A model of a polarized mixture is developed and the effects of migration of ions are also accounted for. The rate of the polarization power in some way furnishes power to the mixture. The electrical external power is calculated and by means of a requirement of invariance of the power, the standard balance laws are deduced. The ions dissolved in the mixture and subject to the electric field are considered like tracers and their migration is discussed. We show that their migration is ruled by the Nernst–Planck equation. In the final section, we adapt the description of the model to the setting of complex bodies and the microstructural evolution equations are derived.
a b s t r a c tIn this paper we propose a mathematical model of a mixture between a porous material and a polarized fluid in the mechanics of complex bodies. We use a variational approach to derive the global and microstructural balance laws for each phase of the mixture and for the mixture as a whole. Such balances differ from those generally proposed in theory of mixtures. We consider an open system and we account for external sources. Moreover, via the Coleman and Noll procedure we point out that the transport equation for the matter in a polarized mixture due to electrical field is governed by the Nernst-Planck equation.
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