Bubble kinetic energy

Fig. 21. Calculated initial bubble kinetic energy vs subcooling (Bll).

At higher vapor loads, the kinetic energy of the vapor rather than the bubble burst supphes the thrust for jets and sheets of hquid that are thrown up as well as the energy from breakup into spray. This yields much higher levels of entrainment. In distillation trays it is the most common limit to capacity. 

The key to the good resolution of ZEKE-PFI is in its discrimination against electrons with >1 cm-1 kinetic energy. This is due to the delayed extraction and time-gated detection. A bubble of 1 cm"1 electrons expands to a radius of 1.6 cm during the 2.0 ps delay. Such kinetic electrons either miss the detector or arrive... 

Vaux (1978), Ulerich et al. (1980) and Vaux and Schruben (1983) proposed a mechanical model of bubble-induced attrition based on the kinetic energy of particles agitated by the bubble motion. Since the bubble velocity increases with bed height due to bubble coalescence, the collision force between particles increases with bed height as well. The authors conclude that the rate of bubble-induced attrition, Rbub, is then proportional to the product of excess gas velocity and bed mass or bed height, respectively,... 

In whichever approach, the common denominator of most operations in stirred vessels is the common notion that the rate e of dissipation of turbulent kinetic energy is a reliable measure for the effect of the turbulent-flow characteristics on the operations of interest such as carrying out chemical reactions, suspending solids, or dispersing bubbles. As this e may be conceived as a concentration of a passive tracer, i.e., in terms of W/kg rather than of m2/s3, the spatial variations in e may be calculated by means of a usual transport equation. 

In the absence of surface tension influences, the drop formation at vertical orifices is expressed by the equation given for bubble formation. The force due to kinetic energy of the liquid is neglected as its component is zero in the vertical direction. The drop ascends right from the beginning according to the equation of motion and detaches when it has covered a distance equal to the diameter of the nozzle. 

No data are available for other orientations, but equations similar to those for bubble formation, taking the appropriate component of the force due to kinetic energy, will be applicable. 

This collapse will be augmented by an increase in the surface tension effect (2cr/R) as the cavity becomes smaller i.e. the total collapse pressure is (Pj( + 2cr/R), but will be opposed by the increase in the pressure within the bubble due to the compression of gas i. e. expanding pressure, By analogy with the empty cavity, the work done by the new hydrostatic pressure (Pj(), minus that of the layer adjacent to the bubble, is equal to the kinetic energy of the liquid. 

The influence of gas density on the gas-liquid interfacial area could be related to the flow patterns and to the interpenetration between gas and liquid. It is probable that the gas-liquid interface results from two distinct mechanisms. The first one is based on the extent of the solid surface where liquid films could develop (wetting of particles), virtually controlled by fluid velocities and liquid properties. The second mechanism depends on the kinetic energy content of the gas phase. The more important the gas inertia, the more important is the contribution of fine gas bubbles penetrating liquid films. 

The bubble energy is conveniently expressed as the sum of the pressure-volume work, 6pV, the surface kinetic energy, eSKl the surface potential energy, eSP, and the volume kinetic energy, eVK, arising from the removal of atoms from the cavity boundary to the bulk of the liquid. 

F-factor F This is the square root of the kinetic energy of the gas, defined by Eq. (14-76). The velocity in Eq. (14-76) is usually (not always) based on the tower cross-sectional area A , the net area A, or the bubbling area AB. The user should beware of any data for which the area basis is not clearly specified. 

Entrainment E is inherent in the bubbling process and can stem from a variety of sources, as shown by Fig. 14-89. However, the biggest practical problem is entrainment generated by the kinetic energy of the flowing vapor rather than the bubbling process. As vapor velocity approaches the flooding limit [Eq. (14-168)], the entrainment rises approximately with (velocity)8. 

A height of three to four meters above the bed is required to allow solids entrained by the bubble wakes into the freeboard to return to the bed surface. The initial velocity of the solids that splash into the freeboard is 4 to 8 times the bubble rise velocity (100) and the freeboard height is determined by the kinetic energy of the larger particles for which drag forces are relatively unimportant. For a bubble rise velocity of 3.2 m/s (estimated from + 0.71 /gd (29) and a bubble diameter of... 

Injectors are two-component nozzles which utilize the kinetic energy of the liquid propulsion jet to disperse the gas continuum into very fine gas bubbles and to distribute them into the liquid. (In contrast, with ejectors, the kinetic energy is utilized to produce suction.) Their advantage over stirrers is that the liquid jet causes gas dispersion directly while the stirrer has to set the entire contents of the vessel in motion in order to generate the necessary shear rate in the liquid. Their disadvantage is the predominance of severe coalescence on account of the high gas bubble density in the free jet of the G/L dispersion. However, in contrast to stirrers, the injector cannot cause redispersion of the large gas bubbles. 

To give an example of the dramatic influence which the geometric parameters can have on coalescence behavior, Fig. 77 shows Y(X) correlations for the industrial-size slot injector which were obtained in a vessel of 30 x 8 m water height. The injector was positioned 1 m above the bottom at the vessel wall in such a way that its axis formed an angle of 0°, + 35° resp. - 35° with the horizontal. Only in the last case, the free jet was pointed towards the floor and decomposed into the bubble swarm just above it. Near the floor, the suction of the free jet is weakest on account of bottom friction. Furthermore, the bubble swarm which has formed does not exert a chimney effect there. Consequently, liquid entrainment into the free jet is suppressed at exactly that point at which it would be particularly supportive of coalescence on account of the weakened kinetic energy of the free jet. 

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