Bubble-induced

Figure 8. Distributor design suggested by Werther and Xi (1993) to separate the jet attrition and bubble-induced attrition.

Modeling ofBubble-Induced Attrition. Merrick and Highley (1974) have modeled bubble-induced attrition as a comminution process. According to Rittinger s law of size reduction by abrasion (cfi, Perry, 1973), the rate of creation of new surface area AS Al is proportional to the rate of energy input Ah. At... 

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,... 

Modeling of Cyclone Attrition. A very simple model of cyclone attrition may be formulated in analogy to the models discussed with respect to jet attrition and bubble-induced attrition (Reppenhagen and Werther, 1997). 

In the emulsion phase/packet model, it is perceived that the resistance to heat transfer lies in a relatively thick emulsion layer adjacent to the heating surface. This approach employs an analogy between a fluidized bed and a liquid medium, which considers the emulsion phase/packets to be the continuous phase. Differences in the various emulsion phase models primarily depend on the way the packet is defined. The presence of the maxima in the h-U curve is attributed to the simultaneous effect of an increase in the frequency of packet replacement and an increase in the fraction of time for which the heat transfer surface is covered by bubbles/voids. This unsteady-state model reaches its limit when the particle thermal time constant is smaller than the particle contact time determined by the replacement rate for small particles. In this case, the heat transfer process can be approximated by a steady-state process. Mickley and Fairbanks (1955) treated the packet as a continuum phase and first recognized the significant role of particle heat transfer since the volumetric heat capacity of the particle is 1,000-fold that of the gas at atmospheric conditions. The transient heat conduction equations are solved for a packet of emulsion swept up to the wall by bubble-induced circulation. The model of Mickley and Fairbanks (1955) is introduced in the following discussion. 

External energy sources for active mixing are, for example, ultrasound [22], acoustic, bubble-induced vibrations [23,24], electrokinetic instabilities [25], periodic variation of flow rate [26-28], electrowetting induced merging of droplets [29], piezoelectric vibrating membranes [30], magneto-hydrodynamic action [31], small impellers [32], integrated micro valves/pumps [33] and many others, which are listed in detail in Section 1.2. 

Other micromixers based on various principles have also been constructed. These principles include vortex [492], eddy diffusion [493-501,654,955], rotary stirring [502], turbulence [495,503], EK instability [504—506], chaotic advection [248,507-513], magnetic stirring [514], bubble-induced acoustic mixing [515], and piezoelectric actuation [516,517]. 

Bubble induced secondary flow Moving bubbles generate secondary flows and wakes which promote local mixing near the membrane surface. Slug flow also results in an annular falling film as displaced liquid flows downward between the slug and the tube wall. 

The lateral distribution of gas bubbles induces bulk recirculation of the emulsion phase. For teeter beds, the flow pattern of solid particles has been studied by Werther (W7, W8), Bui ess and Calderbank (B17), Oki and Shirai (03) and Whiteheade/a/. (W12), in experiments carried out with alumina particles, quartz sand, and petroleum coke under conditions of dp s 83 /Ltm and (f/, - Umd/Umf — 14. The mode of bulk circulation was centrally descending and peripherally ascending for If/Dr 1. while the ascending flow moved toward the center with increasing Lf/Dx. Werther (W8) showed that this circulation flow is caused entirely by bubbles which carry solid particles upward in their wakes. 

There is no substantial literature on direct sparging of non-porous microcarrier cultures. As is discussed in section 4.6, the difficulty is that the presence of bubbles induces bead flotation, i.e. attachment of beads to bubbles, and the formation of large bead-bubble aggregates that tend to rise and accumulate at the surface of the culture vessel, which is a highly undesirable characteristic. Nevertheless, it is possible slowly to sparge microcarrier cultures without undue cellular injury if suitable surfactants/antifoams (e.g. Pluronic F-68 or Medical Emulsion AF see section 4.6) are used. 

To account for the process of bubble-induced gas exchange we modify the gas transfer equation to include both the transfer at the air-water interface, Fawi (Eq. (10.1)), and the flux caused by bubbles, Fb. The total flux, Fj, is now... 

A schematic diagram of steady-state gas supersaturation caused by bubble processes when there is no net flux at the air-water interface. The small symbols represent gas molecules in the air and dissolved in the water. The greater concentration of these symbols in the water relative to air on the left side of the diagram indicates that the dissolved gas is supersaturated in the water. The bubble-induced flux, Fb, into surface waters, illustrated on the right side of the diagram, is balanced by a diffusive flux across the air-water interface, Eawi. indicated on the left side. 

The degree of supersaturation necessary to maintain a diffusive flux equal to the bubble-induced flux is determined by dividing both sides of the above equation by, substituting the Henry s Law relation, assuming and using the definition of Gq in... 

Anode + rod and clamp voltage drop Bubble induced voltage drop... 

The spouted bed technique has become established as an alternative to fluidization for handling particulate solids that are too coarse and uniform in size for good fluidization. Although the areas of application of spouted beds overlap with those of fluidized beds, the flow mechanisms in the two processes are very different. Agitation of particles in a spouted bed is caused by a steady axial jet and, as compared with the more random and complex bubble-induced particle flow patterns in most fluidized beds, is regular as well as cyclic. 

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