Current density, spatial variation

Wang15 investigated heat and mass transport and electrochemical kinetics in the cathode catalyst layer during cold start, and identified the key parameters characterizing cold-start performance. He found that the spatial variation of temperature was small under low current density cold start, and thereby developed the lumped thermal model. A dimensionless parameter, defined as the ratio of the time constant of cell warm-up to that of ice... 

Bearing in mind that phenomena occurring in nature are too complex to be completely described by mathematical equations, the required details to be described by the model must be goal-driven, i.e. the complexity of the model, and the related results, must be strictly connected to the main goal of the analysis itself. When, for example, the main purpose of the model is to provide the fuel cell performance, in order to analyze the whole system in which it is embedded, the spatial variation in the physical and chemical variables (such as gas concentration, temperature, pressure and current density, for example) are not relevant however the performances, in terms of efficiency, electrical and thermal power and input requirements are important [1-4],... 

In STM, image contrast is derived from spatial variations in current flowing between the proximal probe and the sample.126 Tunneling in an STM relies on the spatial overlap of the tip and sample electronic orbitals. Therefore, the tunneling current falls off very rapidly (on atomic length scales) as a function of distance between the tip and a particular sample feature such as an isolated atom. Tunneling current variations and information on surface chemistry are specifically derived from the associated atomic-scale variations in the density of states near the sample surface. 

Figure 9. Simulated spatial variation of the time-averaged current density (solid line) and wall shear (dotted hne) downstream of a cylinder at Re = 100. For comparison, experimental current densities (symbols) for Re = 110 are shown.

To describe the spatial variations in current density, we assume first-order kinetics in the cupric-ion-concentration ci with inhibition due to the blocking of surface sites by the leveling agent ... 

The two-dimensional case is clearly more difficult. Even for a current-biased sample the current density in the perturbed region does not have to remain constant, and it is only the integral of the current density over a complete cross-sectional area which stays constant. A quantitative LTSEM analysis of Tc variations is possible only under some restrictive conditions. An example would be the case where the current flow is essentially one-dimensional (along the x-direction) and the equipotential lines are predominantly parallel to the y-direction. However, qualitative results can always be obtained in the more complicated general case, and in many cases spatial inhomogeneities of can be detected. 

The standard methods for EIS determine an average impedance for the whole exposed area of a sample. Many samples, in particular coated samples or those undergoing localized corrosion, have spatial variations in behavior. A local EIS method has been developed to measure these variations [24-26]. The local AC solution current density is mapped across a surface using a two-electrode microprobe. The ratio of the applied AC voltage (using distant reference and counterelectrodes) to the local current density gives the local impedance. It is possible to obtain a full EIS spectrum at each location, or to map the impedance at a fixed frequency. This method provides information on the location of the attack, and can detect failure prior to visual observation. 

Because there are no spatial compositional variations complicating the data, it is easy to conclude that the inert gas reduces mass transport across the gas diffusion layer, moving the onset of the mass transport polarization regime to lower current densities. 

Fig. 34. True critical current densities in various oxygen-deficient thin films versus reduced temperature. The solid lines correspond to flux pinning due to spatial fluctuations of the mean fiee path and the dashed line to pitming due to spatial variations of the transition temperature (van Dalen et al. 1996).

The rhs of Eq. (24) is the local density of states of the metal. While this result is useful for analysis of spatial variation of the tunneling current on a given metal surface, the contributions from the coupling matrix elements in Eq. (23) cannot be disregarded when comparing different metals and or different adsorbates [20]. 

The spatial variation on the electrode of current density i is often referred to as the current distribution. Since the current density is related to reactirai rate through Faraday s law, the current distribution is thus a manner of expressing the variation of reaction rate within an electrochemical cell. As for traditional chemical reactors, nonuniformities in reaction rate may be anticipated if the fluid flow is inadequate to prevent concentration gradients. However, electrical field effects also influence the current distribution in an electrochemical cell, and thus reaction rates can be nonuniform even if perfect mixing is achieved in the reactor. Electrochemical cells of course have two electrodes, and sometimes optimizing a current distribution of one electrode is more important than the other. Depending on the proximity of the two electrodes, the current distributions of the electrodes may or may not influence each other. 

