Two-phase mixture, density

The data of Fig. 20 also point out an interesting phenomenon—while the heat transfer coefficients at bed wall and bed centerline both correlate with suspension density, their correlations are quantitatively different. This strongly suggests that the cross-sectional solid concentration is an important, but not primary parameter. Dou et al. speculated that the difference may be attributed to variations in the local solid concentration across the diameter of the fast fluidized bed. They show that when the cross-sectional averaged density is modified by an empirical radial distribution to obtain local suspension densities, the heat transfer coefficient indeed than correlates as a single function with local suspension density. This is shown in Fig. 21 where the two sets of data for different radial positions now correlate as a single function with local mixture density. The conclusion is That the convective heat transfer coefficient for surfaces in a fast fluidized bed is determined primarily by the local two-phase mixture density (solid concentration) at the location of that surface, for any given type of particle. The early observed parametric effects of elevation, gas velocity, solid mass flux, and radial position are all secondary to this primary functional dependence. 

Ap = absolute value of the difference in density between the liquids a= interfacial tension between the liquid phases D - fractional holdup in the tank of the dispersed liquid phase pM= two-phase mixture density, given by... 

Dukler constant slip two phase mixture density used to calculate static head, Ih/ft3 see Eq. (16p). Dukler no slip two phase mixture density, see Eq. (15b). 

A gas-liquid mixture will have a lower density than the liquid alone. Therefore, if in a U-tube one limb contains liquid and the other a liquid-gas mixture, the equilibrium height in the second limb will be higher than in the first. If two-phase mixture is discharged at a height less than the equilibrium height, a continuous flow of liquid will take place from the first to the second limb, provided that a continuous feed of liquid and gas is maintained. This principle is used in the design of the air lift pump described in Chapter 8. 

Profiles of foam density, derived from gamma ray scans of the separators, showed that no discrete foam layer was in the vessels, but a two-phase mixture of gas and liquid occupied a substantial pan of the total height of the vessel. 

It appears that the power requirements for liquid-liquid agitated systems can generally be dealt with in the same manner as for the case of one-liquid-phase systems. The appropriate effective mean viscosity of the two-phase mixture must be used as indicated above. Similarly, the average density must be used. In the power studies cited, a simple volume-average was used ... 

Vaporization processes may be divided into pool boiling, in which the hot surface is immersed in a pool of liquid and the vapor bubbles may flow freely away from the hot surface, driven by the difference in phase densities, and convective vaporization, where the liquid and vapor flow together along or away from the hot surface, driven either by natural convection of the two-phase mixture (termed thermosiphon action) or by an externally forced convection (e.g., by a circulating pump). 

This is a ratio of the average density of the two-phase mixture to the liquid density (it approaches unity for lightly aerated liqnids). Equation (12.62) may thns be modified by Eqnation (12.63) to give... 

A significant density difference between solvent and raffinate to ensure good separation of two-phase mixtures. 

This relative velocity can be expressed in terms of a where the continuous phase density in the buoyancy density of the two-phase mixture p . Thus, after noting and Fg act downward while F acts upward, we obtain modified form of (13-3) term is replaced by the for the case here that F ... 

Circulation. Natural circulation occurs because of the density difference between the liquid in the bottom of the column and the two-phase mixture in the heated tubes. 

Mean density of two phase mixture in the downcomer region 0m = [Pg.436]

Since the gas generated ascends along the electrode, the void fiacdon and the resistivity of the two-phase mixture increases with height. The effect on current density is shown in Fig. 10.3.12, where the ordinate is the reduced height, the abscissa is the reduced current density, h is the electrode height, and I o is the average current density over the working surface of the electrode. 

FIGURE 18.1 Four models of the density difference of a two-phase mixture of ammonia and humid air as a function of concentration. 

To accelerate the diffusion rate and shorten the time for the formation of gas/polymer solutions, we must raise the temperature and shorten the diffusion distance. This is done by deforming the two-phase mixture of polymer and gas through shear distortion to decrease the diffusion path. This type of deformation occurs in an extruder under laminar-flow conditions. The bubbles are stretched by the shear field of the two-phase mixture and eventually break up to minimize the surface energy when a critical Weber number is reached (4). The disintegrated bubble size is calculated to be about 1 mm and the initial striation thickness after bubble disintegration is calculated to be about twice the bubble diameter (5). This striation thickness decreases with further shear, and the gas diffusion occurs faster as a result of the increase in the surface area and the decrease in striation thickness. The striation thickness in an extruder is estimated to decrease to about 100 /xm. At this thickness, the diffusion time is about 1 min in PET, from 10 to 20 s in polystyrene (PS), polyfvinyl chloride) (PVC), and high density polyethylene (HDPE), and in the range of a few seconds in low density polyethylene (LDPE). 

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