Showing papers on "Mixture theory published in 1997"

A theory of mixtures with different constituent temperatures

Abstract: In this article we derive the basic equations of a nonlinear theory for binary mixtures of elastic materials in which the constituents may have different temperatures. The independent constitutive variables are the displacement fields, the first displacement gradients, the temperatures of the constituents, and the temperature gradients. The basic equations of the linear theory are established, and the displacement-temperature equations in the case of homogeneous and isotropic materials are derived.

On the description of the consolidation phenomenon by means of a two-component continuum

Abstract: THE PURPOSE of the present paper is the consistent formulation of the initial-boundary value problem for the consolidation phenomenon within the frame of a new two-component continuum model. The new class of models of two-component continua characterized by the balance equation for porosity is presented. The initial-boundary value problem with regard to the physical features of the consolidation is formulated. Some additional constitutive relations for the boundary quantities are proposed. Bearing in mind these constitutive relations, an example of a one-dimensional structure is calculated. The results of the numerical simulation are the basis for the parameter study of some constants of the model.

On the Constituent Structure of a Classical Mixture

Abstract: Thiw work is concerned with the formulation of constituent interactions and corresponding balance relations in classical mixture theory as based on a model for the (classical) constituent structure of such a mixture.

An Introduction to Continuum Physics

Abstract: Classical continuum physics deals with materials without a visible microstructure. That is, the scale of observation is large compared to the molecular scale, but small relative to other heterogeneities within the system. More modern continuum theories allow for a visible microstructure; amongst such theories are polar [65], mixture [21], nonlocal [63], and hybrid mixture [78]. In this chapter we concentrate mainly on setting out a general framework for classical continuum physics, however, toward the end of the chapter we set out the field equations for mixture and hybrid mixture theory. Fig. 1.1.1 illustrates the type of systems we concentrate on in this chapter. On the smallest scale (Figure 1.1.1a) individual molecules evince. Statistical mechanical theories and some micropolar field theories may be applicable on this scale. On a slightly larger scale the body appears locally uniform with no distinct microstructure. This is the scale-of-observation on which classical continuum theories apply. On yet a larger scale-of-observation large heterogeneities evince. Such media may require polar, mixture, hybrid mixture, or nonlocal continuum theories.

Effect of buoyancy and externally induced forces on the solidification of binary mixtures. Final report, August 1, 1987--July 31, 1997

Abstract: Research performed under this contract originated with the premise that much could be done to improve existing techniques for modeling the effects of convection on solidification in mixtures by eliminating arbitrary characterizations of the mushy region and its coupling with the melt. It was therefore proposed that a set of continuum conservation equations be derived from the principles of classical mixture theory and that the model concurrently treat melt, mushy and solid regions as a single domain (a continuum). The conservation equations would accommodate all pertinent convection effects, and closure would be achieved by assuming local composition equilibrium at phase interfaces. The need for simplifying assumptions concerning the geometric regularity of the interfaces would be eliminated, along with the need for separately tracking the interfaces and using moving numerical grids and/or coordinate mapping procedures. Accordingly, specific objectives of the work have been to (i) develop models and procedures for simultaneously solving the coupled set of conservation equations which govern mass, momentum, energy and species transfer for solidification in a mixture, (ii) use the models to predict, as a function of time and over a representative range of operating conditions, velocity, temperature, and composition fields throughout solid, mushy and liquid regions of analog and metal alloys, (iii) validate model predictions by visualizing flows and performing temperature and concentration measurements under test cell conditions which simulate those of the computations, and (iv) delineate mechanisms responsible for macrosegregation and develop control strategies for its suppression. Studies were performed for the unidirectional solidification of NH{sub 4}Cl-H{sub 2}O and Pb-Sn and Pb-Sn-Sb alloys.

Use of mixture theory to represent a cohesive elastic-viscoplastic material

Abstract: The analysis of material properties depends upon detailed information of the physical, geometric* and chemical properties of the materials. Relating these properties to a set of mathematical models is the principle objective of mechanics. Mixtures of materials made up of several constituents require special consideration since the constituent behavior must be reconciled with the overall behavior of the mixture. Mathematical models and their validity must be established to represent these materials. This thesis establishes a methodology whereby a logical sequence of considerations may be followed to represent complex mixtures adequately. Several existing theories of mechanics are assimilated into a cohesive theory to demonstrate the validity of the mathematical model used to represent mixtures. A structured development Of the second law of thermodynamics is constructed to allow additional constraint equations which will restrict the form of new parameters. An example of a wOod-snow mixture is used to show how the analysis is to be completed. Laboratory tests were run to use as a means of constructing the values of the new constitutive parameters. Proposed ways of including more constituents and spatial dimensions suggested.

A Local Model for the Energy Transfer in a Saturated Static Mixture

Abstract: In the present work the transient energy transfer in a nonsaturated porous medium is studied, using a mixture theory viewpoint. The porous matrix is assumed homogeneous, rigid and isotropic, while the fluid is a Newtonian incompressible one and both are assumed static. Since the homogeneous matrix is not saturated, gradients of concentration are present. The porous medium and the fluid (a liquid) will be regarded as continuous constituents of a mixture that will have also a third constituent, an inert gas, assumed with zero mass density and thermal conductivity. The problem is described by a set of two partial differential equations which represent the energy balances for the fluid and the solid constituents. Isovalues for these two constituents are plotted, considering representative time instants and selected values for the energy equations coefficients and for the saturation.