1. by P. Vainshtein and M. Shapiro Technion - Israel Institute of Technology Faculty of Mechanical Engineering An acoustic channel for aerosol particle focusing

2. Technion - Israel Institute of Technology Faculty of Mechanical Engineering 2 Background Particles in gases are focused in aerodynamic lens arrays (P. McMurry and co-authors) Ions are focused in quadrupole electrodynamic lenses (W. Paul and co-authors,1955) Particles focusing in liquids by ultrasonic waves (Goddard, Martin, Graves, Kaduchak, 2006)

3. Technion - Israel Institute of Technology Faculty of Mechanical Engineering 3 Aerosol Aerodynamic lens arrays. Liu et al. (1995) Particle Beam particle r 0 =1 cm gas To vacuum chambers

4. Technion - Israel Institute of Technology Faculty of Mechanical Engineering 4 Disadvantages of aerodynamic lens arrays: - particles mix back into the flow as a result of transition to turbulence loss of particles, reduced instrument resolution. - Use of small orifices (required to reduce gas flow rate and pumping capacity) is problematic because particle passages are blocked - No control over beam broadening caused by particle diffusion poor focusing of nanoparticles -No possibility of focusing at low gas velocities and constant gas pressures limits possibilities of implementation

5. Technion - Israel Institute of Technology Faculty of Mechanical Engineering 5 Our solution Use acoustic field for focusing. Advantages: No particles loss (characteristic of aerodynamic lenses) Possibility to use at atmospheric pressures No need of high gas velocity No beam broadening due to side drift of nonspherical particles Control over diffusion broadening Improve transmission efficiency (transmit more particles) When used in mass-spectrometers - improved sensitivity and resolution

6. Technion - Israel Institute of Technology Faculty of Mechanical Engineering 6 Physical principles of acoustic focusing Need narrow channels (small ) (larger acoustic effect, required in micro- nano-particle applications) Need low acoustic frequencies to reduce attenuation Therefore acoustic wave length no velocity nodes within the channel – no focusing? Examples Pressure oscillations Particles are either stagnant or move to the wall Solution: use convex shaped channel (W. Paul, Electrodynamic quadrupole channel)

7. Technion - Israel Institute of Technology Faculty of Mechanical Engineering 7 Quadrupole acoustic channel x Aerosol particle flow Focused particles ’ beam L

8. Technion - Israel Institute of Technology Faculty of Mechanical Engineering 8 Streamlines and trajectories in quadrupole channel cross-section Channel axis is the velocity node

9. Technion - Israel Institute of Technology Faculty of Mechanical Engineering 9 Model Condition of flow incompressibility Small amplitude of pressure oscillations Incompressible Navier-Stokes Eqs., creeping flow Boundary conditions: quadrupole acoustic pressure disturbances at channel walls

10. Technion - Israel Institute of Technology Faculty of Mechanical Engineering 10 Solution of Laplace equation for pressure Fluid velocity Axial component Cross-sectional components

11. Technion - Israel Institute of Technology Faculty of Mechanical Engineering 11 Equations of particle motion initial particle velocities coincide with those of air Dimensionless parameters: axial fluid velocity Stokes number acoustic strength Mathieu equations Non-diffusive particles

12. Technion - Israel Institute of Technology Faculty of Mechanical Engineering 12 First marginal stability curve a=1 µm r0=0.5 cm f=1 kHz SPL=140dB stability 0.4 3.16

13. Technion - Israel Institute of Technology Faculty of Mechanical Engineering 13 Calculated particle cross-sectional trajectories

14. Technion - Israel Institute of Technology Faculty of Mechanical Engineering 14 Calculated particle axial trajectories

15. Technion - Israel Institute of Technology Faculty of Mechanical Engineering 15. Dimensionless time of 10-fold focusing

16. Technion - Israel Institute of Technology Faculty of Mechanical Engineering 16 Diffusive low inertia particles

17. Technion - Israel Institute of Technology Faculty of Mechanical Engineering 17 Achievable focusing width systematic velocity Velocity balance yields achievable focusing width random velocity for estimate Recall acoustic strength

18. Technion - Israel Institute of Technology Faculty of Mechanical Engineering 18 Conclusions Practically interesting values of the frequency parameter and acoustic strength parameter lie well in the stability region There exists critical value determining the maximal focusing efficiency of non-diffusive particles Acoustic oscillations can focus micron size particles on axial distance comparable to channel cross-sectional size. The achievable focusing width of small diffusive particles can be small enough. It is determined by the balance of random and systematic (acoustic) particle velocities.