Cross-flow velocity adjustment

In the cross-flow operation, the inlet feed stream entering the module at a certain composition and it flows parallel to the membrane surface. The composition of the stream changes along the module, and the stream is separated into two parts a permeate stream and a retentate stream. Flux decline is relatively smaller with cross-flow and can be controlled and adjusted by proper module configuration and cross-flow velocities. 

For industrial applications, a cross-flow operation is preferred because of the lower fouling tendency relative to the dead-end mode (figure VIII - 14b). In the cross-flow operation, the feed flows parallel to the membrane surface with the inlet feed stream entering the membrane module at a certain composition. The feed composition inside the module changes as a function of distance in the module, while the feed stream is separated into two a permeate stream and a retentate stream. The consequences of fouling in dead-end systems are shown schematically in figure VUI - 15. In dead-end filtration, the cake grows with time and consequently the flux decreases with time.Hux decline is relatively smaller with cross-flow and can be controlled and adjusted by proper module choice and cross-flow velocities. 

The feed pump is used to pressurize the feed to a required pressure. In ultrafiJtration and microfiltraiion flux decline is very severe due to concentration polarization and fouling. To reduce this effect as much as possible, the mass transfer in the boundary layer must be improved and this can be achieved by increasing the cross-flow velocity. In most cross-flow membrane operations, two pumps are employed, a feedpump to pressurize the feed and a circulation pump to adjust the cross-flow velocity. The aim of the circulation pump is to maintain a high cross-flow velocity. Since low hydrodynamic pressures 4 ° "cquired in... 

Even though fouHng remains a serious problem, many solutions exist these days to cope with it Some of them can be easily automated so that fouling does not have to be a real worry once a process is running. An appropriate pre-treatment of the feed (adjustment of pH and T, the use of additives, adsorption, prefiltration,...) can avoid many problems. At the level of membrane development, special attention should be paid to narrow pore-size distributions and a careful selection of the membrane hydrophobidty and the presence on the membranes of charged or functional groups with specific interactions. On the level of module and process conditions, turbulence promoters and high feed-flow velocities in cross-flow filtration... 

All the tests were conducted in under-critical flow conditions (Fr <1). 3 water depths were tested. For each water-depth condition, several flow discharges or cross-sectional averaged flow velocities were obtained through adjusting the power of the driving water pumps. Flow velocity was measured by the propeller velocimeter. For each test, the water pumps kept at a constant power value so that the flow can be considered steady. Several stem densities of vegetation were used for each flow depth and velocity condition. 

A major advantage of the dilution principle is that CD profiles of main fiber orientation can be rectified (Fig. 5.36 ). As mentioned before local slice bar adjustment causes cross flow in the nozzle chamber and in the exiting jet. Even a small angle of the jet velocity vector against the machine direction results in a large main fiber orientation angle. The main fiber orientation angle describes the direction of the plurality of the fibers in the paper and can be measured by laser or by ultrasonic devices. It has an impact on other important paper properties. 

Holdup and Flooding. The volume fraction of the dispersed phase, commonly known as the holdup h. can be adjusted in a batch extractor by means of the relative volumes of each liquid phase added. However, in a countercurrent column contactor, the holdup of the dispersed phase is considerably less than this, because the dispersed drops travel quite fast through the continuous phase and therefore have a relatively short residence time in the equipment. The holdup is related to the superficial velocities V of each phase, defined as the flow rate per unit cross section of the contactor, and to a slip velocity Us ... 

In the case of pressure conduits, we have dealt with uniform and nonuniform flow without drawing much distinction between them. This can be done because in a closed pipe the area of the water section, and hence the mean velocity, is fixed at every point. But in an open channel these conditions are not fixed, and the stream adjusts itself to the size of cross section that the slope of the hydraulic gradient requires. 

Some types of electrophoretic cells are stationary layer problem free , but in the other cells the electroosmotic flow can lead to erroneous results. The observed velocity of particles is a sum of the electroosmotic flow of the fluid and the velocity of particles with respect to the fluid. The latter is a function of the potential of the particles and the former is a function of the position in the cell cross section. Hydrodynamic calculations make it possible to find the stationary levels, i.e. the positions in the cell cross section where the electroosmotic flow equals zero. Certainly the position of stationary levels in commercial electrophoretic cells can be found in the user s manual, and there is no need to perform any calculations. The fastest method to determine the electrophoretic mobility is from the velocity at one stationary level, but such a procedure can lead to substantial errors. For example, when the cell position is adjusted at room temperature and then measurements taken... 

The next step is to determine the flooding vapor velocity, which is a function of the vapor and liquid flow rates and their densities. The design vapor velocity is then calculated by multiplying the flooding vapor velocity by a flood factor such as 0.85. The vapor velocity is based on the vapor volumetric flow and the net flow area between the trays, that is, the column cross-sectional area minus the area blocked by the downcomers. With known vapor velocity, vapor flow, and fraction of the column cross section occupied by the downcomers, the net area can be calculated. The total area is then calculated, from which the tray diameter is determined. The actual column diameter is obtained by rounding off the tray diameter to the next larger standard size. The vapor velocity is then adjusted to the new diameter to calculate the expected flood factor. 

Figure 3 is a curve of specific flow area for. a mixture of liquid and vapor when expanded isentropically from saturated liquid. These areas are based on the adjusted velocities shown in Fig. 1. The areas were determined by calculating the cross-sectional area required to...

When the column dimensions are changed to optimize a separation, or to scale a separation to be preparative or narrow bore, the mobile-phase flow rate is adjusted in proportion to the cross sectional area of the column. This then maintains consistent linear velocity and retention times. 

Experimental evidence show that the liquid axial velocity is far from being flat and independent of the radial space coordinate [29], and the use of a cross-sectional average velocity variable seems not to be sufficient. The back mixing induced by the global liquid flow pattern was commonly accounted for by adjusting the axial dispersion coefficient accordingly. However, while (slurry) bubble column performance... 

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