Water sorption pore model

The subsequently presented model of water sorption in PEMs reconciles vapor sorption and porosity data. At sufficiently large water contents exceeding the amount of surface water, T > equilibrium water uptake is controlled by capillary forces. Deviations from capillary equilibrium arising at A < can be investigated by explicit ab initio calculations of water at dense interfacial arrays of protogenic surface groups. ° In the presented model, the problem of Schroeder s paradox does not arise and there is no need to invoke vapor in pores or hydrophobicity of internal channels. Here, we will present a general outline... 

Figure 9. Dissolved arsenate and monomethyl arsonic acid (MMAA) concentrations in pore waters of sediments spiked with MMAA and predictions of sorption/ kinetic model. Model parameters k = 0.07 day, T o mmaa = 4.5 fxmol g, Kmmaa = 5.0 fxmol L Tcc,AsOi = 3.5 fxmol g Ka. o, = 5.0 fxmol L k (a) Inorganic arsenic, measured (b) arsenate, predicted (c) MMAA, measured (d) MMAA, predicted.

The transfer rate in the mixed side-pore model is proportional to the difference in concentration between the flowing-water and immobile-water phases. The transfer-rate constant kgA is a characteristic-rate parameter for diffusion in the immobile-water phase. Without the Freundlich sorption mechanism, this third model is the same as the dead-end pore model developed by Coats and Smith (19). The Freundlich sorption isotherm was included by van Genuchten and Wierenga (18) in their study, but they solved for the linear case only. Grove and Stollenwerk (20) described a similar model but included Langmuir sorption and a continuous immobile-water film phase. 

Recent models of proton and water transport in PEMs tend to support the notion of cylindrical pore networks. A qualitative distinction between superstructures will be made below, based on the analysis of water sorption data and evaluation of the implications of pore network reorganization upon water uptake. 

While several simplifying assumptions needed to be made so as to derive an analytical model, the model captures all relevant physical processes. Specifically, it employed thermodynamic equilibrium conditions for temperature, pressure, and chemical potential to derive the equation of state for water sorption by a single cylindrical PEM pore. This equation of state yields the pore radius or a volumetric pore swelling parameter as a function of environmental conditions. Constitutive relations for elastic modulus, dielectric constant, and wall charge density must be specified for the considered microscopic domain. In order to treat ensemble effects in equilibrium water sorption, dispersion in the aforementioned materials properties is accounted for. 

Macroscale models of PEM operation that do not include the proper pressure-controlled equilibrium conditions at the single pore level fail in predicting correctly the responses of membrane water sorption, transport properties, and fuel cell operation to changes in external conditions. Single pore models, on the other hand, that do not account for statistical spatial fluctuations in microscopic membrane properties must fail because they cannot predict the dispersion in pore sizes and the evolution of the pore size distribution upon water uptake. 

In general, pores swell nonuniformly, as seen in the section Water Sorption and Swelling of PEMs. As a simplification, the random network was assumed to consist of two types of pores. Nonswollen or dry pores (referred to as red pores) permit only a small residual conductance resulting from tightly bound surface water. Swollen or wet pores (referred to as blue pores) contain extra water with high bulklike conductance. Water uptake corresponds to the swelling of wet pores and to the increase of their relative fraction. In this model, proton transport in the PEM is mapped as a percolation problem, wherein randomly distributed sites represent pores of variable size and conductance. The distinction of red and blue pores accounts for variations of proton transport properties due to different water environments at the microscopic scale, as discussed in the section Water in PEMs Classification Schemes. ... 

Fig. 6 The distribution of 3-chlorophenol in the pore water of a model soil column from Na bentonite irreversibly precharged by the pollutant for the case of sorption equilibrium and nonequilibrium ( kinetics ) after 1.5 days...

The bioavailability of contaminants to wildlife and humans is also an area of critical importance, where contaminants can be taken up in pore water and by dermal contact, particle ingestion, or particle inhalation. The dynamics of sorption/desorption are not currently incorporated into exposure and risk assessment models for organic compounds, where availability, in most cases, is assumed to be 100% [224]. Recently, the following have been demonstrated and reported ... 

Because of the similarity of transport in biotilms and in stagnant sediments, information on the parameters that control the conductivity of the biofilm can be obtained from diagenetic models for contaminant diffusion in pore waters. Assuming that molecular diffusion is the dominant transport mechanism, and that instantaneous sorption equilibrium exists between dissolved and particle-bound solutes, the vertical flux ( ) through a stagnant sediment is given by (Berner, 1980)... 

