Analysis of Steady Compaction Waves in Porous Materials

1989 ◽  
Vol 56 (1) ◽  
pp. 15-24 ◽  
Author(s):  
J. M. Powers ◽  
D. S. Stewart ◽  
Herman Krier
Keyword(s):  
Porous Materials ◽  
Volume Fraction ◽  
Matrix Material ◽  
Wave Structure ◽  
Solid Matrix ◽  
Tait Equation ◽  
Two Phase ◽  
Piston Velocity ◽  
Zone Length ◽  
Compaction Waves

A two-phase continuum mixture model is used to analyze steady compaction waves in porous materials. It is shown that such a model admits both subsonic and supersonic steady compaction waves in response to a piston-driven boundary condition when a Tait equation is used to describe a solid matrix material and a generic static compaction relation is used to describe collapse of the matrix. Parameters for the Tait equation are chosen to match shock and compaction wave data. The model is able to predict compaction wave speed, final pressure, and final volume fraction in porous HMX. The structure of the compaction wave is also studied. A shock preceding the compaction wave structure is predicted for compaction waves travelling faster than the ambient sound speed of the solid. For subsonic compaction waves no leading shock is predicted. The compaction zone length is studied as a function of initial volume fraction, piston velocity, and compaction viscosity.

VELOCITY AND ATTENUATION OF SEISMIC WAVES IN TWO‐PHASE MEDIA: PART I. THEORETICAL FORMULATIONS

Geophysics ◽  
1974 ◽  
Vol 39 (5) ◽  
pp. 587-606 ◽  
Author(s):  
Guy T. Kuster ◽  
M. Nafi Toksöz
Keyword(s):  
Elastic Moduli ◽  
Seismic Waves ◽  
Matrix Material ◽  
Composite Medium ◽  
Solid Matrix ◽  
Seismic Velocities ◽  
Displacement Fields ◽  
Two Phase ◽  
The Matrix ◽  
In Series

The propagation of seismic waves in two‐phase media is treated theoretically to determine the elastic moduli of the composite medium given the properties, concentrations, and shapes of the inclusions and the matrix material. For long wavelengths the problem is formulated in terms of scattering phenomena in an approach similar to that of Ament (1959). The displacement fields, expanded in series, for waves scattered by an “effective” composite medium and individual inclusions are equated. The coefficients of the series expansions of the displacement fields provide a relationship between the elastic moduli of the effective medium and those of the matrix and inclusions. The expressions are derived for both solid and liquid inclusions in a solid matrix as well as for solid suspensions in a fluid matrix. Both spherical and oblate spheroidal inclusions are considered. Some numerical calculations are carried out to demonstrate the effects of fluid inclusions of various shapes on the seismic velocities in rocks. It is found that the concentration, shapes, and properties of the inclusions are important parameters. A concentration of a fraction of one percent of thin (small aspect ratio) inclusions could affect the compressional and shear velocities by more than ten percent. For both sedimentary and igneous rock models, the calculations for “dry” (i.e.,air‐saturated) and water‐saturated states indicate that the compressional velocities change significantly while the shear velocities change much less upon saturation with water.

scholarly journals Effective modules of two-phase construction composites with grain filler

2019 ◽  
Vol 15 (6) ◽  
pp. 407-414
Author(s):  
Vladimir T. Erofeev ◽  
Aleksej S. Tyuryahin ◽  
Tatyana P. Tyuryahina ◽  
Aleksandr V. Tingaev
Keyword(s):  
Building Materials ◽  
Materials Science ◽  
Volume Fraction ◽  
Matrix Material ◽  
Flat Space ◽  
Upper And Lower Bounds ◽  
Two Phase ◽  
The Matrix ◽  
Dimensionless Function ◽  
Visual Graphic

In the book of R.M. Christensen, “Introduction to the Mechanics of Composites” (1982), a calculation formula is given for the bulk module of polydisperse composites with spherical inclusions. This formula has been known to the Russianspeaking reader for almost 40 years, but unfortunately, it is not used in the practice of building materials science. To identify applied possibilities, R.M. Christensen's formula is modified and reduced to a dimensionless function k = k ( w , η, θ), which depends on three dimensionless parameters, i.e., it depends on three quantities: w is the volume fraction of the inclusion, η - the ratio of the shear modulus of the matrix material to the volume modulus of the same matrix, θ is the ratio of the volume moduli of the matrix materials and inclusion. Numerical studies of this function reveal that in two-phase granular composites, the range of effective moduli is significantly narrowed compared to the region limited by Voigt and Reuss estimates (in the sense of the upper and lower bounds of real values). At the same time, the lower Christensen score is the same as the Reuss score. Numerical and graphically presented results are given on the examples of the study of two characteristic groups of composite materials. In addition, the dimensionless form of the effective module allows to construct a system of visual graphic dependencies of the functions k ( w ) in a flat space k - w . For different values of θ, the function k = k ( w , η) displays a bunch of curved segments, which sets the position of the plane figure in flat space. Examples of constructing figures for characteristic regions of the values of the function k (η, θ, w ) are given.

