Comparison of two entropy principles and their applications in granular flows with/without fluid

Abstract

Two entropy principles that are commonly used are: (i) the Clausius-Duhem inequality with the procedure of exploitation due to Coleman-Noll (CD-CN), and (ii) the entropy principle of Müller-Liu (ML). CD-CN makes a priori postulates about the entropy flux and entropy supply and assumes external source terms in (most) balance laws. ML postulate the entropy flux to be a general constitutive variable and treat all field equations as constraints for the exploitation of the entropy principle. These and further differences are explained, and results are presented with the use of both principles for (i) a granular solid with a scalar structure equation, and (ii) for a saturated mixture of granular/fluid constituents with scalar structure equations for each constituent. It is shown that the two entropy principles yield different results. It is further indicated which theories are likely to be problematic when the CD-CN approach is used. These theories are then applied to analyses of steady fully-developed gravity flows down an inclined plane.