In Part 2 of the PCB story, we introduced the exchange between the water column and the surface sediments in exactly the same way as we describe air/water exchange. That is, we used an exchange velocity, vsedex, or the corresponding exchange rate, ksedex (Table 23.6). Since at this stage the sediment concentration was treated as an external parameter (like the concentration in the air, Ca), this model refinement is not meant to produce new concentrations. Rather we wanted to find out how much the sediment-water interaction would contribute to the total elimination rate of the PCBs from the lake and how it would affect the time to steady-state of the system. As shown in Table 23.6, the contribution of sedex to the total rate is about 20% for both congeners. Furthermore, it turned out that diffusion between the lake and the sediment pore water was much more important than sediment resuspension and reequilibration, at least for the specific assumptions made to describe the physics and sorption equilibria at the sediment surface. 

Selim et al. (1976b) developed a simplified two-site model to simulate sorption-desorption of reactive solutes applied to soil undergoing steady water flow. The sorption sites were assumed to support either instantaneous (equilibrium sites) or slow (kinetic sites) first-order reactions. As pore-water velocity increased, the residence time of the solute decreased and less time was allowed for kinetic sorption sites to interact (Selim et al., 1976b). The sorption-desorption process was dominated by the equilib-... 

Predicting fast and slow rates of sorption and desorption in natural solids is a subject of much research and debate. Often times fast sorption and desorption are approximated by assuming equilibrium portioning between the solid and the pore water, and slow sorption and desorption are approximated with a diffusion equation. Such models are often referred to as dual-mode models and several different variants are possible [35-39]. Other times two diffusion equations were used to approximate fast and slow rates of sorption and desorption [31,36]. For example, foraVOCWerth and Reinhard [31] used the pore diffusion model to predict fast desorption, and a separate diffusion equation to fit slow desorption. Fast and slow rates of sorption and desorption have also been modeled using one or more distributions of diffusion rates (i.e., a superposition of solutions from many diffusion equations, each with a different diffusion coefficient) [40-42]. 

The content of non-evaporable water, relative to that in a fully hydrated paste of the same cement, was used as a measure of the degree of hydration. Portland cement paste takes up additional water during wet curing, so that its total water content in a saturated, surface dry condition exceeds the initial w/c ratio. Evidence from water vapour sorption isotherms indicated that the properties of the hydration product that were treated by the model were substantially independent of w/c and degree of hydration, and only slightly dependent on the characteristics of the individual cement. The hydration product was thus considered to have a fixed content of non-evaporable water and a fixed volume fraction, around 0.28, of gel pores. 

Brunauer and co-workers (B55,BI08) considered that the gel particles of the Powers-Brownyard model consisted of either two or three layers of C S-H, which could roll into fibres. D-drying caused irreversible loss of interlayer water, and the specific surface area could be calculated from water vapour sorption isotherms, which gave values in the region of 200m g for cement paste. Sorption isotherms using N2 give lower values of the specific surface area this was attributed to failure of this sorbate to enter all the pore spaces. 

Parrott and co-workers (P30,P32,P35,P33) described a more sophisticated method for modelling the hydration process. The fraction of the total water porosity that was below 4nm was calculated by multiplying the volume fraction of C-S- H by an appropriate factor, which depended on whether the C-S-H was formed from alite or belite, the temperature and the amount of space available. The constants assumed were based on experimental data obtained using a procedure based on methanol sorption (Section 8.3.4). The effect of drying was allowed for (P35) by introducing a factor of 0.7 - -1.2(RH — 0.5) for 0.5 < RH < 1, or of 0.7 for RH 0.5. These refinements allow some deviation from the Powers-Brownyard postulate of a fixed volume ratio of gel porosity to product. Typical results for the volume fractions of pores larger than 4 nm in mature pastes of a cement with an alite content of 56% were approximately 0.26, 0.16 and 0.07 for w/c ratios of 0.65, 0.50 and 0.35, respectively (P32). For the two higher w/c ratios, these results are near the capillary porosities of Powers and Brownyard, but for w/c 0.35 the latter value is zero. 

Kotdawala et al.415 develop a mean-field perturbation theory for the study of polar molecules in slit pores and validate their model by comparison with MC simulations. Their theory incorporates the electrostatic interactions, and allows prediction of adsorption isotherms for molecules confined between two parallel plates. The model is used to study sorption of water molecules, and results of this model are compared with others in the literature. 

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