Formation and Stability of Quasicrystalline and Hexagonal Approximant Phases in an Al–Mn–Be Alloy

2002 ◽  
Vol 17 (7) ◽  
pp. 1671-1677 ◽  
Author(s):  
G. S. Song ◽  
E. Fleury ◽  
S. H. Kim ◽  
W. T. Kim ◽  
D. H. Kim
Keyword(s):  
Thermal Stability ◽  
Phase Formation ◽  
Melt Spinning ◽  
Volume Fraction ◽  
Icosahedral Phase ◽  
Primary Phase ◽  
Solid Matrix ◽  
Two Phase ◽  
Large Volume Fraction ◽  
Faceted Particles

Phase formation and thermal stability for an Al–Mn–Be alloy have been investigated by melt-spinning and conventional casting. Significant differences in the phase formation and the thermal stability of the microstructure were found as a result of the different cooling rates. In the melt-spun ribbons, a large volume fraction of a metastable icosahedral phase was found to coexist with an Al solid solution. In the bulk cast ingots, the primary phase formed in the two-phase microstructure was a hexagonal approximant phase of quasicrystals. This phase that solidified in the form of faceted particles embedded in the Al solid matrix proved to be thermodynamically stable during annealing at 540 °C for 100 h. The effect of Be addition on the formation of the stable approximant phase is discussed in terms of the Hume–Rothery mechanism.

Fabrications of cellulose nanocomposite for tailor-made applications

2020 ◽  
pp. 096739112093205
Author(s):  
Muhamad Fareez Ismail ◽  
Ainil Hawa Jasni ◽  
Der Jiun Ooi
Keyword(s):  
Volume Fraction ◽  
Low Cost ◽  
Cellulose Nanofibers ◽  
Matrix Material ◽  
Atomic Layer ◽  
High Volume ◽  
Two Phase ◽  
Layer Deposition ◽  
The Matrix ◽  
Low Toxicity

The unique properties of nanocelluloses (NCs), including nanodimension, renewability, low toxicity, biocompatibility, biodegradability, easy availability, and low cost, render them the ideal nanomaterials for diverse applications. Composite material consists of matrix material with low volume fraction and self-assembled NC fibers with a high volume fraction of reinforcing domain. These two-phase components are often combined to promote stiffness and improve toughness (by dissipating materials fracture energy). The challenge, however, is to control the alignment and distribution of NC within the matrix. Recent research has been focusing on the production of composites using different methodologies such as electrospun cellulose nanofibers, polymer-grafted NC, nanoparticle binding on NCs, assembly of NCs at the air/water and oil/water interfaces, protein-mediated interactions on NCs, and atomic layer deposition on NCs. In this case, NC serves as an appropriate candidate for composites preparation in comparison to the non-biodegradable nanofillers (e.g. carbon nanoclay and nanotube).

scholarly journals Numerical Study on an Interface Compression Method for the Volume of Fluid Approach

Fluids ◽  
2021 ◽  
Vol 6 (2) ◽  
pp. 80
Author(s):  
Yuria Okagaki ◽  
Taisuke Yonomoto ◽  
Masahiro Ishigaki ◽  
Yoshiyasu Hirose
Keyword(s):  
Linear Theory ◽  
Volume Fraction ◽  
Numerical Study ◽  
Volume Of Fluid ◽  
Interfacial Wave ◽  
Validation Process ◽  
Two Phase ◽  
Numerical Diffusion ◽  
Mesh Resolution ◽  
Water Reactors

Many thermohydraulic issues about the safety of light water reactors are related to complicated two-phase flow phenomena. In these phenomena, computational fluid dynamics (CFD) analysis using the volume of fluid (VOF) method causes numerical diffusion generated by the first-order upwind scheme used in the convection term of the volume fraction equation. Thus, in this study, we focused on an interface compression (IC) method for such a VOF approach; this technique prevents numerical diffusion issues and maintains boundedness and conservation with negative diffusion. First, on a sufficiently high mesh resolution and without the IC method, the validation process was considered by comparing the amplitude growth of the interfacial wave between a two-dimensional gas sheet and a quiescent liquid using the linear theory. The disturbance growth rates were consistent with the linear theory, and the validation process was considered appropriate. Then, this validation process confirmed the effects of the IC method on numerical diffusion, and we derived the optimum value of the IC coefficient, which is the parameter that controls the numerical diffusion.

