Modulation of capillary oscillations of a charged drop of low-viscosity liquid by its elastic oscillations

A second-order linear differential equation describing the temporal evolution of the amplitudes of capillary waves in a drop of low-viscosity liquid with elastic properties is given with a complex coefficient multiplying the first derivative. It is shown that the capillary oscillations of the drop are modulated by its oscillations associated with the relaxation of the viscosity of the liquid. Pis’ma Zh. Tekh. Fiz. 24, 83–87 (April 12, 1998)     

Experimental investigation of charged liquid jet efflux from a capillary

The shapes and electrical characteristics of charged liquid (water, ethanol, glycerol, castor oil) jets emitted from a metal capillary have been experimentally studied depending on the applied high voltage. A map of efflux regimes in the flow velocity-applied voltage coordinates is constructed for water. The effects of medium viscosity, surface tension, and charge relaxation time on the laws of jet efflux are analyzed.     

On the elastic deformation of non-saturated swelling soils

Summary This paper aims at completing and extending the theories as they have been applied to swelling media for the last 50 years, to swelling non-saturated soils. However, having regard to the complicated behaviour of swelling soils, it was thought necessary to keep the state of stress as simple as possible when discussing swelling in cylindrical specimens in which drainage is completely prevented. Definitions of the parameters are attemptedbased on equilibrium thermodynamics. Contributions to swelling stress calculation, when expansion is considered in relation to vapor pressure and moisture content, are also given.Notation u _w hydrostatic pressure of soil water - total stress - effective stress - m _c soil mass - m _w water mass - H=(m _w/m _c) moisture content (gravimetric) - A=(m _w/m _c)_Xi (i=x,y,z orr, ,z) moisture content at constant swelling pressure (gravimetric) - n=(m _w/m _c)_h moisture content at constant vapor pressure (gravimetric) - n _a amount of a constituant phase - h _v vapor pressure of soil water - h ₀ vapor pressure of pure water - h=(h _v/h ₀) relative vapor pressures - M molecular weight of water - specific volume of the soil water vapor - R gas constant (8.3144 Joules/mole·^oK) - T absolute temperature - P swelling pressure of an isotropic soil swelling without constrain - S entropy of a sample of volumeV - O oncotic energy - O _r residual oncotic energy - U internal energy - F Helmholtz free energy - G Gibb's free energy - partial molar Gibb's free energy of constituenta - chemical potential which equals the partial molar Gibb's free energy of constituenta - _v chemical potential of water vapor - _v chemical potential of soil water - V volume - V _H volume at constant moisture content - W _a specific energy for the adsorbed water - W _a0 specific osmotic energy of adsorbed solutes - W ₀ specific osmotic energy of free solutes - x, y, z Cartesian coordinate system - r, ,z cylindrical coordinate system - u, v, z _w displacement components along the strain variablesx, y, andz - z _w height of the water column - P _i (i=x, y, z) loads along the strain variablesx, y, z - P _i (i=x, y, z) orr, ,z mechanical pressure along the strain variables - X _i (i=x, y, z orr, ,z) swelling pressures along the strain variablesx, y, z - P _k hydrostatic swelling pressure defined byp _k=(X _x+X _y+X _z)/3 - P _{k, H} hydrostatic swelling pressure under constant moisture content - l _i (i=x, y, z) extential displacements along the strain variablesx, y, z - s _i ^* (i=x, y, z orr, ,z) differential swelling - s _i (i=x, y, z orx, ,z) differential swelling per unit volume - s _k hydrostatic differential swelling defined bys _k=(s _x+s _y+s _z)/3 - s _h differential swelling under constant vapor pressure - Q effective swelling pressure defined as the energy encompassing all the unknown effects contributing to swelling against the mechanical pressure and the vapor pressure of soil water per unit volume - Q coefficient of swelling - E _i (i=r, ,z orx, y, z) Young's moduli in the directioni - E _{i, h} (i=x, y, z) Young's moduli at constant vapor pressure - B _h Bulk modulus under constant vapor pressure - G _{ij. h} (i, j=x, y, z) Shear modulus under constant vapor pressure - v _ij (i, j=r, ,z orx, y, z) Poisson's coefficient which characterizes the compression in the directioni for tension in the directionj, etc. - e _i (i=r, ,z) final radial, tangential and axial strains - e _{i, s} (i=r, ,z) radial, tangential and axial strains due to swelling - loads along the strain variablesr, ,z - G _ij (i, j=x, y, z) rigidity modulus - g acceleration due to gravity - a radius of the cylinder - r ₁,r ₂ roots of the characteristic equation - W work done by the surroundings on the system     

