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On the added mass effect for porous media

Kosiński W., Kubik J., Hutter K.

Archives of Mechanics

2002

Vol. 54, nr 5-6

479-495

Consider a porous solid skeleton saturated with N fluid constituents. To describe the saturation condition and the immiscibility of the mixture constituents (phases), N+1 volume fraction parameters are introduced. In the energy equation an added mass effect is incorporated in the form of a constitutive assumption. This allows to include, on the phenomenological level, the influence of the pore structure of the solid constituent on the kinetic energy formulation of the whole mixture. Its consequences are deduced; they lead to a new form of the kinetic energy in the balance law of energy, from which a new form of motion equations are deduced. A particular case of one fluid component in the isotropic case is considered.

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

Wang Y., Hutter K.

Archives of Mechanics

1999

Vol. 51, nr 5

605-632

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 Mueller-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.