Boundary conditions bipolar

Studies of double carrier injection and transport in insulators and semiconductors (the so called bipolar current problem) date all the way back to the 1950s. A solution that relates to the operation of OLEDs was provided recently by Scott et al. [142], who extended the work of Parmenter and Ruppel [143] to include Lange-vin recombination. In order to obtain an analytic solution, diffusion was ignored and the electron and hole mobilities were taken to be electric field-independent. The current-voltage relation was derived and expressed in terms of two independent boundary conditions, the relative electron contributions to the current at the anode, jJfVj, and at the cathode, JKplJ. 

When carrying out experiments with a bipolar membrane, the hydrogen penetration steady state rate in diffusion mode can be represented by the following equations obtained for two typical boundary conditions [7—11] ... 

Textures correspond to various arrangements of defects. When the isotropic liquid is cooled, the nematic phase may appear at the deisotropization point in the form of separate small, round objects called droplets (Fig. 12). These can show extinction crosses, spiral structures, bipolar arrangements, or some other topology depending on boundary conditions. Theoretical studies based on a simple model confirm the stability of radial or bipolar orientation (Fig. 5) [22]. Considerations based on improved theoretical models yield stable twisted... 

Combinations of Dirichlet and Neumann boundary conditions are used to solve the electronic and protonic potential equations. Dirichlet boundary conditions are applied at the land area (interface between the bipolar plates and the gas diffusion layers). Neumann boundary conditions are applied at the interface between the gas charmels and the gas diffusion layers to give zero potential flux into the gas charmels. Similarly, the protonic potential field requires a set of potential boimdary condition and zero flux boundary condition at the anode catalyst layer interface and cathode catalyst layer interface respectively. 

Figure 3. Nematic order parameter P2) versus temperature for the radial, toroidal and bipolar boundary conditions (J = 1) and for the bulk. All the results have been obtained from simulations of a droplet carved from a 10 x 10 x 10 lattice. 

We have described lattice spin models for the simulation of polymer-dispersed liquid crystals. The biggest advantage of Monte Carlo simulations is the possibility of investigating the system at a microscopic level, and to calculate thermodynamic properties and their specific order parameters suitable for different types of PDLC. Molecular organizations can be investigated by calculating the order parameters point by point across the droplet. Moreover, it is possible to calculate experimental observables like optical textures and, as discussed here, NMR line shapes. We have given an overview of the method and some applications to models of PDLC with radial and bipolar boundary conditions, and considered the effect of orientational and translational diffusion on the spectra. We have examined in particular under what conditions the NMR spectra of the deuterated nematic can provide reliable information on the actual boundaries present in these submicron size droplets. 

Indeed, air temperature at the inlet is fixed and thanks to a high Nusselt number at x = 0, the inlet rate of heat transfer between air flow and bipolar plate is very high. For this reason, at the inlet the stack temperature is strongly coupled to the temperature of air flow. In other words, the inlet boundary condition for stack temperature (the first of Eq. (5.34)) can be replaced by the condition... 

Physically, Eqs (5.120) and (5.121) describe heat transfer between the bipolar plate and the anode flow at the channel inlet and outlet. The boundary condition for the methanol solution temperature is... 

Figure 5.25 To the boundary conditions for the 3D Laplace equation for bipolar plate potential.

This reaction is currently unavoidable and appears to be favored at hot and dry operating conditions of the fuel cell. The peroxide decomposition forms reactive radials such as hydroxyl, OH, and peroxyl, OOH, that cause oxidative degradation of both the fuel cell membrane and catalyst support [67]. Both electrodes currently use Pt or Pt alloys to catalyze both the HOR and ORR reactions. The catalyst particles are typically supported on a high surface area, heat-treated carbon to both increase the effectiveness of the catalyst and to provide a path for the electrons to pass through to the external circuit via the gas diffusion media (which is typically also made of carbon) and the current collecting bipolar plates. In addition, the catalyst particles are coated in ionomer to facilitate proton transport however, the electrode structure must also be porous to facilitate reactant gas transport. A schematic of a typical PEM MEA is shown in Fig. 17.1. A boundary condition exists at the catalyst particle where protons from the ionomer, electrons from the electrically conducting Pt and carbon, and reactant gases meet. This is usually referred to as the three-phase boundary. The transport of reactants, electrons, and protons must be carefully balanced in terms of the properties, volume, and distribution of each media in order to optimize operation of the fuel cell. 

On the cylinder surfaces, the boundary conditions in the bipolar coordinates can be expressed as [13]... 

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