Diffusion-Reaction-Conduction Processes in Porous Electrodes: The Electrolyte Wedge Problem

This work studies mathematical issues associated with steady-state modelling of diffusion-reaction-conduction processes in an electrolyte wedge (meniscus corner) of a current-producing porous electrode. The discussion is applicable to various electrodes where the rate-determining reaction occurs at the electrolyte-solid interface; molten carbonate fuel cell cathodes are used as a specific example. New modelling in terms of component potentials (linear combinations of electrochemical potentials) is shown to be consistent with tradition concentration modelling. The current density is proved to be finite, and asymptotic expressions for both current density and total current are derived for sufficiently small contact angles. Finally, numerical and asymptotic examples are presented to illustrate the strengths and weaknesses of these expressions

Laboratory and theoretical studies of baroclinic processes

An understanding is being developed for processes which may be important in the atmosphere, and the definition and analysis of baroclinic experiments utilizing the geophysical fluid flow cells (GFFC) apparatus in microgravity space flights. Included are studies using numerical codes, theoretical models, and terrestrial laboratory experiments. The numerical modeling is performed in three stages: calculation of steady axisymmetric flow, calculation of fastest-growing linear eigenmodes, and nonlinear effects (first, wave-mean flow interactions, then wave-wave interactions). The code can accommodate cylindrical, spherical, or channel geometry. It uses finite differences in the vertical and meridional directions, and is spectral in the azimuthal. The theoretical work was mostly in the area of effects of topography upon the baroclinic instability problem. The laboratory experiments are performed in a cylindrical annulus which has a temperture gradient imposed upon the lower surface and an approximately isothermal outer wall, with the upper and inner surfaces being nominally thermally insulating

Compact Modeling for a Double Gate MOSFET

MOSFETs (metal-oxide-silicon field-effect transistors) are an integral part of modern electronics. Improved designs are currently under investigation, and one that is promising is the double gate MOSFET. Understanding device characteristics is critical for the design of MOSFETs as part of design tools for integrated circuits such as SPICE. Current methods involve the numerical solution of PDEs governing electron transport. Numerical solutions are accurate, but do not provide an appropriate way to optimize the design of the device, nor are they suitable for use in chip simulation software such as SPICE. As chips contain more and more transistors, this problem will get more and more acute. There is hence a need for analytic solutions of the equations governing the performance of MOSFETs, even if these are approximate. Almost all solutions in the literature treat the long-channel case (thin devices) for which the PDEs reduce to ODEs. The goal of this problem is to produce analytical solutions based on the underlying PDEs that are rapid to compute (e.g. require solving only a small number of algebraic equations rather than systems of PDEs). Guided by asymptotic analysis, a fast numerical procedure has been developed to obtain approximate solutions of the governing PDEs governing MOSFET properties, namely electron density, Fermi potential and electrostatic potential. The approach depends on the channel’s being long enough, and appears accurate in this limit

Spot-on: Safe Fuel/Air Compression

The emission of fuel vapors into the atmosphere from underground storage tanks at filling stations is a common occurrence in many parts the world. The conditions of the vapor in the tanks vary significantly over a 24 hour period such that evaporation and excess air ingestion during the refueling process can cause tank over pressurization and subsequent emissions. At other times during a 24 hour cycle, pressures can fall below atmospheric pressure. The state of California has recognized this emissions problem and has enacted regulations to address it. Due to these low-emission environmental requirements in California, solutions must be implemented that do not entail release of these vapors into the atmosphere. One solution requires that the vapors fill a balloon during the appropriate times. However, the size of the balloon at typical inflation rates requires a significant amount of physical space (approximately 1000-2000 liters), which may not necessarily be available at filling stations in urban areas. Veeder-Root has a patent pending for a system to compress the vapors that are released to a 10:1 ratio, store this compressed vapor in a small storage tank, and then return the vapors to the original underground fuel tank when the conditions are thermodynamically appropriate (see Figure 1 for the schematic representation of this system). The limitation of the compressor, however, is that the compression phase must take place below the ignition temperature of the vapor. For a 10:1 compression ratio, however, the adiabatic temperature rise of a vapor would be above the ignition temperature. Mathematical modeling is necessary here to estimate the performance of the compressor, and to suggest paths in design for improvement. This report starts with a mathematical formulation of an ideal compressor, and uses the anticipated geometry of the compressor to state a simplified set of partial differential equations. The adiabatic case is then considered, assuming that the temporary storage tank is kept at a constant temperature. Next, the heat transfer from the compression chamber through the compressor walls is incorporated into the model. Finally, we consider the case near the valve wall, which is subject to the maximum temperature rise over the estimated 10,000 cycles that will be necessary for the process to occur. We find that for adiabatic conditions, there is a hot spot close to the wall where the vapor temperature can exceed the wall temperature. Lastly, we discuss the implications of our analysis, and its limitations

