Specific flux

A further excellent demonstration of the need to interpret experimental results in terms of a specific flux model is provided by the dynamic test... 

Mean annual specific fluxes (oornptete years)... 

At first sight Eq. 19-63 does not resemble the type of equation that we found earlier for bottleneck boundaries (e.g., Eq. 19-19). That is not surprising since XF is an integrated flux (mass per unit time), while in the case of flat boundaries we have always dealt with specific fluxes (mass per unit area and time). If we divide XF by the surface of the sphere, 4n r, after some algebraic rearrangements we get ... 

This is an extremely useful result. The specific flux now looks like Eq. 19-3 where the boundary layer thickness 8 is replaced by the effective thickness 8eff given by Eq. 19-65. To understand the meaning of the latter, we discuss the following cases ... 

We define the specific flux rate of a chemical between sediment and water,... 

Specific flux is sometimes discussed in comparing the performance of one type of membrane with another. Specific flux is approximated by taking the overall system flux and dividing by the applied driving pressure ... 

In comparing membranes, the higher the specific flux the lower the driving pressure required to operate the RO system. Specific flux is also defined as the permeability of the membrane. 

Specific flux calculated by dividing the flux by the net driving pressure. The higher the specific flux, the greater the permeability of the membrane. Low permeability corresponds to fouling, scaling, or compaction. 

Specific flux The specific flux, allows for the normahzation of the transmembrane flux with the transmembrane pressure [20],... 

Information on the model-specific flux free(0 can be obtained from eq. (3.67), which can be written after rearrangement ... 

Figure 4.10. Acrylonitrile conversion to acrylamide and membrane specific flux evolution in a ultrafiltration MBR using the strain Brevibacterium imperialis CBS 489-74. Each arrow indicates the restoration of the initial acrylonitrile concentration, The Ap indicates the transmembrane pressure applied. Adapted from Cantarella et al. [4.28], with permission from Elsevier Science.

We have above introduced concentrations and relations between concentrations of species of interest The area-specific flux (flux density) of a species, i, resulting from a driving force, F, is proportional to its concentration and to its mechanical mobility (ease of movement) j j = Cj Bj Fj as we come back to in the next section. First we briefly recall from textbooks that for species with an activated diffusion, the self-diffusion coefficient, D, mechanical mobility, B, charge mobility, u, and conductivity, a, are linked through the Nemst-Einstein relation (1.14) ... 

The process of permeation through a membrane gives rise to a flux, or permeation. Commonly used units are mol s i and mL min = mb min (STP). In order to obtain (area specific) flux densities we divide by area and get, for eiample, units of mol s i cm 2 or mLn mim cm . ... 

Three 16 in. diameter and 60 in. long RO-ULP elements from Koch Membrane Systems were evaluated parallel with two commercially available 8 in. diameter elements [75]. The overall specific flux for 16 in. was comparable to that of 8 in. element. Slightly higher fouling was observed for the former element. Cost evaluation revealed that for a 185 million gpd plant, 16 in. element can save as much as 12.4% in total cost. The capital cost saving alone is 27%. 

Microfibers with an inner diameter of 20 pm and a wall thickness of 10 to 20 pm have been proposed, too. The specific flux through such a homogeneous membrane would be low, but outbalanced by high packing density and low membrane costs. The fiber length would be of the order of 20 cm, arranged in a modified module, in which the fibers would be potted in the axial direction into the wall of a tube. So far no reports are known on any application of such a module. 

From Eq. (2) it is evident that the cross-sectional area of the plant part examined may be taken as unity. Transport intensity therefore means mass transfer across the total cross-sectional area. This now is probably the only appropriate unit which auxin transfer of a plant part may be referred to, although evidence is increasing from surgical and autoradiographic studies that the different cell types contribute very differently to the total amount of auxin transported (see Sect. 3.3.6). Thus, the calculation of a specific mass transfer (Canny 1960, p 509, Kaldewey 1967b, p 487), i.e., mass transfer per unit area (e.g., flux mm of the plant part s cross section), may well be misleading since the specific area is not known. However, comparisons of specific fluxes in similar plant parts of different size may give information of their efficiency. 

With the time-integrated flux operator F being Hermitian, the optimization of the channel- and field-specific flux functional ( /(0) IFI /(0)> with respect to the coefficients C employed in Equation 7.3 leads to the Rayleigh-Ritz eigenvalue problem " ... 

The permeation performance of dense membranes is often characterized in terms of a transmembrane flux, ji, at a given temperature and pressure gradient. Alternatively, a specific flux, /, can be defined as a normalized membrane flux based on the thicloiess and logarithm of the partial pressure gradient as a reminiscence of the Wagner equation. The specific flux can be related to the membrane permeability as follows ... 

A gas separation membrane that can separate oxygen from air is constracted from La2Ni04+d, a material where we for simplicity may assume that the defect stracture is dominated by doubly ionized oxygen interstitials compensated by electron holes. In the following assume further that the cell is operated at 1000°C and that the membrane is 100 thick and has no surface kinetics limitations. Assume also that the oxygen ion conductivity (by interstitials) is 1 S/cm at 1 atm O2 and that the electronic (hole) conductivity is 200 S/cm at 1 atm O2. The membrane is operated with atmospheric air on one side and pumped to effectively 0.1 atm at the other side. What is the area-specific flux of oxygen ... 

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