19th INTERNATIONAL CONGRESS ON ACOUSTICS MADRID, 2-7 ...

19th INTERNATIONAL CONGRESS ON ACOUSTICS MADRID, 2-7 SEPTEMBER 2007

ULTRASONIC PARTICLE MANIPULATION DEVICES FORMED BY RESONANTLY-EXCITED, CYLINDRICAL STRUCTURES PACS: 43.25.Uv Kaduchak, Gregory1; Ward, Michael D.2; Goddard, Gregory R.3 1 Acoustic Cytometry Systems; 3500 Trinity, Los Alamos, NM 87544, USA; [email protected] 2 Acoustic Cytometry Systems; 3500 Trinity, Los Alamos, NM 87544, USA; [email protected] 3 Los Alamos National Laboratory, PO Box 1663, Los Alamos, NM 87545, USA; [email protected] ABSTRACT The present research is an overview of acoustic particle manipulation devices that are constructed from resonantly-excited cylindrical structures. These devices, in their most efficient mode of excitation, rely upon matching the structural mode of an elastic cylindrical shell to a cavity mode set up in its confined volume. In applications, discussed for both particles in air and liquids, the structural vibrations are tuned such that desired modal responses are obtained. Lowest order axisymmetric modes will be discussed as well as more localized particle concentration modes that result from breaking the cylindrical symmetry of the system. Specific designs have demonstrated that these devices can be engineered into power efficient assemblies for aerosol manipulation. Examples of applications include line-driven cylindrical capillaries for real-time sample positioning of biological samples in flow cytometers and cylindrical piezoelectric shells driven under multiple symmetry conditions for aerosol concentration and positioning. INTRODUCTION Particle handling and trapping based upon acoustic radiation pressure is becoming an important tool in biology, chemistry, environmental monitoring and clinical research. Capture of particles at predetermined locations within flow channels (fluid streams or gas streams) or modification of their trajectories has found increasing utility in many applications. In early research in aerosol applications, scientists implemented acoustics to position macroscopic samples (usually on the order of a millimeter or larger) in applications where the sample must not contact the wall of a containment vessel. Many studies in containerless processing have been conducted to observe, for example, the growth of freely forming crystals and measurements of the physical properties of substances in both terrestrial and low gravity environments.1,2 More recently, an interest in in-line monitoring of aerosols has made the promise of using acoustics to position particles in flow streams for real time analysis appealing for environmental monitoring applications. With the popularity of microfluidic systems, acoustic trapping, transport, and positioning of particles in fluid streams has become an expanded field of research.3-7 Over the past several decades a number of acoustic particle manipulation systems based upon planar geometries have been proposed and successfully demonstrated, but systems with cylindrical geometries are few. This paper gives a general overview of the development of acoustic particle handling and trapping devices that are based upon cylindrical geometries. Force on particles The force on a particle resulting from acoustic radiation pressure depends upon frequency of excitation, pressure amplitude within the medium, particle size, and the density/compressibility contrast between the particle and the host medium. Within an acoustic standing wave, it is a time-averaged drift force which transports the particles to a stable equilibrium resting position. The expression for the acoustic radiation force FU(x) on a compressible, spherical particle in an acoustic standing wave is given by:8

FU = − ∇U

(1)

⎧⎪ ⎡ p 'in 2 ⎤ ⎫⎪ v 'in 2 3 FU = −∇ ⎨2π a ρ ⎢ 2 2 f1 − f2 ⎥ ⎬ 2 ⎢⎣ 3ρ c ⎥⎦ ⎪⎭ ⎩⎪

(2)

where p’in2 and v’in2 are the mean square fluctuations of the fluid pressure and velocity at the location of the particle,

f1 = 1 − f2 = 2

c2 ρ c02 ρ 0

(3)

