Dynamics of Vapor Bubble

Zuber N (1961) The dynamics of vapor bubbles in non-uniform temperature fields. Int J Heat Mass Transfer 2 83-98... 

Forster, K. and Zuber, N. (1955) AIChE J 1, 531. Dynamics of vapor bubbles and boiling heat transfer. 

Tokuda, N. Dynamics of vapor bubbles in binary liquid mixtures with translatory motion. 4th Int. Heat Transfer Conf., Paris 1970, B 7.5... 

M. S. Plesset and A. Prosperetti, Bubble dynamics and cavitation, Annu. Rev. Fluid Mech. 9, 145-85 (1977). Two more recent papers are Y. Hao and A. Prosperetti, The dynamics of vapor bubbles in acoustic pressure fields, Phys. Fluids 11, 2008-19 (1999) A. Prosperetti, The thermal behavior of oscillating gas bubbles, 1 Fluid Mech. 222, 587-615 (1991). 

ASME JSME Thermal Eng loint Conf Proc 5 455 62 Nigmatulin IR (1991) Dynamics of multiphase media and 2. Hemisphere, London Ory E, Yuan H, Prosperetti A, Popinet S, Zaleski S (2000) Growth and coUapse of vapor bubble in a narrow tube. Phys Fluids 12 1268-1277... 

Mukheqee, A. and Dhir, V.K. (2004) Numerical and experimental study of bubble dynamics associated with lateral merger of vapor bubbles during nucleate pool boiling. In Press, Journal of Heat Tranter. 

Cavitation-erosion is the loss of material caused by exposure to cavitation, which is the formation and collapse of vapor bubbles at a dynamic metal-liquid interface—for example, in rotors of pumps or on traihng faces of propellers. This type of corrosion causes a sequence of pits, sometimes appearing as a honeycomb of small relatively deep fissures (see Uhlig s Corrosion Handbook, 2nd edition, R. W. Revie, editor, Wiley, New York, 2000, Fig. 12, p. 261). 

Transient cavitation is generally due to gaseous or vapor filled cavities, which are believed to be produced at ultrasonic intensity greater than 10 W/cm2. Transient cavitation involves larger variation in the bubble sizes (maximum size reached by the cavity is few hundred times the initial size) over a time scale of few acoustic cycles. The life time of transient bubble is too small for any mass to flow by diffusion of the gas into or out of the bubble however evaporation and condensation of liquid within the cavity can take place freely. Hence, as there is no gas to act as cushion, the collapse is violent. Bubble dynamics analysis can be easily used to understand whether transient cavitation can occur for a particular set of operating conditions. A typical bubble dynamics profile for the case of transient cavitation has been given in Fig. 2.2. By assuming adiabatic collapse of bubble, the maximum temperature and pressure reached after the collapse can be estimated as follows [2]. 

The bubble formed in stable cavitation contains gas (and very small amount of vapor) at ultrasonic intensity in the range of 1-3 W/cm2. Stable cavitation involves formation of smaller bubbles with non linear oscillations over many acoustic cycles. The typical bubble dynamics profile for the case of stable cavitation has been shown in Fig. 2.3. The phenomenon of growth of bubbles in stable cavitation is due to rectified diffusion [4] where, influx of gas during the rarefaction is higher than the flux of gas going out during compression. The temperature and pressure generated in this type of cavitation is lower as compared to transient cavitation and can be estimated as ... 

In this section we develop a dynamic model from the same basis and assumptions as the steady-state model developed earlier. The model will include the necessarily unsteady-state dynamic terms, giving a set of initial value differential equations that describe the dynamic behavior of the system. Both the heat and coke capacitances are taken into consideration, while the vapor phase capacitances in both the dense and bubble phase are assumed negligible and therefore the corresponding mass-balance equations are assumed to be at pseudosteady state. This last assumption will be relaxed in the next subsection where the chemisorption capacities of gas oil and gasoline on the surface of the catalyst will be accounted for, albeit in a simple manner. In addition, the heat and mass capacities of the bubble phases are assumed to be negligible and thus the bubble phases of both the reactor and regenerator are assumed to be in a pseudosteady state. Based on these assumptions, the dynamics of the system are controlled by the thermal and coke dynamics in the dense phases of the reactor and of the regenerator. 

If at any point the local velocity is so high that the pressure in a liquid is reduced to its vapor pressure, the liquid will then vaporize (or boil) at that point and bubbles of vapor will form. As the fluid flows on into a region of higher pressure, the bubbles of vapor will suddenly condense—in other words, they may be said to collapse. This action produces very high dynamic pressures upon the solid walls adjacent, and as this action is continuous and has a high frequency, the material in that zone will be damaged. Turbine runners, pump impellers, and ship screw propellers are often severely and quickly damaged by such... 

The distillation column used in this study is designed to separate a binary mixture of methanol and water, which enters as a feed stream with flow rate F oi and composition Xp between the rectifying and the stripping section, obtaining both a distillate product stream D oi with composition Ad and a bottom product stream 5vo/ with composition Ab. The column consists of 40 bubble cap trays. The overhead vapor is totally condensed in a water cooled condenser (tray 41) which is open at atmospheric pressure. The process inputs that are available for control purposes are the heat input to the boiler Q and the reflux flow rate L oi. Liquid heights in the column bottom and the receiver drum (tray 1) dynamics are not considered for control since flow dynamics are significantly faster than composition dynamics and pressure control is not necessary since the condenser is opened to atmospheric pressure. 

During ultrasonic irradiation of aqueous solutions, OH radicals are produced from dissociation of water vapor upon collapse of cavitation bubbles. A fraction of these radicals that are initially formed in the gas phase diffuse into solution. Cavitation is a dynamic phenomenon, and the number and location of bursting bubbles at any time cannot be predicted a priori. Nevertheless, the time scale for bubble collapse and rebound is orders of magnitude smaller than the time scale for the macroscopic effects of sonication on chemicals (2) (i.e., nanoseconds to microseconds versus minutes to hours). Therefore, a simplified approach for modeling the liquid-phase chemistry resulting from sonication of a well-mixed solution is to view the OH input into the aqueous phase as continuous and uniform. The implicit assumption in this approach is that the kinetics of the aqueous-phase chemistry are not controlled by diffusion limitations of the substrates reacting with OH. 

In general, the temperatures in the gas and liquid both will change with time primarily because of the release (or use) of latent heat at the interface as vapor condenses (or liquid vaporizes). However, for present purposes, we neglect this effect and consider that T = Too = constant everywhere in the system. In terms of practical application, this is a severe assumption, and it is well known that thermal effects can have an important influence on the dynamics of gas/vapor bubbles. However, the isothermal problem retains many of the interesting qualitative features of the lull problem and is sufficiently general for our present illustrative purposes. Thus we assume that... 

Each of these tiny bubbles is enclosed in a spherical shell of liquid particles. The shell acts as a surface that, except for its shape, is the same as the surface at the top of the liquid. Particles can escape from the surface (evaporate) into a vapor phase inside the bubble, and when particles in that vapor phase collide with the surface of the bubble, they return to the liquid state (condense). A dynamic equilibrium can form in the bubble between the rate of evaporation and the rate of condensation, just like the liquid-vapor equilibrium above the liquid in the closed container (Figure 14.11). 

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