Hydraulic water flux

What are the mechanisms and the transport coefficients of water fluxes (diffusion, convection, hydraulic permeation, electro-osmotic drag) ... 

Continuity of fhe wafer flux fhrough the membrane and across the external membrane interfaces determines gradients in water activity or concentration these depend on rates of water transport through the membrane by diffusion, hydraulic permeation, and electro-osmofic drag, as well as on the rates of interfacial kinetic processes (i.e., vaporization and condensafion). This applies to membrane operation in a working fuel cell as well as to ex situ membrane measuremenfs wifh controlled water fluxes fhat are conducted in order to study transport properties of membranes. 

Weber and Newman do the averaging by using a capillary framework. They assume that the two transport modes (diffusive for a vapor-equilibrated membrane and hydraulic for a liquid-equilibrated one) are assumed to occur in parallel and are switched between in a continuous fashion using the fraction of channels that are expanded by the liquid water. Their model is macroscopic but takes into account microscopic effects such as the channel-size distribution and the surface energy of the pores. Furthermore, they showed excellent agreement with experimental data from various sources and different operating conditions for values of the net water flux per proton flux through the membrane. 

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. 

Generally, 70 to 75% of the water vaporized on land is transpired by plants. This water comes from the soil (soil also affects the C02 fluxes for vegetation). Therefore, after we consider gas fluxes within a plant community, we will examine some of the hydraulic properties of soil. For instance, water in the soil is removed from larger pores before from smaller ones. This removal decreases the soil conductivity for subsequent water movement, and a greater drop in water potential from the bulk soil up to a root is therefore necessary for a particular water flux density. 

Rm is the hydraulic resistance of the clean membrane that is deduced from water flux, while An and Rc are estimated through water and solution fluxes of the prefouled element. Another work conducted by Matsumoto et al. [16] also compared the resistances due to internal and surface fouling with ovalbumin. From all these data, it may be concluded that ... 

Ultrafiltration experiments were performed with an Amicon 8050 cell at 25 0 using a stirrer speed of approximately 700 rpm. Water fluxes (hydraulic conductivities) were measured at Ap = 1 psi dextran rejection was measured for feed solutions containing 0.2% T40, 0.2% TIO and 0.1% T500 (see Materials) under conditions of low concentration polarization. Transmembrane fluxes of dextran solutions were of the order of 0.2 x 10 cm/s at Ap = 1 psi. Feeds and permeates were analyzed by size-exclusion chromatography as described in Reference 9, and the chromatographs were used to calculate the rejection curves (Figure 1). 

Temporal variations over short time scales have also been accounted for in this model. They are a result of the diurnal pattern of water uptake which peaks at midday and is zero at night. At night, however, the direction of water fluxes can revert, this hydraulic lift being responsible for water efflux from roots at the top of the root system, especially from those roots growing in the topsoil when it dries out (Caldwell et al., 1998). 

Hollow fibers appear to be the best in terms of surface area/volume, but they have serious hydraulic problems that cause the water flux lo be much lower than other configurations. 

A typical field site, varying in area from about 1 to 10 ha, may include several soil series. The model parameter values may be different not only for each of these soil series, but may also vary considerably within a single series. Such variability in a number of soil hydraulic properties (e.g., soil hydraulic conductivity, soil water flux, etc.) has been widely reported in the literature ( 5 - 1 ). The model parameter values for a given location in the field may also vary with profile depth depending upon soil horizonation as well as a function of the soil and environmental factors (e.g., soil aeration, temperature, etc.). Since soil and environmental factors undergo dynamic changes with time, model parameters are also expected to exhibit temporal variability. At present, only limited data are available to characterize such spatial and temporal variability in pesticide sorption and degradation parameters required in several simulation models. 

Because for salt water, the osmotic pressure difference, Air, acts in opposition to the applied hydraulic pressure, the water flux becomes... 

The reason for this breakthrough resided in the asymmetric structure of the membrane. When the product of the water flux and the total membrane thickness was calculated, the value was 666 times greater than Sourirajan s CA films. The most obvious explanation was that the effective membrane thickness was much less than the total membrane thickness. Loeb postulated the existence of a dense skin less than 1 ju in thickness supported by a relatively porous substrate. Thus, the substrate provided mechanical strength and the thin skin minimized the resistance to hydraulic permeability through the membrane. For the first time in history, it became possible to remove salt from water (95 to 98%) at pressures of 50 to 75 atmospheres with flux values of 10 to 15 gallons of product water per day per square foot of membrane area (GSFD). 

Once the gel-layer is formed, it is often the limiting resistance to flow. Figure 3.32 shows two membranes with widely different membrane resistances (Rm). The pure water flux differs by a factor of 3.75 yet in the presence of protein (retained by both), the water flux differs by a factor of only 1.11, for pressures over the threshold pressure of 20 psi. It will be noted that the higher hydraulic permeability of PM 30 membrane results in a much lower threshold pressure (7 psi). 

Tests with Relatively Nonporous Films. First a set of experiments was carried out on ordinary untreated cellophane film. A 3.5% NaCl brine, under a hydraulic pressure of 1250 p.s.i.g., was used as the feed solution. Product water flux was on the order of 0.3 gallon per day for 1 sq. foot of membrane (gallons per square foot per day). However, no measurable desalinization occurred (experiment 1, Table ). 

One of the most important uncertainty about in-situ parameter concerns materials intrinsic conductivity. They can vary by one or even two order of magnitude. This is quite important because, according to equation 3, darcean liquid flow is directly proportional to this parameter. Theoretically, if the conductivities ratio between the EB and the site remains constant, and, if darcean water flux is dominating, the saturation time should be proportional to EB intrinsic conductivity. To check this, three hydraulic calculations were performed, with EB intrinsic conductivity of respectively lO , 10 ° and... 

FIGURE 14.30 Flux of solutes as influenced by evapotranspiration in wetlands. Solute flux from water column to soil is influenced by hydraulic mass flux caused by water uptake and transpiration by vegetation. (Modified from Martin et al., 2003.)... 

Starling s Law The relationship between water flux through the endothelium and the difference between the hydraulic and osmotic transmural pressures. 

Modeling approaches that explore membrane water management have been reviewed in [16]. Overall, the complex coupling between proton and water mobility at microscopic scale is replaced by a continuiun description involving electro-osmotic drag, proton conductivity and water transport by diffusion or hydraulic permeation. Essential components in every model are the two balance equations for proton flux (Ohm s law) and for the net water flux. Since local proton concentration is constant due to local electroneutrality of the membrane, only one variable remains that has to be solved for, the local water content. 

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