Basic mechanisms of ultrasound-assisted agglomeration

Acoustic agglomeration is a process in which acoustic forces cause particles to interact and, eventually, to collide. The complex mechanisms behind this process involve orthoki-netic and hydrodynamic interactions. The orthokinetic interaction is founded on the hypothesis that collisions are produced due to the different acoustic entrainments experienced by particles of different size and weight. In order to describe this mechanism, an agglomeration volume is defined around each particle as a volume where another particle can be captured [49], However, this mechanism, which constitutes the basis for most existing interaction models, can explain neither the agglomeration of monodispersed aerosols nor the way in which the agglomeration volume is refilled once the initial particles are captured. 

Hydrodynamic mechanisms are those which produce particle interactions through the surrounding fluid due to hydrodynamic forces and the asymmetry of the flow field around each particle. These mechanisms, which are not dependent on the relative differences in acoustic particle entrainments, can act from distances larger than the acoustic displacement and have to be considered as the main mechanism in the agglomeration of monodispersed aerosols, where particles are equally entrained. There are two main types of hydrodynamic mechanisms, namely mutual radiation pressure [50] and the acoustic wake effect [51,52]. The radiation pressure is a second-order effect which produces a force on a particle immersed in an acoustic field due to the transfer of momentum from the acoustic wave to the particle. This force moves the particles towards the pressure node or antinode planes of the applied standing wave, depending on the size and density of the particles. The mutual radial pressure can be computed from the primary wave as well as from other wave fields of nearby scatters. In fact, it gives rise to particle interactions as the result of forces produced on two adjacent particles by a non-linear combination of incident and scattered waves. 

As a consequence, particles on the acoustic axis converge during a number of oyoles and eventually oollide. Equations for the dynamios of partioles under standing waves that include the mass, radius and velocity of the partioles, the kinetio and dynamio velooities of the fluid and its velocity due to the aooustio wave have been derived [53], 

The orthokinetio effect has been shown to ooour mainly in solid-gas systems and to be irrelevant in liquid suspensions. The radiation pressure seems to be the most important effect in the latter case with a view to agglomerating partioles or at least bringing them together. 

A standing wave oan induoe three types of aooustic forces, namely  

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