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End date: 2024 × Start date: 2020 × Type: article × Sponsor: Leibniz_Fonds × WGL Institute: WIAS ×

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    Galilean Bulk-Surface Electrothermodynamics and Applications to Electrochemistry
    (Basel : MDPI, 2023) Müller, Rüdiger; Landstorfer, Manuel
    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 (Formula presented.), which is divided into (Formula presented.) and (Formula presented.) by a possibly moving singular surface S, where a charged reacting mixture of a viscous medium can be present on each geometrical entity (Formula presented.). By the restriction to the Galilean limits of the Maxwell equations, we achieve that only subsystems of equations for matter and electromagnetic fields are coupled that share identical transformation properties with respect to observer transformations. Moreover, the application of an entropy principle becomes more straightforward and finally helps 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 in the analysis of the stress tensor and the momentum balance in the general case of non-constant scalar susceptibility. Finally, we summarise the application of the derived model framework to an electrochemical system with surface reactions.
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    Weak-strong uniqueness and energy-variational solutions for a class of viscoelastoplastic fluid models
    (Boston, Mass. : De Gruyter, 2022) Eiter, Thomas; Hopf, Katharina; Lasarzik, Robert
    We study a model for a fluid showing viscoelastic and viscoplastic behavior, which describes the flow in terms of the fluid velocity and a symmetric deviatoric stress tensor. This stress tensor is transported via the Zaremba-Jaumann rate, and it is subject to two dissipation processes: one induced by a nonsmooth convex potential and one by stress diffusion. We show short-time existence of strong solutions as well as their uniqueness in a class of Leray-Hopf-type weak solutions satisfying the tensorial component in the sense of an evolutionary variational inequality. The global-in-time existence of such generalized solutions has been established in a previous work. We further study the limit when stress diffusion vanishes. In this case, the above notion of generalized solutions is no longer suitable, and we introduce the concept of energy-variational solutions, which is based on an inequality for the relative energy. We derive general properties of energy-variational solutions and show their existence by passing to the nondiffusive limit in the relative energy inequality satisfied by generalized solutions for nonzero stress diffusion.