Nonlinear Stability of MHD Contact Discontinuities with Surface Tension

ON THE NONLINEAR STABILITY OF MARANGONI–BÉNARD PROBLEM WITH FREE SURFACE IN THE BOUSSINESQ APPROXIMATION

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202505003873 ◽

2005 ◽

Vol 15 (01) ◽

pp. 1-22 ◽

Cited By ~ 4

Author(s):

GIOVANNA GUIDOBONI ◽

BUM JA JIN

Keyword(s):

Surface Tension ◽

Free Surface ◽

Exponential Stability ◽

Nonlinear Stability ◽

Sufficient Conditions ◽

Marangoni Effect ◽

Boussinesq Approximation ◽

Energy Functional ◽

Bénard Problem ◽

Benard Problem

We study the Bénard problem in the Boussinesq approximation with upper free surface in the presence of surface tension. Both buoyancy and Marangoni effect are taken into account. Defining a suitable energy functional, we obtain sufficient conditions for nonlinear exponential stability of the rest state.

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Immunoferritin localization of intracellular antigens in positively stained frozen sections

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s042482010008170x ◽

1978 ◽

Vol 36 (2) ◽

pp. 168-169

Author(s):

K. T. Tokuyasu

Keyword(s):

Surface Tension ◽

Water Surface ◽

Thin Layers ◽

The Other ◽

Positive Staining ◽

Frozen Sections ◽

The Past ◽

Ultrathin Frozen Sections ◽

Definition Of

During the past investigations of immunoferritin localization of intracellular antigens in ultrathin frozen sections, we found that the degree of negative staining required to delineate u1trastructural details was often too dense for the recognition of ferritin particles. The quality of positive staining of ultrathin frozen sections, on the other hand, has generally been far inferior to that attainable in conventional plastic embedded sections, particularly in the definition of membranes. As we discussed before, a main cause of this difficulty seemed to be the vulnerability of frozen sections to the damaging effects of air-water surface tension at the time of drying of the sections.Indeed, we found that the quality of positive staining is greatly improved when positively stained frozen sections are protected against the effects of surface tension by embedding them in thin layers of mechanically stable materials at the time of drying (unpublished).

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The Critical Point Drying Method Applied to Scanning Electron Microscopy of L-929 Cells

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100068382 ◽

1970 ◽

Vol 28 ◽

pp. 278-279

Author(s):

Charles TurnbiLL ◽

Delbert E. Philpott

Keyword(s):

Electron Microscopy ◽

Carbon Dioxide ◽

Surface Tension ◽

Critical Point ◽

Freeze Drying ◽

Attractive Alternative ◽

Crystal Formation ◽

Critical Point Drying ◽

Time Required ◽

Scanning Electron

The advent of the scanning electron microscope (SCEM) has renewed interest in preparing specimens by avoiding the forces of surface tension. The present method of freeze drying by Boyde and Barger (1969) and Small and Marszalek (1969) does prevent surface tension but ice crystal formation and time required for pumping out the specimen to dryness has discouraged us. We believe an attractive alternative to freeze drying is the critical point method originated by Anderson (1951; for electron microscopy. He avoided surface tension effects during drying by first exchanging the specimen water with alcohol, amy L acetate and then with carbon dioxide. He then selected a specific temperature (36.5°C) and pressure (72 Atm.) at which carbon dioxide would pass from the liquid to the gaseous phase without the effect of surface tension This combination of temperature and, pressure is known as the "critical point" of the Liquid.

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The Use of Styrenes as Embedding Media for Electron Microscopy

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100066498 ◽

1971 ◽

Vol 29 ◽

pp. 488-489

Author(s):

Edward D. De-Lamater ◽

Eric Johnson ◽

Thad Schoen ◽

Cecil Whitaker

Keyword(s):

Electron Microscopy ◽

Surface Tension ◽

Ultraviolet Light ◽

Methyl Ethyl Ketone Peroxide ◽

Methyl Ethyl ◽

Styrene Polymerization ◽

Radical Initiation ◽

Tertiary Butyl ◽

Low Viscosity ◽

Free Radical Initiation

Monomeric styrenes are demonstrated as excellent embedding media for electron microscopy. Monomeric styrene has extremely low viscosity and low surface tension (less than 1) affording extremely rapid penetration into the specimen. Spurr's Medium based on ERL-4206 (J.Ultra. Research 26, 31-43, 1969) is viscous, requiring gradual infiltration with increasing concentrations. Styrenes are soluble in alcohol and acetone thus fitting well into the usual dehydration procedures. Infiltration with styrene may be done directly following complete dehydration without dilution.Monomeric styrenes are usually inhibited from polymerization by a catechol, in this case, tertiary butyl catechol. Styrene polymerization is activated by Methyl Ethyl Ketone peroxide, a liquid, and probably acts by overcoming the inhibition of the catechol, acting as a source of free radical initiation.Polymerization is carried out either by a temperature of 60°C. or under ultraviolet light with wave lengths of 3400-4000 Engstroms; polymerization stops on removal from the ultraviolet light or heat and is therefore controlled by the length of exposure.

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The nucleation of cavities at grain boundaries

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100126299 ◽

1987 ◽

Vol 45 ◽

pp. 288-291

Author(s):

P. J. Goodhew

Keyword(s):

Surface Tension ◽

Surface Energy ◽

Grain Boundaries ◽

Radiation Damage ◽

Impurity Concentration ◽

Driving Force ◽

Nucleation And Growth ◽

Phase Boundaries ◽

Cavity Nucleation ◽

Spherical Bubble

Cavity nucleation and growth at grain and phase boundaries is of concern because it can lead to failure during creep and can lead to embrittlement as a result of radiation damage. Two major types of cavity are usually distinguished: The term bubble is applied to a cavity which contains gas at a pressure which is at least sufficient to support the surface tension (2g/r for a spherical bubble of radius r and surface energy g). The term void is generally applied to any cavity which contains less gas than this, but is not necessarily empty of gas. A void would therefore tend to shrink in the absence of any imposed driving force for growth, whereas a bubble would be stable or would tend to grow. It is widely considered that cavity nucleation always requires the presence of one or more gas atoms. However since it is extremely difficult to prepare experimental materials with a gas impurity concentration lower than their eventual cavity concentration there is little to be gained by debating this point.

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