ρ0 − ρ , 2ρ0 + ρ

(4)

and ρ = mass density of the fluid ρ0 = mass density of the particle a = radius of the particle c = speed of sound in the fluid c0 = speed of sound in the particle. The brackets correspond to a time-averaged quantity. For pressure wave in planar devices, general solutions (plane waves) possess a spatial dependence where the velocity antinodes and pressure nodes coincide. When plane wave solutions are used to compute the force potential in Eq. (2), the potential minima occur at the locations of either pressure nodes or pressure antinodes (or equivalently, velocity antinodes or velocity nodes) depending upon the signs of the contrast factors f1 and f2.9 When analyzing wavefields with different symmetries such as a cylindrical wavefield, collocation of pressure nodes and velocity antinodes is no longer generally valid and the calculation of the positions to where particles migrate becomes more complex. A good description showing the complexities of the force potential generated by cylindrical and spherical wavefields (in a modal format) in rigidwalled resonators is given by Barmatz.10 CYLINDRICAL ACOUSTIC CONCENTRATION DEVICES FOR PARTICLES IN AIR Viscosity effects in air For particles in air, both f1 and f2 are positive in Eq. (2) and particles are expected to be driven to a spatial position where the velocity magnitude is large (minima in U) as a result of acoustic radiation pressure. However, it was recognized that for small particles in air, effects of the medium viscosity can be quite large. The findings of other researchers have suggested that at low frequencies and for particles below a given size, the particles can migrate to regions of 11-13 high pressure magnitude. According to the theory (under a plane wave approximation), the smallest particles are isolated at the pressure antinodes in the field as a result of a dominant viscosity effect. As the frequency is increased, a ‘cross-over’ frequency is reached where the particle position transitions from the pressure antinode to the pressure node. One of the first embodiments of this effect was experimentally demonstrated by Mazumder where the ‘crossover’ frequency was used in a particle sizing instrument that sized particles in air down to 0.3 microns at acoustic frequencies of tens of kilohertz.14-15 Axisymmetric excitation of a cylindrical resonator We have developed aerosol concentration devices that utilize acoustic forces in a coupled cylindrical drive/cavity system.16-18 These devices can concentrate and position aerosols quickly and inexpensively using sound waves created inside a vibrating tube. We have shown that for certain embodiments, the solid-state device requires very little power (~0.1 W in certain configurations) to operate and have the potential to greatly increase the efficacy of the current generation of aerosol detection devices (e.g., particle sizers, optical classifiers, particle fluorescence monitors, etc.,). This can be done by precisely positioning or ‘steering’ 2 th

19 INTERNATIONAL CONGRESS ON ACOUSTICS – ICA2007MADRID

aerosol particles in a flowing air stream for detectors that require knowledge of the aerosol particle location for proper detection and classification.

PZT tube

concentrated aerosol Figure 1. – Axisymmetric drive cylindrical acoustic concentrator. The concentric rings correspond to the approximate locations of the pressure nodes within the cavity. Aerosol particles in the size range 10 – 20 microns are seen concentrated at these positions. The diameter of this device is approximately 42 mm and operates at 25 kHz. The cylindrical concentrator is constructed from a hollow, cylindrical piezoelectric tube. The tube vibrates in a quasi-breathing mode wherein the wall of the tube vibrates with an appreciable radial component. Within the cavity, aerosol particles experience a time-averaged force that directs them to the vicinity of a pressure node or antinode within the resident sound field depending on the particle size, particle density and compressibility, excitation frequency, and the sound pressure level within the cavity.

low particle concentration elsewhere

antinode

particle concentration along antinode

100 microns

Figure 2. – Photograph of 10 micron particles trapped onto a filter after passing through an axisymmetric driven cylindrical device like shown in Fig. 1. The particles are aligned tightly along a pressure antinode that was created as an annular ring about the central axis of the tube. Figure 1 displays the cross section of an acoustic concentrator driven in an axisymmetric mode. In this mode, the potential minima within the cavity are concentric rings. For the particle size and excitation frequency used in the experiment, the aerosol particles (> 10 3 th


microns) migrate to concentric positions that are in the vicinity of pressure nodes. Concentration factors of greater than 40 have been observed. An experiment conducted at a lower excitation frequency shows the ‘cross-over’ effect where particles migrate to the vicinity of pressure antinodes is shown in Fig. 2. Symmetry breaking of the cavity Though the axisymmetric-driven cylindrical tube with particles collecting at pressure nodes lends to the simplest design, it does not lend to simple aerosol collection or interrogation of aerosol particles due to the spatial geometry of particles arranged in concentric rings within the cavity. It is difficult to collect concentrated aerosols from concentric rings, but more importantly, due to the flow rates experienced in our testing ( < 200 LPM) and the spatial scales involved, this technology is not yet positioned to replace high volume aerosol concentrators (e.g. impactors, cyclones) which can achieve much higher flow rates and concentration factors. Presently, these devices are well suited as a possible front-end for portable detectors where high flow rates are not a requirement.

