On gravity currents confined by porous boundaries in containers of general cross-sections

2021 ◽  
Author(s):  
T. Zemach
Keyword(s):  
Cross Sections ◽  
Gravity Currents ◽  
Porous Boundaries

Non-Boussinesq gravity currents and surface waves generated by lock release in a circular-section channel: theoretical and experimental investigation

2019 ◽  
Vol 869 ◽  
pp. 610-633 ◽  
Author(s):  
L. Chiapponi ◽  
M. Ungarish ◽  
D. Petrolo ◽  
V. Di Federico ◽  
S. Longo
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Cross Section ◽  
Cross Sections ◽  
Density Ratio ◽  
Circular Cross Section ◽  
Gravity Currents ◽  
Numerical Code ◽  
Long Distance ◽  
Front Speed

We present a combined theoretical and experimental study of lock-release inertial gravity currents (GCs) propagating in a horizontal channel of circular cross-section with open-top surface in the non-Boussinesq regime. A two-layer shallow-water (SW) model is developed for a generic shape of the cross-section with open top, and then implemented in a finite difference numerical code for the solution in a circular-cross-section channel of the type used in the experiments. The model predicts propagation with (almost) constant speed for a fairly long distance, accompanied by a depression of the ambient free open-top surface behind the front of the current. Sixteen experiments were conducted with a density ratio $r=0.587{-}0.939$ in full-depth and part-depth release conditions, measuring the front speed and the free-surface time series at four cross-sections. The channel was a circular tube 409 cm long, with a radius of 9.5 cm; the lengths of the locks were 52 and 103.5 cm. Density contrast was obtained by adding sodium chloride and dipotassium phosphate to fresh water. The theoretical values of the front speed and of the depression overestimate the experimental values, but they predict correctly their trend for varying parameters and provide reliable insights into the underlying mechanisms. In particular, we demonstrate that the circular cross-section increases the speed of propagation as compared to the standard rectangular cross-section case (for the same initial height and density ratio). The discrepancies between the SW predictions and the present experiments are of the same order of magnitude as those of previously published results for simpler systems (Boussinesq, rectangular). In addition to the depression, which is a wave bound to, and following the front of, the GC, the system also displays two kinds of free-surface waves, namely the initial bump (its amplitude is of the same order as the depression) and some short-length and low-amplitude waves in the tail of the bump. These free waves propagate with a celerity well predicted by the ‘fast’ eigenvalues of the mathematical model. Comparison is provided with the celerity of a solitary wave. It is expected that discrepancies between theory and experiments can be partly attributed to the presence of these waves. The reported insights and SW prediction method can be applied to a variety of cross-sections of practical interest (triangles, trapezoids, etc.).

scholarly journals Propagation of viscous gravity currents inside confining boundaries: the effects of fluid rheology and channel geometry

2015 ◽  
Vol 471 (2178) ◽  
pp. 20150070 ◽  
Author(s):  
S. Longo ◽  
V. Di Federico ◽  
L. Chiapponi
Keyword(s):  
Cross Sections ◽  
Rheological Behaviour ◽  
Gravity Currents ◽  
Channel Cross Section ◽  
Rigid Boundary ◽  
Cross Sectional ◽  
Self Similar ◽  
Similar Solutions ◽  
Fluid Rheology ◽  
Asymptotic Validity

A theoretical and experimental investigation of the propagation of free-surface, channelized viscous gravity currents is conducted to examine the combined effects of fluid rheology, boundary geometry and channel inclination. The fluid is characterized by a power-law constitutive equation with behaviour index n . The channel cross section is limited by a rigid boundary of height parametrized by k and has a longitudinal variation described by the constant b ≥0. The cases k ⋛ 1 are associated with wide, triangular and narrow cross sections. For b >0, the cases k ≷ 1 describe widening channels and squeezing fractures; b =0 implies a constant cross-sectional channel. For a volume of released fluid varying with time like t α , scalings for current length and thickness are obtained in self-similar forms for horizontal and inclined channels/fractures. The speed, thickness and aspect ratio of the current jointly depend on the total current volume ( α ), the fluid rheological behaviour ( n ), and the transversal ( k ) and longitudinal ( b ) geometry of the channel. The asymptotic validity of the solutions is limited to certain ranges of parameters. Experimental validation was performed with different fluids and channel cross sections; experimental results for current radius and profile were found to be in close agreement with the self-similar solutions at intermediate and late times.

