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The acoustic contrast factor is a number used to describe the relationship between the densities and the sound velocities (or, equivalently because of the form of the expression, the densities and compressibilities) of two media. It is most often used in the context of biomedical ultrasonic imaging techniques using acoustic contrast agents and in the field of ultrasonic manipulation of particles (acoustophoresis) much smaller than the wavelength using ultrasonic standing waves. In the latter context, the acoustic contrast factor is the number which, depending on its sign, tells whether a given type of particle in a given medium will be attracted to the pressure nodes or anti-nodes.
Example - particle in a medium
The figure shows the cross-section of a straight, hard-walled (grey), water-filled channel (blue) with a one-dimensional standing ultrasonic half-wavelength pressure resonance (green curve). Frad is the radiation force on a small suspended particle. Particles that have a positive (red) contrast factor in water are moved to the pressure nodes, while particles with a negative (yellow) contrast factor in water are moved to the anti-pressure nodes.

In an ultrasonic standing wave field, a small spherical particle ( \( {\displaystyle a\ll \lambda } \), where a is the particle radius, and \( \lambda \) is the wavelength) suspended in an inviscid fluid will move under the effect of an acoustic radiation force. The direction of its movement is governed by the physical properties of the particle and the surrounding medium, expressed in the form of an acoustophoretic contrast factor \( \phi \). [1][2]

Given the compressibilities \( \beta_m \) and \( \beta _{p} \) and densities \( \rho_m \) and \( \rho_p \) of the medium and particle, respectively, the acoustic contrast factor ϕ {\displaystyle \phi } \phi can be expressed as:[2]

\( {\displaystyle \phi ={\frac {5\rho _{p}-2\rho _{m}}{2\rho _{p}+\rho _{m}}}-{\frac {\beta _{p}}{\beta _{m}}}} \)

For a positive value of \( \phi \) , the particles will be attracted to the pressure nodes.

For a negative value of \( \phi \), the particles will be attracted to the pressure anti-nodes.
See also

Acoustic impedance
Acoustic tweezers

References

Bruus, Henrik (2012). "Acoustofluidics 7: The acoustic radiation force on small particles". Lab on a Chip. 12 (6): 1014. doi:10.1039/c2lc21068a. ISSN 1473-0197. PMID 22349937.
Lenshof, Andreas; Laurell, Thomas (2010). "Continuous separation of cells and particles in microfluidic systems". Chemical Society Reviews. 39 (3): 1203. doi:10.1039/b915999c. ISSN 0306-0012. PMID 20179832.

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