Liquid cell model

Mann, J. A., Hessami, S., Simha, R., Elastic-moduli of monolayers on liquids - cell model. Abstracts of Papers of the American Chemical Society, 190, pp. 121-COL (1985). 

The above picture of slowly cooled SCLs allows considering the liquid cell model of Lennard-Jones and Devonshire [34] (Figure 10.1 and its various elaborations [35]. In the figure, we show a cell representation of a dense liquid in (a) and of a crystal in (b). Each cell is occupied by a particle in which the particle vibrates. A defect in the cell representation corresponds to some empty cells. The regular lattice in (b) is in accordance with Einstein s model of a crystal. In the liquid state, this regularity is absent. We consider the conjiguratiorud partition JunctionZ T, V) (Appendix lO.A),... 

Fig. 3. Diagrams of electrochemical cells used in flow systems for thin film deposition by EC-ALE. A) First small thin layer flow cell (modeled after electrochemical liquid chromatography detectors). A gasket defined the area where the deposition was performed, and solutions were pumped in and out though the top plate. Reproduced by permission from ref. [ 110]. B) H-cell design where the samples were suspended in the solutions, and solutions were filled and drained from below. Reproduced by permission from ref. [111]. C) Larger thin layer flow cell. This is very similar to that shown in 3A, except that the deposition area is larger and laminar flow is easier to develop because of the solution inlet and outlet designs. In addition, the opposite wall of the cell is a piece of ITO, used as the auxiliary electrode. It is transparent so the deposit can be monitored visually, and it provides an excellent current distribution. The reference electrode is incorporated right in the cell, as well. Adapted from ref. [113],...

Given the character of the water-water interaction, particularly its strength, directionality and saturability, it is tempting to formulate a lattice model, or a cell model, of the liquid. In such models, local structure is the most important of the factors determining equilibrium properties. This structure appears when the molecular motion is defined relative to the vertices of a virtual lattice that spans the volume occupied by the liquid. In general, the translational motion of a molecule is either suppressed completely (static lattice model), or confined to the interior of a small region defined by repulsive interactions with surrounding molecules (cell model). Clearly, the nature of these models is such that they describe best those properties which are structure determined, and describe poorly those properties which, in some sense, depend on the breakdown of positional and orientational correlations between molecules. 

The theoretical description based on the lattice or cell models of the liquid uses the language contributing states of occupancy . Nevertheless, these states ot occupancy are not taken to be real, and the models are, fundamentally, of the continuum type. The contribution to the free energy function of different states of occupancy of the basic lattice section is analogous to the contribution to the energy of a quantum mechanical system of terms in a configuration interaction series. 

Just as in our abbreviated descriptions of the lattice and cell models, we shall not be concerned with details of the approximations required to evaluate the partition function for the cluster model, nor with ways in which the model might be improved. It is sufficient to remark that with the use of two adjustable parameters (related to the frequency of librational motion of a cluster and to the shifts of the free cluster vibrational frequencies induced by the environment) Scheraga and co-workers can fit the thermodynamic functions of the liquid rather well (see Figs. 21-24). Note that the free energy is fit best, and the heat capacity worst (recall the similar difficulty in the WR results). Of more interest to us, the cluster model predicts there are very few monomeric molecules at any temperature in the normal liquid range, that the mole fraction of hydrogen bonds decreases only slowly with temperature, from 0.47 at 273 K to 0.43 at 373 K, and that the low... 

Through the use of a transparent fuel cell, Spernjak et al. [87] were able to visualize the anode FF plate (and DL without MPL) while operating the fuel cell with a cathode that had MPL on the DL. It was observed that liquid water was present in the anode flow field only when an MPL on the cathode side was used. Again, this is an indication that the cathode side creates a pressure barrier that pushes the water toward the anode. These observations agree with the ones presented mathematically by Weber and Newman [148]. Although they did not do any experimental work, their two-phase fuel cell model concluded that the MPL acts as a valve that pushes water away from the DL toward the anode though the membrane. 

MSE.IO. I. Prigogine et L. Saraga, Sur la tension superficielle et le modele ceUulaire de I etat liquide (On the surface tension and the cell model of liquid state), J. Chim. Phys. 49, 399-407 (1952). 