a

piezo-ceramic

pressure nodes

b PZT tube

concentrated aerosol Figure 3. – Cross section of ‘three node’ acoustic concentrator. (a) By symmetry breaking the acoustic cavity, it is possible to create localized nodal configurations. (b) Experiment demonstrating the symmetry breaking effect within the cavity of a cylindrical acoustic concentrator. Symmetry is broken by inserting a small perturbation into the cavity. Aerosol is pumped into the cavity and instantaneously transported to three localized pressure nodes. The device is 27 mm in diameter and operates at 52 kHz. Experiments in our laboratory have demonstrated that highly localized concentration regions can be generated by breaking the symmetry of the circular cross section of the tube. For the symmetry breaking application, a slight perturbation in the cross section of the circular 4 th


geometry (e.g. by making the cross section slightly oblate as shown in Fig. 3(a)), can reduce the concentric rings displayed in the experimental results in Fig. 1 to localized potential minima. Experimental results demonstrating this effect are shown in Fig. 3(b). The creation of localized minima allows for aerosol particles to be forced into several parallel streams for parallel processing in detection and identification platforms. The number of aerosol streams can be adjusted by altering the cavity design and the drive frequency of the tube. Designs with as few as one and as many as six streams have been demonstrated. CYLINDRICAL ACOUSTIC CONCENTRATION DEVICE FOR PARTICLES IN LIQUID

Figure 4. – Diagram of linedriven capillary. Forces due to acoustic radiation pressure carry particles to the location of an axial pressure node along the central axis of a glass capillary.

Line-driven capillary Using the properties of acoustic radiation pressure in a line-driven capillary, an acoustic focusing flow cell has been developed that uses ultrasonic radiation pressure to tightly focus micron size (and above) particles to the center of a flowing stream. This device has been constructed to replace hydrodynamic particle focusing in flow cytometry systems. It is constructed from a capillary that is driven by a piezoceramic source in line-contact with its outer wall. Vibration of the structure creates a localized pressure node along the central axis where an axial particle trap is formed. A diagram of this device is given in Fig. 4. Particles in a dilute suspension enter the device from the top and experience a radial force that transports them to the pressure node as they flow through the system. In a flow cytometer, the particles contained in a sample are simultaneously concentrated and aligned in single file as they are then transported through the interrogation laser.

focused particle stream

Figure 5. – Sequence of photographs showing 3 micron latex spheres focused along the axis of a line-drive capillary. On the far left, the particles are sparsely distributed throughout the capillary and cannot be seen. The middle scene is 0.1 seconds after activation of the ultrasonic field. The particles transport to the center of the capillary. After 0.2 seconds elapsed time (far right), the particles are focused in a tight line approximately 1-2 particles in width.

This type of drive methodology yields large acoustic energy transfer into the flow chamber due to the large source aperture. Because the entire structure is acoustically driven, the system performs concentration over the entire length of the flow chamber thus increasing the residence time of the particles in the acoustic field and allowing the use of lower power levels (100’s of milliWatts). Low power levels alleviate problems that may arise from thermal convection or cavitation. Figure 5 is a sequence of photographs taken from a cylindrical line-driven capillary during activation of the ultrasonic field. Each picture is separated by approximately 0.10 s. The capillary is 0.500 mm inner diameter and the flow rate is 2 milliliters per minute. The excitation frequency is 1.78 MHz. The particles used in the experiment are 3 micron latex spheres. The device operation has demonstrated both stable and repeatable over long time periods. Similar results are shown in Fig. 6 where 20 µm fluorescent particles are registered in single file as they 5 th


