The effects of small vibrations on a particle-fluid system relevant to material processing such as crystal growth in space have been investigated experimentally and theoretically. An inviscid model for a spherical particle of radius, $R0$, suspended by a thin wire and moving normal to a cell wall in a semi-infinite liquid-filled cell subjected to external horizontal vibrations, was developed to predict the vibration-induced particle motion under normal gravity. The wall effects were studied by varying the distance between the equilibrium position of the particle and the nearest cell wall, $H$. The method of images was used to derive the equation of motion for the particle oscillating in an inviscid fluid normal to the nearest cell wall. The particle amplitude in a semi-infinite cell increased linearly with the cell vibration amplitude as expected from the results for an infinite cell, however, the particle amplitude also changed with the distance between the equilibrium position of the particle and the nearest wall. The particle amplitude was also found to increase or decrease depending on whether the cell vibration frequency was below or above the resonance frequency, respectively. The theoretical predictions of the particle amplitudes in the semi-infinite cell agreed well with the experimental data, where the effect of the wall proximity on the particle amplitude was found to be significant for $(H∕R0<2)$ especially near the resonance frequency. Experiments performed at high frequencies well above the resonance frequency showed that the particle amplitude reaches an asymptotic value independent of the wire length.

1.
Coimbra
,
C. F. M.
, and
Rangel
,
R. H.
, 2001, “
Spherical Particle Motion in Harmonic Stokes Flows
,”
AIAA J.
0001-1452,
39
(
9
), pp.
1673
1682
.
2.
Trolinger
,
J. D.
,
Rottenkolber
,
M.
, and
Elandaloussi
,
F.
, 1997, “
Development and Applications of Holographic Particle Image Velocimetry Techniques for Microgravity Applications
,”
Meas. Sci. Technol.
0957-0233,
8
, pp.
1573
1583
.
3.
Gamache
,
O.
, and
Kawaji
,
M.
, 2005, “
Experimental Investigation of Marangoni Convection and Vibration-Induced Crystal Motion During Protein Crystal Growth
,”
Microgravity Sci. Technol.
0938-0108,
XVI-I
, pp.
342
347
.
4.
Basset
,
A. B.
, 1888,
A Treatise on Hydrodynamics
,
Deighton
, Bell and Co., Cambridge, Vol.
2
, Chap. 21. (Also New York: Dover Publications, Inc., 1961).
5.
Boussinesq
,
J. V.
, 1885, “
Sur la Resistance Qu’oppose un Liquide Indefeni au Repos, sans Pesanteur, au Mouvememt d’une Sphere Solide qu’il Mouille sur toute sa Surface
,”
C. R. Seances Acad. Sci. III
0249-6313,
100
, pp.
935
937
.
6.
Oseen
,
C. W.
, 1910, “
Uber die Stokes’sche Formel und Uber eine Verwandte Aufgabe in der Hydrodynamik
,”
Ark. Mat., Astron. Fys.
0365-4133,
6
(
29
), pp.
1
20
.
7.
Oseen
,
C. W.
, 1927,
Hydromechanik
,
, Leipzig.
8.
Stokes
,
C. G.
, 1851,
Mathematical and Physical Papers
,
Johnson Reprint Corp.
, New York, Vol.
3
, pp.
25
35
.
9.
Maxey
,
M.
, and
Riley
,
J.
, 1982, “
Equation for a Small Rigid Sphere in a Non-Uniform Flow
,”
Phys. Fluids
0031-9171,
26
, pp.
883
889
.
10.
Tchen
,
C. M.
, 1947, “
Mean Value and Correlation Problems Connected With the Motion of Small Particles Suspended in a Turbulent Fluid
,” Ph.D. thesis, Delft University.
11.
Lamb
,
H.
, 1932,
Hydrodynamics
,
Cambridge University Press
, London.
12.
Milne-Thomson
,
L. M.
, 1968,
Theoretical Hydrodynamics
,
5th ed.
,
Macmillan
, London.
13.
Eames
,
I.
,
Hunt
,
J. C.
, and
Belcher
,
S. E.
, 1996, “
Displacement of Inviscid Fluid by a Sphere Moving Away From a Wall
,”
J. Fluid Mech.
0022-1120,
234
, pp.
33
53
.
14.
Houghton
,
G.
, 1961, “
The Behaviour of Particles in a Sinusoidal Vector Field
,”
Proc. R. Soc. London, Ser. A
1364-5021,
272
, pp.
33
43
.
15.
Li
,
L.
,
Schultz
,
W. W.
, and
Merte
,
H.
, 1993, “
The Velocity Potential and the Interacting Force of Two Spheres Moving Perpendicularly to the Line Joining Their Centers
,”
J. Eng. Math.
0022-0833,
27
, pp.
147
160
.
16.
Magnaudet
,
J.
, and
Eames
,
I.
, 2000, “
The Motion of High Reynolds-Number Bubbles in Inhomogeneous Flows
,”
Annu. Rev. Fluid Mech.
0066-4189,
32
, pp.
659
708
.
17.
Magnaudet
,
J.
, 2003, “
Small Inertial Effects on a Spherical Bubble, Drop or Particle Moving Near a Wall in a Time-Dependent Linear Flow
,”
J. Fluid Mech.
0022-1120,
485
, pp.
115
142
.
18.
Hassan
,
S.
,
Kawaji
,
M.
,
Lyubimova
,
T. P.
, and
Lyubimov
,
D. V.
, 2006, “
Motion of a Sphere Suspended in a Vibrating Liquid-Filled Container
,”
ASME J. Appl. Mech.
0021-8936,
73
, pp.
72
78
.
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