PDF
Acoustic Levitator
Introduction
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 acoustic tweezers 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.
Note: This model requires the Particle Tracing module.
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.
References
1. A. Brask and others, “High-Temperature Ultrasonic Levitation for Investigating Drying Kinetics of Single Droplets,” 6th Int’l Conf. Multiphase Flow (ICMF 2007), paper 789, 2007.
2. E.G. Lierke and L. Holitzner, “Perspectives of an Acoustic-Electrostatic/Electrodynamic Hybrid Levitator for Small Fluid and Solid Samples,” Measurement Sci. and Tech., vol. 19, no. 11, pp. 115803, 2008.
Application Library path: Acoustics_Module/Nonlinear_Acoustics/acoustic_levitator
Modeling Instructions
From the File menu, choose New.
New
In the New window, click  Model Wizard.
Model Wizard
1
In the Model Wizard window, click  2D.
2
In the Select Physics tree, select Acoustics > Pressure Acoustics > Pressure Acoustics, Frequency Domain (acpr).
3
Click Add.
4
In the Select Physics tree, select Fluid Flow > Particle Tracing > Particle Tracing for Fluid Flow (fpt).
5
Click Add.
6
Click  Study.
7
In the Select Study tree, select Preset Studies for Some Physics Interfaces > Frequency Domain.
8
Click  Done.
Study 1
In this model, you first solve for the acoustic field in the frequency domain. Therefore, deselect the Particle Tracing for Fluid Flow physics.
Step 1: Frequency Domain
As a second step, you solve for the particle movement in the time domain.
Add Study
1
In the Home toolbar, click  Add Study to open the Add Study window.
2
Go to the Add Study window.
3
Find the Physics interfaces in study subsection. In the table, clear the Solve checkbox for Pressure Acoustics, Frequency Domain (acpr).
4
Find the Studies subsection. In the Select Study tree, select General Studies > Time Dependent.
5
Click the Add Study button in the window toolbar.
6
In the Home toolbar, click  Add Study to close the Add Study window.
Global Definitions
Parameters 1
1
In the Settings window for Parameters, locate the Parameters section.
2
Click  Load from File.
3
Browse to the model’s Application Libraries folder and double-click the file acoustic_levitator_parameters.txt.
The parameters loaded here define the geometrical dimensions, the driving frequency, typical wavelength, and particle properties. Because the geometry is now parameterized, changing the dimensions in the parameters list will update the geometry automatically.
Geometry 1
Circle 1 (c1)
1
In the Model Builder window, expand the Component 1 (comp1) > Geometry 1 node.
2
Right-click Geometry 1 and choose Circle.
3
In the Settings window for Circle, locate the Size and Shape section.
4
In the Radius text field, type H.
5
In the Sector angle text field, type 180.
6
Click  Build Selected.
Rectangle 1 (r1)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type Dr.
4
In the Height text field, type H.
5
Locate the Position section. In the x text field, type -Dr/2.
6
Click  Build Selected.
Intersection 1 (int1)
1
In the Geometry toolbar, click  Booleans and Partitions and choose Intersection.
2
Click in the Graphics window and then press Ctrl+A to select both objects.
3
In the Settings window for Intersection, click  Build Selected.
Point 1 (pt1)
1
In the Geometry toolbar, click  Point.
2
In the Settings window for Point, locate the Point section.
3
In the x text field, type -Dt/2.
4
Click  Build Selected.
Point 2 (pt2)
1
In the Geometry toolbar, click  Point.
2
In the Settings window for Point, locate the Point section.
3
In the x text field, type Dt/2.
4
Click  Build Selected.
Add Material
1
In the Materials toolbar, click  Add Material to open the Add Material window.
2
Go to the Add Material window.
3
In the tree, select Built-in > Air.
4
Click the Add to Component button in the window toolbar.
5
In the Materials toolbar, click  Add Material to close the Add Material window.
Pressure Acoustics, Frequency Domain (acpr)
Normal Acceleration 1
1
In the Physics toolbar, click  Boundaries and choose Normal Acceleration.
2
Select Boundaries 3 and 4 only.
3
In the Settings window for Normal Acceleration, locate the Normal Acceleration section.
4
In the an text field, type a0.
Plane Wave Radiation 1
1
In the Physics toolbar, click  Boundaries and choose Plane Wave Radiation.
2
Select Boundaries 1, 2, 5, and 6 only.
Particle Tracing for Fluid Flow (fpt)
Particle Properties 1
1
In the Model Builder window, under Component 1 (comp1) > Particle Tracing for Fluid Flow (fpt) click Particle Properties 1.
2
In the Settings window for Particle Properties, locate the Particle Properties section.
3
From the ρp list, choose User defined. In the associated text field, type rho_p.
4
In the dp text field, type d_p.
