Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Free Field Characterization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

Normal-mode approach to wave propagation in the turbulent atmosphere

Recent studies have used the superposition principle (extended Huygens-Fresnel principle) to characterize completely the statistics of a field that has propagated through a thick slab of turbulent air in terms of the statistics for spherical-wave sources. In this paper, we consider the normal-mode decomposition associated with this linear system propagation model. In particular, we use the statistics of the atmospheric impulse response (Green's function) to show that the atmospheric mode decomposition exhibits far-field and near-field regimes very similar to those of free-space propagation. The significance of these results for optical communication through the atmosphere is briefly discussed.

Shapiro, J. H.↗
NASA NTRS1983

Geomagnetism of earth's core

Instrumentation, analytical methods, and research goals for understanding the behavior and source of geophysical magnetism are reviewed. Magsat, launched in 1979, collected global magnetometer data and identified the main terrestrial magnetic fields. The data has been treated by representing the curl-free field in terms of a scalar potential which is decomposed into a truncated series of spherical harmonics. Solutions to the Laplace equation then extend the field upward or downward from the measurement level through intervening spaces with no source. Further research is necessary on the interaction between harmonics of various spatial scales. Attempts are also being made to analytically model the main field and its secular variation at the core-mantle boundary. Work is also being done on characterizing the core structure, composition, thermodynamics, energetics, and formation, as well as designing a new Magsat or a tethered satellite to be flown on the Shuttle.

Benton, E. R.↗
NASA NTRS2005

Gases and Aerosols over North America and the Atlantic: First results from INTEX-A

Intercontinental Chemical Transport Experiment (INTEX; http://cloud1.arc.nasa.gov) is an ongoing two-phase integrated atmospheric field experiment being performed over North America (NA). Its first phase (INTEX-A) was performed in the summer of 2004 and the second phase (INTEX-B) is planned for the early spring of 2006. The main goal is to characterize the sources and distribution of gases and aerosols over NA and to understand their transport and transformation on transcontinental/intercontinental scales in order to assess their impact on air quality and climate. Central to achieving this goal is the need to relate space-based observations with those from airborne and surface platforms. During JNTEX-A, NASA s DC-8 was joined by some dozen other aircraft from a large number of European (U. K., France, and Germany) and North American partners to explore the composition of the troposphere over NA and the Atlantic in a coordinated manner. Global and regional models along with satellite observations were extensively used to plan, coordinate, and implement this field mission. Aircraft were instrumented to measure a comprehensive suite of gases and aerosols utilizing in-situ and remote sensors. The NASA DC-8 alone was equipped with some 20 instruments capable of measuring species at concentrations as low as 10(exp -15) v/v. Measurements included major atmospheric gaseous constituents (O3, NO(x), HNO3, HNO4, PANS, SO2, VOC/OVOC, CO, and CO2), free radicals and precursors (OH, HO2, H2O2, HCHO), aerosols and radiation (microphysics, composition, optical depth, radiative flux), as well as multiple tracers of pollution. Validation of instruments aboard Terra, Aqua, and Envisat satellites was given high priority. Some of the highest pollution levels were present in the upper troposphere due to widespread deep convection. Although unexpected, frequent instances of Asian pollution over NA were encountered during these summer months. The soil uptake of CO2 over NA was characterized over large regions of NA helping to understand the continents CO2-sink potential. DC-8 sampling of smoke from Alaskan fires and formaldehyde over forested regions, and simultaneous satellite observations of these provided excellent opportunities for the interplay of these platforms. Outflow of pollution from NA was sampled again over the Atlantic after several days to assess its evolution during transport. Models of chemistry and radiation are presently being employed to help in the interpretation of JNTEX-A data. The planning for INTEX-B (spring 2006) is currently underway. First results from INTEX-A and plans for INTEX-B will be discussed

Singh, Hanwant B.↗
NASA NTRS1993

Microwave emission from a sunspot. II - The center-to-limb variation

The center-to-limb variation of both the spectral and spatial brightness distributions is investigated using a series of microwave observations of a sunspot in the active region NOAA 4741. Depending on the heliocentric position of the sunspot, the microwave emission appears in two typical profiles: either a ring structure near the center of the disk or a single-peak structure near the limb. Due to the increase of the gyroresonance opacity of the field lines near the spot center as the viewing angle increases, the brightness temperature at high, optically thin frequencies increases slightly as the spot approaches the limb. In addition, a change of effective harmonic, which accompanies a discontinuous change in the degree of polarization, characterizes the center-to-limb variation of the gyroresonance spectrum. Finally, the height of the gyroresonance layer, low in the corona of the active region, is determined from a change of spectrum from gyroresonance to free-free emission as the spot passes over the solar limb.

