Cross-flow velocity

Membrane Characterization Membranes are always rated for flux and rejection. NaCl is always used as one measure of rejection, and for a veiy good RO membrane, it will be 99.7 percent or more. Nanofiltration membranes are also tested on a larger solute, commonly MgS04. Test results are veiy much a function of how the test is run, and membrane suppliers are usually specific on the test conditions. Salt concentration will be specified as some average of feed and exit concentration, but both are bulk values. Salt concentration at the membrane governs performance. Flux, pressure, membrane geome-tiy, and cross-flow velocity all influence polarization and the other variables shown in Fig. 22-63. 

FIG. 22-64 Cascade arrangement for membrane processing to maintain cross-flow velocity as permeate is removed. 

The factors to consider in the selection of cross-flow filtration include the cross-flow velocity, the driving pressure, the separation characteristics of the membrane (permeability and pore size), size of particulates relative to the membrane pore dimensions, and the hydrodynamic conditions within the flow module. Again, since particle-particle and particle-membrane interactions are key, broth conditioning (ionic strength, pH, etc.) may be necessary to optimize performance. 

The baffle cut determines the fluid velocity between the baffle and the shell wall, and the baffle spacing determines the parallel and cross-flow velocities that affect heat transfer and pressure drop. Often the shell side of an exchanger is subject to low-pressure drop limitations, and the baffle patterns must be arranged to meet these specified conditions and at the same time provide maximum effectiveness for heat transfer. The plate material used for these supports and baffles should not be too thin and is usually minimum thick-... 

The baffle used in the preceding equation has 20% segmental cuts. Shell-side cross-flow velocity ... 

The maximum cross flow velocity under the bit, vjft/s), is [48]... 

Fig. 16.13. Time dependence of membrane permeation rate during cross-flow filtration (a) low cross-flow velocity, (b) increased cross-flow velocity, (c) back flushing at the bottom of each saw-tooth .

Fig. 16.15. Dependence of membrane permeation rate J on (a) applied pressure difference, (b) feed solute concentration Cf and (c) cross-flow velocity ( ) for ultrafiltration.

The velocity, viscosity, density, and channel-height values are all similar to UF, but the diffusivity of large particles (MF) is orders-of-magnitude lower than the diffusivity of macromolecules (UF). It is thus quite surprising to find the fluxes of cross-flow MF processes to be similar to, and often higher than, UF fluxes. Two primary theories for the enhanced diffusion of particles in a shear field, the inertial-lift theory and the shear-induced theory, are explained by Davis [in Ho and Sirkar (eds.), op. cit., pp. 480-505], and Belfort, Davis, and Zydney [/. Membrane. Sci., 96, 1-58 (1994)]. While not clear-cut, shear-induced diffusion is quite large compared to Brownian diffusion except for those cases with very small particles or very low cross-flow velocity. The enhancement of mass transfer in turbulent-flow microfiltration, a major effect, remains completely empirical. 

The spacing in the end zones will often be increased to provide more flow area at the inlet and outlet nozzles. The velocity in these zones will then be lower and the heat transfer and pressure drop will be reduced slightly. The effect on pressure drop will be more marked than on heat transfer, and can be estimated by using the actual spacing in the end zone when calculating the cross-flow velocity in those zones. 

Cross-file patent searches, 18 243-244 CrossFire Beilstein, 6 19 Cross-flow filtration, 11 383 15 827, 829 in porous pipes, 11 387-388 with rotating elements, 11 383-387 Cross flow model, 21 706 Cross-flow packed scrubber, 26 687-688 Crossflow plates, 6 762-763 Cross-flow screens, 22 282 Cross-flow velocity, 15 725 Crosshead mandrel, in VDC film extrusion, 25 732-733 Cross-lapping, 17 501 Cross-linkable epoxy thermoplastic system (CET), 10 436... 

Figure 8.8. Dependence of membrane flux J on (a) Applied pressure difference AP, (b) Feed solute concentration Cf, (c) Cross-flow velocity (u) for ultrafiltration...

The membranes in electrodialysis stacks are kept apart by spacers which define the flow channels for the process feed. There are two basic types(3), (a) tortuous path, causing the solution to flow in long narrow channels making several 180° bends between entrance and exit, and typically operating with a channel length-to-width ratio of 100 1 with a cross-flow velocity of 0.3-1.0 m/s (b) sheet flow, with a straight path from entrance to exit ports and a cross-flow velocity of 0.05-0.15 m/s. In both cases the spacer screens are... 

Though erosive burning is highly dependent on the cross-flow velocity, the physical structure of the propellant also plays a dominant role in determining the erosive... 

Fig. 13.9 Computed blow-off parameter as a function of cross-flow velocity.

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