Entropy flux and Korteweg-type constitutive equations
Received: 2 May 2006
Mathematics Subject Classification (2000): 74A30 - 76A05 -74A15
Abstract Korteweg-type constitutive equations describe smooth properties of capillarity through the dependence on higher-order density (or deformation) gradients. Such constitutive equations are compatible with thermodynamics provided the scheme is appropriately modified. The purpose of the paper is to show that constitutive equations with density gradients may be framed within a thermodynamic scheme in which the entropy flux is different from the heat flux over the absolute temperature. This is shown in two steps. First, thermodynamic restrictions on the constitutive functions are derived as necessary conditions placed by the second law inequality. Next a scheme is set up which satisfies the necessary conditions, proves sufficient - in that satisfies the second law - and gives the constitutive equations in terms of the chosen free energy. The immediate connection with Korteweg’s equation is established.