We derive a novel thermodynamically consistent diffuse-interface model for compressible electrolytes undergoing phase transitions. The fluid mixtures may contain N constituents in liquid and vapor phases, with the possibility of phase coexistence. Furthermore, all constituents are assumed to exhibit polarizable and magnetizable properties. Our proposed thermodynamically consistent model serves as a generalized framework of the Allen–Cahn/Navier–Stokes/Poisson type, tailored for multi-component flows involving phase transitions and electrochemical reactions. Using matched asymptotic techniques, we analyze the physically admissible sharp interface limits of the model. Two scaling regimes are considered: a non-coupled regime and a coupled regime, where coupling occurs between the smallness parameter in the Poisson equation and the interface width. In the sharp interface limit, we derive a generalized Allen–Cahn/Euler/Poisson system that governs mixtures with electrochemical reactions in the bulk phases, complemented by admissible interfacial conditions. These conditions include, for example, a generalized Gibbs–Thomson law and a dynamic Young–Laplace law.

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Phase Field Modeling and Sharp Interface Limits of Multi-component Gas-Liquid Flows with Electrochemical Reactions and Phase Transition Effects

  • Wolfgang Dreyer,
  • Jan Giesselmann,
  • Christiane Kraus

摘要

We derive a novel thermodynamically consistent diffuse-interface model for compressible electrolytes undergoing phase transitions. The fluid mixtures may contain N constituents in liquid and vapor phases, with the possibility of phase coexistence. Furthermore, all constituents are assumed to exhibit polarizable and magnetizable properties. Our proposed thermodynamically consistent model serves as a generalized framework of the Allen–Cahn/Navier–Stokes/Poisson type, tailored for multi-component flows involving phase transitions and electrochemical reactions. Using matched asymptotic techniques, we analyze the physically admissible sharp interface limits of the model. Two scaling regimes are considered: a non-coupled regime and a coupled regime, where coupling occurs between the smallness parameter in the Poisson equation and the interface width. In the sharp interface limit, we derive a generalized Allen–Cahn/Euler/Poisson system that governs mixtures with electrochemical reactions in the bulk phases, complemented by admissible interfacial conditions. These conditions include, for example, a generalized Gibbs–Thomson law and a dynamic Young–Laplace law.