Fractional holdup of dispersed phase

In extraction column design, the model equations are normally expressed in terms of superficial phase velocities, L and G, based on unit cross-sectional area. The volume of any stage in the column is then A H, where A is the cross-sectional area of the column. Thus the volume occupied by the total dispersed phase is h A H, where h is the fractional holdup of dispersed phase, i.e., the droplet volume in the stage, divided by the total volume of the stage and the volume occupied by the continuous phase, in the stage, is (1-h) A H. 

To estimate the total interfacial area in a given volume, the ad value is multiplied by the fractional holdup of dispersed phase in the total volume. 

Holdup relation parameters Organic, dispersed phase flow velocity Fractional holdup of dispersed phase... 

Et Transfer efficiency, over-all F Holdup, fractional volume of dispersed phase in column / Coefficient, function of (Npc)c G Superficial velocity, ft /hr/ft ... 

Figure 3.55. Correlation of dispersed phase fractional holdup values with aqueous (L ) and solvent (O ) flow rates.

As explained in Sec. 3. 3. 1.11, the fractional holdup of the dispersed phase in agitated extraction columns will vary with changing phase flow rate. This dynamic variation in the holdup along the column will cause a dynamic velocity profile in both phases. 

The fractional holdup of the dispersed phase in agitated extraction columns varies as a function of flowrate. Under some circumstances it may be important to model the corresponding hydrodynamic effect. The system is represented below as a column containing seven agitated compartments or stages. 

Interfacial tension MOSCED polarity parameter NRTL model parameter Volume fraction Volume fraction of dispersed phase (holdup)... 

Holdup and Interfacial Area The dispersed-phase holdup in a packed-column extractor may be placed into two categories (1) a small portion that is held in the column for extended periods (essentially permanent) and (2) a larger portion that is free to move through the packing. This is the portion that participates in transfer of solute between phases. The total is which here refers to the volume of dispersed phase expressed as a fraction of the void space in the packed section. Pratt and coworkers [Tram. Inst. Chem. Eng.,... 

CHARACTERISTICS OF DISPERSED PHASE MEAN DIAMETER. Despite these variations, a basic relationship exists between the holdup (the volume fraction of dispersed phase in the system), the interfacial area a per unit volume, and the bubble or drop diameter D. If the total volume of the dispersion is taken as unity, the volume of dispersed phase, by definition, is f. Let the number of drops or bubbles in this volume be N. Then if all the drops or bubbles were spheres of diameter their total volume would be given by... 

Fractional holdup of the gas phase at the critical speed for gas dispersion (—) Power inpnt per unit volnme (kW/m )... 

Additional terms are often included to take into account dispersed phase viscosity and coalescence due to holdup. They usually depend on the volume fraction of dispersed phase ... 

This is the holdup as a volume fraction of fluid in the vessel. It is the volume of dispersed phase (e.g., gas) in the vessel divided by the total volume. This is a variable strongly affected by the mixing conditions. In Chapter 11 there are several correlations for this variable. Holdup (d>) times a gives total mass transfer surface area per unit vessel volume, which is often called a. Thus, one often sees correlations of kta versus mixing parameters. It should always be remembered that this value contains implicitly the holdup and the bubble size. One way to think of holdup is as the ratio of the superficial gas velocity to the bubble rise velocity. This comes from a simplistic picture of the motion of the gas phase ... 

Holdup and Flooding. The volume fraction of the dispersed phase, commonly known as the holdup can be adjusted in a batch extractor by means of the relative volumes of each Hquid phase added. In a continuously operated weU-mixed tank, the holdup is also in proportion to the volume flow rates because the phases become intimately dispersed as soon as they enter the tank. 

The volume of droplets within the contactor at any time is referred to as the operational holdup of the dispersed phase, generally expressed as a fraction of the contactor volume. 

An evaluation of the retardation effects of surfactants on the steady velocity of a single drop (or bubble) under the influence of gravity has been made by Levich (L3) and extended recently by Newman (Nl). A further generalization to the domain of flow around an ensemble of many drops or bubbles in the presence of surfactants has been completed most recently by Waslo and Gal-Or (Wl). The terminal velocity of the ensemble is expressed in terms of the dispersed-phase holdup fraction and reduces to Levich s solution for a single particle when approaches zero. The basic theoretical principles governing these retardation effects will be demonstrated here for the case of a single drop or bubble. Thermodynamically, this is a case where coupling effects between the diffusion of surfactants (first-order tensorial transfer) and viscous flow (second-order tensorial transfer) takes place. Subject to the Curie principle, it demonstrates that this retardation effect occurs on a nonisotropic interface. Therefore, it is necessary to express the concentration of surfactants T, as it varies from point to point on the interface, in terms of the coordinates of the interface, i.e.,... 

The dispersed-phase holdup fraction is, for example, responsible for many important interactions. These are indicated by the dashed lines of Fig. 1, which show the main interrelationships that govern the capacity of a given dispersion. Some of these interrelationships, such as the effects of residence-time... 

Under changing flow conditions, it can be important to include some consideration of the hydrodynamic changes within the column (Fig. 3.53), as manifested by changes in the fractional dispersed phase holdup, h , and the phase flow rates, Ln and G . which, under dynamic conditions, can vary from stage to stage. Such variations can have a considerable effect on the overall dynamic characteristics of an extraction column, since variations in hn also... 

The fractional dispersed phase holdup, h, is normally correlated on the basis of a characteristic velocity equation, which is based on the concept of a slip velocity for the drops, VgUp, which then can be related to the free rise velocity of single drops, using some correctional functional dependence on holdup, f(h). 

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