Lee, Jeongwoo W.↗
NASA NTRS1984

An experimental investigation of two-dimensional thrust augmenting ejectors, part 2

The flow-field within a two-dimensional thrust augmenting ejector has been documented experimentally. Results are presented on the mean velocity field and the turbulent correlations by Laser Doppler Velocimeter, surface pressure distribution, surface temperature distribution, and thrust performance for two shroud geometries. The maximum primary nozzle pressure ratio tested was 3.0. The tests were conducted at primary nozzle temperature ratios of 1.0, 1.8 and 2.7. Two ejector characteristic lengths have been identified based on the dynamics of the ejector flow field, i.e., a minimum length L sub m below which no significant mixing occurs, and a critical length L sub c associated with the development of U'V' correlation in the ejector. These characteristic lengths divide the ejector flow field into three distinctive regions: the entrance region where there is no direct interaction between the primary flow and the ejector shroud; the interaction region where there is an increased momentum of induced flow near the shroud surface; and a pipe flow region characterized by an increased skin friction where x is the distance downstream from the ejector inlet. The effect of the coflowing induced flow has been shown to produce inside the ejector a centerline velocity that has increased over the free-jet data.

Bernal, L.↗
NASA NTRS2005

Interstellar PAH in the Laboratory and in Space. What have we Learned from the New Generation of Laboratory and Observational Studies?

Polycyclic Aromatic Hydrocarbons (PAHs) are an important and ubiquitous component of carbon-bearing materials in space. PAHs are the best-known candidates to account for the IR emission bands (UIR bands) and PAH spectral features are now being used as new probes of the ISM. PAHs are also thought to be among the carriers of the diffuse interstellar absorption bands (DIBs). In the model dealing with the interstellar spectral features, PAHs are present as a mixture of radicals, ions and neutral species. PAH ionization states reflect the ionization balance of the medium while PAH size, composition, and structure reflect the energetic and chemical history of the medium. A major challenge for laboratory astrophysics is to reproduce (in a realistic way) the physical conditions that exist in the emission and/or absorption interstellar zones. An extensive laboratory program has been developed at NASA Ames to assess the physical and chemical properties of PAHs in such environments and to describe how they influence the radiation and energy balance in space and the interstellar chemistry. In particular, laboratory experiments provide measurements of the spectral characteristics of interstellar PAH analogs from the ultraviolet and visible range to the infrared range for comparison with astronomical data. This paper will focus on the recent progress made in the laboratory to measure the direct absorption spectra of neutral and ionized PAHs in the gas phase in the near-UV and visible range in astrophysically relevant environments. These measurements provide data on PAHs and nanometer-sized particles that can now be directly compared to astronomical observations. The harsh physical conditions of the IS medium - characterized by a low temperature, an absence of collisions and strong VUV radiation fields - are simulated in the laboratory by associating a molecular beam with an ionizing discharge to generate a cold plasma expansion. PAH ions are formed from the neutral precursors in an isolated environment at low temperature (of the order of 100 K). The spectra of neutral and ionized PAHs are measured using the high sensitivity methods of cavity ring down spectroscopy (CRDS). These experiments provide unique information on the spectra of free, cold large carbon molecules and ions in the gas phase. Intrinsic band profiles and band positions of cold gas-phase PAHs can now be measured with high-sensitivity spectroscopy and directly compared to the astronomical data. The electronic bands measured for ionized PAH are found to be intrinsically broad (about 20 cm(sup -1)) while the bands associated with the neutral precursors are narrower (of the order of 2 - 10 cm(sup -1)). The laboratory data are discussed and compared with recent astronomical spectra of large and narrow DIBs and with the spectra of circumstellar environments of selected carbon stars and the implications for the interstellar PAH population are derived. Preliminary results also show that carbon nanoparticles are formed during the short residence time of the precursors in the plasma.

