198 research outputs found
A Maxwell-Amp\`{e}re Nernst-Planck Framework for Modeling Charge Dynamics
Understanding the properties of charge dynamics is crucial to many practical
applications, such as electrochemical energy devices and transmembrane ion
channels. This work proposes a Maxwell-Amp\`{e}re Nernst-Planck (MANP)
framework for the description of charge dynamics. The MANP model is shown to be
a gradient flow of a convex free-energy functional, and demonstrated to be
equivalent to the Poisson-Nernst-Planck model. By the energy dissipation law,
the steady state of the MANP model reproduces the charge conserving
Poisson-Boltzmann (PB) theory, providing an alternative energy stable approach
to study the PB theory from the perspective of a gradient flow. In order to
achieve the curl-free condition, the MANP model is equipped with a local
curl-free relaxation algorithm, which is shown to naturally preserve the
Gauss's law and have robust convergence and linear computational complexity.
One of the main advantages of our work is that the model can efficiently deal
with space-dependent permittivity instead of solving the variable-coefficient
Poisson's equation. Many-body effects such as ionic steric effects and Coulomb
correlations can be incorporated within the MANP framework to derive modified
MANP models for problems in which the mean-field approximation fails. Numerical
results on the charge dynamics with such beyond mean-field effects in
inhomogeneous dielectric environments are presented to demonstrate the
performance of the MANP models in the description of charge dynamics,
illustrating that the proposed MANP model provides a general framework for
modeling charge dynamics
Electrochemical transport modelling and open-source simulation of pore-scale solid-liquid systems
The modelling of electrokinetic flows is a critical aspect spanning many
industrial applications and research fields. This has introduced great demand
in flexible numerical solvers to describe these flows. The underlying phenomena
is microscopic, non-linear, and often involving multiple domains. Therefore
often model assumptions and several numerical approximations are introduced to
simplify the solution. In this work we present a multi-domain multi-species
electrokinetic flow model including complex interface and bulk reactions. After
a dimensional analysis and an overview of some limiting regimes, we present a
set of general-purpose finite-volume solvers, based on OpenFOAM(R), capable of
describing an arbitrary number of electrochemical species over multiple
interacting (solid or fluid) domains. We provide a verification of the
computational approach for several cases involving electrokinetic flows,
reactions between species, and complex geometries. We first present three
one-dimensional verification test-cases for single- and multi-domain cases and
then show the capability of the solver to tackle two- and three-dimensional
electrically driven flows and ionic transport in random porous structures. The
purpose of this work is to lay the foundation of a general-purpose open-source
flexible modelling tool for problems in electrochemistry and electrokinetics at
different scales
Physics of Ionic Conduction in Narrow Biological and Artificial Channels
The book reprints a set of important scientific papers applying physics and mathematics to address the problem of selective ionic conduction in narrow water-filled channels and pores. It is a long-standing problem, and an extremely important one. Life in all its forms depends on ion channels and, furthermore, the technological applications of artificial ion channels are already widespread and growing rapidly. They include desalination, DNA sequencing, energy harvesting, molecular sensors, fuel cells, batteries, personalised medicine, and drug design. Further applications are to be anticipated.The book will be helpful to researchers and technologists already working in the area, or planning to enter it. It gives detailed descriptions of a diversity of modern approaches, and shows how they can be particularly effective and mutually reinforcing when used together. It not only provides a snapshot of current cutting-edge scientific activity in the area, but also offers indications of how the subject is likely to evolve in the future
Low Mach Number Fluctuating Hydrodynamics for Electrolytes
We formulate and study computationally the low Mach number fluctuating
hydrodynamic equations for electrolyte solutions. We are interested in studying
transport in mixtures of charged species at the mesoscale, down to scales below
the Debye length, where thermal fluctuations have a significant impact on the
dynamics. Continuing our previous work on fluctuating hydrodynamics of
multicomponent mixtures of incompressible isothermal miscible liquids (A.
Donev, et al., Physics of Fluids, 27, 3, 2015), we now include the effect of
charged species using a quasielectrostatic approximation. Localized charges
create an electric field, which in turn provides additional forcing in the mass
and momentum equations. Our low Mach number formulation eliminates sound waves
from the fully compressible formulation and leads to a more computationally
efficient quasi-incompressible formulation. We demonstrate our ability to model
saltwater (NaCl) solutions in both equilibrium and nonequilibrium settings. We
show that our algorithm is second-order in the deterministic setting, and for
length scales much greater than the Debye length gives results consistent with
an electroneutral/ambipolar approximation. In the stochastic setting, our model
captures the predicted dynamics of equilibrium and nonequilibrium fluctuations.
We also identify and model an instability that appears when diffusive mixing
occurs in the presence of an applied electric field.Comment: 37 pages, 5 figure
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