Analysis of STEM micrographs of thick objects

1978 ◽  
Vol 36 (2) ◽  
pp. 106-107
Author(s):  
S. Golladay
Keyword(s):  
Inelastic Scattering ◽  
Multiple Scattering ◽  
Mass Distribution ◽  
Cross Sections ◽  
Phase Contrast ◽  
Image Point ◽  
Contrast Effects ◽  
Total Cross Sections ◽  
Elastic And Inelastic Scattering

The theory of multiple scattering has been worked out by Groves and comparisons have been made between predicted and observed signals for thick specimens observed in a STEM under conditions where phase contrast effects are unimportant. Independent measurements of the collection efficiencies of the two STEM detectors, calculations of the ratio σe/σi = R, where σe, σi are the total cross sections for elastic and inelastic scattering respectively, and a model of the unknown mass distribution are needed for these comparisons. In this paper an extension of this work will be described which allows the determination of the required efficiencies, R, and the unknown mass distribution from the data without additional measurements or models. Essential to the analysis is the fact that in a STEM two or more signal measurements can be made simultaneously at each image point.

Direct Observation of Heat Exchanger Deposits by Cross Sectioning

1967 ◽  
Vol 25 ◽  
pp. 364-365
Author(s):  
R. W. Anderson ◽  
D. L. Senecal
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
Heat Exchanger ◽  
Direct Observation ◽  
Cross Sections ◽  
Preparation Method ◽  
Specimen Preparation ◽  
Flowing Water ◽  
Transmission Electron ◽  
Deposit Layer

A problem was presented to observe the packing densities of deposits of sub-micron corrosion product particles. The deposits were 5-100 mils thick and had formed on the inside surfaces of 3/8 inch diameter Zircaloy-2 heat exchanger tubes. The particles were iron oxides deposited from flowing water and consequently were only weakly bonded. Particular care was required during handling to preserve the original formations of the deposits. The specimen preparation method described below allowed direct observation of cross sections of the deposit layers by transmission electron microscopy.The specimens were short sections of the tubes (about 3 inches long) that were carefully cut from the systems. The insides of the tube sections were first coated with a thin layer of a fluid epoxy resin by dipping. This coating served to impregnate the deposit layer as well as to protect the layer if subsequent handling were required.

An Analysis of Dissociation of Molecules in a High Resolution Electron Microscope

1973 ◽  
Vol 31 ◽  
pp. 486-487
Author(s):  
Mihir Parikh
Keyword(s):  
Electron Microscope ◽  
High Resolution ◽  
Cross Sections ◽  
Resolving Power ◽  
Peak Intensity ◽  
Molecular Film ◽  
Resolution Electron ◽  
Dissociation Cross Section ◽  
High Resolution Electron Microscope ◽  
The Stability

It is well known that the resolution of bio-molecules in a high resolution electron microscope depends not just on the physical resolving power of the instrument, but also on the stability of these molecules under the electron beam. Experimentally, the damage to the bio-molecules is commo ly monitored by the decrease in the intensity of the diffraction pattern, or more quantitatively by the decrease in the peaks of an energy loss spectrum. In the latter case the exposure, EC, to decrease the peak intensity from IO to I’O can be related to the molecular dissociation cross-section, σD, by EC = ℓn(IO /I’O) /ℓD. Qu ntitative data on damage cross-sections are just being reported, However, the microscopist needs to know the explicit dependence of damage on: (1) the molecular properties, (2) the density and characteristics of the molecular film and that of the support film, if any, (3) the temperature of the molecular film and (4) certain characteristics of the electron microscope used

Surface ultrastructure of danazol treated rat endometrium: A SEM study

1983 ◽  
Vol 41 ◽  
pp. 556-557
Author(s):  
R.P. Apkarian ◽  
J.S. Sanfilippo
Keyword(s):  
Cross Sections ◽  
Reproductive Tract ◽  
Preliminary Investigation ◽  
Breast Disease ◽  
Distal Segment ◽  
Uterine Horn ◽  
Female Reproductive Tract ◽  
Ultrastructural Changes ◽  
Cycle Phase ◽  
Sprague Dawley

The synthetic androgen danazol, is an isoxazol derivative of ethisterone. It is utilized in the treatment of endometriosis, fibrocystic breast disease, and has a potential use as a contraceptive. A study was designed to evaluate the ultrastructural changes associated with danazol therapy in a rat model. The preliminary investigation of the distal segment of the rat uterine horn was undertaken as part of a larger study intended to elucidate the effects of danazol on the female reproductive tract.Cross-sections (2-3 mm in length) of the distal segment of the uterine horn from sixteen Sprague-Dawley rats were prepared for SEM. Ten rats in estrus served as controls and six danazol treated rats were noted to have alterations of the estrus cycle i.e. a lag in cycle phase or noncycling patterns. Specimens were fixed in 3% glutaraldehyde in 0.05M phosphate buffer containing CaCl2 at pH 7.0-7.4 and chilled to 4°C. After a brief wash in distilled water, specimens were passed through a graded series of ethanol, critical point dryed in CO2 from absolute ethanol, and coated with 6nm Au. Observations were made with an IS1-40 SEM operated at 15kV.

