Electroosmotic flux

Process Concept The application of a direct elec tric field of appropriate polarity when filtering should cause a net charged-particle migration away from the filter medium. This electrophoretic migration will prevent filter-cake formation and the subsequent reduction of filter performance. An additional benefit derived from the imposed electric field is an electroosmotic flux. The presence of this flux in the membrane and in any particulate accumulation may further enhance the filtration rate. 

An electroosmotic flux is formed as a result of the effect of the electric field in the direction normal to the pores in the membrane, delectric diffuse layer in the pore with a charge density p. The charges move in the direction of the x axis (i.e. in the direction of the field), together with the whole solution with velocity v. At steady state... 

Because of the electroosmotic flux, a cation-exchanger membrane is less resistant to cation flux than to anion flux. 

The sign of the cross coefficient Lv< determines the direction of the electroosmotic flux and of the cation flux. From Eq. (6.2.12) we have... 

If water movement in the membrane is also to be considered, then one way to do this is to again use the Nernst—Planck equation. Because water has a zero valence, eq 29 reduces to Pick s law, eq 17. However, it is also well documented that, as the protons move across the membrane, they induce a flow of water in the same direction. Technically, this electroosmotic flow is a result of the proton—water interaction and is not a dilute solution effect, since the membrane is taken to be the solvent. As shown in the next section, the electroosmotic flux is proportional to the current density and can be added to the diffusive flux to get the overall flux of water... 

Peck, K.D., et al. 1996. Quantitative description of the effect of molecular size upon electroosmotic flux enhancement during iontophoresis for a synthetic membrane and human epidermal membrane. J Pharm Sci 85 (7) 781. 

As we turn to the discussion of the cross-processes, it would be worth pointing out that when kt 1, the mutual displacement of dispersion medium layers occurs only within a thin layer of liquid in a direct vicinity to the wall. Consequently, the velocity distribution in the medium inside the capillary has the profile shown in Fig. V-13, b. The electroosmotic flux of the medium, QE, is thus equal to the product between the capillary cross-section and the net electrioosmotic phase displacement velocity, % described by the Helmholtz -Smoluchowski equation (V.26), i.e. ... 

V.33). This allows one to determine the electrokinetic potential of disperse system with an unknown structure. By determining the electroosmotic flux and current passing through the investigated system (provided that the additional amount of electrolyte is added to satisfy the X-Xq condition) at some particular value of the potential difference, AT, one may estimate the electrokinetic potential from the equation... 

Electrokinetic processing of soils, by application of a direct current through a wet soil mass, results in the development of electrical, hydraulic, and chemical gradients. The formation of an acidic front at the anode from water electrolysis and the induced electroosmotic flux of the pore fluid enable the removal of those contaminants that can be solubilized, desorbed from the soil, or simply carried by the pore fluid. The fundamental basis of each of these two main processes is described below. 

Equation 2.13 does not consider the effect of electroosmosis explicitly since in electrokinetic processing, the ion flux would be affected by the electroosmotic transport, as well as the excess water transport in the direction of the positive concentration gradient. Yet, since in high ionic concentration cases the electromigration flux can be several orders of magnitude higher than that contributed by electroosmosis, hence electroosmotic flux may safely be neglected (Acar and Alshawabkeh, 1993). 

The electroosmotic flux is analogous to Darcy s law and can be formulated as shown in Equation 26.2 ... 

The last assumption means that local electroosmotic flux of water in membrane is exactly counterbalanced by back diffusion. Recent studies [14,27] have shown that in a wide range of operating conditions total transfer coefficient of water from the anode to the cathode does not exceed 0.2. Since electroosmotic drag coefficient in Nafion is 1.5 [28], we conclude that the average over the cell surface electroosmotic flux in the membrane is almost fully compensated for by back diffusion. Note that the local value of total water flux in the membrane may significantly deviate from the surface-averaged value, e.g. close to the outlet of the oxygen channel [27]. Nevertheless, assumption 5 seems to be a reasonable approximation. 

On the cathode side of a PEFC under normal operating conditions, one is concerned about excessive amounts of liquid water and flooding of gaseous supply charmels due to a net electroosmotic flux through the PEM and the production of water. Under these conditions, it is reasonable to assume full hydration of the ionomer phase in the CCL. Proton conductivity of the layer is, thus, eonsidered constant. Due to the assumption of capillary equilibrium in pores, pore-filling is... 

The couphng between mobilities of protons and water by the electroosmotic effect is normally an undesired effect, as the resulting electroosmotic flux shuffles water molecules Ifom the anode to the cathode. Backflux of water toward the anode side caused by diffusion or hydrauhc permeation partly balances this flux. However, this flux requires estabhshment of internal gradients in water concentration or hydraulic pressure, which implies depletion of water at the anode side of the PEM. The drying of the PEM on the anode side by electroosmosis could drastically diminish its conductive abilities, since the conductivity of presently available PEMs is a strong function of local water content. 

Electrokinetic remediation of groundwater and soil usually involves the use of electroosmosis and electromigration. Electroosmosis describes the phenomenon of water flow induced by application of an electrical field on porous media (14). Electromigration describes the transport of ions under the influence of an electrical field (75). The electroosmotic flux, qeo, can be written as... 

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