Motion bubble dynamics

Ettehadieh, B., Yang, W. C., and Haldipur, G. B., Motion of Solids, Jetting and Bubbling Dynamics in a Large Jetting Fluidized Bed, Powder Tech., 54 243 (1988)... 

Another flaw of the earlier investigations on the bubble dynamics was that al though there has been ample discussion on whether the compressibility of the cavitating medium plays an important role on the cavity motion, there have been no illustrations, where the difference between the predictions of equations considering the compressibility of the medium (e.g. Gilmore model [Gilmore, 1954]... 

Moholkar and Pandit (2001b) have also extended the nonlinear continuum mixture model to orifice-type reactors. Comparison of the bubble-dynamics profiles indicated that in the case of a venturi tube, a stable oscillatory radial bubble motion is obtained due to a linear pressure recovery (with low turbulence) gradient, whereas due to an additional oscillating pressure gradient due to turbulent velocity fluctuation, the radial bubble motion in the case of an orifice flow results in a combination of both stable and oscillatory type. Thus, the intensity of cavitation... 

In addition to the boiling curve measurements, the bubble dynamics have been photographed along the entire heated surface of the platinum wire at a saturated boiling heat flux of 0.358 + 0.006 W.mm for the Natrosol 250 HHR and Separan AP-30 solutions. Both polymer solutions have been tested only at a relative viscosity of 1.08. Slow motion films of the bubble dynamics have been analyzed to determine the average number density of active nucleation sites, and the frequency distribution of bubble departure diameters. 

In the foregoing demonstration, we had limited ourselves to include only the kinematic aspects of bubble motion. A dynamic model including force balances on bubble motion would have called for adding the bubble velocity also as a particle state variable. Such a model could also have been considered allowing for bubble velocity to be a random process satisfying a stochastic differential equation of the type (2.11.14). The basic objective of this example has been to demonstrate applications in which particle state can be a random process. The next and the last example in this chapter considers a similar application, but with a distinction that can help address an entirely different class of problems. 

Ettehadieh B, Yang WC, Hadipur GB. Motion of solids, jetting and bubbling dynamics in a large jetting fluidized bed. Powder Technol 54 243-254, 1988. 

Fig. 4. Dynamics of bubble motion. Laser-induced cavitation in silicone oil upper portion is the experimental observations at 75,000 frames/second lower curve compares the experimentally observed radius versus theory. [W. Lauterborn (47).]...

Auton, T. R., The dynamics of bubbles, drops and particles in motion in liquids, PhD thesis, University of Cambridge (1983). 

In any cavitation field most of the visible bubbles will be oscillating in a stable manner and it is perhaps pertinent that we concentrate our discussions first on the fate of such bubbles in the acoustic field. If we assume that we have a bubble with an equilibrium radius, R, existing in a liquid at atmospheric pressure Pjj, then the oscillation of the bubble and in particular the motion of the bubble wall, under the influence of the applied sinusoidal acoustic pressure (P ) is a simple dynamical problem, akin to simple harmonic motion for a spring. 

The scope of kinetics includes (i) the rates and mechanisms of homogeneous chemical reactions (reactions that occur in one single phase, such as ionic and molecular reactions in aqueous solutions, radioactive decay, many reactions in silicate melts, and cation distribution reactions in minerals), (ii) diffusion (owing to random motion of particles) and convection (both are parts of mass transport diffusion is often referred to as kinetics and convection and other motions are often referred to as dynamics), and (iii) the kinetics of phase transformations and heterogeneous reactions (including nucleation, crystal growth, crystal dissolution, and bubble growth). 

A. H. Zewail Prof. Chetgui s observations are very interesting. As discussed in this conference, coherent wavepacket motion has been observed in condensed phases in many laboratories. In Prof. Chergui s experiment it is now possible to study the time scale for bubble formation. Molecular dynamics should tell us the nature of forces which maintain any coherence in such systems. 

P 11] Simulations were carried with a simplified chamber and air-bubble pocket geometry. Details on this geometry and the several assumptions taken for describing the fluid dynamics can be found in [23] and are not described further here. Generally, the experimental known fluid dynamic features were taken into account, e.g. the convective motion based on vortices was assumed also in the model. 

Fig. 12. Typical results reported by Tomiyama ei al. (1993) on the effect of the Morton number M (atEotvSs number Eo = 10) on the shape and dynamics of a single bubble rising in (a) a Newtonian liquid, and (b) graphical correlation due to Grace (1973) and Grace et al. (1976). [Part (a) reprinted from Nuclear Engineering and Design, Volume 141, Tomiyama, A., Zun, I., Sou, A., and Sakaguchi, T., Numerical analysis of bubble motion with the VOF method, pp. 69-82, Copyright 1993, with permission from Elsevier Science. Part (b) reprinted from Grace, R., Clift, R., and Weber, M.E., Bubbles, Drops, and Particles. Academic Press, Orlando, 1976. Reprinted by permission of Academic Press.)...

Currently available data for the flow properties of the fluidized catalyst bed are fragmentary, since the local motion of the emulsion phase is diflicult to measure experimentally. Therefore, it is useful to clarify the flow properties of the bed in terms of our knowledge of bubble columns. First, the fluid-dynamic properties of the bubble columns will be explained then, the available data will be adapted to apply to fluid catalyst beds. The reader will be able to picture an emulsion phase of carefully prepared catalyst particles operating in intense turbulence for fluidized beds under conditions of practical interest. This turbulence distinguishes the flow properties of fluid catalyst beds from those of widely studied teeter beds. 

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