Begell House Inc.
Multiphase Science and Technology
MST
0276-1459
17
4
2005
ANALYSIS OF VOID WAVE PROPAGATION AND SONIC VELOCITY USING A TWO-FLUID MODEL
293-320
10.1615/MultScienTechn.v17.i4.10
Richard T.
Lahey, Jr.
Center for Multiphase Research, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA
J.
Yin
Center for Multiphase Flow, Rensselaer Polytechnic Institute, Troy, NY, USA
P.
Tiwari
Center for Multiphase Flow, Rensselaer Polytechnic Institute, Troy, NY, USA
In this study, a state-of-the-art, ensemble-averaged, two-fluid model, which is an extension of the model proposed by Park et al. [1998], was used for the analysis of void wave propagation. Ensemble-averaging is the most fundamentally rigorous form of averaging [Buyevich, 1971], [Batchelor, 1970], since, in the ensemble averaging process, the ensemble is a set of flows that can occur at a specified position and time. Thus, the ensemble-average may include all the phasic interactions without specifying the time and length scales, in contrast to space/time averaging techniques [Drew and Passman, 1998].Since the properties of void waves have been found to be sensitive to the two-fluid model's closure relations [Boure, 1982], [Pauchon and Banerjee, 1988], [Park et al., 1990a], [Biesheuvel and Gorrisen, 1990], [Lahey, 1991], the well-posedness of the incompressible two-fluid model was studied by considering the mathematical system's void wave characteristics. The model was found to be well-posed within a range of void fractions which depends on an interfacial pressure parameter, Cp. When Cp has physically realistic values, the incompressible two-fluid model is well-posed over the whole range of void fractions.Void wave propagation phenomenon was also analyzed by performing a dispersion analysis of the linearized incompressible two-fluid model. The celerity, stability and damping of the frequency dependent void waves were obtained and regions of instability for the incompressible two-fluid model were identified. Finally, the two-phase sonic velocity implied by the compressible two-fluid model was evaluated and shown to agree with bubbly flow data.
SOME APPLICATIONS OF LASER TRAPPING ON THE DYNAMICS OF MICROBUBBLES
321-342
10.1615/MultScienTechn.v17.i4.20
H.
Takahira
Dept. of Energy Systems Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Sakai, Osaka 599-8531, Japan
T.
Nagata
Graduate Student, Graduate School of Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Sakai, Osaka 599-8531, Japan
T.
Hozumi
Graduate Student, Graduate School of Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Sakai, Osaka 599-8531, Japan
The growth or shrinkage of a laser-trapped microbubble and the merger of microbubbles are observed with a high-speed camera. We investigate the influence of gas diffusion on the stability of trapped or merged microbubbles. Two kinds of equilibrium radii are observed for shrinking microbubbles. The first one is related to the equilibrium surface concentration of surfactant. The other is related to the decrease of the surface tension due to the compression of the surface area at the maximum surfactant concentration. The experimental results are compared with numerical solutions by taking the influence of the variation of surface tension on the gas diffusion into account. The simulations agree with the experimental results. The laser trapping technique is also applied to the motion of a microbubble in a shear flow. We observe the motion of a microbubble initially trapped in a narrow channel under shear flows. It is shown that as the radius of a microbubble becomes small, the bubble escapes from the laser trap being more repelled by the optical force. The oscillatory translation, which is induced by the rotation of the laser cone, is observed when the bubble is inside the laser cone. The theoretical predictions in which the buoyancy force, the fluid dynamics forces and the optical force are taken into account agree with the experiments.
STRUCTURE FORMATION IN ACOUSTIC CAVITATION
343-371
10.1615/MultScienTechn.v17.i4.30
S.
Konovalova
Institute of Mechanics, Ufa Branch of the Russian Academy of Sciences, Ufa, Russia
I. S.
Akhatov
Dept. of Mechanical Engineering & Applied Mechanics, North Dakota State University, Fargo, ND, USA
Bubble clouds forming in a liquid subject to a strong acoustic excitation, that is called acoustic cavitation, show a complicated slowly varying filamentary structure. This bubbly mixture represents a multiphase system whose physical origin is still not completely understood. Basic physical interactions in such bubbly liquid comprised of nonlinear bubble dynamics, Bjerknes and drag forces, interaction between bubbles, wave dynamics, etc. In the introduction section a brief overview of various theoretical approaches to this phenomenon is presented. The paper gives a systematic representation of particle model for describing the structure formation process in a bubbly liquid. In the framework of the particle model all bubbles are treated as interacting objects that move in the liquid.A mathematical model for coupled, radial and translational, motion of a small spherical cavitation bubbles driven below its resonance frequency in a strong acoustic field (Pa > 1 bar, f = 20 kHz) is presented. Numerical analysis of the dynamics of a single bubble shows that, within the limits of harmonic resonances of the system, period-doubling bifurcations cascades with transitions to chaos and back to regular dynamics take place. A possible mechanism for the erratic dancing mode of bubble motion is proposed. Besides erratic dancing, the low-frequency quasi-periodic translational motion (periodic dancing) mode is observed at certain values of bubble radii. For a pair of interacting bubbles various dynamic modes are obtained: simple attraction, periodic motion and asymptotic motion, when the bubbles tend to take steady positions on a vertical line crossing the pressure antinode. In the last two cases bubbles do not coalesce, but are bound into couples, which cannot be predicted by a classic linear theory. This is explained by so-called giant response of small bubbles. Thus, the nonlinear effects can result in self-organization of bubble clouds. Structure formation processes in bubble clouds are simulated numerically. The characteristic bubble sizes in the structures, as well as dimension and shape of the structures are in qualitative agreement with the experimental observations.