A Continuum Theory of Fluid Saturated Porous Media

1971 ◽  
Vol 38 (1) ◽  
pp. 1-7 ◽  
Author(s):  
A. Bedford ◽  
J. D. Ingram
Keyword(s):  
Constitutive Relations ◽  
Deformation Gradient ◽  
Continuum Theory ◽  
Elastic Solid ◽  
Entropy Inequality ◽  
Heat Conducting ◽  
Saturated Porous Media ◽  
Theory Of Mixtures ◽  
Biot Equations ◽  
The Continuum

A continuum theory, for a heat-conducting, porous elastic solid saturated by a mixture of heat-conducting, viscous compressible fluids, is developed using the continuum theory of mixtures. Gradients of the fluid densities and the second deformation gradient of the solid constituent are included among the independent constitutive variables as proposed by Mu¨ller [17]. The Clausius-Duhem entropy inequality and the principle of material indifference are used to obtain rational constitutive relations for the medium. Linear constitutive equations are presented, and a theory equivalent to a generalization of the Biot equations is obtained.

Applications of material coordinates in the soil and plant sciences.

1987 ◽  
Vol 35 (3) ◽  
pp. 361-370
Author(s):  
P.A.C. Raats
Keyword(s):  
Soil Water ◽  
Solid Phase ◽  
Continuum Theory ◽  
Central Problem ◽  
Plant Tissues ◽  
Common Basis ◽  
Plant Sciences ◽  
Theory Of Mixtures ◽  
The Common ◽  
The Continuum

The continuum theory of mixtures is used to show the common basis of models in three areas. In each, the central problem is the description of the deformation and motion of a reference continuum and of the movement of one or more constituents relative to this reference continuum. The three applications concern the movement of solutes relative to soil water, the movement of soil water relative to the solid phase of swelling/shrinking soils, and the movement of water, solutes, and gases relative to growing plant tissues. (Abstract retrieved from CAB Abstracts by CABI’s permission)

scholarly journals Application of a mixture theory to stress waves in snow

1993 ◽  
Vol 18 ◽  
pp. 274-280
Author(s):  
George E. Austiguy ◽  
Robert L. Brown
Keyword(s):  
Wave Speed ◽  
Mixture Theory ◽  
Continuum Theory ◽  
Elastic Solid ◽  
Stress Waves ◽  
Low Frequencies ◽  
High Frequencies ◽  
Wave Velocities ◽  
Rotational Wave ◽  
Theory Of Mixtures

A continuum theory of mixtures is applied to model snow as a mixture of an elastic solid and an elastic fluid. Three wave types, two dilational and one rotational, are shown to exist. Numerical evaluation shows velocity and attenuation increasing with frequency for all three waves. Wave velocity increases with increasing density while attenuation decreases with increasing density for all three waves. The first dilational wave is associated with the pore fluid, has a slow wave speed and is highly attenuated. This wave exhibits diffusive behavior at low frequencies and nondispersive behavior at high frequencies. The second dilation wave is associated with the solid ice material. It is the fastest of the three wave types and does not appreciably attenuate. Nondispersive wave behavior characterizes this wave at low and high frequencies. The rotational wave occurs only in the solid, is the least attenuated of all three waves, and propagates at velocities greater than that of the first, but less than that of the second, dilational wave. The rotational wave exhibits nondispersive behavior at low and high frequencies. Wave velocities and attenuation show behavior that is in agreement with existing experimental data.

Toward A Diffusing Continuum Theory of Composite Materials

1971 ◽  
Vol 38 (1) ◽  
pp. 8-14 ◽  
Author(s):  
A. Bedford ◽  
M. Stern
Keyword(s):  
Composite Materials ◽  
Dynamical Behavior ◽  
Continuum Theory ◽  
Relative Displacement ◽  
Classical Solutions ◽  
Longitudinal Wave Propagation ◽  
Theory Of Mixtures ◽  
The Individual ◽  
Laminated Materials ◽  
The Continuum

A theory of composite materials is proposed which is based on the continuum theory of mixtures. The constituents of a composite are modeled as superimposed continua which undergo individual deformations. Effects of structure on dynamical processes in composite materials are then simulated by specifying the coupling between the individual constituent motions. A novel feature of this model is the inclusion of diffusion with relative displacement coupling for perfectly bonded composites. A simple one-dimensional form of such a theory is presented, and, when compared with classical solutions for longitudinal wave propagation in laminated materials, predicts some aspects of the dynamical behavior extremely well.

scholarly journals Application of a mixture theory to stress waves in snow

1993 ◽  
Vol 18 ◽  
pp. 274-280
Author(s):  
George E. Austiguy ◽  
Robert L. Brown
Keyword(s):  
Wave Speed ◽  
Mixture Theory ◽  
Continuum Theory ◽  
Elastic Solid ◽  
Stress Waves ◽  
Low Frequencies ◽  
High Frequencies ◽  
Wave Velocities ◽  
Rotational Wave ◽  
Theory Of Mixtures

A continuum theory of mixtures is applied to model snow as a mixture of an elastic solid and an elastic fluid. Three wave types, two dilational and one rotational, are shown to exist. Numerical evaluation shows velocity and attenuation increasing with frequency for all three waves. Wave velocity increases with increasing density while attenuation decreases with increasing density for all three waves. The first dilational wave is associated with the pore fluid, has a slow wave speed and is highly attenuated. This wave exhibits diffusive behavior at low frequencies and nondispersive behavior at high frequencies. The second dilation wave is associated with the solid ice material. It is the fastest of the three wave types and does not appreciably attenuate. Nondispersive wave behavior characterizes this wave at low and high frequencies. The rotational wave occurs only in the solid, is the least attenuated of all three waves, and propagates at velocities greater than that of the first, but less than that of the second, dilational wave. The rotational wave exhibits nondispersive behavior at low and high frequencies. Wave velocities and attenuation show behavior that is in agreement with existing experimental data.

