Back-transport flux

The concentration boundary layer forms because of the convective transport of solutes toward the membrane due to the viscous drag exerted by the flux. A diffusive back-transport is produced by the concentration gradient between the membranes surface and the bulk. At equiUbrium the two transport mechanisms are equal to each other. Solving the equations leads to an expression of the flux ... 

The simplest practicable approach considers the membrane as a continuous, nonporous phase in which water of hydration is dissolved.In such a scenario, which is based on concentrated solution theory, the sole thermodynamic variable for specifying the local state of the membrane is the water activity the relevant mechanism of water back-transport is diffusion in an activity gradient. However, pure diffusion models provide an incomplete description of the membrane response to changing external operation conditions, as explained in Section 6.6.2. They cannot predict the net water flux across a saturated membrane that results from applying a difference in total gas pressures between cathodic and anodic gas compartments. 

This water back-transport index is expressed as the normalized through-plane water flux from the cathode side to the anode side divided by the water generation rate at the cathode. Consequently, a... 

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... 

Permeation in PAMPA experiments is also expressed as a flux rate Papp with the unit [cm/sec] under the assumption that transport equilibrium is not reached and back-transport can be neglected in course of the experiment. Papp values represent kinetic information and describe the flux of compounds over the membrane. 

Equation 8.1 highlights the importance of shear rate in raising critical flux, and illustrates why the majority of performance enhancing techniques involve methods of increasing surface shear phenomena. Table 8.1 shows the coefficients in Equation 8.1 for different back transport mechanisms. 

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. 

Given that neither a pore blocking mechanism nor a reduced cake thickness due to aggregate back-transport can account for the obsen ed differences in flux for cakes formed from rapidly-formed compared to slowly-formed aggregates, we must conclude that the differences in permeation velocity arise from differences in permeability of the cakes formed under the different aggregation regimes. The order of magnitude difference in specific resistances of cakes developed at 20 mM and 100 mM KCl concentrations (approx. 1 10 tti.g versus approx. 0.1 10 respectively) supports the... 

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. 

Concentration polarization is the reversible buildup of dissolved or suspended species in the solution phase, as depicted in Figure 10.1. The concentration profile of the retained solutes depends on the balance between the convective drag toward and through the membrane (resulting from the permeation flux) and back transport away from the membrane. The properties of this deposited layer could be reversible or irreversible. The influence of concentration polarization on performance varies with different membrane processes. For RO and NF, concentration polarization can result in a significant increase in osmotic pressure. As a result, higher delivery pressure is required to provide the driving force to achieve... 

A recent report with improved solvent containing 0.01 M DTBCH18C6 in 20% 1-octanol + 80% toluene has yielded rapid Sr(II) transport initially that was subsequently overwhelmed by large acid cotransport resulting in Sr(ll) back transport [75]. Recently, near quantitative transport of Sr(ll) from 3 M HNOj solution has been reported using the crown ether in 2-nitrophenyl-octyl ether (2-NPOE) and n-dodecane mixture [80]. The flux, however, was low that necessitated the use of HFSLM technique to increase the throughput for possible application on large scale. 

The effect of slip coefficient on concentration polarisation (CP) was mathematically modeled for flat membrane and tubular membrane systems [12,13,15,16]. Lowering of CP due to slip coefficient as a function of product water recovery ( ) for different normalised diffusion coefficients (a) is shown in Figure 6.8. The data show that CP decreases both with and a. Since a is a measure of particle diffusion from the membrane surface to the bulk solution, slip-flow possibly augments diffusive back-transport of particles from the membrane surface to the bulk solution. Thus, the slip-flow velocity model possibly accounts for higher or actual UF/MF flux, which is under-predicted by the gel polarisation model discussed in Chapter 1. 

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