Wall 2
1
In the Physics toolbar, click  Boundaries and choose Wall.
2
Select Boundaries 1, 2, 5, and 6 only.
3
In the Settings window for Wall, locate the Wall Condition section.
4
From the Wall condition list, choose Disappear.
Particles are set to freeze on the solid walls but they disappear where the system is open (at the radiation boundaries).
Release 1
1
In the Physics toolbar, click  Domains and choose Release.
2
Select Domain 1 only.
Acoustophoretic Radiation Force 1
1
In the Physics toolbar, click  Domains and choose Acoustophoretic Radiation Force.
2
In the Settings window for Acoustophoretic Radiation Force, locate the Domain Selection section.
3
From the Selection list, choose All domains.
4
Locate the Acoustic Fields section. From the p list, choose Acoustic pressure (acpr).
5
From the u list, choose Total acoustic velocity (acpr).
6
Locate the Advanced Settings section. Select the Use piecewise polynomial recovery on field checkbox.
Gravity Force 1
1
In the Physics toolbar, click  Domains and choose Gravity Force.
2
In the Settings window for Gravity Force, locate the Domain Selection section.
3
From the Selection list, choose All domains.
Drag Force 1
1
In the Physics toolbar, click  Domains and choose Drag Force.
2
In the Settings window for Drag Force, locate the Domain Selection section.
3
From the Selection list, choose All domains.
Mesh 1
Proceed and generate the mesh using the Physics-controlled mesh functionality. In general, 5 to 6 second-order elements per wavelength are needed to resolve the waves. For more details, see Meshing (Resolving the Waves) in the Acoustics Module User’s Guide. In this model, use 8 elements per wavelength; the default Automatic is to have 5.
1
In the Model Builder window, under Component 1 (comp1) click Mesh 1.
2
In the Settings window for Mesh, locate the Physics-Controlled Mesh section.
3
In the table, clear the Use checkbox for Particle Tracing for Fluid Flow (fpt).
4
Locate the Pressure Acoustics, Frequency Domain (acpr) section. From the Maximum mesh element size control parameter list, choose Frequency.
5
In the fmax text field, type f0.
6
From the Number of mesh elements per wavelength list, choose User defined.
7
In the text field, type 8.
8
Click  Build All.
Study 1
Step 1: Frequency Domain
1
In the Model Builder window, under Study 1 click Step 1: Frequency Domain.
2
In the Settings window for Frequency Domain, locate the Study Settings section.
3
In the Frequencies text field, type f0.
4
In the Model Builder window, click Study 1.
5
In the Settings window for Study, type Study 1 - Acoustic Field in the Label text field.
6
In the Study toolbar, click  Compute.
Results
Acoustic Pressure (acpr)
1
Click the  Zoom Extents button in the Graphics toolbar.
This first figure should look like the one in Figure 2.
Sound Pressure Level (acpr)
The sound pressure level plot should look like Figure 3.
Study 2
Step 1: Time Dependent
1
In the Model Builder window, under Study 2 click Step 1: Time Dependent.
2
In the Settings window for Time Dependent, locate the Study Settings section.
3
In the Output times text field, type range(0,0.0005,0.3).
4
Click to expand the Values of Dependent Variables section. Find the Values of variables not solved for subsection. From the Settings list, choose User controlled.
5
From the Method list, choose Solution.
6
From the Study list, choose Study 1 - Acoustic Field, Frequency Domain.
7
In the Model Builder window, click Study 2.
8
In the Settings window for Study, type Study 2 - Particle Tracing in the Label text field.
9
In the Study toolbar, click  Compute.
Results
Particle Trajectories (fpt)
In the Model Builder window, expand the Results > Particle Trajectories (fpt) node.
Color Expression 1
1
In the Model Builder window, expand the Results > Particle Trajectories (fpt) > Particle Trajectories 1 node, then click Color Expression 1.
2
In the Settings window for Color Expression, locate the Coloring and Style section.
3
From the Color table list, choose Rainbow.
4
From the Scale list, choose Linear.
Particle Trajectories (fpt)
1
In the Model Builder window, under Results click Particle Trajectories (fpt).
2
In the Settings window for 2D Plot Group, locate the Color Legend section.
3
Select the Show units checkbox.
4
Select the Show maximum and minimum values checkbox.
5
Locate the Data section. From the Time (s) list, choose 0.01.
6
In the Particle Trajectories (fpt) toolbar, click  Plot.
The particle position at t = 0.01s is reproduced in Figure 4 (top).
7
From the Time (s) list, choose 0.3.
8
In the Particle Trajectories (fpt) toolbar, click  Plot.
The particle position at t = 0.3s is reproduced in Figure 4 (bottom).
As an optional extension of the model, you can go on to the Export node and animate the particle plot.