Potential, chemical water

This finally leads to the (T, a, A< ) phase diagram shown in Fig. 5.10 (Plate 5.1). The plot in Fig. 5.10a shows the modified interfacial free energy y" of different adsorbate overlayers as a function of the water chemical potential and the electrode... 

Equation 5.23 shows that an increased filling of the cavities causes a decrease in the value of so that the hydrate becomes more thermodynamically stable. In the large cavities particularly, the fractional occupation Oj, frequently approaches unity, causing the water chemical potential is to be substantially lowered because the logarithm of a small fractions (1 — Oji) is a large negative number. 

Like any other membrane distillation, in OMD the membrane material is also hydrophobic, so that water in liquid form cannot enter the pores unless a hydrostatic pressure exceeds the LEP [37]. In the absence of such pressure difference, a liquid-vapor interface is formed on either side of the membrane pores. In some aspects membrane distillation and OMD can be considered as closely related, although there are some remarkable differences between them. In both cases, it is necessary to maintain a vapor pressure difference across the membrane pores to get a difference in water chemical potential. However, the means of obtaining this vapor pressure difference is different in both the cases. Whereas it is a temperature difference in the case of membrane distillation, it is a concentration difference in the case of OMD. 

Finally from the Gibbs-Duhem equation and Equations 6 we obtain Equation 7 which gives the solvent (water) chemical potential in terms of solute molalities and the aforementioned coefficients. 

Donaldson (9) applied water chemical potential arguments to explain lower leakage currents measured in encapsulated microelectronic devices exposed to sugar-water solutions, relative to devices exposed to pure water. The differences reported by Donaldson are smaller than those reported here, since a saturated sugar solution has less effect on the water chemical potential than a saturated CaCl2 solution. 

Let us consider a water solution (flat surface) at constant temperature T and pressure p in equilibrium with the atmosphere. Water equilibrium between the gas and aqueous phases requires equality of the corresponding water chemical potentials in the two phases (see Chapter 10) ... 

The boundary conditions used in conjunction with the above equations can vary and are to some degree simulation dependent. Normally, the current density, water flux, reference potential, and water chemical potential are specified but two water chemical potentials or the potential drop in the membrane can also be used. If modeling more regions than just a membrane, additional mass balances and internal boundary conditions must be specified. In addition, for modeling the membrane in the catalyst layers, rate equations are required for kinetics and water transfer among its various phases [40]. The above equations are also valid only for the steady-state case (the time-dependent terms have been ignored). 

To simplify the analysis, the cell is first allowed to equilibrate its water chemical potential zf/iw = /iw(l)-/ w(0) occurring in Eq. (26) and achieve a turgor pressure above the atmospheric pressure corresponding to its osmotic potential. As the H pump is switched on, the flux of water into the cell will raise its turgor pressure above Pq. This pressure difference P—Po will be written a Ap, and in the above equations (25) and (26) Ap will be replaced by V Ap, where Fvv is the partial molal volume of water. ... 

The osmosis phenomenon, stemming from biological systems with biological semipermeable membrane, initially represents a nature net transport of solvent molecules from a region of higher water chemical potential (e.g., dilute solution) to a region of lower water chemical potential (e.g., concentrate solution). The driving force is the pure chemical potential difference, i.e., osmotic pressure difference, across the membrane. 

The mass transport (both water and solute) in the FO processes is illustrated in Figure 14.1. The water in the FS of higher water chemical potential will permeate through the membrane into the DS of lower water chemical potential. Meanwhile, the draw solute in the DS will reversely diffuse into the FS due to the concentration gradient across the membrane. Solute diffusion in this fashion is referred to as reverse solute diffusion. Coupled with reverse solute diffusion, solute in the FS will forwardly diffuse into the DS if its concentration in FS is greater than that in DS. Solute diffusion in this fashion is referred to as forward solute diffusion. This section will introduce the fundamentals of the mass transport and solute rejection in FO processes. 

The work of Adachi et al. (2009) represented a first attempt to correlate and validate ex situ and in situ water permeation phenomena in PEMs. Water permeabilities of Nafion PEMs and water transport in operating PEFCs were investigated under comparable ex situ and in situ values of temperature and RH. The examined parameters included the type of driving forces (RH, pressure), the phases of water at PEM interfaces, PEM thickness, and the effect of catalyst layers at the membrane interfaces. Several experimental setups and schemes were designed and explored. Water permeability at 70°C was determined for Nafion membranes exposed to either liquid or vapor phases of water. Chemical potential gradients of water across the membrane are controlled through the use of differences in RH (38-100%), in the case of contact with water vapor, and hydraulic pressure (0-1.2 atm), in the case of contact with liquid water. Three types of water permeation experiments were performed, labeled as vapor-vapor permeation (VVP), liquid-vapor permeation (LVP), and liquid-liquid permeation (LLP). Ex situ measurements revealed that the flux of water is largest... 

Reaction free energy for the formation of various Fe O H complexes in ZSM-5 (AT) as a function of oxygen chemical potential (A/(q) and water chemical potential ( A/j q ). Figi re from Ref f45] with... 

Here j stands for the different types of ions (or different solute components). The water chemical potential does not appear, because it may adjust to the same value inside and outside the cell. And the outside water chemical potential is constant of course. According to Eqs.(3.72) and (3.73) we may express the change of the y-ion s chemical potential via... 

In Fig.4.4 we had included the experimental saturation pressure, Psat(T), along the gas-liquid saturation line for water. In the temperature range of interest here we may consider water vapor as being ideal. The ideal water chemical potential was calculated before in the example on p. 197 (vapor pressure of ice), i.e. I H2 O gas (T, Psat) Psat) + P%o T Pjaf). Along the Saturation Unewc... 

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