Acoustic radiation force (ARF) is a physical phenomenon resulting from the interaction of an
acoustic wave with an obstacle placed along its path. Generally, the force exerted on the obstacle is evaluated by integrating the
acoustic radiation pressure (due to the presence of the sonic wave) over its time-varying surface.
The magnitude of the force exerted by an acoustic plane wave at any given location can be calculated as:
where
is a force per unit volume, here expressed in kg/(s2cm2);
The effect of
frequency on acoustic radiation force is taken into account via intensity (higher pressures are more difficult to attain at higher frequencies) and absorption (higher frequencies have a higher absorption rate). As a reference, water has an acoustic absorption of 0.002
dB/(MHz2cm).[3](page number?) Acoustic radiation forces on compressible particles such as
bubbles are also known as
Bjerknes forces, and are generated through a different mechanism, which does not require sound
absorption or
reflection.[4] Acoustic radiation forces can also be controlled through sub-wavelength patterning of the surface of the object.[5]
When a particle is exposed to an acoustic standing wave it will experience a time-averaged force known as the primary acoustic radiation force ().[6] In a rectangular microfluidic channel with coplanar walls which acts as a
resonance chamber, the incoming acoustic wave can be approximated as a
resonant,
standing pressure wave of the form:
.
where is the
wave number.
For a
compressible, spherical and
micrometre-sized particle (of radius ) suspended in an
inviscid fluid in a rectangular micro-channel with a 1D planar standing ultrasonic wave of wavelength , the expression for the primary radiation force (at the far-field region where )becomes then [7][8][9][6]:
^McAleavey, S. A.; Nightingale, K. R.; Trahey, G. E. (June 2003). "Estimates of echo correlation and measurement bias in acoustic radiation force impulse imaging". IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control. 50 (6): 631–641.
doi:
10.1109/tuffc.2003.1209550.
PMID12839175.
S2CID12815598. (subscription required)