Plug Velocity

The experimental results were compared (Fig. 4.19) with the empirical models proposed for the bubble velocity during gas-liquid Taylor flow and the analytical approach of Bretherton (1961) (Table 2.3), as well as with the analytical solution 

4 Liquid-Liquid Flows in Micro and Small Channels. .. 

Pressure drop was measured in 4 different channel sizes from 0.22 to 2 mm ID made of Teflon over a length of 10 cm, for different flow rates and flow rate ratios. As mentioned earlier, in the Teflon channels ionic liquid was always the continuous phase. The results shown in Fig. 4.20 indicate that pressure drop increases by increasing mixture velocity (at flow rate ratio equal to 1) and decreases by increasing channel size. Pressure drop was always higher than that of the single phase ionic liquid having the same flow rate as in the two-phase mixture. 

The model seems to over-predict the experimental results for the bigger channels and this is attributed to the fact that the interfacial pressure drop calculated by Eq. (2.2.30) assumes ideally semi-spherical caps, which is not the case at all experimental conditions. By substituting the constant C in Eq. (2.2.31) to C = 1.7, the correlation was able to predict pressure drop during plug flow in the channels with 0.5, 1, and 2 mm ID with mean relative error of 14 % (red highlighted symbols). 

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D. Tubes, laminar, uniform plug velocity, developing concentration profile, constant wall concentration... 

It should be emphasized that these results are applicable only to fully developed flow. However, if the fluid enters a pipe with a uniform ( plug ) velocity distribution, a minimum hydrodynamic entry length (Lc) is required for the parabolic velocity flow profile to develop and the pressure gradient to become uniform. It can be shown that this (dimensionless) hydrodynamic entry length is approximately Le/D = 7VRe/20. 

The velocity of the plug in the downchannel (z) and tangential (0) directions can be vectorially visualized in Fig. 5.3. Notice that the volumetric flow rate, 0, as well as all of the plug velocities are dependent upon the unknown solids forwarding angle q>. 

What is the maximum pressure in the system, the maximum plug velocity, and the final position of the plug ... 

Fig. 9.27 Axial increment of the solid plug. Velocities given relative to a stationary screw Vpi is the axial velocity of the plug, which is independent of the radial position Vpq and Vpz are the tangential and down-channel components of the plug surface velocity.

Experimental Conditions 7),/m/rpm/screw type Melt Temperature °C Solid-Plug Velocity Holding Time per Lobe Predicted Number of Lobes Observed Number of Lobes... 

L= 1.2 in. Examine and discuss the difference between the observed and calculated throughput rate feeder capabilities, as it relates to the plug velocity assumption. 

The fluid moves in a flat (pistonlike or plug ) velocity profile. 

The retention-time calculations are based on the volume between the perforated plate and the weir plate. The cross-sectional area available to the phases (oil, water (or liquid), and gas) is calculated and the mean plug velocity and retention times are given. The cross-sectional area below a level /j in a horizontal cylinder is generally given by the geometric relation ... 

The plug velocity of a phase is then found by dividing a phase flow by its respective cross-sectional area, and the retention time is given by the ratio between the effective separator length and this plug velocity. 

A plug of stationary phase solution is run into the front of the column (sufficient solution should be added to fill about 10% of the column length) and a gas pressure is applied to the front of the column so that the plug velocity through the column is about 3 mm/second. After the plug has passed through the column, the gas flow is continued for about an hour. It is important not to increase the gas flow too soon, otherwise the stationary phase solution adhering to the walls of the tube is displaced forward in the form of ripples, which produces a very uneven film. After an hour, the flow rate is increased and the column stripped of solvent by evaporation. This procedure requires some practice to provide... 

The quasi-one-dimensional approximation was initially introduced in the theory of capillary jet breakup. The mass and longimdinal momentum balance under the assumption of plug velocity and stress profiles in jet cross-sections reads according to Yarin [29]... 

In the annular area Rp < r < R, the velocity will gradually decrease from the constant plug velocity to zero at the pipe wall. The expression for this velocity distribution will now be derived. 

Figure 3.19 Dimensionless plug velocity and plug size for laminar Bingham plastic flow in an annulus...

Knowledge of the plug velocity is key parameter in the design of contactors, since it defines the residence time, i.e. the time that the droplet remains in the contactor, while it affects the intensity of the internal circulations within the plug and thus the... 

In the following studies, the hydrodynamics and mass transfer during liquid-liquid flow with ionic liquids in channels with a range of diameters are presented. How patterns, as well as several hydrodynamic characteristics, such as plug length, plug velocity, film thickness, and pressure drop have been investigated. 

Fig. 4.18 Plug velocity Up as a function of the flow rate ratio Qil/Qhno3 at constant mixture velocity of 0.01 m s ...

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