On the added mass effect for porous media

Abstract

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.