Application of Newton's second law

Date: 2015-10-07; view: 759.

Primary and secondary acoustic force

The primary transverse force acts normal to the wave propagation. Of the three forces, the primary axial radiation force generally has the greatest magnitude.

The proposed technology can be implemented in a rectangular narrow channel of upward fluid flow. Two walls of the channel can be made with a piezoelectric transducer and rigid reflecting surface, as shown in Fig. 2. When the transducer is energized at the proper frequency to maintain a resonant acoustic field, there will be a pressure node located on the mid-plane of the chamber, and pressure antinodes located on the chamber walls. The acoustic force on a suspended particle results from the particle–fluid interaction that arises when the particle and suspending fluid have different acoustic properties. When the particle is at the pressure node at quarter wavelength, mid-plane of the chamber width, the magnitude of this force is the maximum. For a dilute suspension, the secondary radiation forces, the body forces and the hydrodynamic interactions are neglected. The rate of change of particle momentum is equal to:

where v is the particle velocity and g is the gravitational acceleration. The mass in the momentum term is the “virtual mass” of the particle, m. Since the particle's velocity is v, the drag force is given by Stokes' law (F_D = −6πμrv), where μ is the viscosity of the fluid and r is the radius of the particle in suspension. The summation of the forces in the direction of the acoustic wave propagation gives:

Thus the acoustic force, F_ac, on a particle in an acoustic field is due to the primary axial radiation force and can be used to calculate the particle trajectories.

Fig. 2. Schematic showing the mechanics of the proposed technology.