Multi-component Constitutive Equations

Abstract

The theory of mixtures has been the subject of intensive study in contemporary mechanics (Truesdell 1957, Truesdell 1969, Truesdell and Toupin 1960, Green and Naghdi 1965, Green and Naghdi 1978, Goodman and Cowin 1972, Passman 1977, Nunziato and Walsh 1980) and has spawned as many controversies about the statement and application of the Second Law of Thermodynamics as studies of single component materials. Most mixture theories assume that each component of the mixture occupies space simultaneously and is required to satisfy its own set of balance laws involving additional “growth” terms that allow the components to exchange mass, momentum, and energy among themselves in such a way that these quantities are conserved for the mixture as a whole. Generally, such treatments make use of different temperatures for each component. Controversies arise over which entropy inequality the components are required to satisfy and whether entropy inequalities that apply to the mixture as a whole can be validly applied to each component individually.