Transport crossflow

The concept of critical flux ( Jcrit) was introduced by Field et al. [3] and is based on the notion that foulants experience convection and back-transport mechanisms and that there is a flux below which the net transport to the membrane, and the fouling, is negligible. As the back transport depends on particle size and crossflow conditions the Jcrit is species and operation dependent. It is a useful concept as it highlights the... 

In the fourth subtechnique, flow FFF (F/FFF), an external field, as such, is not used. Its place is taken by a slow transverse flow of the carrier liquid. In the usual case carrier permeates into the channel through the top wall (a layer of porous frit), moves slowly across the thin channel space, and seeps out of a membrane-frit bilayer constituting the bottom (accumulation) wall. This slow transverse flow is superimposed on the much faster down-channel flow. We emphasized in Section 7.4 that flow provides a transport mechanism much like that of an external field hence the substitution of transverse flow for a transverse (perpendicular) field is feasible. However this transverse flow—crossflow as we call it—is not by itself selective (see Section 7.4) different particle types are all transported toward the accumulation wall at the same rate. Nonetheless the thickness of the steady-state layer of particles formed at the accumulation wall is variable, determined by a combination of the crossflow transport which forms the layer and by diffusion which breaks it down. Since diffusion coefficients vary from species to species, exponential distributions of different thicknesses are formed, leading to normal FFF separation. 

Eor a given crossflow filtration, the dominant particle back transport mechanism may depend on the shear rate and the particles size [4]. Brownian diffusion is only important for particles smaller than only a few tenths of a micron in diameter with relative low shear, whereas inertial lift is important for particles larger than several tens of microns with higher shear rates. Shear-induced back transport appears to be important for intermediate particle sizes and shear rates. Li et al. [7] reported that the shear-induced mechanism was able to predict fluxes comparable with the critical fluxes identified by the DOTM. 

Although it has been reported that an external DC electric field can induce an electrophoretic back transport that can significantly enhance flux in crossflow membrane filtration, its commercial implementation appears to be restricted by several factors. These include lack of suitably inexpensive corrosion-resistant electrode materials, concerns about energy consumption, and the complexity of module manufacture. 

For the UF of proteins, the concentration polarization model has been found to predict the filtration performance reasonably well [56]. However, this model is inherently weak in describing the two-dimensional mass transport mechanism during crossflow filtration and does not take into account the solute-solute interactions on mass transport that occur extensively in colloids, especially during MF [21,44,158,159]. The diffusion coefficient, which is inversely proportional to the particle radius, is low and underestimates the movement of particles away from the membrane [56]. This results to the well-known flux paradox problem where the predicted permeate flux is as much as two orders of magnitude lower than the observed flux during MF of colloidal suspensions [56,58,158]. This problem has then been underlined by the experimental finding of a critical flux for colloids, which demonstrates the specificity of colloidal suspension filtration wherein just a small variation in physicochemical or hydrodynamic conditions induces important changes in the way the process has to be operated [21]. 

The heart of a scrubber column is the slurry-gas contact zone, where gases are intimately combined with the absorbent slurry so that the pollutants can be captured by the reactions given previously. There are a number of possible methods for designing the contacting zone, including sprays, crossflow plates, baffle plates, counterflow plates, and packed columns. These all have the purpose of maximizing the interfacial area between the gas phase and the liquid phase, to allow rapid transport of gases across the surface. ... 

Theoretical analysis of crossflow filtration is often based on a steady state analysis of convective and diffusive transport of retained species between the membrane surface and the bulk fluid in the retentate. The build up of retained species at the membrane surface, which then acts as the major resistance to permeate flow, is known as concentration polarization. This analysis predicts that flux declines linearly with the log of the concentration of retained species (6) ... 

Chellam S., Wiesner M.R, (1997), Particle back-transport and permeate flux behaviour in crossflow membrane filters. Environmental Science and Technology, 31, 3, 819-824. 

Xu X., Spencer H.G. (1997), Transport of electrolytes through a weak acid nanofiltration membrane effects of flux and crossflow velocity interpreted using a fine-porous membrane model. 

Spiral drier, roHa- transport, mild crossflow... 

From this brief summary of the data for crossflow OSN transport processes, we... 

If there is essentially no pressure drop in the transport of these permeated gases through the porous substrate, then P p = Pp, which is the pressure in the bulk gas on the permeate side. Further, if this gas mixture does not mix with any other gas stream emerging from other membrane locations, then only x = Xip and x jp = Xjp, leading to the crossflow relation (7.2.2a). 

In all the FFF techniques considered so far, the flow took place in the environment of a channel between two wide flat plates. The channel plate widths are orders of magnitude larger than the gap between the plates (e.g. 2 cm X 200-300 pm). However, there is always an edge effect at the two ends of the width of the plate. Much more important, however, is the requirement in flow FFF and electrical FFF that there be a membrane lining the channel to allow crossflow permeation in flow FFF and buffer ion transport in electrical FFF. 

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