Bubbling and Hydrodynamic Considerations

In membrane processing the application of surface shear is required to control concentration polarization and fouling for high solids feeds or to assist cake removal for batch membrane filtration of low solids feeds. For submerged membranes the common practice is to use two-phase bubbly flow to induce surface shear. This section deals with the role of bubbles as well as other hydrodynamic aspects of submerged membranes. 

There have been few experimental measurements of Ul in submerged systems, but the reported values are in the range 0.1-0.5 m/s (Liu et ah, 2003 Madec, 2004). A decrease in fouling rate (dTMP/df) as Ul increased was reported by Liu et al. (2003). However, this is probably only part of the story, as decreased fouling rate appears to be linked to bubble-induced instabilities as well as average shear stress effects. 

In MBRs bubbling also has a role in mixing the reactor contents, presumably through the induced liquid circulation [Eq. (10.11)]. There is some evidence from tracer studies that mixing induced by bubbles may be a httle more effective with submerged hollow fibers than flat-sheet membranes because the latter act as baffles in the vessel (Wang et al., 2008). 

The amount of air sparging required to control fouling in submerged membrane systems is an important operating cost. This is because the power required, P i, is a function of the 

Specificalions for airflow rate requirements for MBRs are based on experience rather than theoretical analyses, although there is a growing hterature on the effect of bubble flow on fouling control [see reviews by Cui et al. (2003) and Le Clech et al. (2006)]. Judd (2006) has summarized a wide range of available data for submerged MBRs as the specific air demand (SAD) and defines two parameters  

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LaFrance and Grasso [29] report an application of MD methods (again, termed trajectory analysis ) to the dissolved air flotation of nitrocellulose particles of 2.3 fim diameter. This work also neglected Brownian motion considerations, but included electrostatic, van der Waals, the Lewis acid-base interaction forces, and hydrodynamic forces. Lafrance and Grasso found limiting trajectories by successions of forward integrations, and from this calculated the capture efficiency per air bubble as a function of solution chemistry. 

At first the effect of sedimentation on collision efficiency is taken into account since it can strongly decrease the role of the hydrodynamic field of bubble and DAL. This consideration proves to be more obvious when the method of collision efficiency calculation is used as proposed by Dukhin Derjaguin (1958). 

Rulyov (1988) considered the inertial hydrodynamic interaction of a bubble with a conical particle with its axis perpendicular to the bubble surface. The consideration of BCS (similar to that described in Sections 11.1-11.2) was supplemented by the consideration of ACS and special attention was paid to the energy dissipation. 

The theory of Dukhin (1981) was generalised by Listovnichiy Dukhin (1986) where the effect of stabilisation is considered under arbitrary hydrodynamic flow conditions around a bubble and the effect of convective transfer of surfactant into the adsorption layer was taken into account. Numerical estimations of 0, were carried out and it was shown that the effect of the liquid interlayer stabilisation by a DAL decreases the flotation efficiency over a wide range of system parameters by more than an order of magnitude. Numerical estimations also point to the fact that the effects under consideration have a much smaller influence on flotation of spherical particles than of disk-shaped particles. 

Electrolyte circulation can be improved by hybridized EMM with low-frequency tool vibration [5]. It necessitates the development of a suitable microtool vibration system in EMM for effective micromachining operation. Piezoelectric transducer (PZT) can be used for vibrating microtools [6]. Vibration has hydrodynamic effects on the bubble behavior, which has been utilized for the effective removal of sludge, hydrogen bubbles, and the replenishment of fresh electrolyte. The microtool vibrates longitudinally with the definite combination of amplitude of vibration and frequency of vibration. Vibrations within the machining zone, in the stagnant electrolyte, have considerable influence on the diffusion and convection of dissolved metal ions. 

The main advantage of the Eulerian-Lagrangian formulation comes from the fact that each individual bubble is modeled, allowing consideration of additional effects related to bubble-bubble and bubble-liquid interactions. Mass transfer with and without chemical reaction, bubble coalescence, and redispersion, in principle, can be added directly to an Eulerian-Lagrangian hydrodynamic model. The main disadvantage of the Eulerian-Lagrangian approach is that only a limited number of particles (bubbles) can be tracked, such as when the superficial gas velocity is low (Chen et al., 2005), due to computer limitations. 