Comparison of Crystal Plasticity and Isotropic Hardening Predictions for Metal-Matrix Composites

1993 ◽  
Vol 60 (1) ◽  
pp. 70-76 ◽  
Author(s):  
A. Needleman ◽  
V. Tvergaard
Keyword(s):  
Volume Fraction ◽  
Matrix Material ◽  
Isotropic Hardening ◽  
Slip Systems ◽  
Matrix Composites ◽  
Plastic Deformations ◽  
Crystalline Plasticity ◽  
Planar Crystal ◽  
Crystal Model ◽  
Flow Theory Of Plasticity

In a numerical micromechanical study of the tensile properties of a metal reinforced by short whiskers, the elastic-plastic deformations of the metal are described in terms of crystalline plasticity, using a planar crystal model that allows for either two or three slip systems. Plane strain analyses are carried out for a periodic array of aligned whiskers for whisker volume fractions of 10 percent to 30 percent, and comparison is made with predictions based on a corresponding flow theory of plasticity with isotropic hardening. The predicted trend for composite strengthening with whisker volume fraction is the same for the various matrix material constitutive characterizations. It is found that the crystal model can give rise to shear localization, initiating at the sharp whisker edges. As a consequence of this localization, the stress carrying capacity eventually drops.

Heat Transfer in Porous Media Heated From Above With Evaporation, Condensation, and Capillary Effects

1983 ◽  
Vol 105 (3) ◽  
pp. 485-492 ◽  
Author(s):  
K. S. Udell
Keyword(s):  
Stable State ◽  
Superheated Liquid ◽  
Phase Zone ◽  
Two Phase ◽  
Water Steam ◽  
Zone Length ◽  
Compressed Liquid ◽  
Pressure Lowering ◽  
Darcy’S Equations ◽  
Convection Dominated

Heat and mass transfer characteristics of a sand-water-steam system heated at the top and cooled at the bottom were studied. It was found that at steady-state conditions the system segregated into three regions. The top region was conduction-dominated with the voids containing a stationary superheated steam. The middle region was convection-dominated, nearly isothermal, and exhibited an upward flow of the liquid by capillary forces and a downward flow of steam due to a slight pressure gradient. The bottom portion contained a stationary compressed liquid and was also conduction dominated. The length of the two-phase convection zone was evaluated through the application of Darcy’s equations for two-phase flow and correlations of relative permeabilities and capillary pressure data. The model was in excellent agreement with the observed results, predicting a decreasing two-phase zone length with increasing heat flux. The thermodynamics of the two-phase zone were also analyzed. It was found that the vapor phase was in a superheated state as described by the Kelvin equation for vapor pressure lowering. Also, it was evident that the liquid must also be superheated for thermodynamic equilibrium to result. A stability analysis demonstrated that the superheated liquid can exist in an unconditionally stable state under conditions typical of porous systems. The degree of liquid superheat within the two-phase zone of these experiments was obtained.

scholarly journals Effects of Polydispersity on the Phase Behavior of Additive Hard Spheres in Solution

Molecules ◽  
2021 ◽  
Vol 26 (6) ◽  
pp. 1543
Author(s):  
Luka Sturtewagen ◽  
Erik van der Linden
Keyword(s):  
Phase Behavior ◽  
Critical Point ◽  
Volume Fraction ◽  
Hard Spheres ◽  
Second Virial Coefficient ◽  
Two Phase ◽  
Different Types ◽  
Asymmetric Partitioning ◽  
Average Size ◽  
Liquid Liquid Phase Separation

The ability to separate enzymes, nucleic acids, cells, and viruses is an important asset in life sciences. This can be realised by using their spontaneous asymmetric partitioning over two macromolecular aqueous phases in equilibrium with one another. Such phases can already form while mixing two different types of macromolecules in water. We investigate the effect of polydispersity of the macromolecules on the two-phase formation. We study theoretically the phase behavior of a model polydisperse system: an asymmetric binary mixture of hard spheres, of which the smaller component is monodisperse and the larger component is polydisperse. The interactions are modelled in terms of the second virial coefficient and are assumed to be additive hard sphere interactions. The polydisperse component is subdivided into sub-components and has an average size ten times the size of the monodisperse component. We calculate the theoretical liquid–liquid phase separation boundary (the binodal), the critical point, and the spinodal. We vary the distribution of the polydisperse component in terms of skewness, modality, polydispersity, and number of sub-components. We compare the phase behavior of the polydisperse mixtures with their concomittant monodisperse mixtures. We find that the largest species in the larger (polydisperse) component causes the largest shift in the position of the phase boundary, critical point, and spinodal compared to the binary monodisperse binary mixtures. The polydisperse component also shows fractionation. The smaller species of the polydisperse component favor the phase enriched in the smaller component. This phase also has a higher-volume fraction compared to the monodisperse mixture.

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