Salama, Farid↗
NASA NTRS2006

Astrochemistry: Recent Advances in the Study of Carbon Molecules in Space

Carbon molecules and ions play an important role in space. Polycyclic Aromatic Hydrocarbons (PAHs) are the best-known candidates to account for the infrared emission bands (UIR bands) and PAH spectral features are now being used as probes of the interstellar medium in Galactic and extra-galactic environments. PAHs are also thought to be among the carriers of the diffuse interstellar absorption bands (DIBs). In the model dealing with the interstellar spectral features, PAHs are present as a mixture of radicals, ions and neutral species. PAH ionization states reflect the ionization balance of the medium while PAH size, composition, and structure reflect the energetic and chemical history of the medium. A major challenge for laboratory Astrochemistry is to reproduce (in a realistic way) the physical conditions that exist in the emission and absorption interstellar zones. An extensive laboratory program has been developed in various laboratories to characterize the physical and chemical properties of PAHs in astrophysical environments and to describe how they influence the radiation and energy balance in space and the interstellar chemistry. In particular, laboratory experiments provide measurements of the spectral characteristics of interstellar PAH analogs from the ultraviolet and visible range to the infrared range for comparison with astronomical data. The harsh physical conditions of the interstellar medium - characterized by a low temperature, an absence of collisions and strong ultraviolet radiation fields - are simulated in the laboratory by associating a molecular beam with an ionizing discharge to generate a cold plasma expansion. PAH ions are formed from the neutral precursors in an isolated environment at low temperature (of the order of 100 K). The spectra of neutral and ionized PAHs are measured using the high sensitivity methods of cavity ring down spectroscopy (CRDS). These experiments provide unique information on the spectra of free, cold large carbon molecules and ions in the gas phase.

Salama, Farid↗
NASA NTRS2005

PAHs and the Diffuse Interstellar Bands. What have we Learned from the New Generation of Laboratory and Observational Studies?

Polycyclic Aromatic Hydrocarbons (PAHs) are an important and ubiquitous component of carbon-bearing materials in space. PAHs are the best-known candidates to account for the IR emission bands (UIR bands) and PAH spectral features are now being used as new probes of the ISM. PAHs are also thought to be among the carriers of the diffuse interstellar absorption bands (DIBs). In the model dealing with the interstellar spectral features, PAHs are present as a mixture of radicals, ions and neutral species. PAH ionization states reflect the ionization balance of the medium while PAH size, composition, and structure reflect the energetic and chemical history of the medium. A major challenge for laboratory astrophysics is to reproduce (in a realistic way) the physical conditions that exist in the emission and/or absorption interstellar zones, An extensive laboratory program has been developed at NASA Ames to characterize the physical and chemical properties of PAHs in astrophysical environments and to describe how they influence the radiation and energy balance in space and the interstellar chemistry. In particular, laboratory experiments provide measurements of the spectral characteristics of interstellar PAH analogs from the ultraviolet and visible range to the infrared range for comparison with astronomical data. This paper will focus on the recent progress made in the laboratory to measure the direct absorption spectra of neutral and ionized PAHs in the gas phase in the near-W and visible range in astrophysically relevant environments. These measurements provide data on PAHs and nanometer-sized particles that can now be directly compared to astronomical observations. The harsh physical conditions of the IS medium - characterized by a low temperature, an absence of collisions and strong V W radiation fields - are simulated in the laboratory by associating a molecular beam with an ionizing discharge to generate a cold plasma expansion. PAH ions are formed from the neutral precursors in an isolated environment at low temperature (of the order of 100 K). The spectra of neutral and ionized PAHs are measured using the high sensitivity methods of cavity ring down spectroscopy (CRDS). These experiments provide unique information on the spectra of free, cold large carbon molecules and ions in the gas phase. Intrinsic band profiles and band positions of cold gas-phase PAHs can now be measured with high- sensitivity spectroscopy and directly compared to the astronomical data. The electronic bands measured for ionized PAH are found to be intrinsically broad (about 20/cm) while the bands associated with the neutral precursors are narrower (of the order of 2 - 10/cm).

