Internal constraints in the theories of immiscible mixtures for soils

In this paper we formulate balance principles for an immiscible mixture of continua with microstructure in the broadest sense to include, e.g., diffusion and adsorption phenomena, strain gradient effects and chemical reactions, and introduce an additional balance of micromomentum for each constituent to describe the microstructural effects. Next, we describe a method for taking into account the general internal constraints in entropy inequality, based on an ‘extended’ principle of thermodynamic determinism, and obtain a set of ‘pure’ constitutive equations. Finally we consider some examples of interest for thermo-mechanics of soils, such as granular materials dispersed in a fluid or the flow of fluids in a porous solid. Particular solutions are obtained in linear approximations for mixtures of packed granular materials in rarefied air, and solids with nano-pores filled by a gas.