Bjerknes forces are translational forces on
bubbles in a
sound
In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid.
In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' b ...
wave. The phenomenon is a type of
acoustic radiation force. ''Primary'' Bjerknes forces are caused by an external sound field; ''secondary'' Bjerknes forces are between pairs of bubbles in the same sound field. They were first described by
Vilhelm Bjerknes
Vilhelm Friman Koren Bjerknes ( , ; 14 March 1862 – 9 April 1951) was a Norwegian physicist and meteorologist who did much to found the modern practice of weather forecasting. He formulated the primitive equations that are still in use in num ...
in his 1906 ''Fields of Force''.
Theory
The force on a small particle in a sound wave is given by:
:
where V is the volume of the particle, and
P is the acoustic pressure gradient on the bubble.
Assuming a sinusoidal
travelling wave
In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from List of types of equilibrium, equilibrium) of one or more quantities. Waves can be Periodic function, periodic, in which case those quantities ...
, the time-averaged pressure gradient over a single acoustic cycle is zero, meaning a solid particle (with fixed volume) experiences no net force. However, because a bubble is compressible, the oscillating pressure field also causes its volume to change; for spherical bubbles this can be described by the
Rayleigh-Plesset equation. This means the time-averaged product of the bubble volume and the pressure gradient can be non-zero over an acoustic cycle. Unlike
acoustic radiation forces on incompressible particles, net forces can be generated in the absence of attenuation or reflection of the sound wave.
Bubbles with
resonance frequency
Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscillat ...
above the acoustic driving frequency travel up the pressure gradient, while those with a lower resonance frequency travel down the pressure gradient. In acoustic
standing waves, small bubbles accumulate at pressure
antinode
A node is a point along a standing wave where the wave has minimum amplitude. For instance, in a vibrating guitar string, the ends of the string are nodes. By changing the position of the end node through frets, the guitarist changes the effect ...
s, whereas large bubble accumulate at pressure
nodes.
[Leighton, T.G., Walton, A.J. and Pickworth, M.J.W., 1990. Primary bjerknes forces. European Journal of Physics, 11(1), p.47.]
References
Acoustics
Fluid dynamics
External links
* {{Cite journal , last=Ball , first=Philip , date=2022-06-24 , title=Manipulating Objects Using Air Bubbles and Sound Waves , url=https://physics.aps.org/articles/v15/92 , journal=Physics , language=en , volume=15