Vertical density flow

The basic mechanism for transition from bubble to slug flow appears to be the same as in vertical pipe flow. That is, as the gas flow rate is increased for a given liquid flow rate, the bubble density increases, many collisions occur and cell-type Taylor bubbles are formed, and the transition to slug flow takes place. As shown in the case of vertical pipe upflow, Taitel et al. (1980) assumed that this transition takes place when ac = 0.25. This criterion is also applicable here. However, because of the preferable geometry in the rod bundle, where the bubbles are observed to exist, instead of in the space between any two rods, this void fraction of 0.25 applies to the local preferable area only, a.L. The local voids, aL, can be related to the average void by (Venkateswararao et al., 1982)... 

Figure 11.13. Velocity and density distributions in vertical pipe flows at negligible gravity effect (from Soo, 1990) (a) NDF = 0.25 (b) NDF = 0.025.

Chemiluminescence photographs of the flow field taken perpendicular to the optic axis indicated no such nonuniformities, because any such photos only give spatially integrated particle density data. Consequently, vertical density gradients... 

At this point, the vertical density structure for the past ocean can be reconstructed using benthic foraminifera only where the seafloor intersects the upper water column (ocean margins, islands, shallow seamounts). Although planktonic foraminifera calcify at various depth within the upper water column, we have no way to quantitatively reconstruct the depth at which they calcified. However, deep dwelling planktonic foraminifera can be used to reconstruct the spatial pattern of upper ocean flows (Matsumoto and Lynch-Stieglitz, 2003). 

In summary, transport and spreading of dissolved landfill leachate pollutants in aquifers are governed by advection/dispersion. The local hydrogeology at the site in terms of water table mounds and seasonal variation in flow field may enhance the spreading horizontally and vertically. Density effects due to high concentrations of inorganic compounds may increase vertical transport, but the understanding of density transport in leachate plumes is poor. Density transport is likely to be most important close to landfills but less so as dilution of the plume increases. 

Fingering can cause the displacing solution to run ahead of the average displacement front when a concentrated solution displaces a more dilute one during vertical saturated flow (Mulqueen Kirkham, 1972). Density differences as small as 0.0002 g cm-3 have been shown to significantly alter the shape of the breakthrough curve, and thus estimates of K (Rose Passioura, 1971 James Rubin, 1972). 

At low compression of the active block, the gas accumulated at the interface plate/AGM separator will increase in volume. Under the action of gravitation, the gas flow will be directed vertically. The electrolyte has three times higher density than that of the gas, so it will push the gas upwards to the gas space above the active block. Thus, oxygen will leave the active block. The rate of this vertical gas flow depends on the current flowing through the cell, the electrolyte temperature and the service condition of the cell (i.e. new or after long service). 

A reasonable value for Kp is 1.2. If the exchanger is vertical and flow is upward, the outlet pressure is further reduced by the height of the heat exchanger times the fluid density. If the flow is downward, the outlet pressure is increased by the same amount. 

In countercurrent flow extraction columns, the heavy phase is charged at the top of the column and the light phase at the bottom of the column. Vertical countercurrent flow of the phases is caused by gravity and density difference. If the light phase is the dispersed phase, the phase separation level has to be high. The reverse is true in the case of the heavy phase as the dispersed phase. 

In a horizontal pipeline the velocity of the particles will typically be about 80% of that of the air. This is usually expressed in terms of a slip ratio, defined in terms of the velocity of the particles divided by the velocity of the air transporting the particles, and in this case it would be 0.8. The value depends upon the particle size, shape and density, and so the value can vary over an extremely wide range. In vertically upward flow in a pipeline a typical value of the slip ratio will be about 0.7 in comparison. 

Effect of positive and negative pipe inclination on velocity ratio for medium density capsules is illustrated in Fig. 6, where a good transportability of capsules even for vertical upward flow direction is illustrated. 

In general, heat transfer is calculated based on quiescent vapor. In case of vapor flow cocurrent to the vertical film flow, the heat transfer is calculated by an enhancement factor relative to the heat transfer to unmoved vapor. The enhancement factor depends on the shear stress at the film boundary [61]. Thus, for high-pressure processes, the increase in heat transfer depends not only on the relative velocity between the liquid and gas phase but also on the increased gas density. 

Two related gravity-driven flows are chute flow [3,33,146-155] and vertical tube flow [156-159]. Chute flow generally differs from hopper discharge in that the chute is opened so that the flow experiences a free surface. Vertical tube flow is similar to hopper flow, but there is no narrowing of the flow chamber at the outlet. A similar flow-rate scaling holds for vertical tubes [156] but the velocity profile tends to be plug like [157] for slow flows. For faster flows, density waves have been observed [159]. 

The earliest large-scale continuous industrial extraction equipment consisted of mixer—settlers and open-spray columns. The vertical stacking of a series of mixer—settlers was a feature of a patented column in 1935 (96) in which countercurrent flow occurred because of density difference between the phases, avoiding the necessity for interstage pumping. This was a precursor of the agitated column contactors which have been developed and commercialized since the late 1940s. There are several texts (1,2,6,97—98) and reviews (99—100) available that describe the various types of extractors. 

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