Effect of elastic stresses on free oscillations in ferroelectric liquid crystals

It is shown experimentally that an elastic mechanical stress in a crystal structure is a necessary factor for the appearance of free oscillations of the director of a ferroelectric liquid crystal. Such a mechanical stress arises as a result of internal textural perturbations in the presence of regions with a different orientation of the director or is produced by external pressure applied to one of the cell plates in the appropriate direction. Pis’ma Zh. Tekh. Fiz. 25, 74–80 (March 26, 1999)     

Anti-plane shear deformations of swelling porous elastic soils

This paper is concerned with the theory of anti-plane shear deformations of swelling porous elastic soils in the case of fluid saturation or gas saturation. The formulation belongs to the theory of mixtures for porous elastic solids filled with fluid or gas. These problems propose some new mathematical difficulties. We prove the exponential decay of solutions, a uniqueness result and the spatial decay of solutions (in the dynamical and the quasi-static cases). Some remarks are presented in the last section.     

Extraction of water from a capillary specimen in an acoustic field

The authors present results of experiments on drying of a model capillary specimen in a subheated air flow in an acoustic field. It is established that the acoustic field causes considerable intensification of the drying process. The influence of the specimen position relative to the front of an acoustic wave and the flow velocity is established that the acoustic field causes considerable intensification of the drying process. The influence of the specimen position relative to the front of the acoustic wave and the flow velocity is investigated. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 73, No. 4, pp. 686–687, July–August, 2000.     

Motion and thermodynamic instability of a liquid in a variable capillary

The flow of a liquid in a capillary of variable cross section formed by moving surfaces is analyzed. It is shown that a liquid flow with definite parameters (viscosity, surface tension, etc.) is characterized by a definite negative (relative to atmospheric) pressure, which is responsible for thermodynamic instability of the liquid layer and the formation of discontinuities in it. The theoretical results are consistent with the experimental.     

Hysteresis and metastability of the transition from evaporative to droplet flow of a liquid through a capillary

A model is constructed for the transition from evaporative to droplet flow of a liquid through a capillary in a gravitational field allowing for the mutual influence of the droplets. An S-shaped dependence of the flow on the pressure drop at the capillary is obtained which for certain (critical) values of the control parameter gives a monotonic curve. Values of the pressure drop are determined for which the droplet flow regime and the droplet-free regime become unstable. It is shown that in a certain range of pressure drops in the presence of noise transitions may take place from evaporative to droplet flow and back (intermittence). Pis’ma Zh. Tekh. Fiz. 25, 30–36 (December 26, 1999)     

Propagation of a transient shear wave from a crack in an elastic plate

A simple analytical technique based on the methods of transverse resonance and group velocity is developed in order to predict the propagation of shear (SH) waves emitted from a crack in elastic plates. Since a total solution of the Rayleight Lamb waves propagation inside the plate is very complicated, the simple SH mode was used to demonstrate the argument of this paper. The effects of varying distances between the crack and the sensor are also discussed.

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Résumé On développe une technique analytique simple basée sur les procédés de résonance transversale et de vitesse de trains d'onde en vue de prédire la propagation d'ondes SH émises à partir d'une fissure dans une plaque élastique.Comme une solution complète pour la propagation des ondes de Rayleight-Lamb est très compliquée à mettre en oeuvre, on s'est restreint à utiliser le mode SH pour démontrer la validité de l'étude.On discute également des effets d'une distance variable entre la fissure et le palpeur.

     

Detachment of an elastic matrix from a rigid spherical inclusion

An approximate theoretical treatment is given for detachment of an elastomer from a rigid spherical inclusion by a tensile stress applied to the elastomeric matrix. The inclusion is assumed to have an initially-debonded patch on its surface and the conditions for growth of the patch are derived from fracture energy considerations. Catastrophic debonding is predicted to occur at a critical applied stress when the initial debond is small. The strain energy dissipated as a result of this detachment, and hence the mechanical hysteresis, are also evaluated. When a reasonable value is adopted for Young's modulus E of the elastomeric matrix, it is found that detachment from small inclusions, of less than about 0.1 mm in diameter, will not occur, even when the level of adhesion is relatively low. Instead, rupture of the matrix near the inclusion becomes the preferred mode of failure at an applied stress given approximately by E/2. For still smaller inclusions, of less than about 1 m in diameter, rupture of the matrix becomes increasingly difficult, due to the increasing importance of a surface energy term. These considerations account for the general features of reinforcement of elastomers. Small-particle fillers become effectively bonded to the matrix, whereas larger inclusions induce fracture near them, or become detached from the matrix, at applied stress that can be calculated from the particle diameter, the strength of adhesion, and the elasticity of the matrix material.     

