55 research outputs found
Models and numerical methods for electrolyte flows
The most common mathematical models for electrolyte flows are based on the dilute solution assumption, leading to a coupled system of the Nernst--Planck--Poisson drift-diffusion equations for ion transport and the Stokes resp. Navier--Stokes equations for fluid flow. This contribution discusses historical and recent model developments beyond the dilute solution assumption and focuses on the effects of finite ion sizes and solvation. A novel numerical solution approach is presented and verified here which aims at preserving on the discrete level consistency with basic thermodynamic principles and structural properties like independence of flow velocities from gradient contributions to external forces
On a drift-diffusion system for semiconductor devices
In this note we study a fractional Poisson-Nernst-Planck equation modeling a
semiconductor device. We prove several decay estimates for the Lebesgue and
Sobolev norms in one, two and three dimensions. We also provide the first term
of the asymptotic expansion as .Comment: to appear in Annales Henri Poincar\'
Global solutions to the Nernst-Planck-Euler system on bounded domain
We show that the Nernst-Planck-Euler system, which models ionic
electrodiffusion in fluids, has global strong solutions for arbitrarily large
data in the two dimensional bounded domains. The assumption on species is
either there are two species or the diffusivities and the absolute values of
ionic valences are the same if the species are arbitrarily many. In particular,
the boundary conditions for the ions are allowed to be inhomogeneous. The proof
is based on the energy estimates, integration along the characteristic line and
the regularity theory of elliptic and parabolic equations
Discontinuous Galerkin Methods for Mass Transfer through Semi-Permeable Membranes
A discontinuous Galerkin (dG) method for the numerical solution of
initial/boundary value multi-compartment partial differential equation (PDE)
models, interconnected with interface conditions, is presented and analysed.
The study of interface problems is motivated by models of mass transfer of
solutes through semi-permeable membranes. More specifically, a model problem
consisting of a system of semilinear parabolic advection-diffusion-reaction
partial differential equations in each compartment, equipped with respective
initial and boundary conditions, is considered. Nonlinear interface conditions
modelling selective permeability, congestion and partial reflection are applied
to the compartment interfaces. An interior penalty dG method is presented for
this problem and it is analysed in the space-discrete setting. The a priori
analysis shows that the method yields optimal a priori bounds, provided the
exact solution is sufficiently smooth. Numerical experiments indicate agreement
with the theoretical bounds and highlight the stability of the numerical method
in the advection-dominated regime
On existence and uniqueness of the equilibrium state for an improved Nernst--Planck--Poisson system
This work deals with a model for a mixture of charged constituents introduced in [W. Dreyer et al. Overcoming the shortcomings
of the Nernst-Planck model. \emph{Phys. Chem. Chem. Phys.}, 15:7075-7086, 2013]. The aim of this paper is to give a first
existence and uniqueness result for the equilibrium situation. A main difference to earlier works is a momentum balance
involving the gradient of pressure and the Lorenz force which persists in the stationary situation and gives rise to the
dependence of the chemical potentials on the particle densities of every species
Further developments on theoretical and computational rheology
Tese financiada pela FCT - FundaĆ§Ć£o para a CiĆŖncia e a Tecnologia, CiĆŖncia.InovaĆ§Ć£o2010, POPH, UniĆ£o Europeia FEDERTese de doutoramento. Engenharia QuĆmica e BiolĆ³gica. Faculdade de Engenharia. Universidade do Porto. 201
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