 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| L. E. Ukrainskii, "On the motion of rigid particles in wave fields," Mech. Solids. 41 (3), 45-54 (2006) |
| Year |
2006 |
Volume |
41 |
Number |
3 |
Pages |
45-54 |
| Title |
On the motion of rigid particles in wave fields |
| Author(s) |
L. E. Ukrainskii (Moscow) |
| Abstract |
Transformation of a wave fluid flow into a unidirectional motion of solid
particles suspended in the fluid is considered. Equations describing this type
of the particle motion relative to the fluid are obtained in two limiting cases
where the dominant force in the fluid-particle interaction process is accounted
for by the added mass effect and where this force is accounted for by viscous
drag obeying the Stokes law. For a number of particular wave fields, the
characteristics of the particle motion are obtained, and the appearance of
stable and unstable quasi-equilibrium positions of the particles is
established. The stable positions are due to the particle localization effect
and the unstable ones are due to the formation of advective motions.
Unidirectional motions of rigid particles suspended in a carrying medium, their
localization or advective motion near the saddle equilibrium positions have
been repeatedly observed experimentally [1-3]. Some particular cases of such
motions were studied theoretically for ideal [4, 5] and viscous [6] carrying
media. In this paper, an approach originally proposed by the author in [7, 8]
is described. According to this approach, the cases where the transformation of
the wave fluid motion into the unidirectional motion of suspended particles
occurs can be systematically established by a standard procedure based on the
asymptotic methods of nonlinear mechanics [9, 10]. In the current study, this
approach is applied to the simplest types of the carrying medium flow for which
the particle motion can be described using the assumption of
quasi-incompressibility. Using this approach, not only the mechanisms of
transformation of the wave motion of the medium into the unidirectional
particle motion obtained earlier by other authors could be re-established, but
also some new mechanisms of such transformations have been identified, which
can find practical applications. Examples have shown that in the wave fields,
three particular modes of particle motion can occur: (i) unidirectional motion
with respect to the carrying medium, (ii) particle localization related to the
occurrence of stable quasi-equilibrium particle positions in the wave field,
and (iii) advection caused by the presence of saddle equilibrium positions
(when the phase space dimension exceeds 2 and doubly asymptotic Poincaré's
solutions [11] of the particle motion equations are not reduced to a
separatrix). |
| References |
| 1. | L. Bergman, Ultrasound and its Applications in Science and
Technology [Russian translation], Izd-vo Inostr. Lit-ry, Moscow, 1957. |
| 2. | L. K. Zarembo and V. A. Krasil'nikov, Introduction to
Nonlinear Acoustics [in Russian], Nauka, Moscow, 1966. |
| 3. | L. D. Rosenberg (Editor), Physics and Engineering of Powerful Ultrasound.
Volume 3.
Physical Foundations of Ultrasonic Technology [Russian translation],
Mir, Moscow, 1970. |
| 4. | L. P. Gor'kov, "On the forces acting on a small particle in the
acoustic field of an ideal fluid," Doklady AN SSSR, Vol. 140, No. 1, pp. 88-91, 1961. |
| 5. | L. V. King, On the acoustic radiation pressure on sphere,
Proc. Roy Soc. London, Ser. A, Vol. 147, No. 861, pp. 212-240, 1934. |
| 6. | S. S. Dukhin, "Drift theory of an aerosol particle in a standing sound wave,"
Kolloidnyi Zhurnal, Vol. 22, No. 1, pp. 128-130, 1960. |
| 7. | R. F. Ganiev and L. E. Ukrainskii, "On the motion of rigid particles suspended
in an oscillating compresible medium," Prikl. Mekhanika, Vol. 11, No. 2, pp. 3-14, 1975. |
| 8. | R. F. Ganiev and L. E. Ukrainskii, Dynamics of Particles Affected by Vibration,
Kiev, Naukova Dumka, 1975. |
| 9. | V. F. Zhuravlev and D. M. Klimov,
Applied Methods in the Theory of Oscillations [in Russian],
Nauka, Moscow, 1988. |
| 10. | N. N. Bogolyubov and Yu. A. Mitropol'skii,
Asymptotic Methods in the Theory of Nonlinear Oscillations
[in Russian], Fizmatgiz, Moscow, 1963. |
| 11. | A. Poincaré, Selected Works [Russian Translation], Volume 2, Nauka,
Moscow, 1972. |
| 12. | R. I. Nigmatulin, Dynamics of Multi-phase Media. Parts 1 and 2 [in Russian],
Nauka, Moscow, 1987. |
| 13. | Kh. A. Rakhmatulin, "Foundations of the dynamics of interpenetrating motions
of compressible media," PMM [Applied Mathematics and Mechanics], Vol. 20, No. 1, pp. 184-195, 1956. |
| 14. | R. Beyer, Nonlinear Acoustics. Physical Acoustics [Russian translation],
Vol. 2, Part 6, pp. 266-301, Moscow, Mir, 1969. |
| 15. | R. I. Nigmatulin, "Small-scale flows and surface effects in
multiphase fluid dynamics," PMM [Applied Mathematics and Mechanics], Vol. 35, No. 3, pp. 453-463, 1971. |
| 16. | H. Aref, "Stirring by chaotic advection," J. Fluid Mech.,
Vol. 143, pp. 1-21, 1984. |
| 17. | A. V. Il'in, V. P. Kuznetsov, B. G. Novitskii, and V. M. Fridman,
"Mechanism of flotation action of pulsating gas bubbles," Akust. Zhurnal,
Vol. 18, No. 4, pp. 537-545, 1972. |
|
| Received |
13 May 2005 |
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