Bubble Subject

It has been pointed out by numerical experiments that pulsating bubbles subject to acoustic waves can exhibit chaotic behavior [51]. A second-order model for the pulsating bubbles which is governed by slow variations in amplitude was analyzed in [51]. The ehect of parameters such as amplitude and frequency of the external wave was found to induce chaotic behavior. 

Experiments with bubbles of 50 fxm diam showed that such bubbles initiate an explosion provided they contain a gas with a high y. It was also observed that smaller bubbles took less time to initiate reaction because smaller bubbles respond more quickly to shock and the time to reach minimum volume is reduced. A comparison of the efficiency of different sized bubbles subjected to the same shock is given by the sequence in Figure 5. The diameters of the bubbles B, bi, b2, ba, and b4 are 1.75 mm, 50 /rni, 80 jum, 80 /rni, and 250 /xm, respectively. The smallest bubble caused initiation first (frame 3), and at this stage there was very little change in the volume of the largest bubble. In frame 4, initiation took place at other small bubbles. 

Equation 5.22 is known as Rayleigh-Plesset-Noltingk-Neppiras-Poritsky (RPNNP) [33, 34] equation. This equation determines the temporal evolution of the radius of a bubble subjected to a pressure change at infinity. For the case of a nonviscous liquid, the last term on the right-hand side vanishes. 

Tsiglifis, K., N. A. Pelekasis Nonlinear oscillations and collapse of elongated bubbles subject to weak viscous effects effect of internal overpressme, Phys. Fluids 19, 072106 (2007). 

In the case of two bubbles the situation becomes more complex since the bubbles will interact with each other through acoustic coupling. Typical experimental results of two bubbles subjected to Pm = —2 MPa, but with different interdistances d, are shown in Fig. 7.6. In the left case (d = 400 pm), both bubbles remain essentially spherical during their whole lifetime (so-called "weak... 

On the microscale (tissue level), surface tension forces located at the air-Uquid interface of the progressing bubble subject the EpC lining of closed airways and alveoli to a nonuniform, time-dependent, micromechanical stress field. In order to predict the magnitude of the microscale stresses imparted by the interfacial flows, fluid mechanical models are developed that are founded upon fundamental investigations of multiphase flows. 

The vapour pressure of a liquid increases with rising temperature. A few typical vapour pressure curves are collected in Fig. 7,1, 1. When the vapour pressure becomes equal to the total pressure exerted on the surface of a liquid, the liquid boils, i.e., the liquid is vaporised by bubbles formed within the liquid. When the vapour pressure of the liquid is the same as the external pressure to which the liquid is subjected, the temperature does not, as a rale, rise further. If the supply of heat is increased, the rate at which bubbles are formed is increased and the heat of vaporisation is absorbed. The boiling point of a liquid may be defined as the temperature at which the vapour pressure of the liquid is equal to the external pressure dxerted at any point upon the liquid surface. This external pressure may be exerted by atmospheric air, by other gases, by vapour and air, etc. The boiling point at a pressure of 760 mm. of mercury, or one standard atmosphere, may be termed the normal boiling point. 

Two main operational variables that differentiate the flotation of finely dispersed coUoids and precipitates in water treatment from the flotation of minerals is the need for quiescent pulp conditions (low turbulence) and the need for very fine bubble sizes in the former. This is accompHshed by the use of electroflotation and dissolved air flotation instead of mechanically generated bubbles which is common in mineral flotation practice. Electroflotation is a technique where fine gas bubbles (hydrogen and oxygen) are generated in the pulp by the appHcation of electricity to electrodes. These very fine bubbles are more suited to the flotation of very fine particles encountered in water treatment. Its industrial usage is not widespread. Dissolved air flotation is similar to vacuum flotation. Air-saturated slurries are subjected to vacuum for the generation of bubbles. The process finds limited appHcation in water treatment and in paper pulp effluent purification. The need to mn it batchwise renders it less versatile. 

The minimum ignition energy of Hquid acetylene under its vapor, when subjected to electrostatic sparks, has been found to depend on the temperature as indicated in Table 3 (86). Ignition appears to start in gas bubbles within the Hquid. 

The mechanism of hole- or bubble-forrning in metal or dye polymer layers continues to be a subject of intensive investigation (7). 