Salama, Farid↗
NASA NTRS1992

Variance of phase fluctuations of waves propagating through a random medium

As an electromagnetic wave propagates through a random scattering medium, such as a forest, its energy is attenuated and random phase fluctuations are induced. The magnitude of the random phase fluctuations induced is important in estimating how well a Synthetic Aperture Radar (SAR) can image objects within the scattering medium. The two-layer random medium model, consisting of a scattering layer between free space and ground, is used to calculate the variance of the phase fluctuations induced between a transmitter located above the random medium and a receiver located below the random medium. The scattering properties of the random medium are characterized by a correlation function of the random permittivity fluctuations. The effective permittivity of the random medium is first calculated using the strong fluctuation theory, which accounts for large permittivity fluctuations of the scatterers. The distorted Born approximation is used to calculate the first-order scattered field. A perturbation series for the phase of the received field in the Rytov approximation is then introduced and the variance of the phase fluctuations is also calculated assuming that the transmitter and receiver are in the paraxial limit of the random medium, which allows an analytic solution to be obtained. Results are compared using the paraxial approximation, scalar Green's function formulation, and dyadic Green's function formulation. The effects studied are the dependence of the variance of the phase fluctuations on receiver location in lossy and lossless regions, medium thickness, correlation length and fractional volume of scatterers, depolarization of the incident wave, ground layer permittivity, angle of incidence, and polarization.

Chu, Nelson C.↗
NASA NTRS1991

Real time quantitative imaging for semiconductor crystal growth, control and characterization

A quantitative real time image processing system has been developed which can be software-reconfigured for semiconductor processing and characterization tasks. In thermal imager mode, 2D temperature distributions of semiconductor melt surfaces (900-1600 C) can be obtained with temperature and spatial resolutions better than 0.5 C and 0.5 mm, respectively, as demonstrated by analysis of melt surface thermal distributions. Temporal and spatial image processing techniques and multitasking computational capabilities convert such thermal imaging into a multimode sensor for crystal growth control. A second configuration of the image processing engine in conjunction with bright and dark field transmission optics is used to nonintrusively determine the microdistribution of free charge carriers and submicron sized crystalline defects in semiconductors. The IR absorption characteristics of wafers are determined with 10-micron spatial resolution and, after calibration, are converted into charge carrier density.

Wargo, Michael J.↗
NASA NTRS2005

Spectroscopy of Jet-Cooled Neutral and Ionized PAHs: Implications for Interstellar Dust

We present the gas-phase spectroscopy of neutral and ionized polycyclic aromatic hydrocarbons (PAHs) measured in the W-Visible-NIR range in an astrophysically relevant environment. These measurements provide data on PAHs and nanometer sized particles that can now be directly compared to astronomical observations. The harsh physical conditions of the IS medium - characterized by a low temperature, an absence of collisions and strong VUV radiation fields - are simulated in the laborat'ory by associating a molecular beam with an ionizing discharge to generate a cold plasma expansion. PAH ions are formed from the neutral precursors in an isolated environment at low temperature ($\sim lOO$-K). The spectra of neutral and ionized PAHs are measured using the high sensitivity methods of cavity ring down spectroscopy (CRDS) and multiplex integrated cavity output spectroscopy (MICOS). These experiments provide unique information on the spectra of free, cold large carbon molecules and ions in the gas phase. The electronic bands measured for ionized PAH are found to be intrinsically broad ($\geq$20 cm$^{-l}$) while the bands associated with the neutral precursors are narrower (of the order of 2 - 10 cm$^{-l}$). The laboratory data are discussed and compared with recent astronomical spectra of large and narrow DIBs and with the spectra of circumstellar environments of selected carbon stars (see contribution of Cami et al.) and the implications for the interstellar PAH population are derived. Preliminary results also show that carbon nanoparticles are formed during the short residence time of the precursors in the plasma. This finding holds great potential for understanding the formation process of interstellar grains.

Salama, F.↗
NASA NTRS2006

Laboratory Spectroscopy of Large Carbon Molecules and Ions in Support of Space Missions. A New Generation of Laboratory & Space Studies

Polycyclic Aromatic Hydrocarbons (PAHs) are an important and ubiquitous component of carbon-bearing materials in space. A long-standing and major challenge for laboratory astrophysics has been to measure the spectra of large carbon molecules in laboratory environments that mimic (in a realistic way) the physical conditions that are associated with the interstellar emission and absorption regions [1]. This objective has been identified as one of the critical Laboratory Astrophysics objectives to optimize the data return from space missions [2]. An extensive laboratory program has been developed to assess the properties of PAHs in such environments and to describe how they influence the radiation and energy balance in space. We present and discuss the gas-phase electronic absorption spectra of neutral and ionized PAHs measured in the UV-Visible-NIR range in astrophysically relevant environments and discuss the implications for astrophysics [1]. The harsh physical conditions of the interstellar medium characterized by a low temperature, an absence of collisions and strong VUV radiation fields - have been simulated in the laboratory by associating a pulsed cavity ringdown spectrometer (CRDS) with a supersonic slit jet seeded with PAHs and an ionizing, penning-type, electronic discharge. We have measured for the {\it first time} the spectra of a series of neutral [3,4] and ionized [5,6] interstellar PAHs analogs in the laboratory. An effort has also been attempted to quantify the mechanisms of ion and carbon nanoparticles production in the free jet expansion and to model our simulation of the diffuse interstellar medium in the laboratory [7]. These experiments provide {\it unique} information on the spectra of free, large carbon-containing molecules and ions in the gas phase. We are now, for the first time, in the position to directly compare laboratory spectral data on free, cold, PAH ions and carbon nano-sized carbon particles with astronomical observations in the UV-NIR range (interstellar UV extinction, DIBs in the NUV-NIR range). This new phase offers tremendous opportunities for the data analysis of current and upcoming space missions geared toward the detection of large aromatic systems Le., the "new frontier space missions" (Spitzer, HST, COS, JWST, SOFIA,...).

