Deformable media

Action of Shock and Explosion in Deformable Media. Engl transin of Rus book by G.I. Pokrovskii St I.S. Fedorov, "Deystviye Udara i Vzryva v Deformiruyemykh Sredakh , Prom-Stroylzdat, Moscow (1957)... 

Yablonovitch [215] proposed using a medium with a rapidly decreasing in time refractive index ( plasma window ) to simulate the so-called Unruh effect [216] the creation of quanta in an accelerated frame of reference. More rigorous and detailed studies of quantum phenomena in nonstationary (deformed) media have been performed [159,160,217-229]. The case when the dielectric constant changes simultaneously with the distance between mirrors (in one dimension) was also considered [230,231]. Johnston and Sarkar compared the spectra of photons created by the motion of mirrors and by the time variations of the dielectric permeability [232]. An analog of the nonstationary Casimir effect in the superfluid 3He, namely, the friction force on the moving interface between two different phases, was discussed by Volovik [233]. 

Li S, Xu B and Duan Y. 2(X31b. Flow through fissured reservoir with deformable media. Chinese J. of Computational Mechanics, 18(2), pp. 133-137. 

This paper presents part of the geo-mechanical modelling work performed by one of the groups involved in the Project. An in-house program, CODE BRlGHT, has been used for that purpose. The main features of the code are described in next section, but basically, it is a finite element program that solves the energy balance equation, the water and air balance equations and the equilibrium equation in a porous deformable media. 

Ketelaars, A. A. J., 1992. Drying deformable media Kinetics, shrinkage and stresses. 

The temperature of an incompressible fluid element in a deforming medium is governed by the equation of thermal energy, Eq. 2.9-14. This excluding the reversible compression term, and in terms of specific heat, is... 

The general expression for the conservation of mass for the solid phase in a deforming medium may be given as (Palciauskas and Domenico, 1989)... 

Relationship between elasticity and orientational order As remarked in chapter I, a uniformly oriented film of nematic liquid crystal may be prepared by prior treatment of the surfaces with which it is in contact. If the preferred orientation imposed by the surfaces is perturbed, let us say by a magnetic field, a curvature strain will be introduced in the medium. The theory of such a deformation will be discussed at length in 3.2 for the present it will suffice to state some of the important results. The free energy per unit volume of the deformed medium relative to the state of uniform orientation is... 

Relations (3) and (4) are true for relaxing medium that has an elastic constant carcass, able to restore its unstrained state. For plastically (finitely) deformable medium in (3) and (4) = 0 is to be introduced. 

Consider a small plane surface of area AA drawn in a deforming medium see Rgure 10.18. The material flows or deforms through AA. For analytic purposes, the vector direction of motion is divided among x, y, and z. The direction of motion is not necessarily normal to the plane of AA. 

We now consider the case when a liquid film A deposited on a substrate B (solid or liquid) is exposed not to air but to a deformable medium R, which can be either another liquid or a soft solid (an elastomer). The spreading parameter S is... 

In conclusion, it is probable that both Fe and Ga are less prone than A1 to form isolated acidic species different from the bridging OH species. Once the bridging species, stable in a zeolite framework, is brought to the surface or embedded in a deformable medium, it becomes destabilized and with either Ga or Fe, the process probably preferentially goes to completion, with the yield of extra-framework oxidic species. 

Balankin, A. S. (1992). Fractal Mechanics of Deformable Mediums and Solid Bodies Fracmre Topology DoWady AN, 322(5), 869-874. 

Medium Critical deformation (%) Medium Critical deformation (%)... 

In solving equation (3) a new parameter, the diffusion length a, is naturally introduced that is most convenient to use when discussing isotopic diffusion in a uniformly deforming medium and its effect on delta profiles. This new parameter is determined by solving the equation... 

The divergence factor (DF) introduced by the asymptotic expansion, accounts for the deformation of the refracted wavefront (initially spherical in the coupling medium). It ensures, under the GO approximation, the energy conservation of a ray-pencil propagating... 

Traditionally, production of metallic glasses requites rapid heat removal from the material (Fig. 2) which normally involves a combination of a cooling process that has a high heat-transfer coefficient at the interface of the Hquid and quenching medium, and a thin cross section in at least one-dimension. Besides rapid cooling, a variety of techniques are available to produce metallic glasses. Processes not dependent on rapid solidification include plastic deformation (38), mechanical alloying (7,8), and diffusional transformations (10). 

