The thermodynamic structure of the two-component model of porous incompressible materials with true mass densities
This paper presents the thermodynamic foundations of a new binary model of an incompressible porous solid saturated with an incompressible liquid. In the previous thermodynamic theory by \textit{R. M. Bowen} [Int. J. Eng. Sci. 18, 1129-1148 (1980; Zbl 0446.73005)] the incompressibility of the \(N\) fluid components was reflected solely by one single scalar constraint, instead of the expected \(N+1\) constraints. Here, additional field equations are proposed following from the balance of the so-called true densities (defined as the ratio of the usual density to the corresponding normalized porosity). This yields the expected number of constraints. The new theory, thermodynamic formulation of which is carried out in the framework of rational thermodynamics [\textit{C. Truesdell}, Rational Thermodynamics, Springer (1984; Zbl 0559.00016)], has, amongst other advantages, the possibility to formulate coherently some boundary problems which led to contradictions in the previous theory. Numerical applications of the theory will be carried out in forthcoming publications.
scientific article; zbMATH DE number 761074