On the capillary instability of a dielectric viscous liquid cylinder surrounded by another viscous fluid in an electric field

Summary The capillary instability of a long, dielectric, incompressible, viscous liquid cylinder when subjected to small axisymmetric disturbances in the presence of a uniform axial electric field is investigated by making a normal mode analysis of the equations describing the perturbed fluid flow. The resulting characteristic equation, which includes the effect of a surrounding unbounded viscous fluid, is solved in order to express graphically the governing dispersion relation as a function of the relative viscous and dielectric properties of the two media when the viscosities of both are dominant. The influence of the various parameters on the modes of capillary instability as well as their effect on the modes of maximum instability are exhibited for this and other special cases.

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Zusammenfassung Die kapillare Instabilität eines langen, dielektrischen, inkompressiblen, zähen Flüssigkeitszylinders wird untersucht, wenn letzterer kleinen axialsymmetrischen Störungen in Gegenwart eines gleichförmigen, elektrischen Axialfeldes ausgesetzt ist. Das zur Behandlung des vorliegenden Problems herangezogene Verfahren macht Gebrauch von einem Normalschwingungsansatz für die das gestörte Strömungsfeld beschreibenden Gleichungen. Die resultierende charakteristische Gleichung, welche den Einfluß der umgebenden, unendlich ausgedehnten, zähen Flüssigkeit berücksichtigt, wird gelöst. Die grundlegende Dispersionsbeziehung wird graphisch als Funktion der relativen zähen und dielektrischen Eigenschaften beider Medien dargestellt, falls der Zähigkeitseinfluß in beiden Medien dominiert. Der Einfluß verschiedener Parameter auf das Schwingungsverhalten der Kapillarinstabilität, ebenso ihr Einfluß auf das Schwingungsverhalten der maximalen Instabilität, wird sowohl für den vorliegenden Fall als auch für verschiedene Sonderfälle dargestellt.

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With 7 Figures

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Presented at the Canadian Congress of Applied Mechanics, Université Laval, Québec, Canada, May 1967; an abstract appears in the proceedings.     

An analysis of the capillary force and optimum liquid volume in a transient liquid phase sintering process

A transient liquid phase sintering process, called the ISM (in situ microfusion) process, has been developed for Al---Fe alloys, where an exothermic reaction in the system is utilized to produce a small volume of liquid and densify the powder compact. The model of an interparticle force, due to the capillary action of a liquid in contact with two solid spheres, and the optimum liquid volume, in the rearrangement process for full densification in conventional liquid phase sintering, are no longer thought to be suitable for this particular process. A model has been established for the ISM process, in which two partly melted spheres are attracted by the molten liquid between them and the liquid volume is equal to that melted from the two spheres. Based on this system, the interparticle force two partly melted spheres was calculated and the optimum liquid volume estimated for the ISM process, both of which are in good agreement with previous experimental work.     

Formation of a gas bubble on a vibrating capillary immersed in a liquid

The formation of a train of bubbles in a low-viscosity liquid is investigated. The dependence of the gas flow rate during formation of the bubble train on the vibrational acceleration of the capillary is determined.Deceased.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 30, No. 4, pp. 665–670, April, 1976.     

Stability of the process of evaporation from a porous structure during displacement of the liquid by capillary forces

It is demonstrated that evaporation can be stable when the driving capillary pressure head varies across the thickness of a porous plate. Expressions are proposed which describe the effect of structural features and process conditions on the stability characteristics of this process.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 5, pp. 870–876, November, 1980.     

Effect of extrusion stem speed on extrusion process for a hollow aluminum profile

Extrusion stem speed is one of important process parameters during aluminum profile extrusion, which directly influences the profile quality and choice of extrusion equipments. In this paper, the extrusion process of a thin-walled hollow aluminum profile was simulated by means of the HyperXtrude commercial software. Through a serial of numerical simulation, the effects of stem speed on extrusion process, such as metal flow behavior at die exit, temperature distribution, extrusion force, and welding pressure, have been investigated. The numerical results showed that there existed an optimum value of stem speed for flow velocity distribution. With the increasing stem speed, the temperature of the extrudate and required extrusion force increased, and the welding quality of extrudate would be improved. Through comprehensive comparison and analysis, the appropriate stem speed could be determined for practical extrusion production. Thus, the research results could give effective guideline for determining initial billet and die temperature and choosing the proper extrusion press in aluminum profile industry.     

Wave propagation in a liquid flowing in a channel with elastic walls

Wave propagation in the ideal liquid flowing in a cylindrical circular channel is described. The channel is considered as an elastic shell and the interaction of density and pressure waves in the liquid with elastic waves in the walls is taken into account. It is shown that the flow may exhibit instability under certain conditions. Conditions for the convective and absolute instability development are determined. The pattern of instability development and the onset of turbulence in this model differs from the analogous scenario in a viscous liquid model.     

Effect of voids on the propagation of waves in an elastic layer

The present paper investigates the propagation of waves in an elastic layer containing voids. Numerical calculations and discussions indicate that the velocity of the propagation of waves decreases due to the presence of voids in the material medium of the layer and the voids cause dispersion of the general waveform.