Acoustic contrast factor

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.
In an ultrasonic standing wave field, a small spherical particle (formula_1, where formula_2 is the particle radius, and formula_3 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 formula_4. 
Given the compressibilities formula_5 and formula_6 and densities formula_7 and formula_8 of the medium and particle, respectively, the acoustic contrast factor formula_4 can be expressed as: 
For a positive value of formula_11, the particles will be attracted to the pressure nodes.
For a negative value of formula_11, the particles will be attracted to the pressure anti-nodes.