Mercury thermometers are subject to separation of the mercury column or to inclusion of bubbles of the fiU gas. These may result from shipping and handling and cause a scale offset which can usually be seen upon visual examination, and they are always recogni2ed by a 0°C verification check. Manufacturers will suggest means by which these temporary defects may be cured. 

Steel forged fittings with screwed ends may be installed without pipe dope in the threads and seal-welded (Fig. 10-130) to secure bubble-tight joints with a minimum of welders labor. They are not subject to deformation by pipe wrenches, and such couplings, bushings, and plugs are often used with the screwed fittings below. 

From Table 13-5 it can be seen that the variables subject to the designer s control are C -i- 3 in number. The most common way to utilize these is to specify the feed rate, composition, and pressure (C -i- 1 variables) plus the drum temperature To and pressure To. This operation will give one point on the equilihrium-flash cuive shown in Fig. 13-26. This cui ve shows the relation at constant pressure between the fraction V/F of the feed flashed and the drum temperature. The temperature at V/F = 0.0 when the first bubble of vapor is about to form (saturated liquid) is the bubble-point temperature of the feed mixture, and the value at V/F = 1.0 when the first droplet of liquid is about to form (saturated hquid) is the dew-point temperature. 

The rate of rise of bubbles has been discussed in many papers, including two that present good reviews of the subject [BenfrateUo, Energ Mettr, 30, 80 (1953) Haberman and Morton, Repoit 802 ... 

Two complementai y reviews of this subject are by Shah et al. AIChE Journal, 28, 353-379 [1982]) and Deckwer (in de Lasa, ed.. Chemical Reactor Design andTechnology, Martinus Nijhoff, 1985, pp. 411-461). Useful comments are made by Doraiswamy and Sharma (Heterogeneous Reactions, Wiley, 1984). Charpentier (in Gianetto and Silveston, eds.. Multiphase Chemical Reactors, Hemisphere, 1986, pp. 104—151) emphasizes parameters of trickle bed and stirred tank reactors. Recommendations based on the literature are made for several design parameters namely, bubble diameter and velocity of rise, gas holdup, interfacial area, mass-transfer coefficients k a and /cl but not /cg, axial liquid-phase dispersion coefficient, and heat-transfer coefficient to the wall. The effect of vessel diameter on these parameters is insignificant when D > 0.15 m (0.49 ft), except for the dispersion coefficient. Application of these correlations is to (1) chlorination of toluene in the presence of FeCl,3 catalyst, (2) absorption of SO9 in aqueous potassium carbonate with arsenite catalyst, and (3) reaction of butene with sulfuric acid to butanol. 

Entrained Sohds Bubble Columns with the Sohd Fluidized by Bubble Action The three-phase mixture flows through the vessel and is separated downstream. Used in preference to fluidized beds when catalyst particles are veiy fine or subject to disintegration in process. 

Most metals are subject to erosion-corrosion in some specific environment. Soft metals, such as copper and some copper-base alloys, are especially susceptible. Erosion-corrosion is accelerated by, and frequently involves, a dilute dispersion of hard particles or gas bubbles entrained in the fluid. 

Cavitation may be defined as the instantaneous formation and collapse of vapor bubbles in a liquid subject to rapid, intense localized pressure changes. Cavitation damage refers to the deterioration of a material resulting from its exposure to a cavitating fluid. 

Damage will be confined to the bubble-collapse region, usually immediately downstream of the low-pressure zone. Components exposed to high velocity or turbulent flow, such as pump impellers and valves, are subject. The suction side of pumps (Case History 12.3) and the discharge side of regulating valves (Fig. 12.6 and Case History 12.4) are frequently affected. Tube ends, tube sheets, and shell outlets in heat exchanger equipment have been affected, as have cylinder liners in diesel engines (Case History 12.1). 

By 1969, when a major survey (Thompson 1969) was published, the behaviour of point defeets and also of dislocations in crystals subject to collisions with neutrons and to the eonsequential collision cascades had become a major field of researeh. Another decade later, the subjeet had developed a good deal further and a highly quantitative body of theory, as well as of phenomenological knowledge, had been assembled. Gittus (1978) published an all-embracing text that eovered a number of new topics chapter headings include Bubbles , Voids and Irradi-ation(-enhanced) Creep . 

---