The University of Southampton
Engineering

Research project: Order to chaos and back again

Currently Active: 
Yes

Most people understand the growth of small disturbances leading to chaos, but the formation of many structures relies on establishing subsequent order out of that chaos.

Project Overview

Faraday waves on a bubble wall
Faraday waves on a bubble wall

A collaboration between Professor Leighton (University of Southampton) and Professor Maksimov (Far Eastern Branch of the Russian Academy of Sciences) explains the eventual choice of the final shapes of stars, viruses, giant gas planets, tumours, and weather patterns in the Earth’s atmosphere and oceans. They show disturbances in shape grow chaotically under the influence of external forces, but then eventually setttle down to a stable form.  The predictions are tested against experimental observations of the shapes of air bubbles in water disturbed by sound fields.

Related videos

Click here for videos of Faraday waves on bubble walls.
Click here for videos of showing increasing numbers of modes being excited on a bubble wall as the amplitude increases, leading eventually to bubble fragmentation (warning: large file).
Click here to see electrochemical signals generate by Faraday waves on the walls of rising bubbles.

The image at the top of this page is a frame from the movie listed under 'useful downloads'. It shows a stable form with icosohedral symmetry is chosen by a bubble, after small disturbances on an initially spherical bubble grow chaotically in a sound field, and then settle down to a regular structure. Below it is the modelled form: the two agree. See the 2012 paper listed below for details.

Faraday waves modelled on a bubble
Faraday waves modelled on a bubble

Curious fact  

Strangely enough, the stable set of waves that eventually occur on the bubble wall are Faraday waves, named after the great Michael Faraday (1791-1867) who first got thinking about them when he saw ripples on the surface of beer in barrels loaded onto a cart moving over cobbled streets! He recreated them by placing a tray of water on an 18 ft long plank of water than then vibrating the plank with a violin bow. Click here to see  the movie of Professor Leighton recreating this experiment.

plank experiment
Recreating Faraday's

Want to know more?

Two clicks (the first one here, then click the request button) will get you a copy of the paper:

Maksimov, A.O. and Leighton, T.G. (2012) Pattern formation on the surface of a bubble driven by an acoustic field, Proceedings of the Royal Society A, 468, 57-75

For related papers, click on the author links below:

Birkin, P.R., Offin, D.G., Vian, C.J.B., Leighton, T.G. and Maksimov, A.O. (2011) Investigation of non-inertial cavitation produced by an ultrasonic horn, Journal of the Acoustical Society of America, 130(5), 3297-3308

Maksimov, A.O., Leighton, T.G. and Birkin, P.R. (2008) Self focusing of acoustically excited Faraday ripples on a bubble wall, Physics Letters A, 372(18), 3210-3216

Maksimov, A., Winkels, K., Birkin, P.R. and Leighton, T.G. (2008) Hopf bifurcation in acoustically excited Faraday ripples on a bubble wall, Nonlinear Acoustics: Fundamentals and Applications Proceedings of the 18th International Symposium on Nonlinear Acoustics, Stockholm, Sweden, 7-10 July, 229-232

Maksimov, A.V., Leighton, T.G. and Birkin, P.R. (2006) Dynamics of a tethered bubble, Proceedings of 17th International Symposium on Nonlinear Acoustics, Pennsylvania, USA, 4pp

Maksimov, A.O., Leighton, T.G. and Birkin, P.R. (2005) Dynamics of a tethered bubble, Innovations in Nonlinear Acoustics: ISNA 17; 17th International Symposium on Nonlinear Acoustics including the International Sonic Boom Forum, State College, Pennsylvania, 18-22 July 2005, 512-15

Leighton, T.G. (2004) From seas to surgeries, from babbling brooks to baby scans: The acoustics of gas bubbles in liquids, Invited Review Article for International Journal of Modern Physics B, 18(25), 3267-314

Maksimov, A.O. and Leighton, T.G. (2001) Transient processes near the threshold of acoustically driven bubble shape oscillations, Acta Acustica, 87(3), 322-32

 

For more information on bubble acoustics click here.

Related research groups

Acoustics Group

Publications

Articles

Book Chapter

  • Maksimov, A., Sosedko, E. V., & Leighton, T. G. (2002). Nonlinear transient bubble oscillations. In Abstracts of the 16th International Symposium on Nonlinear Acoustics, Moscow, Russia, 19-23 August 2002 (pp. 102-103). Moscow, Russia: International Symposium on Nonlinear Acoustics.

Conferences

Staff

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