It is assumed that the ac solution current density at the probe tip is equal to the current density at the electrode surface, which implies that all of the ac current at the tip is assumed to be travelling normal to the electrode. Equation (7-69) implies that the local impedance is deEned as the ratio of the local current and an overall potential perturbation. It does not therefore consider local variations of potential perturbations. A detailed investigation of the spatial resolution and the height dependence of the measurement is given in a recent publication by Zou et al. (1997). 

The application of LEIS, based on the SRET or the SVET, is of interest when anodic and cathodic site are not clearly separated. The local anodic and cathodic currents are only measured by the SVET when they are further apart then the spatial resolution of the used probe. If they are closer than the spatial resolution, the measured resulting current diminishes to zero although the measured site is corroding actively. In this case, the LEIS is still able to detect the activity of the site by measuring the polarization resistance, which can be measured as the slope of the overall current density curve. The LEIS seems to be a promising tool to detect local variations in coating properties, such as capacitance or film resistance. 

We see immediately that does not depend on the actual coil dimensions at all, but depends only on the ratio of the inner and outer coil radius and the relative spatial variations of resistivity and current density. Therefore, F, may be used as a figure of merit for coil design which is independent of coil dimensions. Stating the result another way, at constant magnetic field the coil losses per unit... 

The traditional approach to understanding both the steady-state and transient behavior of battery systems is based on the porous electrode models of Newman and Tobias (22), and Newman and Tiedermann (23). This is a macroscopic approach, in that no attempt is made to describe the microscopic details of the geometry. Volume-averaged properties are used to describe the electrode kinetics, species concentrations, etc. One-dimensional expressions are written for the fluxes of electroactive species in terms of concentration gradients, preferably using the concentrated solution theory of Newman (24). Expressions are also written for the species continuity conditions, which relate the time dependence of concentrations to interfacial current density and the spatial variation of the flux. These equations are combined with expressions for the interfacial current density (heterogeneous rate equation), electroneutrality condition, potential drop in the electrode, and potential drop in the electrolyte (which includes spatial variation of the electrolyte concentration). These coupled equations are linearized using finite-difference techniques and then solved numerically. 

Once the set of equations (7-37 through 7-57) with boundary conditions (Equations 7-58 through 7-65) are simultaneously solved, this model provides useful information about the spatial variation of reaction rate, current density, and oxygen concentration within the modeling domain (Figure 7-6). 

Spatial fluid density variations are frequently inherited from the filling history of the reservoir. The initial fluids expelled from a source rock are relatively dense liquids. As a source rock becomes more thermally mature, it expels progressively lighter fluids and eventually gases. When such fluids fill a reservoir, and fill and spill from compartment to compartment within a reservoir, each part of the reservoir can end up with different proportions of fluids of different maturity and density. Field observations show that the segment of the reservoir closest to the source kitchen has often received the latest, lowest density charge. Those areas farthest away from the source kitchen may contain earlier denser fluids that have filled and spilled to their current location. 

An interesting relation has been observed between thermal conductivity and density for the rock types at Aspo, and this may be used to evaluate the spatial distribution of the thermal properties from density logging. There is currently insufficient knowledge concerning the variation of thermal properties at different scales. If the whole observed variation within a rock type is based on the cm-m scale, the thermal influence at the canister scale is small. This is due to the fact that the small-scale variation in thermal properties is mainly averaged out on the 5-10 m scale. If the main variation within rock types is on the 5-10 m scale, there is probably a significant effect on the canister temperature. However, it is likely that the observed variation occurs on both these scales. 

The capacitance-temperature slope method described above is one manner in which C-Tcurves at different applied bias may be used to independently study the spatial and energy variations of the density of states in a-Si H. This and similar methods, we believe, currently offer the most reliable means of learning about the bulk density of states in undoped a-Si H. 

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