Page 399 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 399
MULTICOMPONENT DIFFUSION IN POROUS MEDIA (MS-42)
Modeling of ion transport by a Maxwell-Stefan approach and numerical
results
Rüdiger Müller, mueller@wias-berlin.de
Weierstraß Institut, Germany
Coauthor: Wolfgang Dreyer
Electro-thermodynamics provides a consistent framework to derive continuum models for the
description of electrochemical systems on the device level, e.g. for batteries or fuel cells. These
models must be equipped with two additional ingredients: (i) a free energy model to calculate
the chemical potentials and (ii) a kinetic model for the kinetic coefficients. Suitable free en-
ergy models for liquid electrolytes incorporating ion–solvent interaction, finite ion sizes and
solvation already exist and have been validated against experimental measurements.
In this work, we apply a Maxwell–Stefan setting for multicomponent transport in order to
derive mobility coefficients. However, instead of these mobility coefficients, often other trans-
port parameters are more insightful for the interpretation of measurements. In the context of
energy conversion systems, the electric conductivity of electrolytes has naturally attracted most
interest. Further relevant parameters are the transference numbers and diffusion coefficients.
Contrary to the equilibrium properties, some of these mentioned transport properties depend on
a combination of chemical potentials and kinetic coefficients, while others depend solely on the
kinetic coefficients.
In a numerical study, we analyze the impact of ion solvation and incomplete salt dissociation
on the transport parameters of a non-dilute electrolyte.
A bi-fluid model for a mixture of two compressible non interacting fluids
with general boundary data
Sarka Necasova, matus@math.cas.cz
Institute of Mathematics, Academy of Sciences of the Czech Republic, Czech Republic
We prove global existence of weak solutions for a version of one velocity Baer-Nunziato sys-
tem with dissipation describing a mixture of two non interacting viscous compressible fluids
in a piecewise regular Lipschitz domain with general inflow/outflow boundary conditions. The
geometrical setting is general enough to comply with most current domains important for appli-
cations as, for example, (curved) pipes of picewise regular and axis-dependent cross sections.
As far as the existence proof is concerned, we adapt to the system the nowaday’s classical
Lions-Feireisl approach to the compressible Navier-Stokes equations which is combined with
a generalization of the theory of renormalized solutions to the transport equations. The results
related to the families of transport equations presented in this paper extend/improve some of
statements of the theory of renormalized solutions, and they are therefore of independent inter-
est.
397
Modeling of ion transport by a Maxwell-Stefan approach and numerical
results
Rüdiger Müller, mueller@wias-berlin.de
Weierstraß Institut, Germany
Coauthor: Wolfgang Dreyer
Electro-thermodynamics provides a consistent framework to derive continuum models for the
description of electrochemical systems on the device level, e.g. for batteries or fuel cells. These
models must be equipped with two additional ingredients: (i) a free energy model to calculate
the chemical potentials and (ii) a kinetic model for the kinetic coefficients. Suitable free en-
ergy models for liquid electrolytes incorporating ion–solvent interaction, finite ion sizes and
solvation already exist and have been validated against experimental measurements.
In this work, we apply a Maxwell–Stefan setting for multicomponent transport in order to
derive mobility coefficients. However, instead of these mobility coefficients, often other trans-
port parameters are more insightful for the interpretation of measurements. In the context of
energy conversion systems, the electric conductivity of electrolytes has naturally attracted most
interest. Further relevant parameters are the transference numbers and diffusion coefficients.
Contrary to the equilibrium properties, some of these mentioned transport properties depend on
a combination of chemical potentials and kinetic coefficients, while others depend solely on the
kinetic coefficients.
In a numerical study, we analyze the impact of ion solvation and incomplete salt dissociation
on the transport parameters of a non-dilute electrolyte.
A bi-fluid model for a mixture of two compressible non interacting fluids
with general boundary data
Sarka Necasova, matus@math.cas.cz
Institute of Mathematics, Academy of Sciences of the Czech Republic, Czech Republic
We prove global existence of weak solutions for a version of one velocity Baer-Nunziato sys-
tem with dissipation describing a mixture of two non interacting viscous compressible fluids
in a piecewise regular Lipschitz domain with general inflow/outflow boundary conditions. The
geometrical setting is general enough to comply with most current domains important for appli-
cations as, for example, (curved) pipes of picewise regular and axis-dependent cross sections.
As far as the existence proof is concerned, we adapt to the system the nowaday’s classical
Lions-Feireisl approach to the compressible Navier-Stokes equations which is combined with
a generalization of the theory of renormalized solutions to the transport equations. The results
related to the families of transport equations presented in this paper extend/improve some of
statements of the theory of renormalized solutions, and they are therefore of independent inter-
est.
397
