Electroosmotic Permeability

As transport numbers can characterize ion transport through a membrane, a water transport number tw can be assigned to characterize solvent carried through a membrane. This number would express a number of moles of water carried through the membrane with one Faraday of electrical charge. 

The solvent transport number is not a characteristic of a membrane or a specific pair of ions. It can have either hnear or nonhnear dependency on Jg because this characteristic would depend on the degree of membrane s heterogeneity, current density, the nature of the polymer matrix and the nature of the ion. It was determined for cation membranes that the solvent transport is higher when a counterforts hydration number is higher. 

The electric current is carried predominantly by only one kind of ion in an ion-exchange membrane - by cations in a cation membrane and by anions in an anion membrane - in contrast to the case in free solution where both kinds of ions carry current. Therefore concentration changes take place in the solution close to the membrane surface. These changes are called concentration polarization. Let us assume that there is a thin nonmixed solution layer near the membrane with thickness 5. The concentration in this layer would change linearly from the bulk concentration Q to the concentration Q on the membrane surface. Let us disregard the electrolyte diffusion on the opposite side of the membrane. Then it is obvious that at certain current density the concentration would approach zero on the receiving membrane surface. This current density is named the limiting current density ium and it can be described by the equation  

Taking into account the electrolyte diffusion on the other side of the membrane, the equation should be [1]  

In the case of turbulent flow passing through a chamber with a mixing screen the thickness of the diffusion layer can be described [1]  

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Near the end of the planned operational period, soil samples were collected from the treatment area to determine if the soil concentrations were reduced to less than 5.6mg/kg. These samples, taken only in areas of known high-preoperation TCE concentrations, were collected to get a conservative estimate of the concentration reductions. This preliminary soil sampling showed that the process had worked and that the ROD limit would be met. The unit was then operated until the end of the contract period. Based on the laboratory-determined electroosmotic permeability (adjusted for temperature), applied voltage, and operational time, a total of 1.6 pore volumes of treatment occurred. No groundwater (or pore water) samples were collected during the operation of Phase Ilb. 

While the hydraulic permeability may vary between about six orders of magnitude (fi om 10 to 10 m/s), the electroosmotic permeability is relatively constant and usually comprised in the range of 10 -10 cm Ws. 

Pikal, M.J., and S. Shah. 1990. Transport mechanisms in iontophoresis. III. An experimental study of the contribution of electroosmotic flow and permeability change in transport of low and high molecular weight solutes. Pharm Res 1 (3) 222. 

One method of transporting solutions and compounds in low permeability soils is the application of an electric current to the soil using a process called Electroosmosis (EO). EO fluid flow is a result of ions movement in the double layer of clay surfaces. For this reason, EO is ideally suited to fine-grained, clay-rich soils. The magnitude of electroosmotic... 

In order to evaluate the steady-state water profile in the membrane of a PEFC under given operating conditions, the necessary membrane transport properties required thus include water uptake by the membrane as function of water activity and membrane pretreatment conditions, A(aw) (covered in Section 5.3.1) the diffusion coefficient of water in the membrane as a function of membrane water content, D ) the electroosmotic drag coefficient as a function of membrane water content, (A) and the membrane hydraulic permeability, A hy(i(A). Section 5.3.2 includes a discussion of water transport modes in ionomeric membranes. 

The initial emphasis on evaluation and modeling of losses in the membrane electrolyte was required because this unique component of the PEFC is quite different from the electrolytes employed in other, low-temperature, fuel cell systems. One very important element which determines the performance of the PEFC is the water-content dependence of the protonic conductivity in the ionomeric membrane. The water profile established across and along [106]) the membrane at steady state is thus an important performance-determining element. The water profile in the membrane is determined, in turn, by the eombined effects of several flux elements presented schematically in Fig. 27. Under some conditions (typically, Pcath > Pan), an additional flux component due to hydraulic permeability has to be considered (see Eq. (16)). A mathematical description of water transport in the membrane requires knowledge of the detailed dependencies on water content of (1) the electroosmotic drag coefficient (water transport coupled to proton transport) and (2) the water diffusion coefficient. Experimental evaluation of these parameters is described in detail in Section 5.3.2. 

Here, the electroosmotic flow is proportional to the proton current density jp with a drag coefficient n (wx). D Arcy flow as the mechanism of water backflow proceeds in the direction of the negative gradient of liquid pressure, which (for A P% = 0) is equal to the gradient of capillary pressure. The density of water, cw, and the viscosity, /1, are assumed to be independent of w. The transport coefficient of D Arcy flow is the hydraulic permeability K wx). 

In addition to the ion-clustered gel morphology and microcrystallinity, other structural features includes pore-size distribution, void type, compaction and hydrolysis resistance, capacity and charge density. The functional parameters of interest in this instance include permeability, diffusion coefficients, temperature-time, pressure, phase boundary solute concentrations, cell resistance, ionic fluxes, concentration profiles, membrane potentials, transference numbers, electroosmotic volume transfer and finally current efficiency. 

C. Fabiani, G. Scibona and B. Scuppa, Correlation between electroosmotic coefficients and hydraulic permeability in Nafion membrane, J. Membr. Sci., 1983,16, 51-61. 

To analyze the flow through a porous medium, we can, as before, model the medium as a collection of parallel cylindrical microcapillaries. As noted in Section 4.7, the actual sinuous nature of the capillaries may be accounted for by the introduction of an empirical tortuosity factor. The results for electroosmotic flow through a capillary are then readily carried over to the porous medium by using Darcy s law (Eq. 4.7.7) and, for example, the Kozeny-Carman permeability (Eq. 4.7.16). 

Velocity profiles across the capillary have a Poisseuille shaped flow and the expression predicts that the electroosmotic coefficient of permeability should vary with the square of the radius. In practice, it is found generally that this law is not as satisfactory as the Helmholtz-Smoluchowski approach for predicting electroosmotic behavior in soils. The failure of small pore theory may be because most clays have an aggregate structure with the flow determined by the larger pores [6], Another theoretical approach is referred to as the Spiegler Friction theory [25,6]. Its assumption, that the medium for electroosmosis is a perfect permselective membrane, is obviously not valid for soils, where the pore fluid comprises dilute electrol d e. An expression is derived for the net electroosmotic flow, Q, in moles/Faraday,... 

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