Breakup of bubbles

Equation (17) indicates that the entire distribution may be determined if one parameter, av, is known as a function of the physical properties of the system and the operating variables. It is constant for a particular system under constant operating conditions. This equation has been checked in a batch system of hydrosols coagulating in Brownian motion, where a changes with time due to coalescence and breakup of particles, and in a liquid-liquid dispersion, in which av is not a function of time (B4, G5). The agreement in both cases is good. The deviation in Fig. 2 probably results from the distortion of the bubbles from spherical shape and a departure from random collisions, coalescence, and breakup of bubbles. 

The final result is very well known in experimental studies and is usually used to evaluate a32 from known and s values. Other studies in this field include the work by Shinnar and Church (S7) who used the Kolmogoroff theory of local isotropy to predict particle size in agitated dispersions, and an analysis by Levich (L3) on the breakup of bubbles. Levich derived an expression for the critical bubble radius (the radius at which breakup begins) ... 

Most studies on heat- and mass-transfer to or from bubbles in continuous media have primarily been limited to the transfer mechanism for a single moving bubble. Transfer to or from swarms of bubbles moving in an arbitrary fluid field is complex and has only been analyzed theoretically for certain simple cases. To achieve a useful analysis, the assumption is commonly made that the bubbles are of uniform size. This permits calculation of the total interfacial area of the dispersion, the contact time of the bubble, and the transfer coefficient based on the average size. However, it is well known that the bubble-size distribution is not uniform, and the assumption of uniformity may lead to error. Of particular importance is the effect of the coalescence and breakup of bubbles and the effect of these phenomena on the bubble-size distribution. In addition, the interaction between adjacent bubbles in the dispersion should be taken into account in the estimation of the transfer rates... 

Almost all flows in chemical reactors are turbulent and traditionally turbulence is seen as random fluctuations in velocity. A better view is to recognize the structure of turbulence. The large turbulent eddies are about the size of the width of the impeller blades in a stirred tank reactor and about 1/10 of the pipe diameter in pipe flows. These large turbulent eddies have a lifetime of some tens of milliseconds. Use of averaged turbulent properties is only valid for linear processes while all nonlinear phenomena are sensitive to the details in the process. Mixing coupled with fast chemical reactions, coalescence and breakup of bubbles and drops, and nucleation in crystallization is a phenomenon that is affected by the turbulent structure. Either a resolution of the turbulent fluctuations or some measure of the distribution of the turbulent properties is required in order to obtain accurate predictions. 

Impaction of water drops on solid surfaces has been studied (G3), and under some circumstances smaller drops are detached and leave the surface. Impingement of drops on thin liquid films may also cause breakup (K3, S5). Breakup of bubbles in fluidized beds due to impingement on fixed horizontal cylinders has also been observed (G4). Sound waves may lead to instability of bubbles in liquids (S2I). 

If the bed has expanded by 50%, a = 1/3, and the bubbles would be almost touching. For higher values of a, the bubbles would be as close as particles in a packed bed or droplets in a concentrated emulsion but since bubbles in a fluid bed have no skin or surface tension, high values of a are unlikely. As h/hg approaches 2 or a approaches 0.5, frequent coalescence and breakup of bubbles will cause a transition to turbulent fluidization. The velocity of individual bubbles varies with the square root of the size. The predicted coefficient p is 0.71 [3], but data show values of 0.5-0.7 [4] ... 

The dispersiveness of a Uquid-gas mixture can be characterized by a continuous volume distribution of bubbles n(V, t, P) at the moment of time f at the point P of the considered volume. The distribution n satisfies the kinetic equation, which, with due regard of the diffusion growth and coagulation, and neglecting the breakup of bubbles, takes the form ... 

The probe measurement shows that the chord-length of bubbles has become smaller at the downstream of the throat. This fact suggests that the energy of absorbed waves has been converted into the surface-tension energy by the breakup of bubbles with increase in the bubbles-liquid interface area. 

One interesting aspect is the breakup of bubbles in turbulent liquid motions. This is one of the main processes which determine the bubble size distribution and hence the specific interfacial area a. 

A.5.1.3 Effect of System Physical Properties Liquid-phase physical properties have a significant effect on the gas holdup in stirred reactors. The main physical properties of interest are (i) surface tension (<7 ), (ii) viscosity p ), and (iii) density ip ) of the liquid phase. The gas holdup in any gas-liquid contactor is intimately related to the average bubble size. The bubble size itself is a complex function of the physical properties of the system and the turbulence prevailing in the contactor. Besides these, the total pressure at which the systan is operaling is also known to affect the bubble size. In the following discussion, some basic aspects of breakup of bubbles in a turbulent system are presented (Walter and Blanch 1986 Parthasarathy and Ahmed 1991). 

A bubble owes its stabihty to the surface tension forces. It can break when the hydrodynamic stresses are sufficiently large to overcome the forces due to surface tension (Hinze 1955). Therefore, a relative estimate of these two opposing forces is necessary to determine the operating conditions that can cause breakup of bubbles. The discussion is limited to highly turbulent flow fields since industrial operations are invariably in the turbulent region. When the two opposing forces are equal, there is a quasi equilibrium. This situation is quantified as follows ... 

Hinze (1955) proposed that bubble breakup is caused by the dynamic pressure and the shear stresses on the bubble surface induced by different liquid flow patterns, e.g., shear flow and turbulence. When the maximum hydrodynamic force in the liquid is larger than the surfaee tension foree, the bubble disintegrates into smaller bubbles. This mechanism can be quantified by the liquid Weber number. When the Weber number is larger than a eritical value, the bubble is not stable and disintegrates. This theory was adopted to prediet the breakup of bubbles in gas liquid systems (Walter and Blaneh, 1986). Calculations by Lin et al. (1998) showed that the theory underprediets the maximum bubble size and cannot predict the effeet of pressure on the maximum bubble size. 

The chain line in Fig. 3.43 denotes the merging distance from the nozzle exit, calculated from (3.26). For z> He the measured values of /b.ci agree well with the broken line, and accordingly, coalescence and breakup of bubbles hardly take place... 

Breakup of bubbles in a water jet is usually used for generating microbubbles [12,13], This is a relatively simple and convenient method. 

Apart from an increased drag force, high gas volume fractions can also lead to occurrence of coalescence and breakup of bubbles. Although the closures derived for these kinds of phenomena are rather mature for droplet-droplet interactions, this is not the case for bubble—bubble interactions. The main reason is probably the role of surfactants, which can have a considerable effect on the rigidness of the bubble surface and hence on the processes occurring on that scale. Given the fact that many closures were derived for water-air systems makes things worse, as the water quahty and in... 

The breakup of bubbles can have different causes, but in most bubbly flow applications, it is induced by the turbulent hquid flow field that exerts shear forces on the bubble surface. If these forces are larger than the surface tension, the bubble wiU break up ... 

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