Homogeneous bubbling flow

Of interest is a recent theoretical relation for eg in gas-liquid bubble columns based on liquid circulation and claimed to be valid both in the homogeneous bubble flow regime and in the chum-turbulent regime, also for non-Newtonian fluids. For power law fluids with... 

In the homogeneous bubble flow regime, the gas phase is generally assumed to move in plug flow and the liquid phase axial mixing is characterized by the axial dispersion coefficient. The axial dispersion coefficient is dependent upon gas velocity and column diameter according to (26,41,42)... 

For one-dimensional homogeneous bubble flow, the wake usually reduces the ascending velocity b of the bubbles. The extent of reduction, however, depends on the rate of wake renewal, as shown in Section V,A,2. For the case of Section V,B,1, the wake has no influence on b. Thus the way by which the wake influences b depends strongly on the physical situation encountered. In what follows the typical recirculation flow under intense turbulence will be treated, since this is the focus of our interest. We now show that the influence of the wake can be neglected in this flow regime. 

For water and dilute aqueous solutions the bubbles are generally uniformly distributed in the liquid at low gas flow rates [132]. The bubble size distribution is relatively narrow and the bubbles rise uniformly through the column. This is known as homogeneous flow and is sketched in Fig 8.3. Homogeneous bubbly flow may occur in small scale apparatus with superficial gas velocities below 5 (cm/s). 

Carteluer, a., Andreotti, M. Secret, P. 2009 Induced agitation in homogeneous bubbly flows at moderate particle Reynolds number. Physical Review E 80, 065301(R). 

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. 

Vertical Downflow Mode hi the case of vertical downflow, only the coaxial and homogeneous bubbly flow regimes have been reported (Ben Brahim et al. 1984 Bhutada and Pangarkar 1987 Panchal et al. 1991). 

For low gas to liquid flow ratio, homogeneous bubble flow with very small bubbles dispersed in the continuous liquid phase is observed. This type of bubbly flow (also referred to as emulsion) regime covers the entire diffuser from its throat to the outlet. 

Since an averaging of physical properties is used, such models are further restricted to the post- mixing shock homogeneous bubble flow regime. 

For zones 2-3, besides neglecting the potential energy component, the following assumptions were made (i) the secondary fluid is an ideal gas and the primary fluid is incompressible (ii) at point 2, the flow is in the homogeneous bubble flow regime, and the flow properties can be represented by weighted mixture properties ... 

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