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Acoustic radiation force (ARF) is a physical phenomenon resulting from the interaction of an
acoustic wave Acoustic waves are types of waves that propagate through matter—such as gas, liquid, and/or solids—by causing the particles of the medium to compress and expand. These waves carry energy and are characterized by properties like acoustic pres ...
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: : , F^, = \frac where :*, F^, is a force per unit volume, here expressed in kg/(s2cm2); :*\alpha is the
absorption coefficient The linear attenuation coefficient, attenuation coefficient, or narrow-beam attenuation coefficient characterizes how easily a volume of material can be penetrated by a beam of light, sound, particles, or other energy or matter. A coefficient val ...
in Np/cm (nepers per cm); :*I is the temporal average
intensity Intensity may refer to: In colloquial use * Strength (disambiguation) *Amplitude * Level (disambiguation) * Magnitude (disambiguation) In physical sciences Physics *Intensity (physics), power per unit area (W/m2) *Field strength of electric, m ...
of the acoustic wave at the given location in W/cm2; and :*c is the
speed of sound The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elasticity (solid mechanics), elastic medium. More simply, the speed of sound is how fast vibrations travel. At , the speed of sound in a ...
in the medium in cm/s. The effect of
frequency Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...
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).''(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. Acoustic radiation forces can also be controlled through sub-wavelength patterning of the surface of the object. When a particle is exposed to an acoustic standing wave it will experience a time-averaged force known as the primary acoustic radiation force ( F_). In a rectangular microfluidic channel with coplanar walls which acts as a resonance chamber, the incoming acoustic wave can be approximated as a
resonant Resonance is a phenomenon that occurs when an object or system is subjected to an external force or vibration whose frequency matches a resonant frequency (or resonance frequency) of the system, defined as a frequency that generates a maximu ...
,
standing Standing, also referred to as orthostasis, is a position in which the body is held in an upright (orthostatic) position and supported only by the feet. Although seemingly static, the body rocks slightly back and forth from the ankle in the ...
pressure wave of the form:
p_1 = p_a\cos.
where k is the
wave number In the physical sciences, the wavenumber (or wave number), also known as repetency, is the spatial frequency of a wave. Ordinary wavenumber is defined as the number of wave cycles divided by length; it is a physical quantity with dimension of r ...
. For a compressible, spherical and micrometre-sized particle (of radius a) suspended in an inviscid fluid in a rectangular micro-channel with a 1D planar standing ultrasonic wave of wavelength \lambda, the expression for the primary radiation force (at the far-field region where a \ll \lambda)becomes then :
F^_= 4\pi\Phi(\tilde,\tilde)a^3kE_\sin \Phi(\tilde,\tilde)= \left -\tilde \right /math> E_=\kappa_fp^2_a=
where * \Phi is the acoustic contrast factor * \tilde is relative
compressibility In thermodynamics and fluid mechanics, the compressibility (also known as the coefficient of compressibility or, if the temperature is held constant, the isothermal compressibility) is a measure of the instantaneous relative volume change of a f ...
between the particle \kappa_p and the surrounding fluid \kappa_f: \tilde=\kappa_p / \kappa_f * \tilde is relative
density Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be u ...
between the particle \rho_p and the surrounding fluid \rho_f: \tilde=\rho_p / \rho_f * E_ is the acoustic
energy density In physics, energy density is the quotient between the amount of energy stored in a given system or contained in a given region of space and the volume of the system or region considered. Often only the ''useful'' or extractable energy is measure ...
* The factor \sin makes the radiation force period doubled and
phase Phase or phases may refer to: Science *State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter), a region of space throughout which all physical properties are essentially uniform *Phase space, a mathematica ...
shifted relative to the pressure wave p_a\cos * c_f is the
speed of sound The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elasticity (solid mechanics), elastic medium. More simply, the speed of sound is how fast vibrations travel. At , the speed of sound in a ...
in the fluid


See also

* Acoustic tweezers *
Radiation pressure Radiation pressure (also known as light pressure) is mechanical pressure exerted upon a surface due to the exchange of momentum between the object and the electromagnetic field. This includes the momentum of light or electromagnetic radiation of ...


References

{{DEFAULTSORT:Acoustic Radiation Force Acoustics