Dispersed-phase holdup

This correlation is valid when turbulent conditions exist in an agitated vessel, drop diameter is significantly bigger than the Kohnogoroff eddy length, and at low dispersed phase holdup. The most commonly reported correlation is based on the Weber number ... 

E] Used as an arithmetic couceutratiou difference. Low <3, disperse-phase holdup of drop swarm. 

The power for agitation of two-phase mixtures in vessels such as these is given by the cuiwes in Fig. 15-23. At low levels of power input, the dispersed phase holdup in the vessel ((j)/ ) can be less than the value in the feed (( )df) it will approach the value in the feed as the agitation is increased. Treybal Mass Transfer Operations, 3d ed., McGraw-HiU, New York, 1980) gives the following correlations for estimation of the dispersed phase holdup based on power and physical properties for disc flat-blade turbines ... 

Direction of extraction, whether from dispersed to continuous, organic hquid to water, or the reverse Dispersed-phase holdup Flow rates and flow ratio of the liquids... 

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... 

In each subreactor, the dispersed-phase holdup fraction should be the same as the overall fraction thus... 

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... 

A dynamic balance for the dispersed phase holdup in stage n gives... 

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). 

The normal method of correlating dispersed phase holdup is normally of the form... 

Figure 3.54. Implicit loop calculation of dispersed-phase holdup.

Fig. 3. Comparison the one- (Eq. 24) and the two dimensional model (Lin et al. [44]) results as a function of dispersed phase holdup at different values of particle distance from the interface...

Fig. 5. Enhancement as a function of the physical mass transfer coefficient without dispersed phase at different particle numbers and dispersed phase holdups (D = 2.3 x 10 m s Dr = 0.56,H = 18,dp= 10 X 10- m,(5o = 0,M = 0)...

Many reviews and several books [61,62] have appeared on the theoretical and experimental aspects of the continuous, stirred tank reactor - the so-called chemostat. Properties of the chemostat are not discussed here. The concentrations of the reagents and products can not be calculated by the algebraic equations obtained for steady-state conditions, when ji = D (the left-hand sides of Eqs. 27-29 are equal to zero), because of the double-substrate-limitation model (Eq. 26) used. These values were obtained from the time course of the concentrations obtained by simulation of the fermentation. It was assumed that the dispersed organic phase remains in the reactor and the dispersed phase holdup does not change during the process. The inlet liquid phase does not contain either organic phase or biomass. 

P = plug flow, M = mixed flow, eD = fractional dispersed phase holdup, td = residence time of the dispersed phase (Doraiswamy Sharma, 1984). 

The physical technique just described directly measures the local surface area. The determination of the overall interfacial area in a gas-liquid or a liquid-liquid mechanically agitated vessel requires the application of this technique at various positions in the vessel because of variations in the local gas (or the dispersed-phase) holdup and/or the local Sauter mean diameter of bubbles or the dispersed phase. The accuracy of the average interfacial area for the entire volume of the vessel thus depends upon the homogeneity of the dispersion and the number of carefully chosen measurement locations within the vessel. 

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