Visualization of acoustic particle interaction and agglomeration: Theory evaluation

Journal of the Acoustical Society of America

Volumn 101, Issue 6, 1997, Pages 3421-3429

  Hoffmann, Thomas L ^a,b   Koopmann, Gary H ^b  

^a Consejo Superior de Investigaciones Científicas   (Spain)

^b The Pennsylvania State University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTIC WAVE SCATTERING; ACOUSTIC WAVE VELOCITY; AGGLOMERATION; FLOW INTERACTIONS; FLOW VISUALIZATION; HYDRODYNAMICS; MATHEMATICAL MODELS; PARTICLES (PARTICULATE MATTER); VISCOSITY;

ACOUSTIC AGGLOMERATION THEORY; ACOUSTIC PARTICLE ENTRAINMENT; ACOUSTIC PARTICLE INTERACTION; ACOUSTIC WAKE EFFECT; MUTUAL RADIATION PRESSURE INTERACTION; MUTUAL SCATTERING INTERACTION;

ACOUSTICS;

ACOUSTICS; ARTICLE; HYDRODYNAMICS; KINETICS; MOLECULAR INTERACTION; PARTICLE SIZE; PARTICULATE MATTER; PRIORITY JOURNAL; THEORY; TUNING CURVE; VELOCITY; VISCOSITY;

EID: 0031172392     PISSN: 00014966     EISSN: None     Source Type: Journal    
DOI: 10.1121/1.418352     Document Type: Article

References (19)

1. T. L. Hoffmann and G. H. Koopmann, "Visualization of acoustic particle interaction and agglomeration: Theory and experiments," J. Acoust. Soc. Am. 99, 2130-2141 (1996).
2. D. V. Dianov, A. A. Podol'skii, and V. I. Turubarov, "Calculation of the hydrodynamic interaction of aerosol particles in a sound field under Oseen flow conditions," Sov. Phys. Acoust. 13, 314-319 (1968).
3. W. König, "Hydrodynamisch-akustische Untersuchungen: I. Über das Mitschwingen einer Kugel in einer schwingenden Flüssigkeit," Ann. Phys. Chem. 42, 352-370 (1891).
4. F. T. Gucker and G. J. Doyle, "The amplitude of vibration of aerosol droplets in a sonic field," J. Phys. Chem. 60, 989-996 (1956).
5. S. Temkin, Elements of Acoustics (Wiley, New York, 1981).
6. S. Temkin and C.-M. Leung, "On the velocity of a rigid sphere in a sound wave," J. Sound Vib. 49, 75-92 (1976).
7. I. González, T. L. Hoffmann, and J. A. Gallego-Juárez, "Measurement of acoustic particle entrainment factors," J. Aerosol Sci. (in preparation).
8. L. Song, "Modeling of acoustic agglomeration of aerosol particles," Ph.D. dissertation, Pennsylvania State University (1990).
9. L. Song, G. H. Koopmann, and T. L. Hoffmann, "An improved theoretical model of acoustic agglomeration," Trans. ASME 116, 208-214 (April 1994).
10. In Section 4.10 (pp. 240-244) on "Oseen's improvement of the equation of flow due to moving bodies at small Reynolds number," Batchelor's (Ref. 11) standard treatise on fluid dynamics refers to the flow region directly behind the sphere as a 'wake' (pp. 242-243 and Figure 4.10.1). In this paper we thus adopt Batchelor's use of the expression 'wake' for the relatively small Reynolds numbers that correspond to the Oseen flow regime.
11. G. K. Batchelor, An Introduction to Fluid Dynamics (Cambridge U.P., Cambridge, 1987).
12. Temkin and Ecker (Ref. 13) (p. 468) identify the reason for an observed attraction between two droplets as "... the transient wake that is produced in the lee side of one droplet, due to the passage of the wave. If a second droplet is in the vicinity of this wake, it will experience smaller fluid forces than the first. The first droplet may therefore move much more rapidly than the second, possibly producing collision."
13. S. Temkin and G. Z. Ecker, "Droplet pair interactions in a shock-wave flow field," J. Fluid Mech. 202, 467-497 (1989).
14. Batchelor (Ref. 11) (p. 256) discusses the physics of low Reynolds number flow fields around particles: "At Reynolds numbers small compared with unity, the dominant process in the flow is the diffusion of vorticity away from the body.... The Oseen improved approximation of §4.10 takes account of inertia forces partially, and the vorticity here diffuses from a source which is moving steadily.... Thus, for R≪1 [R = Reynolds number], when Stokes and Oseen approximations are applicable, the flow has fore-and-aft symmetry near the body with that same symmetry, but distinct asymmetry further out."
15. S. V. Pshenai-Severin, "On the convergence of aerosol particles in a sound field under the action of the Oseen hydrodynamic forces," Dokl. Akad. Nauk SSSR 125, 775-778 (1959).
16. Even though it is not the intention of this paper to prove the different theories for correctness, it should be noted here that both Pshenai-Severin's and Dianov et al.'s theory are based on the superposition of the two particles' individual flow fields. Because of this approximation, neither of the theories strictly satisfies the boundary conditions on the particles' surfaces [see discussion in Fuchs (Ref. 17) pp. 46-47, pp. 101-102, and p. 328].
17. N. A. Fuchs, The Mechanics of Aerosols (Pergamon, Oxford, 1964).
18. W. H. Press, B. P. Flannery, S. A. Teukolsky, and V. T. William, Numerical Recipes: The Art of Scientific Computing (Cambridge U.P., New York, 1986).
19. T. L. Hoffmann and G. H. Koopmann, "A new technique for visualization of acoustic particle agglomeration," Rev. Sci. Instrum. 65, 1527-1536 (1994).