Galilean bulk-surface electrothermodynamics and applications to electrochemistry

Abstract

In this work, the balance equations of non-equilibrium thermodynamics are coupled to Galilean limit systems of the Maxwell equations, i.e. either to (i) the quasi-electrostatic limit or (ii) the quasi-magnetostatic limit. We explicitly consider a volume $Omega$ which is divided into $Omega^+$ and $Omega^-$ by a possibly moving singular surface S, where a charged reacting mixture of a viscous medium can be present on each geometrical entity ($Omega$^+, S, $Omega^-$). By the restriction to Galilean limits of the Maxwell equations, we achieve that only subsystems of equations for matter and electric field are coupled that share identical transformation properties with respect to observer transformations. Moreover, the application of an entropy principle becomes more straightforward and finally it helps to estimate the limitations of the more general approach based the full set of Maxwell equations. Constitutive relations are provided based on an entropy principle and particular care is taken for the analysis of the stress tensor and the momentum balance in the general case of non-constant scalar susceptibility. Finally, we summarize the application of the derived model framework to an electrochemical system with surface reactions.