Planar cell modeling

For an isolated cell the pressure is given by the particle density at the outer cell boundary. As a corollary, it must then also be positive. This is a rigorous statement, true for the spherical, cylindrical, and planar cell model [27], It is a merit of the PB equation that it retains the validity of this exact relation. For the extended density functional theories this no longer holds, and additional terms appear [5]. 

The reliability of the planar cell predictions relays on the accuracy of the model parameters. Eor example, the exchange current density parameters depend on the micro-structural properties such as porosity, pore and particle diameter etc. These parameters strongly influence the three-phase boundary length. For that reason the exchange current density parameters deduced by simulating one set of experimental data may not be valid for a cell with different micro-structural properties. Here, aU the electrochemical model parameters and the micro-structural properties required for the planar cell modeling are the same as the ones presented in Chapter 6 for button cell modeling. The planar cell model predictions are reliable... 

The electrochemical parameters deduced from the modeling of button cell experiments were used for planar cell modeling. Thereby ensuring physically realistic model parameters to assist performance predictions, where there is no direct experimental observation to compare with. Based on a co-flow conflguration, a number of geometrical and operating parameters has been subjected to study their influence on the resulting cell performance, and... 

A Kelvin foam model with planar cell faces was used (a. 17) to predict the thermal expansion coefficient of LDPE foams as a function of density. The expansion of the heated gas is resisted by biaxial elastic stresses in the cell faces. However SEM shows that the cell faces are slightly wrinkled or buckled as a result of processing. This decreases the bulk modulus of the... 

In this section the characteristic phenomena occurring in the tubular cells are shown and the differences with respect to the planar cells are stressed. The model equations are recalled from Chapter 3. 

Another way to assess ion channel conductance is to use artificial phospholipid vesicles (liposomes) as cell models. These structures (described in more detail in the next chapter) are commonly used to transport vaccines, drugs, enzymes, or other substances to target cells or organs. The vesicles, which are several hundred nanometres in diameter, do not suffer from interference from residual natural ion channel peptides or ionophores, unlike purified natural cells. A liposome model was used to test the ion transport behaviour of the redox-active hydraphile 12.36. The compound transports Na+ and the process can also be monitored using 23Na NMR spectroscopy.26 The presence of the ferrocene-derived group in the central relay allows the ion transport to be redox-controlled - oxidation to ferrocinium completely prevents Na+ transport for electrostatic reasons. Some representative data from a planar bilayer measurement is shown for hydraphile 12.36 in Figure 12.16. 

Adhesion of different immune cells to one another or to epithelial cells has also been studied using planar bilayer models. For example, lymphocyte function-associated protein-1 (LFA-1) promotes cell adhesion in inflammation [i.e., a reaction that can be mimicked by binding to purified ICAM-1 in supported membranes (70)]. Similarly, purified LFA-3 reconstituted into supported bilayers mediates efficient CD2-dependent adhesion and differentiation of lymphoblasts (71). This work was followed by a study in which transmembrane domain-anchored and GPl-anchored isoforms of LFA-3 were compared (72). Because this research occurred before the introduction of polymer cushions and because the bilayers were formed by the simple vesicle fusion technique, the transmembrane domain isoform was immobile, whereas the GPl isoform was partially mobile. By comparing results with these two isoforms at different protein densities in the supported bilayer, the authors showed that diffusible proteins at a sufficient minimal density in the supported membrane were required to form strong cell adhesion contacts in this system. 

PNNL (Pacific Northwest National Laboratory) goal 60 (2002) planar, metallic 1C, anode substrate materials, cells, modelling... 

Here, the density profile decays as Cp(r) r , which corresponds to a uniform stretching of the arms in interior region of an annealing PE star. Note that this result differs from that obtained in a simplified quasi-planar model (Cp(r) r / ). The latter predicts an increase in the local stretching of the arms as a function of distance r from the star center. Remarkably, in spite of the difference in the polymer density distributions specified by the two models, the overall size R of the star macromolecule obeys the same power law dependence [123]. One can therefore use either of the two approaches, or even a box-like cell model, to get the power law dependencies for the star size R. 

In planar fuel eells, the membrane is part of a layered sandwich structure (the membrane-eleetrode assembly) eonsisting of a thin eatalyst layer and a porous eleetrode (gas dilfusion layer) on either side of the membrane. The oxygen reduction and hydrogen oxidation reaetions take plaee at the eathode and anode catalyst layers, and the reaetants and produets are transported through the porous electrodes. A fuel eell model thus requires appropriate coupling of the membrane sub-model to the adjacent transport and electrochemical reactions. Detailed strategies for implementing complete fuel cell models have been discussed elsewhere [11-15]. 

Peksen, M., Peters, R., Blum, L., and Stolten, D. (2010) Component design in SOFC technology 3D computational continuum mechanics modelling and experimental validation of a planar type Pre-heater, presented at the 7th Symposium on Fuel Cell Modelling and Experimental Validation, Morges (Lausanne), Switzerland. 

Delphi Corporation has developed a 3-5 kW size SOFC APU system using anode-supported planar cells. This unit is intended to operate on gasoline or diesel, which is reformed through partial oxidation within the APU unit. In 2008, Delphi Coiporation (USA) and Peterbilt Motors Co. (USA) successfully demonstrated the operation of a Delphi s SOFC APU in powering a Peterbilt Model 386 truck s hotel loads (Fig. 9). The Delphi SOFC APU provided power for Model 386 s electrical system and air conditioning and maintained the truck s batteries, all while the truck s diesel engine was turned off. Delphi hopes to commercialize such SOFC APUs in the next few years. 

Various planar membrane models have been developed, either for fundamental studies or for translational applications monolayers at the air-water interface, freestanding films in solution, solid supported membranes, and membranes on a porous solid support. Planar biomimetic membranes based on amphiphilic block copolymers are important artificial systems often used to mimic natural membranes. Their advantages, compared to artificial lipid membranes, are their improved stability and the possibility of chemically tailoring their structures. The simplest model of such a planar membrane is a monolayer at the air-water interface, formed when amphiphilic molecules are spread on water. As cell membrane models, it is more common to use free-standing membranes in which both sides of the membrane are accessible to water or buffer, and thus a bilayer is formed. The disadvantage of these two membrane models is the lack of stability, which can be overcome by the development of a solid supported membrane model. Characterization of such planar membranes can be challenging and several techniques, such as AFM, quartz crystal microbalance (QCM), infrared (IR) spectroscopy, confocal laser scan microscopy (CLSM), electrophoretic mobility, surface plasmon resonance (SPR), contact angle, ellipsometry, electrochemical impedance spectroscopy (EIS), patch clamp, or X-ray electron spectroscopy (XPS) have been used to characterize their... 

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