A thermodynamic theory of mixtures of fluids
About: This article is published in Archive for Rational Mechanics and Analysis.The article was published on 1968-01-01. It has received 416 citations till now. The article focuses on the topics: Thermodynamic equations & Thermodynamic system.
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TL;DR: In this article, a set of continuum conservation equations for binary, solid-liquid phase change systems is presented. But these equations have been cast into forms amenable to clear physical interpretation and solution by conventional numerical procedures.
896 citations
TL;DR: In this article, a systematic procedure for averaging continuum equations over representative regions of multiphase systems is developed, where Mass and areal averages as well as volume averages are defined to ensure that the averaged quantities are physically meaningful.
639 citations
TL;DR: A survey of theories of immiscible mixtures can be found in this article, where it is emphasized that the immiscibility of such mixtures has important consequences concerning the forms of the constitutive equations, and that it can also result in the mixtures exhibiting microstructural effects.
566 citations
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TL;DR: The basic physical concepts of classical continuum mechanics are body, configuration of a body, and force system acting on a body as mentioned in this paper, which can be expressed as follows: a body is regarded as a smooth manifold whose elements are the material points; a configuration is defined as a mapping of the body into a three-dimensional Euclidean space, and a force system is defined to be a vector-valued function defined for pairs of bodies.
Abstract: The basic physical concepts of classical continuum mechanics are body, configuration of a body, and force system acting on a body. In a formal rational development of the subject, one first tries to state precisely what mathematical entities represent these physical concepts: a body is regarded to be a smooth manifold whose elements are the material points; a configuration is defined as a mapping of the body into a three-dimensional Euclidean space, and a force system is defined to be a vector-valued function defined for pairs of bodies1. Once these concepts are made precise one can proceed to the statement of general principles, such as the principle of objectivity or the law of balance of linear momentum, and to the statement of specific constitutive assumptions, such as the assertion that a force system can be resolved into body forces with a mass density and contact forces with a surface density, or the assertion that the contact forces at a material point depend on certain local properties of the configuration at the point. While the general principles are the same for all work in classical continuum mechanics, the constitutive assumptions vary with the application in mind and serve to define the material under consideration.
1,885 citations
TL;DR: In this paper, a dynamical theory of the flow relative to each other of two continua is developed from an energy equation and the use of invariance conditions under superposed rigid body motions, together with an entropy production inequality.
353 citations