arXiv subjects

Wolfgang Dreyer

Publications and source records attributed to Wolfgang Dreyer.

5 recordsLinked to original sources

arXiv2025

Derivation and thermodynamically consistent coupling of a Debye-Hückel type energy to a steric electrolyte model and application to the apparent molar volume and phase boundaries

We derive a Debye-Hückel-like model of the electric ion-ion interaction for non-constant dielectric susceptibility, which does not depend on any kind of charging process due to its foundation in the general framework of non-equilibrium electro-thermodynamics. The derivation, however, leads to a novel thermodynamic consistency condition for the temperature dependence of the susceptibility. Due to its contributions to the total pressure, the consistent coupling of this new contribution to the free energy requires subtle modifications in the derivation of the simple mixture model for electrolytes. The coupled model is then applied to the apparent molar volume for various related monovalent salts over a wider range of salt concentrations and temperatures, and classical tests of the electrolyte theory at phase boundaries are investigated.

physics.chem-ph↗

arXiv2021

A McKean-Vlasov SDE and particle system with interaction from reflecting boundaries

We consider a one-dimensional McKean-Vlasov SDE on a domain and the associated mean-field interacting particle system. The peculiarity of this system is the combination of the interaction, which keeps the average position prescribed, and the reflection at the boundaries; these two factors make the effect of reflection non local. We show pathwise well-posedness for the McKean-Vlasov SDE and convergence for the particle system in the limit of large particle number.

math.PR↗

arXiv2021

Multicomponent incompressible fluids -- An asymptotic study

This paper investigates the asymptotic behavior of the Helmholtz free energy of mixtures at small compressibility. We start from a general representation for the local free energy that is valid in stable subregions of the phase diagram. On the basis of this representation we classify the admissible data to construct a thermodynamically consistent constitutive model. We then analyze the incompressible limit, where the molar volume becomes independent of pressure. Here we are confronted with two problems: (i) Our study shows that the physical system at hand cannot remain incompressible for arbitrary large deviations from a reference pressure unless its volume is linear in the composition. (ii) As a consequence of the second law of thermodynamics, the incompressible limit implies that the molar volume becomes independent of temperature as well. Most applications, however, reveal the non-appropriateness of this property. According to our mathematical treatment, the free energy as a function of temperature and partial masses tends to a limit in the sense of epi- or Gamma-convergence. In the context of the first problem, we study the mixing of two fluids to compare the linearity with experimental observations. The second problem will be treated by considering the asymptotic behavior of both a general inequality relating thermal expansion and compressibility and a PDE-system relying on the equations of balance for partial masses, momentum and the internal energy.

math-ph↗

arXiv2014

Continuum thermodynamics of chemically reacting fluid mixtures

We consider viscous, heat conducting mixtures of molecularly miscible chemical species forming a fluid in which the constituents can undergo chemical reactions. Assuming a common temperature for all components, we derive a closed system of partial mass and partial momentum balances plus a mixture balance of internal energy. This is achieved by careful exploitation of the entropy principle and requires appropriate definitions of absolute temperature and chemical potentials, based on an adequate definition of thermal energy excluding diffusive contributions. The resulting interaction forces split into a thermo-mechanical and a chemical part, where the former turns out to be symmetric in case of binary interactions. For chemically reacting systems and as a new result, the chemical interaction force is a contribution being non-symmetric outside of chemical equilibrium. The theory also provides a rigorous derivation of the so-called generalized thermodynamic driving forces, avoiding the use of approximate solutions to the Boltzmann equations. Moreover, using an appropriately extended version of the entropy principle and introducing cross-effects already before closure as entropy invariant couplings between principal dissipative mechanisms, the Onsager symmetry relations become a strict consequence. With a classification of the factors in the binary products of the entropy production according to their parity--instead of the classical partition into so-called fluxes and driving forces--the apparent anti-symmetry of certain couplings is thereby also revealed. If the diffusion velocities are small compared to the speed of sound, the Maxwell-Stefan equations follow in the case without chemistry, thereby neglecting wave phenomena in the diffusive motion. This results in a reduced model with only mass being balanced individually. In the reactive case ...

physics.flu-dyn↗

arXiv2014

Modeling of compressible electrolytes with phase transition

A novel thermodynamically consistent diffuse interface model is derived for compressible electrolytes with phase transitions. The fluid mixtures may consist of N constituents with the phases liquid and vapor, where both phases may coexist. In addition, all constituents may consist of polarizable and magnetizable matter. Our introduced thermodynamically consistent diffuse interface model may be regarded as a generalized model of Allen-Cahn/Navier-Stokes/Poisson type for multi-component flows with phase transitions and electrochemical reactions. For the introduced diffuse interface model, we investigate physically admissible sharp interface limits by matched asymptotic techniques. We consider two scaling regimes, i.e. a non-coupled and a coupled regime, where the coupling takes place between the smallness parameter in the Poisson equation and the width of the interface. We recover in the sharp interface limit a generalized Allen-Cahn/Euler/Poisson system for mixtures with electrochemical reactions in the bulk phases equipped with admissible interfacial conditions. The interfacial conditions satisfy, for instance, a generalized Gibbs-Thomson law and a dynamic Young-Laplace law.

math.AP↗