Chauffeur braking

An experienced driver will `feather' the brakes so as to unwind the suspension compliance and stop the vehicle with only just enough torque in the brakes to hold the vehicle stationary on any gradient, or against the residual torque from an automatic transmission’s torque converter. An optimal stopping problem that minimises the total jerk was formulated and solved. This model was extended by including a linear relationship between the brake pressure and the acceleration of the car where the coefficients are estimated by linear regression. Finally, a Kalman filter estimates the state of the car using the tone wheel

Maximizing Minimum Pressure in Fluid Dynamic Bearings of Hard Disk Drives

We focus on the central spindle which supports the rotating magnetic platters which hold all of the data. The spindle must operate with great precision and stability at high rotational speeds. Design practice has converged on oil-lubricated hydrodynamic journal bearings as the most common choice for spindles. That is, a layer of viscous oil separates a rotating shaft (the bearing) from the fixed outer sleeve (the journal). In hard drives, it is very important for the shaft to be centered within the sleeve. Plain journal bearings (i.e. both surfaces are circular cylinders) are unstable to perturbations that push the shaft off-center. It was found that this stability problem can be overcome by cutting diagonal grooves into the journal in a pattern called a herring-bone. Another consequence of this design is that very high pressures are generated by the grooves as they drive the oil to the middle of the bearing, away from the top/bottom ends of the spindle. This pumping action generally works to oppose leakage out of the bearing. We examine how choices for the groove pattern can influence the key properties of the bearing. The focus is to understand the effect of the groove geometry on the pumping action. In particular the undesirable behavior caused by the low pressures created near the top/bottom ends of the bearing which, under many conditions, may result in the pressure becoming negative, relative to atmospheric pressure. Negative pressure can result in cavitation or, when it occurs near an air-oil interface, can cause air to be ingested and hence create bubbles. Any bubbles in the oil can corrupt the lubricating layer in the bearing and, as they are created and collapse, can cause significant undesirable vibrations. The negative pressures have therefore been identified as one of the key problems in design of hard disk drive bearings. We will use numerical computations and some analysis to show that by modifying the groove geometry we can reduce the negative pressure while retaining good stability characteristics

Enhanced Leak Detection

A key requirement for Veeder-Root’s Enhanced Leak Detection System is that it be able to test in situ for the presence of leaks at gasoline dispensing facilities. Aside from the obvious issues of safety and lost product, this functionality is obligatory for compliance with environmental standards mandated by federal and state oversight bodies, such as the California State Water Resources Control Board (SWRCB). The SWRCB demands a testing procedure that includes conditions as close to operational as possible, while still using environmentally safe gases as a test fluid. Although the test parameters (e.g., pressure) are allowed to deviate from operating conditions in order to facilitate the test procedure, a prescribed rescaling of the test thresholds must then be applied to account for the deviation. Whether the test is run at operation conditions or in a slightly different parameter regime, the fact that the testing must be done on the product and return lines after installation at a service station presents significant challenges in devising an effective test strategy