Acoustic Levitator

An ultrasonic standing wave levitator, also called acoustic levitator, is a device used for levitating fluid and solid particles in an acoustic field. The standing acoustic waves exert an acoustic radiation force on the particles. The force is a second order effect and stems from a combination of the time-averaged pressure and inertial interaction between the particles and the acoustic field.

By levitating a particle, it is possible to study, for example, its drying kinetics under different external conditions as temperature and humidity (see Ref. 1). The levitator has also been used to study combustion processes, the formation of ice particles and snow flakes, and is also used as an acoustic tweezer in microgravity in space missions, for example.

The model is that of a simplified 2D acoustic levitator geometry driven at a constant frequency. Small elastic particles are released uniformly in the standing acoustic field and their path is determined when influenced by the acoustic radiation force, viscous drag, and gravity.

Model Definition

The levitator consists of a transducer of width Dt and a concave reflector of width Dr and curvature 1/R. The distance between the reflector and the transducer is H. The driving frequency of the system is f0 = 58 kHz and the system is filled with air at 20°C. The geometry is shown in Figure 1. Standard values for the dimensions of the levitator are given in Ref. 2 and are as follows in the model:

Table 1: Standard dimensions and physical values.
Symbol	Value	Description
c0	343 m/s	Speed of sound
f0	58 kHz	Driving frequency
λ0	5.9 mm	Wavelength
Dt = 2λ0	11.8 mm	Transducer diameter
Dr = 3λ0	17.7 mm	Reflector diameter
H = 5λ0/2	14.8 mm	Reflector-transducer distance
R = H	14.8 mm	Radius of curvature of reflector

Figure 1: Levitator geometry.

In this model, the particle diameter dp is assumed to be small compared to the wavelength λ0 as they are modeled as point particles. The condition dp << λ0 is also necessary for the acoustic radiation force term to be physically correct. The second condition is that the particle diameter dp should be larger than the acoustic viscous boundary layer thickness δv. In the present system δv is of the order 10 μm. Table 2 lists the particle properties uses in this model.

Table 2: Particle Properties.
Symbol	Value	Description
dp	0.6 mm	Particle diameter
ρp	500 kg/m3	Particle density
Kp	2.2 GPa	Particle bulk modulus

Results and Discussion

The particles are released in the standing acoustic wave field in the levitator. The pressure field is shown in Figure 2, with plane wave radiation conditions at the open boundaries. The corresponding sound pressure level in the system is shown in Figure 3.

Figure 2: Real part of the pressure field, Re(p).

Note that the sound pressure level reaches as much as 166 dB SPL. Fortunately for the practical application of this device, this is outside the human auditory range. By tuning the amplitude of the normal acceleration of the transducer a0 (under parameters in the model tree), it is possible to determine the value at which the radiation force is no longer large enough to levitate the particles.

Figure 3: Sound pressure levels in the levitator.

The positions of the particles at t = 0.01 s and t = 0.3 s are shown in Figure 4.

Figure 4: Positions of the particles at t = 0.01 s (top) and t = 0.3 s (bottom). The colors refer to the instantaneous particle velocities.

Finally, the particle position and their trajectories is shown in Figure 5 using the magnitude of the radiation potential as color legend. Since the radiation force is defined as the gradient of the radiation potential, it is clear that the particles tend toward the lowest potential value.