The beginning of modeling of polymer-electrolyte fuel cells can actually be traced back to phosphoric-acid fuel cells. These systems are very similar in terms of their porous-electrode nature, with only the electrolyte being different, namely, a liquid. Giner and Hunter and Cutlip and co-workers proposed the first such models. These models account for diffusion and reaction in the gas-diffusion electrodes. These processes were also examined later with porous-electrode theory. While the phosphoric-acid fuel-cell models became more refined, polymer-electrolyte-membrane fuel cells began getting much more attention, especially experimentally. 

In 2000 and 2001, fuel-cell models were produced by the dozens. These models were typically more complex and focused on such effects as two-phase flow ° where liquid-water transport was incorporated. The work of Wang and co-workers was at the forefront of those models treating two-phase flow comprehensively. The liquid-water flow was shown to be important in describing the overall transport in fuel cells. Other models in this time frame focused on multidimensional, transient, and more microscopic effects.The microscopic effects again focused on using an agglomerate approach in the fuel cell as well as how to model the membrane appropriately. 

Figure 4.26 shows a cell model of the three phases. Gas in the upper region has a very low density and the molecules are free to fly around. When the vapor condenses into a liquid (shown lower right), the density is greatly increased so that there is very little free volume space the molecules have limited ability to move around, and they have random orientation that is, they can rotate and point in random directions. When the liquid freezes into a solid (shown lower left), the density is slightly increased to eliminate the void space, the molecules have assigned positions and are not free to move around, and there is now an orientation order that is, they cannot rotate freely and they all point at the same direction. 

Figure 4.26 Cell model of gases, liquids, and solids...

Third, turbulent transport is represented as a succession of simple laminar flows. If the boundary is a solid wall, then one considers that elements of liquid proceed short distances along the wall in laminar motion, after which they dissolve into the bulk and are replaced by other elements, and so on. The path length and initial velocity in the laminar motion are determined by dimensional scaling. For a liquid-fluid interface, a roll cell model is employed for turbulent motion as well as for interfacial turbulence. 

Fig. 8. Roll cell model (a) stream lines in a frame of reference moving with the average liquid velocity (b) stream lines in a fixed frame of reference.

Lamont, J. C., and D. S. Scott, An eddy cell model of mass transfer into the surface of a turbulent liquid , AlChE J., 16,4, 513-519 (1970). 

Evans, E. A., and Hochmuth, R. M. (1977). A solid-liquid composite model of the red cell membrane. J. Membr. Biol. 30, 351-362. 

Using the 2-D saturation maps from the two-phase LB simulation, shown in Fig. 14, the effective ECA can be evaluated and correlated according to Eq. (26). Based on several liquid water saturation levels, the catalytic surface coverage factor for the CL microstructure is estimated and the following correlation can be constructed, which can be used as valuable input to macroscopic two-phase fuel cell models.27,62... 

Figure 23 shows the variation of the effective ECA with liquid water saturation from the evaluated correlation given in Eq. (27) along with the typical correlations with ad-hoc fitting of the coverage parameter otherwise used in the macroscopic fuel cell models.2 It is to be noted that the effect of liquid water is manifested via a reduction of the active area available for electrochemical... 

This estimate could prove to be valuable input for more accurate representation of the pore blockage effect in the macroscopic two-phase fuel cell models. Figure 24 shows the variation of the effective oxygen diffusivity with liquid water saturation from the correlation in Eq. (29) along with the typical macrohomogeneous correlation with m = 1.5 and b = 1.5 otherwise used arbitrarily in the macroscopic fuel cell modeling literature. 

The rate-based models suggested up to now do not take liquid back-mixing into consideration. The only exception is the nonequilibrium-cell model for multicomponent reactive distillation in tray columns presented in Ref. 169. In this work a single distillation tray is treated by a series of cells along the vapor and liquid flow paths, whereas each cell is described by the two-film model (see Section 2.3). Using different numbers of cells in both flow paths allows one to describe various flow patterns. However, a consistent experimental determination of necessary model parameters (e.g., cell film thickness) appears difficult, whereas the complex iterative character of the calculation procedure in the dynamic case limits the applicability of the nonequilibrium cell model. 

The liquid-drop model was used to model the deformation of sea urchin eggs (Yoneda, 1973). This theory assumes that the tensions in the wall during the compression are uniform and isotropic as is stated by Cole (1932) and Yoneda (1964). However, Hiramoto (1963) suggested that the circumferential tensions are actually up to two times greater than the tensions in the meridian direction. This result suggests that the use of the liquid-drop model may not be appropriate to determine material properties of cells. 

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