Inhomogeneous or multiphase reaction systems are characterised by the presence of macroscopic (in relation to the molecular level) inhomogeneities. Numerical calculations of the hydrodynamics of such flows are extremely complicated. There are two opposite approaches to their characterisation [63, 64] the Euler approach, with consideration of the interfacial interaction (interpenetrating continuums model) and the Lagrange approach, of integration by discrete particle trajectories (droplets, bubbles, and so on). The presence of a substantial amount of discrete particles in real systems makes the Lagrange approach inapplicable to study motion in multicomponent systems. Under the Euler approach, a two-phase flow is described... 

Internal thermodynamic and hydrodynamic factors aside for the moment, it should be remembered that foams are sensitive to a number of external environmental stresses, which act to bring about bubble coalescence and foam collapse. Those include vibration, the presence of solid particles, organic contaminants, and temperature differentials. It will therefore be important to take such factors into consideration when carrying out foaming studies or formulating a foam systems. 

During the past five decades, gas-solids hydrodynamics studies principally have concentrated on solids phase measurements and characterization and have largely ignored the gas phase. Pneumatic conveying is an example solids are the commodity of interest the gas phase is only important in the sense that power requirements for blowers and compressors should be minimized. In studies of bubbling and turbulent fluidized beds, experimentalists study the spatial and temporal distribution of bubbles, but, typically, they employ solids measurement devices from which gas phase hydrodynamics are inferred. Circulating fluidized bed researchers also have devoted considerable attention to the solids phase, but since 1988 only 40 publications have appeared that deal with gas phase hydrodynamics. 

This review deals mainly with the discussion of various macroscopic hydro-dynamic, heat, and mass transfer characteristics of bubble columns, with occasional reference to the analogous processes in modified versions of bubble columns with a variety of internals. The hydrodynamic considerations include determination of parameters like flow patterns, holdup, mixing, liquid circulation velocities, axial dispersion coefficient, etc., which all exert strong influence on the resulting rates of heat and mass transfer and chemical reactions carried out in bubble columns. Different correlations developed for estimating the aforementioned parameters are presented and discussed in this chapter. 

In system 1, the 3-D dynamic bubbling phenomena in a gas liquid bubble column and a gas liquid solid fluidized bed are simulated using the level-set method coupled with an SGS model for liquid turbulence. The computational scheme in this study captures the complex topological changes related to the bubble deformation, coalescence, and breakup in bubbling flows. In system 2, the hydrodynamics and heat-transfer phenomena of liquid droplets impacting upon a hot flat surface and particle are analyzed based on 3-D level-set method and IBM with consideration of the film-boiling behavior. The heat transfers in... 

Ultrafast processes 1 and 2 will not further be considered rather they will be used to set a temporal lower limit of t > 10 ps for the electron tunneling dynamics from the bubble. In what follows we shall consider the dynamics of electron tunneling in conjunction with the bubble motion in the cluster. This problem is of considerable interest, because electron tunneling is expected to be extremely sensitive to the spatial hydrodynamic motion of the bubble, providing a microscopic nanoprobe for superfluidity in He clusters [245, 251], as experimentally demonstrated by Northby and co-workers [208, 209] and by Toennies and co-workers [99, 242-245]. 

Three-phase fluidized beds and slurry reactors (see Figs. 30g-l) in which the solid catalyst is suspended in the liquid usually operate under conditions of homogeneous bubbly flow or chum turbulent flow (see regime map in Fig. 33). The presence of solids alters the bubble hydrodynamics to a significant extent. In recent years there has been considerable research effort on the study of the hydrodynamics of such systems (see, e.g., Fan, 1989). However, the scale-up aspects of such reactors are still a mater of some uncertainty, especially for systems with high solids concentration and operations at increased pressures it is for this reason that the Shell Middle Distillate Synthesis process adopts the multi-tubular trickle bed reactor concept (cf. Fig. 30e). The even distribution of liquid to thousands of tubes packed with catalyst, however poses problems of a different engineering nature. 

Extension of these principles to the flotation of small-sized particles require, first, the inclusion of the hydrodynamic factor because particles deposit on a bubble from the stream of liquid flowing around it, and second, the consideration of mobility of the bubble surface if the level of the impurities which retard the surface movement is not very high. The second factor is manifest in flotation, and the specific feature of this process is connected with it. 

For this investigation, the bubbles are assumed to be spherical and their diameters are taken to be of the order of millimetre having a non-retarded surface (this is necessary for the use the theory developed in Section 11.3, which enables to describe the hydrodynamic field of bubble by a potential one). In addition, only spherical particles with smooth surface are considered (this makes it possible to use the results of the consideration of film thinning at the inertia impact of a particle on bubble surface from Section 11.2 and experimented data). Upper and lower limits of particle size are assumed, the necessity of which will be explained later. 

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