Salama, Farid↗
NASA NTRS2011

The Effect of Sonic Booms on Earthquake Warning Systems

Several aerospace companies are designing quiet supersonic business jets for service over the United States. These aircraft have the potential to increase the occurrence of mild sonic booms across the country. This leads to interest among earthquake warning (EQW) developers and the general seismological community in characterizing the effect of sonic booms on seismic sensors in the field, their potential impact on EQW systems, and means of discriminating their signatures from those of earthquakes. The SonicBREWS project (Sonic Boom Resistant Earthquake Warning Systems) is a collaborative effort between Seismic Warning Systems, Inc. (SWS) and NASA Dryden Flight Research Center. This project aims to evaluate the effects of sonic booms on EQW sensors. The study consists of exposing high-sample-rate (1000 sps) triaxial accelerometers to sonic booms with overpressures ranging from 10 to 600 Pa in the free field and the built environment. The accelerometers record the coupling of the sonic boom to the ground and surrounding structures, while microphones record the acoustic wave above ground near the sensor. Sonic booms are broadband signals with more high-frequency content than earthquakes. Even a 1000 sps accelerometer will produce a significantly aliased record. Thus the observed peak ground velocity is strongly dependent on the sampling rate, and increases as the sampling rate is reduced. At 1000 sps we observe ground velocities that exceed those of P-waves from M L 3 earthquakes at local distances, suggesting that sonic booms are not negligible for EQW applications. We present the results of several experiments conducted under SonicBREWS showing the effects of typical-case low amplitude sonic booms and worst-case high amplitude booms. We show the effects of various sensor placements and sensor array geometries. Finally, we suggest possible avenues for discriminating sonic booms from earthquakes for the purposes of EQW.

Wurman, Gilead↗
NASA NTRS1997

The Effect of Vortex Generators on a Jet in a Cross-Flow

The effect of vortex generators in the form of tabs on the penetration and spreading of a jet in a cross-flow has been studied experimentally. It is found that the tab has very little effect when placed on the leeward side, i.e., on the downstream edge of the jet nozzle relative to the free-stream flow. A study of the static pressure distribution reveals significantly lower pressures on the leeward side. Thus, when placed on that side the tab does not produce a "pressure hill" of sufficient magnitude that is the primary source of streamwise vorticity in the flow field over the tab. This qualitatively explains the ineffectiveness. In comparison, there is a significant effect on the flow field when the tab is placed on the windward side, The sense of vorticity generated by the tab in the latter configuration is opposite to that of the bound vortex pair that otherwise characterizes the flow. Thus, the strength of the bound vortex pair is diminished and the jet penetration is reduced.

Zaman, K. B. M. Q.↗
NASA NTRS2007

The EPIC-MOS Particle-Induced Background Spectra

In order to analyse diffuse emission that fills the field of view, one must accurately characterize the instrumental backgrounds. For the XMM-Newton EPIC instrument these backgrounds include a temporally variable "quiescent" component. as well as the strongly variable soft proton contamination. We have characterized the spectral and spatial response of the EPIC detectors to these background components and have developed tools to remove these backgrounds from observations. The "quiescent" component was characterized using a combination of the filter-wheel-closed data and a database of unexposed-region data. The soft proton contamination was characterized by differencing images and spectra taken during flared and flare-free intervals. After application of our modeled backgrounds, the differences between independent observations of the same region of "blank sky" are consistent with the statistical uncertainties except when there is clear spectral evidence of solar wind charge exchange emission. Using a large sample of blank sky data, we show that strong magnetospheric SWCX emission requires elevated solar wind fluxes; observations through the densest part of the magnetosheath are not necessarily strongly contaminated with SWCX emission.

