoroughly mixing the liquids.

References

External links

YouTube video of Faraday waves in corn starch.

YouTube video Yves Couder Explains Wave/Particle Duality via Silicon Droplets

YouTube video of Singing Bowl creating Fountain
{{Use dmy dates, date=May 2020 Wave mechanics Fluid dynamics Michael Faraday

Application

See also

References

External links