Feed flow velocity

The limiting current density is determined by concentration-polarization effects at the membrane surface in the diluate containing compartment that in turn is determined by the diluate concentration, the compartment design, and the feed-flow velocity. Concentration polarization in electrodialysis is also the result of differences in the transport number of ions in the solution and in the membrane. The transport number of a counterion in an ion-exchange membrane is generally close to 1 and that of the co ion close to 0, while in the solution the transport numbers of anion and cations are not very different. 

Since the thickness ofthe laminar boundary in an electrodialysis stack is difficult to determine in an independent measurement, the limiting current density in practical application is generally not calculated by Equation 5.18 but by an experimentally determined relation which describes the limiting current density as a function to the feed-flow velocity in the electrodialysis stack [4]. The limiting current density is expressed by ... 

Notes. 1. Results, represented in columns 3 and 6, were obtained ar various feed flow velocities (column 2) and fixed (IJ = 0.5 cm /s) carrier and strip solutions flow velocities. Results in columns 4 and 7 were obtained at various carrier solution flow velocities and fixed (U = 0.5 cm / s) feed and snip solutions flow velocities. Results in columns 5 and 8 were obtained at various strip solution flow velocities and fixed U = 0.5 cin /s) feed and carrier solutions flow velocities. 

Figure 6.3 The dependence of feed-side and strip-side overall mass-transfer coefficients on feed flow velocities. Initial compositions feed 40 % H3PO4 WPA, containing 55.2 ppm Cd, 55.4 ppm Cu, and 290 ppm Zn LM 0.5 mol/kg PVSH aqueous solution strip 2.0 mol/kg HCl. Membrane barriers Tokayama Soda cation-exchange membrane CM-2. From Ref. [6] with permission.

Electrodialysis as a unit operation is determined by several process and equipment design parameters, such as feed flow velocities, cell and spacer construction, stack design etc. These parameters effect the costs of the process directly and also indirectly by means of the limiting current density and the current utilization [33]. 

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... 

To avoid concentration polarization, an improved mass transfer should be realized in the feed compartment. Determining parameters are feed flow velocity (modified through the hydraulic diameter of the feed cell or the pump characteristics), solute diffusion (changed via the feed temperature), feed viscosity (idem), shape and dimensions of the module (introduction of turbulence promoters, use of pulsating flows to break the boundary layer, increased Reynolds numbers,...). 

From eq. vn - 10 it can be seen that the mass transfer coefficient k is mainly a function of the feed flow velocity (v), the diffusion coefficient of the solute (D), the viscosity, the density and the module shape and dimensions. Of these parameters, flow velocity and diffusion coefficient are the most important, viz. 

Figure 12.17 Effect of feed inlet temperature on MD flux obtained using PP capillary (Accurel S6/2 MD020CP2N, Table 12.1) with feed flow velocity 0.8 m/s. In DCMD (0.8 m/s permeate flow velocity, 20°C permeate inlet temperature) in SGMD (11.3 m/s humid air velocity, 20°C air inlet temperature) in VMD (3500 Pa downstream pressure). The solid lines are theoretical prediction curves. (Adapted from Khayet et al., 2003c.)...

Most of the above apphcations are in clarification duties. The use of HGMS to dewater relatively concentrated, paramagnetic mineral slurries has been demonstrated on 2 to 12 wt % feed concentration of synthetic malachite (7) concentrated to 40%. The magnetic collection was optimized at flow velocities of 1 mm/s, and product concentrations greater than 40% were not possible unless the collected material could be removed from the matrix with less than the equivalent of one canister of washwater. 

Feed or withdraw from both ends, reducing the pipe flow velocity head and required hole pressure drop by a factor of 4. 

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. 

Reduce linear flow velocities to eliminate static charge buildup during feed... 

As more fuel is converted into combustion products per unit of volume and time, expansion flow becomes stronger. Higher flow velocities go hand in hand with more intense turbulence. This process feeds on itself that is, a positive feedback coupling comes into action. In the turbulent stage of flame propagation, a gas explosion may be described as a process of combustion-driven expansion flow with the turbulent expansion-flow structure acting as an uncontrolled positive feedback (Figure 3.2). 

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.

There are many parameters influencing the size-related performance of a reactor where feed mixing is important concentrations of reactants, feed flow rate, feed pipe velocity, geometry and size of both reactor and stirrer, and stirrer rotational speed. The following remarks should be kept in mind when composing an experimental program for engineering studies ... 

Flow Flux, Permeability, Conversion The productivity of a membrane module is described by its flux J = volumetric permeate flow rate/membrane area with units of volume per area per time. Relatively high flux rates imply that relatively small membrane areas are required. The permeate volume is usually greater than the feed volume for a given process. Flux is also the magnitude of the normal flow velocity with units of distance per time. 

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