flow through the capillary. Single file registration and positioning are necessary for high sensitivity flow cytometry applications. CONCLUSIONS Examples of ultrasonic particle manipulation devices that possess cylindrical geometry have been shown. These devices include line-driven cylindrical capillaries for real-time sample positioning of biological samples in flow cytometers and cylindrical piezoelectric shells driven under multiple symmetry conditions for aerosol concentration and positioning. References: [1] Trinh, E. H., “Compact acoustic levitation device for studies in fluid dynamics and material science in the laboratory and microgravity,” Rev. Sci. Instrum. 56, 20592065 (1985). [2] Tuckermann, R., B. Neidhart, E. G. Lierke, and S. Figure 6. – (Left) Flowing solution Bauerecker, “Trapping of heavy gases in stationary containing particles in a glass ultrasonic fields,” Chem. Phys. Lett. 363, 349-354 (2002). capillary with acoustic field OFF. [3] G. Goddard, J. C. Martin, S. W. Graves, G. Kaduchak, “Ultrasonic particle concentration for sheathless focusing of (Right) Same solution once acoustic particles for analysis in a flow cytometer,” Cytometry 69, 66field is turned ON. Spheres are 20 74 (2006). µm diameter, capillary ID 480 µm, [4] A. Haake, J. Dual, “Positioning of small particles by an and excitation frequency 1.8 MHz. ultrasound field excited by surface waves,” Ultrasonics 42, 75-80 (2004). [5] W. T. Coakley, J. J. Hawkes, M. A. Sobanski, C. M. Cousins, J. Spengler, “Analytical scale ultrasonic standing wave manipulation of cells and microparticles,”, Ultrasonics, 38, 638-641 (2000). [6] Z. Wang, P. Grabenstetter, D. L. Feke, J. M. Belovich, “Retention and viability characteristics of mammalian cells in an acoustically driven polymer mesh,” Biotechnol. Prog. 20, 384-387 (2004). [7] J. J. Hawkes, M. J. Long, W. T. Coakley, M. B. McDonnell, “Ultrasonic deposition of cells on a surface,” Biosensors and Bioelectronics 19, 1021-1028 (2004). [8] L.P. Gor'kov, “On the forces acting on a small particle in an acoustical field in an ideal fluid”, Soviet Phys. Dokl., 6, no. 9, 773 (1962). [9] P. L. Marston and D. B. Thiessen, “Manipulation of fluid objects with acoustic radiation pressure,” Ann. N.Y. Acad. Sci. 1027, 414-434 (2004). [10] M. Barmatz and P. Collas,” Acoustic radiation potential on a sphere in plane, cylindrical, and speherical standing wave fields”, J. Acoust. Soc. Am. 77, 928-945 (1985). [11] Holwill, I. L. J., “The use of ultrasonic standing waves to enhance optical particle sizing equipment,” Ultrasonics 38, 650-653 (2000). [12] Doinikov, A., “Acoustic radiation force on a spherical particle in a viscous heat-conducting fluid. I. General formula,” J. Acoust. Soc. Am. 101, 713-721 (1997); Doinikov, A., “Acoustic radiation force on a spherical particle in a viscous heat-conducting fluid. II. Force on a rigid sphere,” J. Acoust. Soc. Am. 101, 722-730 (1997); Doinikov, A., “Acoustic radiation force on a spherical particle in a viscous heat-conducting fluid. III. Force on a liquid drop,” J. Acoust. Soc. Am. 101, 713-721 (1997). [13] Danilov, SD; Mironov, MA, Mean force on a small sphere in a sound field in a viscous fluid, J. Acoust. Soc. Am. 107, 143-53 (2000). [14] Mazumder, M. K., and K. J. Kirsch, “Single particle aerodynamic relaxation time analyzer,” Rev. Sci. Instr. 48, 622-624 (1977). [15] Mazumder, M. K., et al., “SPART Analyzer: Its applicatoin to aerodynamic size distribution measurement,” Aerosol Sci. 10, 561-569 (1979). [16] Kaduchak, G., D. N. Sinha, and D. C. Lizon, “Novel cylindrical, air-coupled acoustic levitation/concentration devices,” Rev. Sci. Instrum. 73, 1332-1336 (2002). [17] Kaduchak, G., and D. N. Sinha, “Low-power acoustic harvesting of aerosols,” 2001 IEEE Ultrasonics Symposium, 607-610 (2001). [18] Kogan, Sh., G. Kaduchak, and D. N. Sinha, “Acoustic concentration of particles in piezoelectric tubes: Theoretical modeling of cavity shape and symmetry breaking,” accepted for publication in J. Acoust. Soc. Am. (2004). [19] G. Goddard and G. Kaduchak, "Particle concentration in a line driven cylindrical tube," J. Acoust. Soc. Am. 117, 3440-3447 (2005).

6 th