Most authors who have studied the consohdation process of soflds in compression use the basic model of a porous medium having point contacts which yield a general equation of the mass-and-momentum balances. This must be supplemented by a model describing filtration and deformation properties. Probably the best model to date (ca 1996) uses two parameters to define characteristic behavior of suspensions (9). This model can be potentially appHed to sedimentation, thickening, cake filtration, and expression. 

Aperture impedance measurements of cell volume must take into account the osmolaUty and pH of the medium. A hypotonic medium causes cells to swell a hypertonic medium causes them to shrink. Some manufacturers of aperture impedance counters deHberately provide hypertonic electrolytic media for red blood cell measurements. The shmnken red cells not only become more nearly spherical and thus less affected by orientation, but also less deformable than cells in isotonic media and thus less affected by differences in hemoglobin content. 

Use of filter aids is a technique frequently applied for filtrations in which problems of slow filtration rate, rapid medium blinding, or un-satisfactoiy filtrate clarity arise. Filter aids are granular or fibrous solids capable of forming a highly permeable filter cake in which veiy fine solids or slimy, deformable floes may be trapped. Application of filter aids may allow the use of a much more permeable filter medium than the clarification would require to produce filtrate of the same quahty by depth filtration. 

Figure 4.11. Diagrammatic sketches of atomic lattice rearrangements as a result of dynamic compression, which give rise to (a) elastic shock, (b) deformational shock, and (c) shock-induced phase change. In the case of an elastic shock in an isotropic medium, the lateral stress is a factor v/(l — v) less than the stress in the shock propagation direction. Here v is Poisson s ratio. In cases (b) and (c) stresses are assumed equal in all directions if the shock stress amplitude is much greater than the material strength.

In addition to these direct long-range forces there may also exist effective long-range forces, produced by some medium or substrate. An especially drastic effect is expected for epitaxial growth on a semiconductor. If adsorbate atoms are different from the substrate, the adsorbed layers have a lattice constant different from that of the substrate. In the case of thick adsorbate layers, an instability then appears on the surface of the crystal such that the surface undergoes wavy deformation, which might even lead to... 

To understand how the dispersed phase is deformed and how morphology is developed in a two-phase system, it is necessary to refer to studies performed specifically on the behavior of a dispersed phase in a liquid medium (the size of the dispersed phase, deformation rate, the viscosities of the matrix and dispersed phase, and their ratio). Many studies have been performed on both Newtonian and non-Newtonian droplet/medium systems [17-20]. These studies have shown that deformation and breakup of the droplet are functions of the viscosity ratio between the dispersity phase and the liquid medium, and the capillary number, which is defined as the ratio of the viscous stress in the fluid, tending to deform the droplet, to the interfacial stress between the phases, tending to prevent deformation ... 

The existence of yield stress Y at shear strains seems to be the most typical feature of rheological properties of highly filled polymers. A formal meaing of this term is quite obvious. It means that at stresses lower than Y the material behaves like a solid, i.e. it deforms only elastically, while at stresses higher than Y, like a liquid, i.e. it can flow. At a first approximation it may be assumed that the material is not deformed at all, if stresses are lower than Y. In this sense, filled polymers behave as visco-plastic media with a low-molecular and low-viscosity dispersion medium. This analogy is not random as will be stressed below when the values of the yield stress are compared for the systems with different dispersion media. The existence of yield stress in its physical meaning must be correlated with the strength of a structure formed by the interaction between the particles of a filler. 

In order to complete the discussion of methodical problems, we should mention two more methods of determining yield stress. Figure 6 shows that for plastic disperse systems with low-molecular dispersion medium, when a constant rate of deformation, Y = const., is given, the dependence x on time t passes through a maximum rm before a stationary value of shear stress ts is reached. We may assume that the value of the maximal shear stress xm is the maximum strength of the structure which must be destroyed so that the flow can occur. Here xm as well as ts do not depend or depend weakly on y, like Y. The difference between tm and xs takes into account the difference between maximum stress and yield stress. For filled polymer melts at low shear rates Tm Ts> i,e- fhese quantities can be identified with Y. 

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