Electron Irradiation Effects in Polyoxymethylene Crystals Grown Inside Trioxane Crystals

1971 ◽  
Vol 29 ◽  
pp. 78-79
Author(s):  
J. P. Colson ◽  
D. H. Reneker
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Detailed Examination ◽  
The Other ◽  
Electron Micrograph ◽  
Irradiation Effects ◽  
Threefold Axis ◽  
Typical Sample ◽  
Polymer Crystals ◽  
Chain Axis

Polyoxymethylene (POM) crystals grow inside trioxane crystals which have been irradiated and heated to a temperature slightly below their melting point. Figure 1 shows a low magnification electron micrograph of a group of such POM crystals. Detailed examination at higher magnification showed that three distinct types of POM crystals grew in a typical sample. The three types of POM crystals were distinguished by the direction that the polymer chain axis in each crystal made with respect to the threefold axis of the trioxane crystal. These polyoxymethylene crystals were described previously.At low magnifications the three types of polymer crystals appeared as slender rods. One type had a hexagonal cross section and the other two types had rectangular cross sections, that is, they were ribbonlike.

A quantitative approach to inner shell losses

1978 ◽  
Vol 36 (1) ◽  
pp. 526-527 ◽  
Author(s):  
R.D. Leapman ◽  
P. Rez ◽  
D.F. Mayers
Keyword(s):  
Energy Transfer ◽  
Cross Section ◽  
Cross Sections ◽  
Accurate Determination ◽  
Background Intensity ◽  
Core Excitation ◽  
Quantitative Basis ◽  
Cross Section Differential ◽  
Bound Electrons

Microanalysis by EELS has been developing rapidly and though the general form of the spectrum is now understood there is a need to put the technique on a more quantitative basis (1,2). Certain aspects important for microanalysis include: (i) accurate determination of the partial cross sections, σx(α,ΔE) for core excitation when scattering lies inside collection angle a and energy range ΔE above the edge, (ii) behavior of the background intensity due to excitation of less strongly bound electrons, necessary for extrapolation beneath the signal of interest, (iii) departures from the simple hydrogenic K-edge seen in L and M losses, effecting σx and complicating microanalysis. Such problems might be approached empirically but here we describe how computation can elucidate the spectrum shape.The inelastic cross section differential with respect to energy transfer E and momentum transfer q for electrons of energy E0 and velocity v can be written as

Oxygen K near edge structures studied with multiple scattering calculations

1988 ◽  
Vol 46 ◽  
pp. 504-505
Author(s):  
Xudong Weng ◽  
Peter Rez
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Partial Cross Section ◽  
Energy Window ◽  
Edge Structure ◽  
Fine Structures ◽  
Hydrogenic Model ◽  
Electron Energy Loss ◽  
Quantitative Chemical

In electron energy loss spectroscopy, quantitative chemical microanalysis is performed by comparison of the intensity under a specific inner shell edge with the corresponding partial cross section. There are two commonly used models for calculations of atomic partial cross sections, the hydrogenic model and the Hartree-Slater model. Partial cross sections could also be measured from standards of known compositions. These partial cross sections are complicated by variations in the edge shapes, such as the near edge structure (ELNES) and extended fine structures (ELEXFS). The role of these solid state effects in the partial cross sections, and the transferability of the partial cross sections from material to material, has yet to be fully explored. In this work, we consider the oxygen K edge in several oxides as oxygen is present in many materials. Since the energy window of interest is in the range of 20-100 eV, we limit ourselves to the near edge structures.

Complex Vesicles, Microtubules, and Cytoplasmic Filaments in the Endothelial Cells of Normal Dog Aorta

1968 ◽  
Vol 26 ◽  
pp. 172-173
Author(s):  
C. N. Sun ◽  
J. J. Ghidoni
Keyword(s):  
Electron Microscopy ◽  
Endothelial Cells ◽  
Cross Sections ◽  
Functional Significance ◽  
Tubular Structures ◽  
Aldehyde Fixation ◽  
Cytoplasmic Filaments

Endothelial cells in longitudinal and cross sections of aortas from 3 randomly selected “normal” mongrel dogs were studied by electron microscopy. Segments of aorta were distended with cold cacodylate buffered 5% glutaraldehyde for 10 minutes prior to being cut into small, well oriented tissue blocks. After an additional 1-1/2 hour period in glutaraldehyde, the tissue blocks were well rinsed in buffer and post-fixed in OsO4. After dehydration they were embedded in a mixture of Maraglas, D.E.R. 732, and DDSA.Aldehyde fixation preserves the filamentous and tubular structures (300 Å and less) for adequate demonstration and study. The functional significance of filaments and microtubules has been recently discussed by Buckley and Porter; the precise roles of these cytoplasmic components remains problematic. Endothelial cells in canine aortas contained an abundance of both types of structures.

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