Pressure electro-osmotic

The theoretical approach generally used "in electro-osmotic dewatering is an electrochemical one in which the Helmholtz-Smoluchowski relation is used to relate the electro-osmotic convective liquid velocity to such parameters as the viscosity and permittivity of the solution, the zeta potential of the clay surface, and the strength of the applied field. Also, electrode kinetic effects are taken into account where the data point to the involvement of electrochemical reactions at the electrodes during the EOD process. " In combined pressure-electro-osmotic dewatering (CPEOD), the effect of pressure is interpreted in an empirical, ad-hoc manner without any attempt to develop a comprehensive theoretical framework that combines the two driving forces, namely, the pressure and the electric field. 

In Chapters 3 and 4, it has been pointed out that on application of force in the form of temperature difference, potential difference or pressure difference, the development of steady thermo-osmotic pressure, electro-osmotic pressure or streaming potential takes some time. Similar situation occurs when these forces are withdrawn, resulting in the decay of steady state. Build-up and decay in the case of electro-kinetic phenomena have been found to be exponential (Section 4.6). Detailed analysis of the relaxation phenomena and co-relations between the relaxation time and membrane composition have been reported. 

A general case of heat transfer under the conditions of combined action of electro-osmotic forces and imposed pressure gradient was considered by Chakra-borty (2006). The analysis showed that in this case the Nusselt number depends not only on parameters z and S, but also on an additional dimensionless group, which is a measure of the relative significance of the pressure gradient and osmotic forces. 

Under fuel cell operation, a finite proton current density, 0, and the associated electro-osmotic drag effect will further affect the distribution and fluxes of water in the PEM. After relaxation to steady-state operation, mechanical equilibrium prevails locally to fix the water distribution, while chemical equilibrium is rescinded by the finite flux of water across the membrane surfaces. External conditions defined by temperature, vapor pressures, total gas pressures, and proton current density are sufficient to determine the stationary distribution and the flux of water. 

The physical mechanism of membrane water balance and the formal structure of modeling approaches are straightforward. Under stationary operation, the inevitable electro-osmotic flux has to be compensated by a back flux of water from cathode to anode, driven by gradients in concentration, activity, or liquid pressure of water. The water distribution in PEMs that is generated in response to these driving forces decreases from cathode to anode. With increasing/o, the water distribution becomes more nonuniform. the water content near the anode falls below the percolation threshold of proton conduction, X < X. This leaves only a small conductivity due to surface transport of water. As a consequence, increases dramatically this can lead to failure of the complete cell. 

The first term in the right-hand side of (6.4.44) represents the common electro-osmotic contribution whereas the second term stands for what could be termed the negative osmotic effect. Note that the pressure term is absent from (6.4.44). 

Figure 8.8—Electrochromatographic separation of aromatic hydrocarbons. The movement of the mobile phase is strictly due to the electro-osmotic flow. In contrast to HPLC, no pressure is exerted at the head of the column. Separations can be carried out with a very high efficiency.

If there is no potential gradient nor a pressure gradient across the membrane and if no electro-osmotic flow occurs, and when also the activity coefficients are ignored, (17) and (18) yield ... 

Most recently, Gallagher et al.21 measured the water uptake of Nafion membrane under subfreezing temperatures, which showed a significant reduction in the maximum water content corresponding to membrane full hydration. The Nafion membrane with 1,100 equivalent weight, for example, uptakes A 8 of water at -25°C when it equilibrates with vapor over ice because of the low vapor pressure of ice compared to supercooled liquid water. They also found the electro-osmotic drag coefficient to be 1 for Nafion membrane under sub freezing temperatures. 

In PEMFC systems, water is transported in both transversal and lateral direction in the cells. A polymer electrolyte membrane (PEM) separates the anode and the cathode compartments, however water is inherently transported between these two electrodes by absorption, desorption and diffusion of water in the membrane.5,6 In operational fuel cells, water is also transported by an electro-osmotic effect and thus transversal water content distribution in the membrane is determined as a result of coupled water transport processes including diffusion, electro-osmosis, pressure-driven convection and interfacial mass transfer. To establish water management method in PEMFCs, it is strongly needed to obtain fundamental understandings on water transport in the cells. 

Electrodriven separations, such as capillary electrophoresis (CE) and capillary electrochromatography (CEC), are based on the different electrophoretic mobilities in an electric field of the molecules to be separated. They provide a higher separation efficiency then conventional HPLC since the electrophoretic flow (EOF) has a plug-flow profile. Whereas the mobile phase in CE is driven only by the electro-osmotic flow, it is generated in CEC by a combination of EOF and pressure. CEC has a high sample capacity which favours its hyphenation with NMR. 

The theoretical foundation for this kind of analysis was, as mentioned, originally laid by Taylor and Aris with their dispersion theory in circular tubes. Recent contributions in this area have transferred their approach to micro-reaction technology. Gobby et al. [94] studied, in 1999, a reaction in a catalytic wall micro-reactor, applying the eigenvalue method for a vertically averaged one-dimensional solution under isothermal and non-isothermal conditions. Dispersion in etched microchannels has been examined [95], and a comparison of electro-osmotic flow to pressure-driven flow in micro-channels given by Locascio et al. in 2001 [96]. 

Electro-osmosis - the movement of liquid relative to a stationary charged surface (e.g. a capillary or porous plug) by an applied electric field (i.e. the complement of electrophoresis). The pressure necessary to counterbalance electro-osmotic flow is termed the electro-osmotic pressure. 

The contribution of free salt ions to the electric conductivity may therefore be negligible and only the adsorbed countercharge of cations will then contribute to electric conduction. The derived values of ke enable the prediction of the electro-osmotic water flux by active application of an electric potential gradient. Thus, at 0.01 M NaCl in the compacted bentonite, a gradient of 1 V/m will, in the absence of a hydraulic pressure gradient, cause a water flux of the order of 10 10 m/s. 

The functioning of grooves was proven under pressure-driven [44] and electro-osmotic flow [156] conditions and both cases are described below. 

This type of pumping is frequently employed in separation chemistry for capillary electrophoresis, traditionally in fused silica capillaries, but recently more and more in planar quartz structures [32-34]. It should be noted that this type of pump is of the current-source type. This means that the pressures that can be obtained depend on the internal resistance in wide glass tubing, with little resistance, very little pressure can be built up, and a very small hydrostatically induced differential in/outlet pressure immediately overrules the electro osmotic-pumping. However, in very small capillaries, relatively high pressures can be obtained (up to tens of bars). 

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