Lubrication With Binary Mixtures: Liquid-Liquid Emulsion

1993 ◽  
Vol 115 (1) ◽  
pp. 46-55 ◽  
Author(s):  
A. Al-Sharif ◽  
K. Chamniprasart ◽  
K. R. Rajagopal ◽  
A. Z. Szeri
Keyword(s):  
Hydrodynamic Lubrication ◽  
Continuum Theory ◽  
Squeeze Film ◽  
Water Emulsion ◽  
Oil In Water ◽  
Squeeze Film Dampers ◽  
Liquid Emulsion ◽  
Theory Of Mixtures ◽  
Oil Water ◽  
The Continuum

There are numerous instances of technical importance in which multicomponent lubricants are utilized either by design or by necessity. In many of these cases one of the components is a liquid while the other component is a gas, as in squeeze film dampers during high frequency operation, or both components are liquids, as in the oil-water emulsion used in metal forming processes. In this paper our objective is to develop a self-consistent theory of hydrodynamic lubrication with bicomponent, liquid-liquid lubricants. The basic scientific method utilized is the continuum theory of mixtures. In this, first instance we test the model on journal bearings lubricated with water-in-oil and oil-in-water emulsions.

Lubricating Properties of Water in Oil Emulsions

2005 ◽  
Vol 128 (2) ◽  
pp. 296-311 ◽  
Author(s):  
James J. Benner ◽  
Farshid Sadeghi ◽  
Michael R. Hoeprich ◽  
Mark C. Frank
Keyword(s):  
Continuum Theory ◽  
Operating Conditions ◽  
Steel Ball ◽  
Lubricant Film Thickness ◽  
Lubricated Contacts ◽  
Steel Disc ◽  
Theory Of Mixtures ◽  
Oil Emulsions ◽  
The Continuum ◽  
Lubricating Properties

In this study the effect of water as a contaminant in lubricated contacts was analytically and experimentally investigated. A steel ball on glass disc apparatus was used to measure lubricant film thickness of pure oil and water in oil emulsions under various operating conditions. A steel ball on steel disc rig was used to measure friction as a function of various loads, slide to roll ratios and water in oil emulsions. A finite difference numerical model was developed using the continuum theory of mixtures and results were corroborated with the experimental measurements. Numerical results are in excellent agreement with the experimental results and indicate that water will flow around the contact. The experimental and analytical results suggest that for heavily loaded contacts water-in-oil emulsions perform essentially the same as pure oils.

Creep and recrystallization of large polycrystalline masses. I. General continuum theory

2006 ◽  
Vol 462 (2069) ◽  
pp. 1493-1514 ◽  
Author(s):  
Sérgio H Faria
Keyword(s):  
Continuum Theory ◽  
Transversely Isotropic ◽  
Current Approach ◽  
Symmetry Groups ◽  
Lattice Orientation ◽  
Balance Equations ◽  
Theory Of Mixtures ◽  
General Continuum ◽  
Continuous Diversity ◽  
The Continuum

This is the first of a series of works on the continuum mechanics and thermodynamics of creep and recrystallization of large polycrystalline masses. The general continuum theory presented here is suited to mono- and multi-mineral rocks. It encompasses several symmetry groups (e.g. orthotropic and transversely isotropic) and diverse crystal classes of triclinic, monoclinic and rhombic systems, among others. The cornerstone of the current approach is the theory of mixtures with continuous diversity, which allows one to regard the polycrystal as a ‘mixture of lattice orientations’. Following this picture, balance equations of mass, linear momentum, lattice spin, energy, dislocations, and entropy are set forth to describe the response of the polycrystal (i.e. the ‘mixture’), as well as of a group of crystallites sharing the same lattice orientation ( viz . a ‘species’). The connection between the balance equations for a species and those for the mixture is established by homogenization rules, formulated for every field of the theory.

A BOUNDARY VALUE PROBLEM IN GROUNDWATER MOTION ANALYSIS — COMPARISON OF PREDICTIONS BASED ON DARCY’S LAW AND THE CONTINUUM THEORY OF MIXTURES

1993 ◽  
Vol 03 (02) ◽  
pp. 231-248 ◽  
Author(s):  
D. MUNAF ◽  
A.S. WINEMAN ◽  
K.R. RAJAGOPAL ◽  
D.W. LEE
Keyword(s):  
Radial Flow ◽  
Darcy’S Law ◽  
Classical Problem ◽  
Mixture Theory ◽  
Continuum Theory ◽  
Darcy's Law ◽  
Low Flow ◽  
Theory Of Mixtures ◽  
Equations Of Motions ◽  
The Continuum

The classical problem of the radial flow to a well in a confined horizontal aquifer is solved using two theories: (1) when the flow is based on Darcy’s law, and (2) when the flow is based on equations of the Continuum Theory of Mixtures. The latter reduce to Darcy’s law when the inertia of the fluid can be neglected, and when the viscosity of the fluid does not enter into the expression for the partial stress for the fluid. A comparison of the two solutions shows that there are conditions when Mixture Theory could predict results that provide a significant departure from those predicted by Darcy’s Law. In this paper we delineate the extent of validity of Darcy’s law, within the context of a more general theoretical framework. The results of our work indicate that Darcy’s law is indeed quite good for low flow rates for a fluid like water. However this is not the case for dense fluids, say oils or effluents, due to the inclusion of inertial effects in the equations of motions.

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