Kuntz, K. D.↗
NASA NTRS2010

Thin-Film Ferro Electric-Coupled Microstripline Phase Shifters With Reduced Device Hysteresis

This work deals with the performance of coupled microstripline phase shifters (CMPS) fabricated using BaxSr 1 -xTiO 3 (BST) ferroelectric thin films. The CMPS were fabricated using commercially available pulsed laser deposition BST films with Ba:Sr ratios of 30:70 and 20:80. Microwave characterization of these CMPS was performed at upper Kuband frequencies, particularly at frequencies near 16 and 18 GHz. X-ray diffraction studies indicate that the 30:70 films exhibit almost a 1:1 ratio between the in-plane and out-of-plane lattice parameters, suggesting that their cubics create strain -free films suitable for producing CMPS devices with reduced hysteresis in the paraelectric state. The quality of performance of the CMPS was studied based on their relative phase shift and insertion loss within the DC bias range of 0 to 400 V (i.e., E-field ranges within 0 to 53 V/micron). The performance of the CMPS was tested as a function of temperature to investigate their operation in the paraelectric, as well as in the ferroelectric, state (i.e., above and below the Curie temperature, respectively). The novel behavior discussed here is based on the experimental observation of the CMPS. This behavior, observed for the aforementioned cation ratio, highlights the relevance of good crystalline structure for high-quality CMPS.

Miranda, Felix A.↗
NASA NTRS2004

Network Theory: A Primer and Questions for Air Transportation Systems Applications

A new understanding (with potential applications to air transportation systems) has emerged in the past five years in the scientific field of networks. This development emerges in large part because we now have a new laboratory for developing theories about complex networks: The Internet. The premise of this new understanding is that most complex networks of interest, both of nature and of human contrivance, exhibit a fundamentally different behavior than thought for over two hundred years under classical graph theory. Classical theory held that networks exhibited random behavior, characterized by normal, (e.g., Gaussian or Poisson) degree distributions of the connectivity between nodes by links. The new understanding turns this idea on its head: networks of interest exhibit scale-free (or small world) degree distributions of connectivity, characterized by power law distributions. The implications of scale-free behavior for air transportation systems include the potential that some behaviors of complex system architectures might be analyzed through relatively simple approximations of local elements of the system. For air transportation applications, this presentation proposes a framework for constructing topologies (architectures) that represent the relationships between mobility, flight operations, aircraft requirements, and airspace capacity, and the related externalities in airspace procedures and architectures. The proposed architectures or topologies may serve as a framework for posing comparative and combinative analyses of performance, cost, security, environmental, and related metrics.

Holmes, Bruce J.↗
NASA NTRS1993

The onset of electrohydrodynamic instability in isoelectric focusing

The onset of electrohydrodynamic motion associated with the imposition of an electric field across a thin layer of liquid has been investigated for the case in which the electrical conductivity varies linearly over the depth of the layer. The variation of the conductivity is due to concentration gradients in the charge-carrying solutes and its spatio-temporal evolution is represented by a convective-diffusion equation. When the viscous relaxation time is long compared to the time for charge relaxation, the analysis reveals that the neutral stability curves for the layer can be characterized by three dimensionless parameters: Ra(sub e) is equivalent to d(epsilon)E(sup 2, sub 0) Delta sigma/mu K(sub eff) sigma(sub 0), an electrical Rayleigh number; delta sigma/sigma(sub 0), the relative conductivity increment; and alpha, the transverse wave number of the disturbance. Here d is the thickness, epsilon is the dielectric constant, and mu is the viscosity of layer, E(sub 0) is the applied field strength at the lower conductivity boundary, and K(sub eff) is an effective diffusivity associated with the Brownian motion of the charge-carrying solutes. With viscous-stress-free boundaries, at which the electrical conductivity and the normal component of the electric field are prescribed, the critical Ra(sub e) is 1.504 x 10(exp 4) at a critical transverse wave number of 1.97 when Delta sigma/sigma(sub 0) is 10. As Delta sigma/sigma(sub 0) increases, the critical Ra(sub e) increases and shifts to shorter wavelength disturbances; the critical imposed field strength, however, passes through a minimum because the lower-conductivity boundary exerts a considerable stabilizing influence in the presence of steep conductivity gradients. Similar trends were obtained for liquid layers with rigid boundaries.

Baygents, James C.↗